Modeling Ca2 -Dependent Regulation of KCC2 ......I am thankful to have had the opportunity to work...

Modeling Ca2+-Dependent Regulation of KCC2 Phosphorylation as aMechanism forInhibitory Synaptic Plasticity

by

Annik Yalnizyan-Carson

A thesis submitted in conformity with the requirementsfor the degree of Master of Science

Graduate Department of Cell and Systems BiologyUniversity of Toronto

c© Copyright 2015 by Annik Yalnizyan-Carson

Abstract

Modeling Ca2+-Dependent Regulation of KCC2 Phosphorylation as a Mechanism for Inhibitory SynapticPlasticity

Annik Yalnizyan-CarsonMaster of Science

Graduate Department of Cell and Systems BiologyUniversity of Toronto

2015

Inhibitory synaptic transmission in the mammalian central nervous system is chiefly mediated by the neuro-

transmitter γ-aminobutryic acid (GABA), which binds the Cl−-permeable ionotropic GABAA receptor. In mature

neurons, low intracellular Cl− is maintained by the K+-Cl− cotransporter KCC2, allowing Cl− influx and hence

hyperpolarization of the cell upon GABA binding. Repetitive coincident activation (within ±20 ms) of pre- and

postsynaptic neurons at inhibitory synapses leads to a depolarizing shift in the GABA reversal potential (EGABA),

diminishing the strength of inhibition. It has been hypothesized that this is due to Ca2+-dependent dephosphoryla-

tion of KCC2 mediated by T-type voltage gated Ca2+ channels (VGCCs). We simulated this proposed mechanism

using a kinetic model of KCC2 phosphorylation. Simulations showed that Ca2+ entry via T-type VGCCs could

produce spike timing-dependent changes in KCC2 phosphorylation leading to removal from the membrane, hence

intracellular Cl− accumulation and reduced strength of inhibition.

ii

Acknowledgements

I would like to thank all of the people who have contributed to the completion of this project, from which Ilearned a great deal. This experience would not have been possible without all of the support I received along theway. First and foremost, I would like to thank my supervisors Dr. Blake Richards and Dr. Melanie Woodin, whohave both been fantastic teachers and mentors. I am especially grateful to have been involved in a multidisciplinaryproject with two supervisors who each bring an incredible breadth of knowledge, and who are both exceptionallyskilled at imparting this to their students. I am thankful to have had the opportunity to work in Dr. Woodin’s labto learn the biological perspective for this project; Dr. Woodin’s enthusiasm for the subject and commitment tothe development of her students has been instrumental in my academic growth. I am also deeply grateful for Dr.Richards’ guidance to formulate the mathematical model and programming skills necessary for this project, andfor his consistent encouragement and patience throughout.

I would also like to thank my supervisory committee, Dr. Frances Skinner and Dr. Steve Prescott, for theirtime and thoughtful guidance of this project throughout the course of its development. I would also like to thankmy colleagues who provided valuable input to the formulation of the model: Jordan Guerguiev, who helped toformulate the kinetic scheme upon which this thesis is based, and Jessica Pressey and Vivek Mahadevan of theWoodin lab for their work which provided experimentally driven parameters necessary to complete the projectand ground results in reality.

Finally I would like to acknowledge the University of Toronto and the National Science and EngineeringResearch Council of Canada (NSERC) for providing the funding to make this project possible.

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Contents

Introduction 1

1.1 Inhibitory Neurotransmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Changes in Inhibitory Neurotransmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Developmental Shift in the Polarity of GABAergic Transmission . . . . . . . . . . . . . . 3

1.2.2 Synaptic Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 The Calcium Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3.1 Voltage Gated Calcium Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Kinase and Phosphatase Activation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4.1 Calcium-sensitive Kinases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4.2 Calcium-sensitive Phosphatases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.5 The K+-Cl− Co-transporter KCC2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.5.1 Phosphorylation of KCC2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.5.2 Activity-Dependent KCC2 Dephosphorylation . . . . . . . . . . . . . . . . . . . . . . . 17

1.6 Changes in Cl− Reversal Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.7 Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.7.1 Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.7.2 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.7.3 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Methods 23

2.1 Computational Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.1.1 Passive Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

iv

2.1.2 Model Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.1.3 Ion Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.1.4 Channels and Transporters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.1.5 Synaptic Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.1.6 Current Clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.1.7 Spike Timing Dependent Plasticity (STDP) Induction Protocol . . . . . . . . . . . . . . . 35

2.2 Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.2.1 Total Internal Reflection Fluorescence (TIRF) Microscopy . . . . . . . . . . . . . . . . . 37

2.2.2 Biotinylation & Western Blot Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.3 Simulation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.3.1 Simulation Analysis and Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.3.2 Establishing Parameters for KCC2 State Dynamics . . . . . . . . . . . . . . . . . . . . . 39

2.3.3 Measures of Plasticity Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Results 42

3.1 Parameter Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.1.1 Rates of Membrane Insertion and Removal of KCC2 . . . . . . . . . . . . . . . . . . . . 44

3.1.2 Rates of Phosphatase Activation and Inactivation . . . . . . . . . . . . . . . . . . . . . . 46

3.1.3 Rates of Phosphorylation and Dephosphorylation . . . . . . . . . . . . . . . . . . . . . . 48

3.2 Ca2+-Dependent Kinase and Phosphatase Activity Effectively Regulates KCC2 State . . . . . . . 50

3.3 KCC2 is Dephosphorylated Following STDP Protocol . . . . . . . . . . . . . . . . . . . . . . . 51

3.3.1 Ca2+ Influx Source Determines Changes in [MP] KCC2 . . . . . . . . . . . . . . . . . . 54

3.3.2 Q Value Determines Magnitude of Changes in [MP] KCC2 . . . . . . . . . . . . . . . . . 57

3.3.3 Changes in ECl in Coincident Spike Timing Intervals Due To KCC2 Dephosphorylationand Synaptic Cl− Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Discussion 63

4.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.2 Model Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

v

4.4 Future Studies and Experimental Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

References 68

Appendices 77

A Enzyme Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

A.1 The Michaelis-Menten Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

A.2 The Hill Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

B Kinase & Phosphatase Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

B.1 The Kinetic Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

B.2 Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

B.3 Assumptions and Simplifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

B.4 Steady-State Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

C Chloride Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

C.1 The Kinetic Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

D Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

E Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

F Supplementary Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

vi

List of Tables

2.1 Ca2+ Channel Conductance Values Used in STDP Induction Experiments . . . . . . . . . . . . . 28

3.1 Four Distinct Regimes for Kinase and Phosphatase Activation in Response to Changing Q Values 48

D.1 KCC2 Regulation Kinetic Scheme Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

E.1 Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

E.2 Compartment Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

E.3 Initial Ion Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

E.4 Hodgkin-Huxley Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

E.5 Calcium Channel Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

E.6 Michaelis-Menten Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

E.7 Kinase and Phosphatase Kinetic Scheme Rate Constants . . . . . . . . . . . . . . . . . . . . . . 93

E.8 Kinetic Parameters of PKC Isozymes α, β, and γ . . . . . . . . . . . . . . . . . . . . . . . . . . 94

E.9 Kinetic Parameters of Kinase and Phosphatase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

E.10 KCC2 Ion Transport Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

E.11 Synaptic Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

E.12 Current Clamp Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

vii

List of Figures

1.1 GABAA Receptor Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Developmental Shift in Polarity of GABA Signaling . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Excitatory Spike Timing-Dependent Plasticity Induction Window . . . . . . . . . . . . . . . . . . 8

1.4 Inhibitory Spike Timing-Dependent Plasticity Induction Window . . . . . . . . . . . . . . . . . . 9

1.5 Proposed Mechanism for Depolarizing Shift in EGABA via Coincident Spiking Activity . . . . . . 20

2.1 Kinetic Scheme of KCC2 Distribution in the Cell . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2 Kinetic Scheme of Cl− Transport via Membrane-Bound, Active KCC2 . . . . . . . . . . . . . . . 31

2.3 Example Voltage Trace for STDP Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4 Measures of Plasticity Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.1 Schematic Diagram of Ca2+-Dependent KCC2 Regulation in the Model . . . . . . . . . . . . . . 43

3.2 Proportion of Kinase and Phosphatase in Active States with Varying Ca2+ and Q Values . . . . . . 47

3.3 Net Phosphorylation Activity Calcium Dose Response Curves for Varying Q Values . . . . . . . . 49

3.4 Effects of Q Value on Steady State Active Phosphatase and Net Phosphorylation Rate . . . . . . . 50

3.5 Calcium Dose Response Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.6 Change in Membrane Phosphorylated KCC2 Following STDP Induction Protocol . . . . . . . . . 53

3.7 Maximum Ca2+ Reached During Plasticity Induction for Q = 7.4 . . . . . . . . . . . . . . . . . . 54

3.8 Change in [MP] Following STDP Induction Protocol for Q = 7.4 . . . . . . . . . . . . . . . . . . 58

3.9 Changes in ECl Following Plasticity Induction for L-type Ca2+Channels . . . . . . . . . . . . . . 61

3.10 Changes in ECl Following Plasticity Induction for T-type Ca2+Channels . . . . . . . . . . . . . . 62

F.1 Ca2+ Dose Response Curve for Q = 0.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96



viii

F.4 Ca2+ Dose Response Curve for Q = 28.45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

F.5 Ca2+ Dose Response Curve for Q = 148.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

F.6 Ca2+ Dose Response Curves for Various Q Values . . . . . . . . . . . . . . . . . . . . . . . . . . 99

F.7 Changes in KCC2 Distribution During Plasticity Induction for a Coincident Spike Timing Interval 100

F.8 Changes in KCC2 Distribution During Plasticity Induction for a Non-Coincident Spike TimingInterval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

F.9 Maximum [PA] Reached During Plasticity Induction for Q = 0.1 . . . . . . . . . . . . . . . . . . 102



F.12 Maximum [PA] Reached During Plasticity Induction for Q = 28.45 . . . . . . . . . . . . . . . . . 103

F.13 Maximum [PA] Reached During Plasticity Induction for Q = 148.0 . . . . . . . . . . . . . . . . . 104

F.14 Changes in ECl Following Plasticity Induction for L- and T-type Ca2+Channels Together . . . . . 105

F.15 Changes in ECl Following Plasticity Induction for Low Conductance T-type Ca2+Channels . . . . 106

ix

Introduction

1.1 Inhibitory Neurotransmission

Inhibitory synaptic transmission in the central nervous system (CNS) is a key process in information storageand transfer between neurons [6]. Inhibitory signaling in the adult brain is mediated by the amino acid neuro-transmitters glycine and γ-aminobutryic acid (GABA), which bind at most synaptic sites to chloride-permeableionotropic receptors [2, 46]. GABA is the major inhibitory neurotransmitter in the brain, and is most highly con-centrated in the substantia nigra and globus pallidus nuclei of the basal ganglia where it is involved in voluntarymovement, in the hippocampus where it plays an important role in learning and memory, and in the cerebral cortexwhere it plays important roles in coordinating neural activity and controlling neural plasticity [6, 30, 68].

In the forebrain, there are two distinct GABA receptor subtypes. The ionotropic GABAA receptor (GABAAR)permits quick hyperpolarization of the cell by allowing the passage of anions into the cell directly through itspore. In contrast, metabotropic GABAB receptors (GABABRs) are linked via G-proteins to potassium (K+)channels and, when activated, decrease intracellular K+ concentrations to hyperpolarize the cell [18]. Becausemetabotropic receptors rely on second messenger signaling, GABABR-mediated hyperpolarization is slower thanvia GABAARs. There is even some difference in the speed of signaling via GABAARs, depending on their loca-tion on the postsynaptic cell [95]. GABAA receptors present on the postsynaptic membrane mediate fast inhibitionon the order of milliseconds, whereas receptors present in the extra-synaptic membrane function to confer tonicinhibitory effects in response to ambient GABA [27, 49]. As GABAARs are the primary receptors responsi-ble for rapid inhibitory synaptic transmission in the hippocampus, their physiology is a major topic of study inneuroscience.

GABAA receptors are heteropentameric transmembrane proteins whose subunits are organized around acentral pore permeable to chloride (Cl−) and, to a lesser extent, bicarbonate (HCO−3 ) ions [46, 49]. There areseveral classes of GABAA receptor subunits (α(1−6), β(1−3), γ(1−3), δ, ε(1−3), θ, π), each of which are composed offour transmembrane α helices [45, 95]. These subunits can be combined in many ways to yield functional recep-tors. Though there is tremendous potential for structural diversity of GABAARs, the majority are composed oftwo α subunits, two β subunits, and one γ subunit (see Figure 1.1A) [45]. The particular subunits composing thereceptor determine the affinity for GABA and the channel’s conductance for Cl− and HCO−3 [21]. GABA bindsat the interface between α and β subunits of the receptor, which then causes a conformational change opening thepore to allow anions to pass across the membrane (see Figure 1.1B) [27, 95]. Some GABAARs containing a γsubunit are also sensitive to the benzodiazepine (BZD) class of drugs, binding between the α and γ subunits [22].BZD binding ultimately changes the receptor affinity – once bound, BDZ causes a conformational change in the

1

Introduction

Figure 1.1: GABAA Receptor Configuration. (A) GABAA receptors (GABAARs) are heteropentameric ionotropicGABA receptors permeable to Cl− and HCO−3 . These receptors are present synaptically, where they mediate fastinhibitory synaptic transmission, as well as extrasynaptically, where they mediate tonic GABA currents. (B)Typical GABAARs consist of two α, two β, and one γ subunit. GABA binds at sites at the junction between α andβ subunits, causing a conformational change to open the Cl−/HCO−3 pore. Benzodiazepines (BZDs) can also bindat the interface of the α and γ subunits, which causes heightened affinity of the receptor for its substrate.

GABAAR which increases its affinity for GABA and increases the frequency of receptor activation and thereforeCl− influx [22].

When GABA binds its receptor on the postsynaptic membrane, the degree of current flow through theGABAA receptors determines the resulting change in membrane potential. The current flow through the receptorcan be described mathematically by Ohm’s law:

I = g · (VM − Ex) (1.1)

where g is the maximal conductance through the receptor. The expression VM − Ex describes the driving forcefor the ion x across the membrane, which is the difference between the membrane potential (VM) and the reversalpotential (Ex). The driving force is determined in large part by the chemical concentration gradient for the ion, asthe reversal potential is given by the Nernst equation for a single ion species:

Ex =RTzF

ln[x]out

[x]in(1.2)

Here R is the universal gas constant, T is absolute temperature, z is the valence of the ion, and F is the Faradayconstant. These constants are summarized in Table E.1, Appendix E. Resting membrane potential (VM) can bedescribed similarly by the Goldman-Hodgkin-Katz equation:

VM =RTF

ln

∑X

i PM+i[M+

i ]out +∑Y

j PA−j [A−j ]in∑X

i PM+i[M+

i ]in +∑Y

j PA−j [A−j ]out

(1.3)

2

Introduction

where M represents any of X monovalent positive ionic species, and A represents any of Y monovalent negativeionic species. The membrane permeability for an ion x is described by Px. R, T, and F are the universal gasconstant, the absolute temperature, and the Faraday constant, as described above.

When GABA binds its receptor, the degree of Cl− flux across the membrane determines the strength ofGABA’s inhibitory action. From equation (1.1), we see that strength of inhibition is dependent on two major fac-tors, conductance of the GABAA receptor, and the driving force through the channel, which can be characterizedby the GABA reversal potential (EGABA). Hence, changes to the strength of GABAA inhibitory currents can bemade by altering the conductance of the receptor or the reversal potential.

Changes to GABAA conductance can occur presynaptically by changes in either the probability of neuro-transmitter release or in the size of discrete neurotransmitter packages (quanta) [50]. Conductance can also bealtered postsynaptically in two ways: first, by changes in the number of postsynaptic GABAARs expressed on thepostsynaptic membrane [89]. Second, the conductance and gating properties of existing receptors can be alteredby changes to the phosphorylation state of specific residues in the β subunit [11].

The current through the GABAA receptor is also dependent on EGABA, as mentioned previously. EGABA

determines the driving force for ions through the receptor pore when the channel opens (see equation (1.1)). AsGABAA receptors are several times more permeable to Cl− than HCO−3 , EGABA is much closer to the reversalpotential for Cl− (ECl) and hence is largely determined by the relative concentrations of Cl− inside and outside ofthe cell [46]. As the extracellular space acts as a sink for Cl− ions, changes in ECl primarily reflect changes in[Cl−]i. Consequently the strength of rapid inhibitory neurotransmission in the brain is determined, in large part,by the regulation of internal Cl− concentration [7, 87].

1.2 Changes in Inhibitory Neurotransmission

As discussed above, both changes in GABAA conductance and reversal potential can influence the currentflow through GABAA receptors upon activation – and therefore the strength of signaling at GABAergic synapses.There are two major changes to GABAA-mediated inhibition that occur in the CNS. First, during the courseof development, the polarity of GABAergic signaling switches from depolarizing to hyperpolarizing. Second,in mature neurons distinct firing patterns of pre- and post-synaptic neurons cause changes in the strength ofinhibition. The details of these changes will be described below.

1.2.1 Developmental Shift in the Polarity of GABAergic Transmission

During the course of development, changes in the transporters which maintain Cl− homeostasis in the celllead to a decrease in the steady state [Cl−]i. This causes a hyperpolarizing shift in EGABA, ultimately renderingGABA inhibitory in mature neurons. In early embryonic development, [Cl−]i is largely controlled by activityof the sodium-potassium-chloride (Na+-K+-Cl−) cotransporter, NKCC1 [6]. NKCC1 maintains high [Cl−]i elec-troneutrally by transporting Na+, K+, and Cl− into the cell with a stoichiometry of 1:1:2, down the Na+ concentra-tion gradient created by the Na+-K+ATPase (see Figure 1.2A) [26]. At this stage of development, NKCC1 is theprincipal transporter responsible for Cl− homeostasis, and maintains high [Cl−]i relative to adult levels (∼25mMearly in development as compared with ∼4-7mM in mature neurons) [2, 6, 46]. This high [Cl−]i maintained by

3

Introduction

NKCC1 causes the reversal potential for GABA to be depolarized relative to the resting membrane potential.Consequently, when GABA binds to the GABAA receptor, Cl− flows down its electrochemical gradient out of thecell, thereby depolarizing the membrane [46]. If NKCC1 expression is sufficiently high so that EGABA is depo-larized relative to the action potential threshold, GABA may even have an excitatory effect on the postsynapticneuron [6].

In maturing neurons, Ca2+-dependent regulation of NKCC1 causes a decrease in its expression [4], whileexpression of the K+-Cl− co-transporter KCC2 increases [6, 86, 87]. The timeline for the switch in polarity ofGABA signaling is strongly correlated with increases in KCC2 mRNA in the cell [107]. In a similar fashionto NKCC1, KCC2 utilizes the concentration gradient for K+ created by the Na+-K+ATPase to transport one K+

and one Cl− out of the cell against the Cl− concentration gradient, thereby maintaining low [Cl−]i and allowinghyperpolarizing influx of Cl− through the GABAA receptor (see Figure 1.2B) [77]. This developmental changefrom NKCC1 to KCC2 as the dominant player in Cl− ion regulation in neurons leads to the shift from high tolow [Cl−]i, and hence contributes to the shift in polarity of GABA signaling from depolarizing to hyperpolarizing[7, 76, 87].

Developmentally, the exact time at which this shift occurs is heterogenous across model animals, and evenacross cell types within the same animal [6]. Neurons born early in development, as in the brainstem, spinalcord, thalamus, hypothalamus, and neocortex, switch from a depolarizing response to GABA to a hyperpolarizingresponse earlier than later born neurons such as pyramidal cells of the hippocampus [107, 109]. In mice and rats,by 15 to 20 days postnatally, the effects of GABA are almost entirely hyperpolarizing in hippocampal pyramidalneurons [34, 117]. Interestingly, this may be reverted in cases of neuronal injury or pathology in mature cells,which may cause GABAergic signaling to reverse polarity [76].

As KCC2 is the primary regulator of [Cl−]i in mature neurons, it plays an important role in maintainingthe strength of inhibition in the adult brain. Greater KCC2 transport activity extrudes more Cl− from the cell,thereby creating a greater driving force for Cl− through GABAA receptors. Hence if KCC2 is highly expressedand actively extruding Cl−, activation of GABAA receptors results in strong hyperpolarization. Importantly, thereis evidence that KCC2 transport efficacy in pyramidal neurons of the hippocampus may be changed by patternedspiking activity of pre- and post-synaptic neurons, leading to altered Cl− flux in response to GABA [111]. Thisform of inhibitory synaptic plasticity has been shown to have an important impact on neuronal integration [90],and thus may be critical for information processing, learning and memory. In the next sections, I provide ageneral overview of synaptic plasticity and a focused discussion on the mechanisms by which inhibitory synapticplasticity is regulated via changes to KCC2 efficacy.

1.2.2 Synaptic Plasticity

After the developmental shift in polarity of GABA signaling, the strength of signaling can be changed throughpatterned activity between cells. This phenomenon, known as activity-dependent synaptic plasticity, occurs at bothexcitatory and inhibitory synapses. This was first proposed in 1949 by the neuropsychologist Donald Hebb:

When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes partin firing it, some growth process or metabolic change takes place in one or both cells such that A’sefficiency, as one of the cells firing B, is increased.

4

Introduction

Figure 1.2: Developmental Shift in Polarity of GABA Signaling. (A) Early in development, NKCC1 expression ishigh relative to KCC2. High [Cl−]i is maintained by NKCC1 transport of Na+, K+ and 2 Cl− ions into the cell downthe gradient for Na+ created by the Na+-K+ATPase. High [Cl−]i (∼25mM at P0) causes EGABA to be depolarizedrelative to the resting membrane potential. Hence, activation of GABAARs leads to Cl− efflux and depolarizationof the membrane. If EGABA is depolarized relative to the action potential threshold (∼45mV, dotted red line),GABA may have an excitatory effect. (B) KCC2 extrudes Cl− and K+ by secondary active transport, along the K+

gradient created by the Na+-K+ATPase. As neurons develop, increased expression of KCC2 allows for increasedCl− extrusion, a lower steady state level of [Cl−]i (∼4-7mM by P20) and consequently a hyperpolarizing shift inEGABA. As maintenance of low [Cl−]i allows EGABA to be hyperpolarized relative to resting membrane potential(RMP), activation of GABAARs leads to Cl− influx and subsequent membrane hyperpolarization.

This is known as Hebb’s postulate, and has been summarized as “cells that fire together, wire together” [92]. Thecorollary of Hebb’s postulate is that persistent failure of cell A to stimulate cell B results in a weakening of thesynaptic connection. The idea behind this is intuitive; if multiple cells commonly fire in concert, there is likely acommon cause for the firing and learning occurs when the connections between these neurons change to reflectthis co-activation.

The existence of a long-term form of activity-dependent synaptic plasticity was discovered in 1972 when ex-periments by Tim Bliss and Terje Lømo focusing on excitatory synapses of hippocampal cells confirmed that con-nections between cells underwent long term potentiation (LTP), a long lasting increase in synaptic strength [10].Later experiments showed weakening of synaptic strength – or long term depression (LTD) – could result fromrepetitive firing of the presynaptic neuron after the postsynaptic neuron [42, 43]. These experiments confirmed,as Hebb predicted, that the order of cellular activation plays a role in the plastic changes induced at the synapse.

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Introduction

While the first plasticity experiments gave credence to the growing consensus that glutamatergic excitatorysynapses can achieve long lasting changes in synaptic strength, it was not initially clear that the same was truefor inhibitory synapses. In the 1990s there were reports of inhibitory LTP and LTD, however these studies used avariety of plasticity induction protocols in a range of preparations, and no consensus was readily apparent aboutthe nature of inhibitory synaptic plasticity [12, 47, 48, 71].

The particular form of LTP shown by Bliss and Lømo was induced by high frequency (100Hz) “tetanic”stimulation of the presynaptic cell, causing high levels of neurotransmitter to be released into the synaptic cleft tostimulate the postsynaptic neuron. At these synapses, high levels of glutamate were necessary to provide sufficientactivation of Na+-permeable α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors to causedepolarization of the postsynaptic cell. AMPA receptors (AMPARs) are primarily responsible for the influx ofcations which cause local depolarizations of the postsynaptic cell in response to glutamate [65]. At the same time,glutamate binds the N-methyl-D-aspartate (NMDA) receptor, which is permeable to Ca2+ and acts to increasedepolarizing postsynaptic currents [2]. At rest, the NMDA receptor (NMDAR) pore is obstructed by an ion ofmagnesium (Mg2+), though local depolarization causes the Mg2+ ion to be expelled, opening the pore for Ca2+

influx [67, 73] The depolarization-dependent expulsion of the Mg2+ ion from the pore allows the NMDAR toserve as a coincidence detector for the presence of presynaptic activation (i.e. glutamate release) and postsynapticdepolarization [83]. Activation of NMDARs allows for Ca2+ influx which triggers downstream kinase activation[64]. This leads to phosphorylation of key AMPAR residues increasing channel conductance, and to increasedtrafficking of AMPARs to the membrane, potentiating the synapse [63, 64, 66].

It is generally believed that Ca2+ influx is also crucial in LTD. Induction of LTD also involves activationof pre- and postsynaptic cells within a short temporal interval, although lower-level postsynaptic depolarizationis required [33]. Sustained repetitive stimulation of the postsynpatic cell preceding presynaptic stimulation leadsprimarily to activation of voltage-gated calcium channels [8, 83]. When the temporal separation between post-and presynaptic activation is small enough, some NMDARs may also be activated [116]. The resulting Ca2+ influxis less substantial than when presynaptic activation precedes postsynaptic depolarization, and leads to LTD ratherthan LTP [33, 114]. Imaging studies have shown that changes in intracellular Ca2+concetration ([Ca2+]i) weresupralinear when presynaptic stimulation immediately preceded postsynaptic depolarization, and sublinear whenthis ordering was switched [52]. Large transient increases in [Ca2+]i can lead to activation of certain kinases, whilesmaller transient increases in [Ca2+]i can lead to activation of phosphatases which dephosphorylate AMPARs,decreasing conductance and depotentiating the synapse [64, 66, 114].

While these experiments showed that long lasting changes in the strength of signaling between cells couldbe induced, the tetanus protocol may fail to faithfully capture how plasticity is induced in vivo, as this protocolinvolves a physiologically unrealistic frequency of presynaptic stimulation in order to generate the necessaryactivity in the postsynaptic cell. Consider for example that the hippocampal theta rhythm seen in active behavioursand REM sleep is within the range of 4-12Hz [100]. To demonstrate that this phenomenon could occur withphysiological levels of presynaptic activity and that this could therefore plausibly be a mechanism for learningand memory, Bi and Poo revisited Hebb’s postulate and designed an experiment involving stimulation of bothpre- and post-synaptic cells at a physiologically realistic frequency [8]. When both pre- and post-synaptic cellsare activated at low frequency (∼5Hz), so long as they are activated within a short time from one another, long-term changes in the strength of the synapse can be achieved [8]. Chiefly, these experiments showed that thedegree of plasticity induction was dependent on both the order and the temporal separation between the pre- andpost-synaptic spikes, a principle known as “Spike Timing-Dependent Plasticity” (STDP) [8].

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Introduction

Spike Timing-Dependent Plasticity

The mechanism by which plasticity was induced at glutamatergic synapses in the tetanus protocol of Terjeand Lømo and the STDP protocol of Bi and Poo was largely the same. Tetanic stimulation of the presynapticcell causes glutamate to be released into the synapse nearly continuously for the duration of the stimulation,such that a great number of AMPA receptors on the postsynaptic membrane can be activated [65]. SufficientAMPAR activation allows enough Na+ influx to locally depolarize the membrane and expel the Mg2+ block fromthe NMDARs [67, 73]. The subsequent Ca2+ influx triggers a signal cascade which ultimately results in increasedsynaptic strength [114]. With the STDP protocol, direct stimulation of the postsynaptic cell creates the necessarydepolarization to activate NMDARs and allow Ca2+ influx to trigger intracellular changes involved in potentiatingthe synapse [8].

The key consideration in plasticity induction using STDP is the timing between presynaptic activation,triggering release of neurotransmitter into the synapse, and the postsynaptic activation, which ultimately affectsthe Ca2+ influx necessary to affect the subcellular changes involved in adjusting synaptic strength [94]. Thetemporal separation between pre- and post-synaptic spike pairs is known as the spike timing interval (denoted∆t), and has been shown experimentally to control the magnitude and polarity (LTP or LTD) of synaptic changesachieved during induction of plasticity [8, 100, 116]. The change in synaptic strength as a function of the relativetiming of pre- and postsynaptic cellular activation is called the STDP function or learning window (see Figures 1.3and 1.4). The shape of this curve varies between synapse types [8, 111, 116] The spike timing window is reflectiveof the sensitivity of the synapse to small differences in temporal separation between pre- and post-synaptic firing,suggesting that precise patterns of spike timing are an important type of information about external stimuli to bestored by the brain.

At excitatory synapses, small positive ∆t values (corresponding to firing of the presynaptic cell immediatelypreceding firing of the postsynaptic cell) causes glutamate release from the presynaptic cell to bind to AMPA andNMDA receptors on the postsynaptic membrane, followed by a postsynaptic depolarization allowing removal ofthe NMDA receptor Mg2+ block leading to Ca2+ influx [67, 73]. High levels of Ca2+ influx lead to potentiationof the synapse by triggering intracellular mechanisms such as phoshporylation of the AMPA receptors to increaseconductance, as well as increasing AMPAR trafficking to the membrane [2, 65]. Conversely, small negative ∆tvalues (representing postsynaptic spiking followed by presynaptic input) lead to depression of the synapse (Figure1.3) [8]. It has been theorized that spiking of the postsynaptic cell a short time before the presynaptic cell leadsto much smaller changes in [Ca2+]i, which leads instead to activation of phosphatases which lead to decreasedAMPA receptor conductance, and reduced receptor membrane expression [65].

Although the precise mechanism of inhibitory synaptic plasticity is not as well understood, spike-timingintervals also affect the potentiation or depression at inhibitory synapses. Though evidence of inhibitory plasticitywas initially inconsistent or difficult to interpret, demonstration of LTP and LTD using STDP induction protocolsgave rise to a new way of studying plasticity at inhibitory synapses. Inhibitory STDP experiments showed thatspecific patterns of pre- and post-synaptic spiking activity could induce consistent and sustained changes in thestrength of GABAergic transmission and, like excitatory synapses, the magnitude of these changes is dependenton the temporal separation between pre- and post-synaptic spikes (see Figure 1.4) [3, 13, 111].

Woodin et al. (2003) showed that precise patterns of pre- and post-synaptic spiking activity led to signifi-cant changes in the strength of GABAergic signaling by shifting EGABA [111]. Importantly, these experiments also

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Introduction

Figure 1.3: Excitatory Spike Timing-Dependent Plasticity Induction Window. The percent change in excitatorypostsynaptic current (EPSC) is shown as a function of separation between pre- and post-synaptic spikes. Negative∆t values correspond to firing of the postsynaptic cell preceding firing of the presynaptic cell (A). Positive ∆tvalues represent intervals for which the presynaptic cell fired before the postsynaptic cell (B,C). Data pointsrepresent individual plasticity induction experiments carried out in [116]. Example traces A,B,C from [116].

showed that, like excitatory STDP, changes in inhibitory transmission were mediated by Ca2+ influx in the postsy-naptic cell via voltage-gated Ca2+ channels [111]. Unlike excitatory synapses (which show an inverse hyperbolicrelationship with potentiation - Figure 1.3), inhibitory synapses show a relationship with potentiation which isnearly symmetric with respect to the temporal separation of pre- and post-synaptic firing (Figure 1.4) [8, 111].Crucially, both excitatory and inhibitory synapses undergo the greatest potentiation or depression when pre- andpost-synaptic spiking occurs with small temporal separation [8, 111]. This tight temporal coupling eliciting thegreatest changes in synaptic strength is referred to as “coincident” activation (when -20 ms < ∆t < +20 ms), thedetails of which are outlined below.

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Introduction

Figure 1.4: Inhibitory Spike Timing-Dependent Plasticity Induction Window. The percent change in GABAergicpostsynaptic current (GPSC) is shown as a function of separation between pre- and post-synaptic spikes. Negative∆t values correspond to firing of the postsynaptic cell preceding firing of the presynaptic cell (A). Positive ∆tvalues represent intervals for which the presynaptic cell fired before the postsynaptic cell (B,C). Data pointsrepresent individual plasticity induction experiments carried out in [111]. Example traces generated in NEURONSimulation Environment (www.neuron.yale.edu).

Coincident and Non-Coincident Spiking

Key experiments investigating STDP showed that the separation between pre- and post-synaptic spike pairsdetermines the magnitude of the change in synaptic strength at both excitatory and inhibitory synapses [8, 13, 111].At excitatory synapses, the necessity for pre- and post-synaptic activation within a short temporal interval is due tothe fact that plasticity is principally mediated by changes in [Ca2+]i from NMDARs [33, 64, 83, 112]. NMDARsrequire both binding of glutamate from presynaptic activation and local depolarization from postsynaptic acti-

9

Introduction

vation, meaning that NMDARs act as molecular coincidence detectors for pre- and postsynaptic activity. Whenthese events are temporally distant, NMDA receptors may not be activated to allow sufficient Ca2+ influx to causechanges in the strength of the synapse [116].

The precise mechanisms for inhibitory STDP are yet to be fully resolved, though it is known that Ca2+ influxis important at these synapses as well [3, 111]. Interestingly, coincident activation of pre- and post-synaptic cellsleads to a depolarizing shift in EGABA for both positive and negative spike timing intervals [111]. The specificdetails of the mechanism accounting for this change in EGABA have not yet been determined experimentally.As KCC2 is the principal protein responsible for management of Cl− homeostasis – and hence responsible forthe steady state EGABA – this suggests that coincident pre- and postsynaptic activation triggers Ca2+ influx inthe postsynaptic cell which in turn triggers a reduction in the extrusion of Cl− via KCC2. This conclusion issupported by data showing that inhibitory STDP is sensitive to furosemide treatment, a general Cl− cotransporterinhibitor [111].

Current evidence suggests that changes in EGABA are mediated by Ca2+ influx through specific VGCCswhich require presynaptic involvement. Unlike excitatory STDP, the inhibitory STDP curve (see Figure 1.4) issymmetric, but it is important to note that the mechanisms by which a change in synaptic strength occurs maybe different for positive and negative spike-timing intervals. The central focus of this thesis is to understandhow coincident activity at inhibitory synapses can produce a change in KCC2 extrusion efficacy via a Ca2+-dependent mechanism. Experimental work studying the mechanisms thought to be involved in inhibitory STDPare presented in further detail below.

1.3 The Calcium Signal

Given the importance of Ca2+ in both excitatory and inhibitory synaptic plasticity induction, it is prudentto understand the precise mechanisms by which Ca2+ effects these changes. As a key signalling molecule, Ca2+

is very tightly regulated by the cell. The concentration of free Ca2+ ions extracellularly is typically around 1.5mM, while intracellular Ca2+ concentration is actively maintained close to 100 nm, a difference of four orders ofmagnitude [2]. Over 99% of intracellular Ca2+ is sequestered in membrane-bound organelles or buffered by othermolecules in the cytoplasm [97]. The purpose of this is twofold: first, it creates a strong inward electrochemicalgradient for Ca2+, hence activation of voltage sensitive receptors such as the glutamatergic NMDA receptor andvoltage-gated Ca2+ channels (VGCCs) allow for transient, although substantial, increases in [Ca2+]i. Second, asa signaling molecule with very diverse effects in the cell, cytosolic Ca2+ must be tightly controlled so precisepathways may be engaged only when appropriate [32, 97].

As described above, NMDAR-mediated Ca2+ influx is crucial to the induction of plasticity at excitatorysynapses [8, 67, 112]. In excitatory STDP protocols, positive spike timing intervals potentiate the synapse byallowing significant increases in [Ca2+]i via both NMDARs and postsynaptic VGCCs. This high level of [Ca2+]i

leads to the activation of kinases which ultimately facilitate increase in conductance of channels in the postsy-naptic membrane, potentiating the synapse [83, 114]. LTD at excitatory synapses is also mediated by NMDAR-dependent Ca2+ influx [64, 66, 114]. Spiking of the postsynaptic cell leads to activation of VGCCs, allowing Ca2+

influx. Subsequent presynaptic activation releases glutamate which can then bind NMDARs on the postsynapticcell. However, because the postsynaptic cell has already been activated, a much smaller proportion of NMDARswill have the Mg2+ block removed to allow for Ca2+ influx [83]. Consequently [Ca2+]i levels are elevated above

10

Introduction

baseline, though to a lesser degree than with positive spike timing intervals [114]. This lower elevation of [Ca2+]i

leads to activation of phosphatases, which in turn lead to lowered AMPAR conductance and hence a depotentiationof the synapse [65, 83, 114].

At inhibitory synapses, Ca2+ influx occurs principally via VGCCs in the postsynaptic membrane activatedby the back-propagating action potential [3, 74]. Woodin et al. (2003) showed that a specific VGCC subtypewas necessary for the induction of STDP at GABAergic synapses, as treatment with the L-type-specific Ca2+

channel blocker nimodipine prevented plasticity induction [111] (see Section 1.3.1 for more details). However,these experiments also showed that these particular VGCCs were not sufficient to induce plasticity, since postsy-naptic stimulation alone could not generate the change in EGABA seen with coincident activation, indicating thatpresynaptic involvement was also necessary [111]. In order to understand the way in which coincident activityinfluences inhibitory synaptic plasticity, the differences between VGCC types should be examined in more detail.

1.3.1 Voltage Gated Calcium Channels

All VGCCs are composed of subunits α1, α2δ, β1−4, and γ, with the α1 subunit conferring voltage sensitivityand forming the Ca2+ conducting pore of the channel [25]. The pore of these channels is especially sensitive toCa2+ over more abundant cations (i.e. Na+ and K+) due to negatively charged glutamate residues within each poreloop [104, 113]. As there are multiple genes which encode the functional unit of the channel, the α1 subunit, manyVGCC subtypes may exist [15]. Moreover, alternative splicing of genes as well as co-assembly of the α1 subunitwith multiple combinations of ancillary calcium channel subunits, further contributes to the great diversity amongVGCCs [96]. VGCCs can be organized into several important classes, each operating under different conditionsand with different dynamics for Ca2+ entry into the cell [14, 15].

VGCCs are typically classified as either High- or Low-Voltage Activated (HVA and LVA), depending onthe level of depolarization of the membrane necessary to activate the voltage sensitive domain in the α1 subunitto open the pore. Two important types of VGCCs found in neurons are the “long-lasting” (L-type) HVA Ca2+

channels and the “transient opening” (T-type) LVA Ca2+ channels [14]. For the purposes of this study, we focuson these two Ca2+ channel types and the role they play in signaling at inhibitory synapses of the adult brain. Weare principally interested in how Ca2+ signals are generated by coincident activity at inhibitory synapses, and howthis translates into changes in ECl via these two channel types.

L-Type Calcium Channels

L-Type Calcium Channels in the brain are activated by large depolarizations in membrane potential; themagnitude of depolarization necessary for activation varies among subtypes [15]. There are 4 subtypes of theL-type channel, each of which perform different functions in different cell types. Subtypes Cav1.2 and Cav1.3are the key members of the L-type VGCCs present in neuronal bodies and dendrites, where they are principallyinvolved in regulation of transcription, neurotransmitter release from sensory cells, and synaptic integration andplasticity [14]. These channels are specifically antagonized by drugs belonging to the phenylalkylamines, ben-zothiazepines, and dihydropyridines (such as nimodipine) [14]. L-type channels are activated when membranepotential is depolarized, though different subtypes have different thresholds for activation, varying from -20mV(Cav1.3) to +14mV (Cav1.1) [14]. L-type Ca2+ channels are typically inactivated between -40mV and -60mV (in2mM Ca2+; HEK cells) [39]. Upon activation, some subtypes of these channels (specifically Cav1.1) can reacha single channel conductance of up to 17pS, but typical conductance for the channels is closer to 9pS [14, 106].

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Introduction

Electron microscopy experiments showed that L-type Ca2+ channels are predominantly – though not exclusively– located in postsynaptic dendritic processes and somata of CA1 pyramidal neurons in rat hippocampus [59].Furthermore, this work indicated that the most distal dendritic processes and spines had proportionally greatermembrane expression of L-type Ca2+ channels than more proximal regions [59].

Results from Woodin et al. (2003) showed that nimodipine blocking of L-type VGCCs on the postsynap-tic membrane prevented plasticity induction. This suggested that these particular channels were necessary forplasticity at inhibitory synapses. However, in protocols stimulating the postsynaptic cell only, plasticity was notinduced. This indicated that a postsynaptic depolarization, which should activate L-type channels and allow Ca2+

influx, was not sufficient to induce plasticity in a spike timing-dependent manner at inhibitory synapses [111].These findings suggested that Ca2+ influx must come from another source, and in particular this source must alsorequire presynaptic inputs.

T-Type Calcium Channels

There exist three types of T-type Ca2+ channels: Cav3.1, Cav3.2, and Cav3.3. All three T-type channelsubtypes are present in neuronal cell bodies and dendrites in many areas of the brain including olfactory bulb,amygdala, cerebral cortex, thalamus, hypothalamus, cerebellum, and brain stem [14]. Measures of T-type channeldensity showed similarly that these channels are localized primarily in the plasma membrane of the cell bodyand postsynaptic dendritic processes [69]. Physiologically, T-type channels have been implicated in thalamicoscillations, and in the Ca2+ influx involved in plasticity induction at inhibitory synapses [3, 14]. Unfortunately,there are currently no known T-type specific antagonists, presenting significant challenges to the experimentalinvestigation of the specific role of T-type VGCCs in inhibitory STDP. Activation of T-type channels occurs at∼-45mV and inactivation at -72mV for all three channel subtypes [14]. Upon activation, T-type channels have asingle channel conductance between 7.5-11pS [14, 58, 80].

T-Type Ca2+ Channels are characterized by the low voltage thresholds at which they may become activated,their fast inactivation, and small single channel conductance [104]. Moreover, T-type channels are fundamentallydifferent from other VGCCs in that they require a hyperpolarization to “prime” them for activation. That is, inorder for the channel to become activated upon depolarization of the membrane, it requires a preceding hyperpo-larization to remove the channel from its “inactivated” state [61, 79]. In this way, the T-Type Ca2+ channel is ableto act as a coincidence detector at inhibitory synapses in a similar fashion to NMDARs at excitatory synapses: ifan inhibitory signal is received a short time prior to an excitatory signal, the preceding hyperpolarization shouldoptimally prime the T-type channel for activation, and subsequent depolarization can lead to Ca2+ entry into thepostsynaptic cell. T-type Ca2+ channels have fast voltage-dependent inactivation compared to other VGCCs, andare therefore well suited to large Ca2+ transients, as they are activated at negative membrane potentials when thedriving force for Ca2+ entry is large [15]. These characteristics make T-type Ca2+ channels a key candidate formediating the postsynaptic Ca2+ currents involved in inhibitory STDP.

At inhibitory synapses, positive spike timing intervals mean that presynaptic activity can provide T-type Ca2+

channels the necessary hyperpolarization to remove them from their inactivated state. Subsequent postsynapticspiking leads to local depolarization via the backpropagating action potential, which can both activate L-typechannels and T-type channels (now “de-inactivated” by GABAergic inputs). The resulting Ca2+ influx ultimatelyleads to a depolarizing shift in EGABA. The reason for similar depolarizing shifts in EGABA with negative spiketiming intervals is less clear. Postsynaptic activation leads to L-type channel activation via the backpropagating

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Introduction

action potential, but the failure of the T-type channels to be removed from inactivation by preceding hyperpolar-ization means that Ca2+ influx should be less substantial than in positive spike timing intervals. It is currentlyunknown what additional source of Ca2+ influx may contribute to the plasticity induced at negative spike timingintervals.

Effects of Changes in [Ca2+]i

The primary effect of the transient Ca2+ signals via VGCCs in the neuron is to further alter the electricalactivity of the cell through changes to the conductance of Na+ and K+ channels, and to trigger neurotransmitterrelease at the synaptic boutons [97]. However, Ca2+ also acts as an important intracellular “second messenger”molecule, wherein it relays signals received extracellularly to the relevant intracellular targets. As such, Ca2+

transients can control a wide range of cellular functions indirectly, as discussed previously in the case of STDP atexcitatory synapses. Many proteins are sensitive to changes in [Ca2+]i, which can have a wide variety of down-stream effects. A significant example of this is calmodulin (CaM), a calcium binding protein, which functions asa modulator of the activity of numerous other proteins in the cell [97]. In this way, CaM acts as a Ca2+ sensorand signal transducer. The importance of CaM is highlighted by how highly conserved this protein is among eu-karyotes; its function is necessary for a variety of critical cellular functions including inflammation, metabolism,and apoptosis, among others [20, 103]. Another important class of proteins which can be affected by changesin [Ca2+]i are kinases and phosphatases. Kinases are enzymes which catalyze the addition of phosphate groups(phosphorylation) on target proteins, lipids, and carbohydrates within the cell. Conversely, phosphatases are en-zymes catalyzing the removal of phosphate groups (dephosphorylation) from these sites. For the purposes of thisstudy, we focus only on those kinases and phosphatases which target proteins, particularly those which targetKCC2. Through changes in phosphorylation state of their targets, these enzymes modulate activity, reactivity, orlocalization [105]. A more detailed discussion of the actions of the kinases and phosphatases which act on KCC2is given below.

1.4 Kinase and Phosphatase Activation

Phosphorylation is one of the most important mechanisms for cellular regulation. Protein function, traffickingand cellular localization, as well as interaction with other proteins, can be modified by changes to phosphorylationstate of key residues. As phosphorylation is a reversible covalent modification, and hence can allow for dynamicresponses to cellular changes, it has been suggested that phosphorylation-dephosphorylation reactions are primar-ily regulatory in nature [54]. While there are many known kinases and phosphatases, all with diverse expressionprofiles and cellular targets, a detailed discussion is beyond the scope of this work. Instead, attention is restrictedto the kinases and phosphatases known to interact with key residues of the protein of interest, KCC2.

1.4.1 Calcium-sensitive Kinases

Activation of kinases may be carried out by a variety of subcellular mechanisms. Many protein kinases maybe activated directly by Ca2+ binding to an activation domain on the enzyme. This is the case with some membersof a group of kinases know as the AGC kinases, including the protein kinases A (PKA), C (PKC), and G (PKG).

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Introduction

Members of the PKC family of protein kinases are activated by transient increases in [Ca2+]i and, when activated,target the C-terminal domain of KCC2 [53, 57]. In particular, PKC has been shown to be responsible for themajority of phosphorylation at key residues controlling KCC2 membrane stabilization [57].

In humans, PKC isozymes are categorized as: (a) conventional isoforms, requiring Ca2+, the second messen-ger signaling lipid diacetylglycerol (DAG), and a phospholipid for activation; (b) novel isoforms requiring DAGbut not Ca2+ for activation; and (c) atypical isoforms requiring neither Ca2+ nor DAG [108]. Studies into the rel-ative abundance of PKC isozymes in mammalian hippocampus showed that early in development, the novel PKCisoforms ε and θ were relatively abundant, while at later stages in development expression of the conventionalisozymes α, β, and γ sharply increases [82]. Moreover, members of the conventional PKC subfamily have beenimplicated in synaptogenesis in the developing brain [82]. As Ca2+ plays an important role in synaptic transmis-sion, which then influences synaptogenesis, it is to be expected that particular PKC isozymes which are crucial inthis process would experience an increase in expression as synaptic connections are established (around P15). Asthe conventional PKC isozymes abundant in mature hippocampal neurons and have been shown to be importantin key processes related to changes in synaptic strength via Ca2+-dependent mechanisms, we restrict our focusto the dynamics of the conventional PKCα, PKCβ, and PKCγ isozymes rather than exploring the differences inactivation patterns of multiple PKC subfamilies.

Structurally, all PKCs consist of a regulatory domain containing membrane targeting motifs C1 and C2,and a catalytic domain, linked together by a hinge region [101]. Once activated, PKCs primarily target mem-brane associated proteins. The C2 domain of PKC is a Ca2+ sensor which serves as a docking trigger in manyCa2+ signaling pathways [53]. Upon Ca2+ binding, the C2 domain is activated to associate with a phospholipidcomponent of the plasma membrane, phosphatidylinositol 4,5-bisphosphate (PIP2) [91]. The C2-PIP2 interactionallows association of the PKC with the membrane, and subsequent interaction of the C1 domain of the proteinwith its membrane-embedded ligand DAG [91]. This results in a high-affinity interaction with the membranewhich releases the autoinhibitory pseudosubstrate segment of the protein from its catalytic domain, thus allowingfor phosphorylation of its target proteins in the membrane [91]. Detailed studies of the molecular interactions ofthe C2 domain with Ca2+ ions showed that both the Hill coefficient, representing the cooperativity of substratebinding, and the affinity of the C2 domain for Ca2+ ions varies among the conventional isoforms (see Table E.8,Section 2.1.4) [53].

It has been shown that PKCα is expressed universally among mammalian cells, while PKCβ is found in thebrain and in endocrine tissues, and PKCγ is found exclusively in the brain and spinal cord [72]. In the rat brain,both PKCα and PKCβ were shown to progressively increase from 3 days before birth to ∼2-3 weeks postnatally,after which point they remained constant [115]. In the same preparations, PKCγ maintained low expression inthe first week postnatally, after which point it sharply increased to reach its maximal concentration around threeweeks after birth [72, 115]. Interestingly, this timeline dovetails with the shift in polarity of GABA signaling,which is a function of changes in the relative expression levels of NKCC1 and KCC2. Furthermore, activityof NKCC1 and KCC2 are thought to be reciprocally regulated by phosphorylation [86]. PKC is the primarykinase responsible for phosphorylation of KCC2 at key residues involved in membrane stability and transportertrafficking, and hence its activity can influence transport efficacy, suggesting that there may be reason to believechanges in PKC expression levels and shift in EGABA are causally related [16, 57]. The details of PKC-dependentphosphorylation of KCC2 are discussed in more detail below (see section 1.5.1).

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Introduction

1.4.2 Calcium-sensitive Phosphatases

As with Ca2+-sensitive kinases, there exist a wide variety of Ca2+-sensitive phosphatases with many down-stream effects. For the purposes of this study, we restrict our attention to those phosphatases that directly influencethe phosphorylation state of KCC2. Independent studies have implicated both protein phosphatase 1 (PP1) [55]and calcineurin (also known as protein phosphatase 3, formerly protein phosphatase 2B) [93] in the dephospho-rylation of KCC2 at key residues which control membrane stabilization. As a result of dephosphorylation at theseresidues, KCC2 becomes destabilized in the membrane, increasing the probability of endocytosis, and thereforedecreasing transport function. Both PP1 and calcineurin are serine/threonine phosphatases responsive to changesin [Ca2+]i.

There exist multiple isoforms for PP1; PP1α, PP1β, PP1γ1 and PP1γ2 [38]. All PP1 isoforms contain ahighly conserved threonine residue near the C terminus (T320) which is normally phosphorylated by Cdk5 toinhibit PP1 activity by blocking the active site for PP1 substrates [38]. NMDA receptor-mediated Ca2+ influxis critical for mediating the dephosphorylation of PP1 residue T320, and hence PP1 is activated indirectly byCa2+ [38]. Findings suggest that the mechanism for dephosphorylation of the inhibitory T320 residue in responseto synaptic stimulation is due to proteasome-dependent degradation of p35, a regulator of Cdk5. Degradation ofp35 results in inactivation of Cdk5, allowing auto-dephosphorylation of the T320 residue by PP1 [38].

The mechanisms by which calcineurin is activated are slightly more nuanced, as it experiences dual regula-tion by Ca2+, meaning that it is activated both directly by Ca2+ at its regulatory domain, calcineurin B, and indi-rectly by Ca2+ via calmodulin (CaM) which itself binds Ca2+ [102]. CaM has four Ca2+-binding domains which,once bound, alter the conformation of the protein to allow it to interact with target proteins such as calcineurin, inorder to modulate their activity [98]. Calcineurin is a heterodimer, consisting of a catalytic subunit calcineurin A(which binds CaM), and a regulatory subunit calcineurin B (which binds Ca2+ directly) [102]. Upon binding ofCa2+, calcineurin B changes its conformation, which in turn induces a conformational shift in calcineurin A, andexposes the CaM binding site [5]. This dual Ca2+ control mediated by two separate Ca2+-dependent proteins, CaMand calcineurin B, is a property which is highly conserved among eukaryotes [40]. Importantly, Ca2+-dependentactivation of calcineurin B in the absence of CaM stimulates calcineurin to less than 10% of the level of activ-ity achieved in the presence of CaM, indicating that CaM is central to the proper function of calcineurin [102].Calcineurin also plays a significant role in the induction of neural plasticity, especially in the hippocampus. Atinhibitory synapses, calcineurin dephosphorylates GABAA receptors via NMDA-dependent Ca2+ influx, result-ing in a reduction in GABAergic drive [5, 19]. At inhibitory synapses, treatment with the calcineurin inhibitorFK506 prevents decreased KCC2 membrane expression at inhibitory synapses, indicating that calcineurin has adirect relationship with the transporter [93]. These results, taken together, suggest that calcineurin is an importantregulator of plasticity at inhibitory synapses.

1.5 The K+-Cl− Co-transporter KCC2

The solute carrier family 12 includes nine electroneutral cation-chloride transporters encoded by the SLC12Agenes, four of which are potassium-chloride cotransporters [29]. KCC2 is unique among these four members ofthe KCC gene family in that it is neuron-specific. Moreover, KCC2 can function under isotonic conditions, afunction conferred by a region of 15 amino acids not present in other KCCs, which can only carry out transport

15

Introduction

under conditions of osmotic stress [1, 107]. KCC2 is a large (∼140kDa) protein with 12 predicted membrane-spanning segments and cytoplasmic carboxy- and amino-terminal domains [77]. In mature neurons, KCC2 is theprimary transporter responsible for neuronal Cl− homeostasis and ultimately the driving force for Cl− throughGABAA receptors (see equation (1.2)). In hippocampal neurons, KCC2 is targeted to the somatodendritic cellsurface, preferentially accumulating at synapses [17]. Though KCC2 membrane expression is necessary forthe maintenance of low [Cl−]i, it has been shown that the reversal potential for GABAA receptors (EGABA) - ameasure of transport efficacy - does not necessarily correlate with KCC2 expression [17, 41]. This suggests thatexpression alone is not sufficient for functionality and that there may be additional, post-translational mechanismsby which KCC2 function is regulated. Alterations to the phosphorylation state of key residues in the C-terminus(specifically between residues 929 and 1043) of KCC2 decrease transporter function, indicating that this regionplays a necessary role in the operational states of KCC2 [1, 70]. There is a growing body of evidence pointing tophosphorylation as one of the primary post-translational modifications responsible for KCC2 regulation [17, 56,57], although some details of this mechanism remain uncertain.

1.5.1 Phosphorylation of KCC2

The C-terminal domain of KCC2 plays an important role in many of its functional properties, and as such ishighly conserved. In addition to structural motifs important for its activity in isotonic conditions, the C-terminaldomain contains sites for post-translational modifications such as phosphorylation important for activity regula-tion [1, 57, 70, 86]. KCC2 phosphorylation and dephosphorylation at key residues found in this key C-terminalregion have profound effects on its localization to the membrane and its transport efficacy [17, 56, 57, 110].Moreover, changes in the phosphorylation of several of these residues are thought to be chiefly controlled by aCa2+-dependent kinase and phosphatase activity [56, 57].

While phosphorylation at different residues can have widely varied effects on KCC2 trafficking and efficacy,the Serine 940 (S940) residue is the primary site of PKC phosphorylation in KCC2 [56, 57]. S940 plays asignificant role in the modulation of KCC2 dynamics; KCC2 phosphorylated at this residue has enhanced cellsurface expression, as well as increased membrane stability and transport efficacy [16, 56, 57]. For the purposesof this study, phosphorylation of KCC2 will refer specifically to phosphorylation at this residue.

S940 was first established as a putative phosphorylation site by point mutation experiments, modifying theamino acid sequence of the KCC2 protein so that Serine was replaced by Alanine at position 940 to eliminatephosphorylation. Mutation of S940 reduced total KCC2 phosphorylation by almost 70% (an effect not observedwith point mutation at other putative phosphorylation sites), suggesting the S940 is the primary site of phospho-rylation on KCC2 [57]. Lee et al. (2007) showed that this site is a direct target of Protein Kinase C (PKC), andthat these events were responsible for increased cell surface expression levels. This phosphorylation has beensuggested to increase membrane stability by decreasing the probability of endocytosis [17]. As a result of thisincreased expression and stability, more efficacious transport is observed [16, 56, 57]. Point mutation experi-ments by Chamma et al. (2013) showed that mutation of S940 to Aspartate (phosphomimetic KCC2) preventedthe increases in membrane diffusion and KCC2 cluster dispersal in cells treated with the K+ channel blocker4-aminopyridine (4-AP), used to increase synaptic activity, indicating that KCC2 phosphorylation state can beregulated in an activity-dependent manner [17].

Dephosphorylation of KCC2 at this site is less well characterized; both Protein Phosphatase 1 (PP1) and

16

Introduction

calcineurin (discussed above, see section 1.4.2), have both been proposed to act on S940 [56, 57, 93]. In pointmutation experiments substituting S940 for Alanine (mimicking dephosphorylated KCC2), KCC2 was 1.4 timesfaster to diffuse through the membrane than controls, indicating that dephosphorylated KCC2 is less stable inthe membrane [17]. Moreover, this group also showed that activity-dependent destabilization of KCC2 withinthe membrane was due to dephosphorylation [17]. In particular, confinement range and dwell time within themembrane are decreased as a result of increased neuronal activity [17].

It is important to remember that the phosphorylation state of the residue is determined by the balance

between the activity of the kinases and phosphatases which act on it. In this project, we will remain agnosticabout the details of KCC2 phosphorylation/dephorylation. Several parameters in our model are taken from studieson the kinetics of PKC and calcineurin activity. However, our model will not capture the specifics of S940phosphorylation, or the dynamics of PKC and calcineurin, per se. Rather, the model is designed to reflect generalprinciples of Ca2+-dependent phosphorylation/dephosphorylation of KCC2 as a potential regulatory mechanism.It has been hypothesized by the Woodin lab, and others, that Ca2+-dependent KCC2 phosphorylation is a majormechanism involved in inhibitory synaptic plasticity. This hypothesis is the focus of this project. Using a kineticmodel of KCC2 phosphorylation and Cl− flux, we will explore whether Ca2+-dependent phosphorylation is aplausible mechanism for inhibitory synaptic plasticity.

1.5.2 Activity-Dependent KCC2 Dephosphorylation

Neuronal activity can alter KCC2 membrane expression and transport function under both normal and patho-logical conditions [28, 41, 55, 88, 111]. During plasticity induction, repetitive pre- and post-synaptic spiking leadsto Ca2+ influx via VGCCs activated by the backpropagating action potential in the postsynaptic cell. While L-type VGCCs are activated by membrane depolarizations from postsynaptic spiking only, T-type VGCCs requireinhibitory inputs resulting from presynaptic spiking to remove them from an inactive state before being activatedby postsynaptic depolarization. Consequently, the temporal separation between pre- and post-synaptic firing de-termines which VGCCs will be activated, and therefore the level of Ca2+ influx into the postsynaptic cell.

Persistent elevation in [Ca2+]i leads to sustained activation of Ca2+-sensitive second messenger proteinssuch as CaM, as well as Ca2+-sensitive kinases and phosphatases such as PKC and calcineurin. CaM, PKCand calcineurin are all differentially responsive to changes in [Ca2+]i, and have different kinetic parameters foractivation (see Tables E.8 and E.9, Appendix) [53, 98, 102]. Consequently the level of [Ca2+]i determines therelative levels of active kinase and phosphatase in the postsynaptic cell. As PKC and calcineurin have bothbeen shown to target key residues in the C-terminal domain of KCC2, the balance between active kinase andphosphatase ultimately determines the probability of phosphorylation of the transporter. Importantly, in the modelpresented in this thesis, it is the balance between kinase and phosphatase activity, dependent on the level of Ca2+

influx, which is ultimately responsible for transforming coincident spiking activity into changes in KCC2 function.

1.6 Changes in Cl− Reversal Potential

Changes in KCC2 phosphorylation state can alter dwell time and clustering of KCC2 proteins in the mem-brane [17]. In particular, point mutation experiments creating phosphomimetic KCC2 (S940 to Aspartate mutant)

17

Introduction

and constitutively dephosphorlyated (S940 to Alanine mutant) KCC2 showed that dephosphorylated KCC2 punctamoved more in the membrane in both distance and speed as compared to their wildtype counterparts. Moreover,phosphomimetic KCC2 did not differ significantly from wildtype in its mobility and clustering in the membrane,suggesting that membrane KCC2 may be phosphorylated under basal conditions [17]. However, the phospho-mimetic KCC2 mutant prevented the increase in lateral diffusion resulting from increased synaptic activity inwildtype controls, suggesting that dephosphorylation may play a key role in the changes in KCC2 membranedynamics in response to synaptic activity [17].

Destabilized KCC2 is more likely to undergo endocytosis, resulting in decreased levels of functional trans-porter in the membrane [55, 56]. This results in intracellular Cl− accumulation, as there is less functional trans-porter available to pump Cl− out of the cell following hyperpolarizing GABAergic inputs. Consequently, there isa depolarizing shift in EGABA which reduces the driving force for Cl− through GABAA receptors upon stimulationof the postsynaptic cell (see equation (1.1)). As there is less Cl− influx upon receptor stimulation, GABAer-gic inputs have a diminished inhibitory effect on the postsynaptic cell. As such, factors influencing changes toCl− homeostatic mechanisms such as extrusion by KCC2 can have profound effects on the efficacy of inhibitoryneurotransmission.

Summary

At inhibitory synapses, repetitive firing of pre- and postsynaptic neurons at a fixed interval can lead tochanges in the GABAergic postsynaptic current (GPSC) [111]. The size of this interval, ∆t, affects the degree ofchange in synaptic strength. Coincident activity (-20 ms < ∆t < +20 ms) leads to a depolarizing shift in EGABA,which results in decreased strength of GABAergic transmission [3, 111]. As GABAA receptors are more perme-able to Cl− than to HCO−3 , EGABA is closer to the reversal potential for Cl−, ECl [6, 46]. In mature neurons, theK+-Cl− cotransporter KCC2 is the primary transporter responsible for Cl− homeostasis and as such is a primecandidate for mediating the shift in EGABA seen during STDP induction.

KCC2 is subject to post-translational modifications such as phosphorylation, which affects its stability inthe membrane and transport efficacy [57]. Moreover, the phosphorylation state of key residues in the C-terminaldomain of the protein can be altered in an activity-dependent manner [17]. Phosphorylation of the particularresidue responsible for membrane stabilization is under the control of specific kinases and phosphatases, namelymembers of the PKC family of kinases and either the phosphatase PP1 or calcineurin [16, 57, 93]. Notably, theseenzymes are sensitive to changes in [Ca2+]i [38, 53, 102].

It has been proposed that the effects of STDP induction are due to changes of key cellular second messengers,such as intracellular Ca2+ signals [94]. Small spike timing intervals allow for GABA release into the synapsewhich binds to postsynaptic GABAA receptors, and also importantly allows for depolarization of the postsynapticcell which activates voltage-gated calcium channels in the postsynaptic membrane [3, 111]. L-type VGCCs arenecessary but not sufficient for plasticity induction at inhibitory synapses, indicating that Ca2+ influx is crucial,yet must also involve presynaptic input [111]. T-type Ca2+ channels are prime candidates for such Ca2+ influx,as these channels require a local hyperpolarization to remove them from an inactivated state preceding activationby depolarization, allowing them to function as inhibitory input coincidence detectors in much the same wayNMDARs act as coincidence detectors at excitatory synapses [14].

18

Introduction

Bringing the current evidence together, we note that the following facts have been demonstrated separatelyin various experimental preparations:

• Woodin et al. (2003) showed that coincident activation of pre- and post-synaptic neurons could lead toa depolarizing shift in ECl in the postsynaptic cell. Moreover, this depolarizing shift in ECl was due toincreases in [Ca2+]i via VGCCs [111].

• Balena et al. (2010) showed that during a coincident STDP protocol at inhibitory synapses, Ca2+ influx wasmediated by T-type VGCCs [3].

• Multiple studies in a variety of cell types have shown that changes in [Ca2+]i can effect both PKC andcalcineurin [38, 53, 102]

• Multiple studies have shown KCC2 phosphorylation at key residues to be responsible for membrane sta-bilization and transport function [17, 55–57, 110]. Moreover, some of these studies have also shown thatphosphorylation of these residues is under the control of specific kinases and phosphatases, namely PKCand PP1 or calcineurin [16, 57, 93].

• A great deal of research suggests that as KCC2 is the primary transporter responsible for Cl− homeostasisin mature neurons, and decreases in the function of KCC2 lead to a depolarizing shift in ECl [6, 76, 86].

This thesis aims to explore the mechanism by which coincident activity between pre- and post-synapticneurons leads to changes in the strength of inhibition at these synapses. Given the above experimental work, it isreasonable to hypothesize the following:

1. Coincident activation of pre- and post-synaptic neurons leads to changes in [Ca2+]i mediated by specificVGCCs in the postsynaptic membrane.

2. Transient increases in [Ca2+]i lead to different relative levels of kinase and phosphatase activation. Acti-vation of these enzymes leads to changes in the phosphorylation state of key residues on the C-terminaldomain of KCC2, the main regulator of [Cl−]i in mature neurons.

3. Dephosphorylation of specific residues leads to destabilization of KCC2 in the membrane, increased endo-cytosis, and consequently diminished transport of Cl−.

4. Reduced extrusion of Cl− leads to intracellular Cl− accumulation and hence the depolarizing shift in EGABA

seen following plasticity induction at inhibitory synapses.

The verification of hypotheses of this nature remain experimentally intractable given current biological in-tervention methods; for example, kinase and phosphatase inhibitors remain too blunt, unable to target the specificaction on KCC2 without having widespread effects on other regulatory processes which these enzymes may beinvolved in. Even experimental preparations which can achieve the desired specificity of intervention have somesignificant limitations in the ability to interpret results. For example, precise control of KCC2 phosphorylationstate can be achieved by mutation of the S940 residue to either aspartate or alanine (as in Chamma et al. (2013)),it is currently unknown to what degree these mutants differ from wildtype in transport function and hence mainte-nance of [Cl−]i. Consequently, utilization of such mutants in experiments to observe effects of changes to KCC2phosphorylation state during STDP induction require many caveats for the interpretation of results.

19

Introduction

However, computational models provide a powerful tool to lend support to the plausibility of this proposedmechanism and generate experimental predictions for inhibitory synaptic plasticity. The focus of my Master’sproject was to create a biologically constrained computational simulation of Ca2+-dependent changes in KCC2phosphorylation state to determine if this is a feasible mechanism for the depolarizing shift in EGABA seen fol-lowing coincident spiking at inhibitory synapses. Figure 1.5 summarizes the proposed steps of this mechanism,which will be discussed in further detail below.

Figure 1.5: Proposed Mechanism for Depolarizing Shift in EGABA via Coincident Spiking Activity. (1) Coinci-dent pre- and post-synaptic spiking activity (∆t ∈ -20 ms, +20 ms) leads to (2) Ca2+ influx via voltage gatedcalcium channels (VGCCs). (3) Ca2+-sensitive inactive kinase and phosphatase ([KI] and [PI], respectively) aredifferentially converted to their active forms ([KA] and [PA]) in response to rising [Ca2+]i (4) Increased levels ofactive phosphatase dephosphorylate key residues of membrane-associated KCC2, leading to destabilization in themembrane and increased likelihood of endocytosis. (5) Increased KCC2 endocytosis leads to less available trans-porter in the membrane, hence decreased capacity for Cl− extrusion. Accumulation of intracellular Cl− resultsin a depolarizing shift in EGABA. (6) This depolarizing shift in EGABA reduces the driving force for Cl− throughGABAA receptors, hence diminished Cl− influx upon activation of GABAARs and consequently reduced strengthof inhibition.

20

Introduction

1.7 Thesis

1.7.1 Rationale

While each of the steps outlined above have been demonstrated experimentally (see Figure 1.5), it is unclearwhether this current scheme for the mechanism of inhibitory synaptic plasticity is reasonable. In particular, thereare several key issues in demonstrating this scheme experimentally:

• For each step in the process outlined in Figure 1.5, the downstream effects are widespread. This is partic-ularly true of Ca2+ influx; as discussed above [Ca2+]i is tightly regulated in the cell in part because it actsas a variable signaling molecule with many downstream targets. Experimentally, this makes it difficult todraw conclusions about its specific role affecting changes in ECl, as it is difficult to rule out other possi-ble ways in which Ca2+ influx may influence ECl. Similar concerns can be raised about other steps in theproposed process. For example, interventions involving PKC and/or calcineurin activity, which both havemany targets in the cell, make it hard to draw specific conclusions about the observed effects.

• It is very difficult to test all of these steps together in the same experimental preparation. Such an experi-ment would require many different techniques, including conditional genetic manipulations, pharmacology,imaging and electrophysiology, simultaneously.

• In the demonstration of one step of the above scheme, we hamper the ability to cleanly show other steps, asone experimental manipulation may give rise to confounding factors for other steps. For example, experi-mental manipulation of VGCCs may have the consequence of altering the activation dynamics of a varietyof kinases and phosphatases, some of which may target other proteins that can also affect Cl− homeostasis.Consequently, it is difficult to then draw conclusions about KCC2 function from such an experiment.

Given that there are several major challenges inherent to designing an experiment to verify a scheme of this scope,it is advantageous to use a computational model to investigate the plausibility of the hypothesis.

Computational modeling lends itself well to the study of complex interacting systems, as it can manage largeamounts of data and can track changes in many parameters simultaneously. Models may be able to reconcile in-consistent data, and provide insights into commonalities among phenomena. Model systems may be more cleanly“lesioned” than experimental systems, and by impairing and restoring isolated features can give information abouttheir particular functions. However, in order to draw any conclusions about functional desiderata, modeling re-quires a well defined set of equations describing the activity of the system, careful definition of parameters, andexplicit declarations of the assumptions about the mechanics of the system. Consequently, successful modelingrevolves around the creation of well constrained experimental questions. Clarity in the rationale, hypothesis, andgoals of the study is crucial to the ability to interpret model results.

1.7.2 Hypothesis

As detailed above, current research indicates that coincident pre- and post-synaptic spiking leads to a Ca2+-dependent depolarizing shift in EGABA [3, 111]. This change in EGABA has been proposed to occur as a result ofdecreased Cl− extrusion due to lowered availability of KCC2 in the membrane [17, 55]. The presence of KCC2

21

Introduction

in the membrane is reduced by Ca2+-dependent dephosphorylation of key residues in the C-terminal domain,which cause destabilization in the membrane and increased rate of internalization via endocytosis [17, 56, 57]. Atthese inhibitory synapses, coincident activation of pre- and post-synaptic cells provide conditions necessary forT-type channel-mediated Ca2+ influx, which could allow for activation KCC2-targeting kinases and phosphatases[16, 57].

In order to examine this mechanism, a detailed kinetic model specified by experimentally derived param-eters was developed. Though many parameters were available in the literature, parameters describing the Ca2+-dependent activation rates for our phosphatase were not available. Consequently, these parameters must be ob-tained by fitting analytical solutions to derived differential equations against existing data. Activation and inacti-vation rates for phosphatase should be such that kinase and phosphatase activity may be dynamically controlledby changes in [Ca2+]i. Furthermore, parameters characterizing rates of KCC2 trafficking to and from the mem-brane, and rates of KCC2 phosphorylation/dephosphorylation are not available in current literature. Therefore,we used experimental data collected by the Woodin lab to either determine these parameters explicitly or fit themto achieve the experimentally observed behaviour.

Importantly, changes in [Ca2+]i can be mediated by different VGCCs on the postsynaptic membrane. WhileL-type VGCCs allow Ca2+ influx in response to small depolarizations of the postsynaptic membrane, the require-ment of T-type VGCCs for preceding hyperpolarization suggests that the effects of inhibitory STDP induction aremediated by these channels [3].

We hypothesize that the depolarizing shift in EGABA resulting from coincident pre- and post-synapticspiking is the result of dephosphorylation and subsequent destabilization and internalization of KCC2 inthe membrane, leading to diminished transport of Cl− out of the cell. Furthermore, we hypothesize that thisdephosphorylation is due to changes in the relative activation of Ca2+-sensitive kinases and phosphatasesmediated by Ca2+ influx via T-type VGCCs.

1.7.3 Goals

The specific goals of this model are:

1. To determine whether the Ca2+-dependent dephosphorylation of KCC2 is a plausible mechanism for thechanges seen experimentally during induction of inhibitory STDP

2. To explore the differences in the Ca2+-dependent dephosphorylation of KCC2 mediated by L- and T-typeVGCCs in the postsynaptic membrane

3. To draw inferences about the nature of Ca2+-dependent dephosphorylation of KCC2 to constrain futureexperimental work

4. To generate empirically testable hypotheses about the mechanisms governing inhibitory synaptic plasticity

22

Methods

2.1 Computational Modeling

All model parameters sourced from literature are presented below in the relevant subsections, and summa-rized in appendices D and E.

2.1.1 Passive Properties

Parallels may be drawn between signal transduction in neurons of the brain and the movement of electricalcurrent through a circuit. The neuron may be seen as a core conductor in that its membrane acts as a capacitorseparating electrically conducting media on either side. Because of this, propagation of neural signals throughoutthe cell can be well characterized by cable theory wherein the cell is represented as a single or segmented cylinder[85]. Cable theory utilizes mathematical expressions to represent the electric current across sections of the neuron,and can be used for modeling both passive and active properties of the membrane. The current through the cellcan be equated to the current flowing across the membrane of a one-dimensional cable (by Kirchoff’s law). Fora continuous cell, a current injected to the cell at position x has an effect on the voltage which is describedmathematically by the partial differential equation:

τ∂V∂t

= λ2 ∂2V∂x2 − V

τ = RMCM

λ =

√RMd4RA

Where τ is the membrane time constant, i.e. how fast the membrane potential will change in response to theinjected current. The length constant λ indicates the distance that a stationary current will influence the membranevoltage, V , which is itself dependent on both time t and position x along the core conductor. Here RM is themembrane resistance, CM the membrane capacitance, RA the cytoplasmic (axial) resistance, and d is the diameterof the cylindrical cellular compartment.

In our model, passive properties of the neuron such as membrane capacitance and the resistivity of thecytoplasm, were selected by using the defaults of the NEURON simulation environment. Membrane capacitancewas set to 1µF/cm2, and cytoplasmic resistivity was set to 35.4Ω, consistent with experimental findings for specificmembrane capacitance [31] and cytoplasmic resistivity [37] in hippocampal neurons. The resting membrane

23

Methods

potential (VM) was set at -70 mV, calculated from the Goldman-Hodgkin-Katz equation (see equation (1.3)), usingknown ion concentrations inside and outside the cell sourced from the literature (details of which are discussedbelow) and estimates of the relative permeability of the membrane to each ion species at rest. The temperatureof the system was set to 36C to reflect the resting body temperature of mammals. Nonspecific ion leak channelsinserted into the membrane were set with conductance (gl) of 0.001 S/cm2 and reversal potential (El) of -70 mV.

2.1.2 Model Geometry

The cell was designed as a single cylindrical section with a volume of 785.4 µm3 (d = 10 µm and length, L

= 10 µm), divided into 11 equal segments. The number was chosen based on analytical estimates of the numberof segments necessary for accurate numerical simulation of voltage changes in a cell of this size. Numericalintegration calculations were calculated at the center point of each segment.

2.1.3 Ion Parameters

The NEURON simulation environment tracks changes in ionic concentrations of ions which have been reg-istered with the program. By default, Ca2+, Na+ and K+ are registered with NEURON, while Cl− and HCO−3were registered by hand. Registering an ion x automatically creates the associated variables Ix, [x]i, [x]o, andEx, representing the inward current (pA), internal concentration (mM), external concentration (mM), and reversalpotential (mV), respectively. The reversal potential for each ion was calculated by NEURON upon simulationinitialization using the Nernst equation. ECl was recalculated for each timestep to account for dynamic fluctua-tions in Cl−. All other ion species were assumed to have unchanging reversal potentials. Additionally, parametersspecifying diffusion dynamics for Cl− within the cell were specified. Details are discussed in further detail inSection 2.1.4 (§ KCC2 Transporter). Ion concentrations for simulation initialization were sourced from relevantliterature, summarized in Table E.3.

2.1.4 Channels and Transporters

Channels and transporters responsible for the management of ion concentrations across the membrane weregiven as distributed mechanisms in the NEURON simulation environment. These mechanisms are also referredto as “density mechanisms” as they are specified with density units, often as conductance or current per unit area.Hodgkin-Huxley currents, voltage-gated calcium channels, and active transport mechanisms such as the KCC2cotransporter were designed as distributed mechanisms in this model.

Hodgkin-Huxley Channels

K+ and Na+ ion management for the compartment was principally performed by Hodgkin-Huxley channels,which mediate their flow across the membrane. Hodgkin-Huxley channel kinetics are sensitive to changes inmembrane voltage, which triggers changes in the state of activation, inactivation, and deactivation gates for Na+

and K+ channels represented as membrane conductances.

The Hodgkin-Huxley model was originally developed to describe the initiation and propagation of action

24

Methods

potentials through the squid giant axon, and has been shown to be largely relevant in the study of neural transmis-sion in mammalian brains as well [36]. This conductance model is a set of nonlinear differential equations whichapproximates the electrical properties of the neuron. The kinetic equations used in this model are given by:

INa = gNa · m3 · h · (V − ENa) (2.4)

IK = gK · n4 · (V − EK) (2.5)

Where gx is the maximal conductance for the ion x. For this model, gNa was set to 0.120 S/cm2, and gK was set to0.005 S/cm2 [90]. The term m represents Na+ channel activation gates, h represents Na+ inactivation gates, and n

represents K+ activation gates. These are voltage-dependent gating variables described by the equations:

dmdt

= m +( αm

αm + βm− m

)(1 − et/τm ) (2.6)

dhdt

= h +( αh

αh + βh− h

)(1 − et/τh ) (2.7)

dndt

= n +( αn

αn + βn− n

)(1 − et/τn ) (2.8)

In this model, αm,h,n and βm,h,n are:

αm = 0.32 · Vtrap((13 − V∗), 4

)(2.9)

βm = 0.28 · Vtrap((V∗ − 40), 5

)(2.10)

αh = 0.128 · e(17−V∗)/18 (2.11)

βh =4

1 + e(40−V∗)/5(2.12)

αn = 0.032 · Vtrap((15 − V∗), 5

)(2.13)

βn = 0.5 · e(40−V∗)/5 (2.14)

(2.15)

The variable V∗ = V - Vtraub where V is the membrane potential and Vtraub is a variable shifting the voltage-dependence of the voltage-gated currents, given as -60 mV.

The function Vtrap is

Vtrap(x, y) =

y − 2x if | xy | < 10−6

xex/y−1 otherwise

(2.16)

Finally, the variable τx (for x = m,h,n) is given by:

τx =3.0(degC−36)/10

αx + βx

25

Methods

Where degC is the temperature (C). In this model, degC = 36C (see Table E.2, Appendix) so this simplifies to

τx =1

αx + βx(2.17)

These equations describe the current flowing through a given ion channel as functions of the membranepotential, via the voltage-sensitive gates m, n, and h. The dynamics of the gates are also determined by the rateconstants α and β, which represent the rates of transitions back and forth between the open and closed states.Here, V is the membrane potential, set to -70 mV at rest. Note that these equations have been modified from theoriginal Hodgkin-Huxley formulation to account for temperature differences between mammals (typically ∼36C)and squid, for which these equations were originally developed. Hodgkin-Huxley parameters are summarized inTable E.4 in the Appendix.

Calcium Channels

Channels involved in Ca2+ ion management were retrieved from ModelDB (https://senselab.med.ya-le.edu/)from files uploaded by Poirazi et al. (2003) used in their work on CA1 pyramidal neurons (Model Accessionnumber 20212) [81]. Parameters for the Ca2+ ion channels used in the Poirazi model, including conductances,were carefully tuned to fit data from earlier experiments exploring single channel properties and studies concernedwith dendritic physiology and synaptic integration, which includes responsiveness of the channels to changes involtage and/or synaptic stimulation [81]. The choice to use Ca2+ channels from this model was primarily due tothe great deal of care that was taken to ensure physiological fidelity to a CA1 pyramidal cell – the supplementarymaterials for Poirazi et al. (2003) available online detail the variety and scope of verification studies used for thismodel. Voltage dependent Ca2+ currents via VGCCs are described below for each Ca2+ channel type. The kineticequations and density distributions used were adapted from Magee and Johnston (1995) [61].

L-Type Calcium Channels

Kinetic equations describing HVA or L-type Ca2+ channels are given by the following set of equations. Calciumcurrent (ICaL ) through the L-type Ca2+ channel is given by:

ICaL = gCaL· m ·

0.001mM0.001mM + [Ca2+]i

· ghk(V, [Ca2+]i, [Ca2+]o) (2.18)

Where gCaLis the maximal conductance for the channel, and ghk(x, y, z) is a modified Goldman-Hodgkin-Katz

(GHK) equation given by:

ghk(V, [Ca2+]i, [Ca2+]o) = −x ·(1 −

[Ca2+]i

[Ca2+]o· eV/x

)· f

(Vx

)(2.19)

With x being a function of the absolute temperature (K) and f (z) being a function to eliminate singularities in theGHK equation:

x =0.0853 · T

2(2.20)

f (z) =

1 − z2 if |z| < 10−4

zez−1 otherwise

(2.21)

26

Methods

Furthermore, the activation gating variable m for the L-type Ca2+ channels were described by:

mt+dt = mt +(1 − e−

dtτm

)·( αm(V)αm(V) + βm(V)

− mt

)(2.22)

Where αm,h(V), βm,h(V) are given by:

αm(V) = −0.055 ·V + 27.01

e−(V+27.01)/3.8 − 1(2.23)

βm(V) = 0.94 · e−V+63.01

17 (2.24)

And τm,h is:

τm =1

5 ·(αm(V) + βm(V)

) (2.25)

Here V is the membrane voltage (mV), T the absolute temperature (K), and dt is the size of time step betweensuccessive computations (ms). For this model, T was set to 309.15K, and dt was 0.025ms. L-type channelswere given a maximal conductance of gCaL

= 7.6 mS/cm2, based on values given in Poirazi et al. (2003) for acompartment of this size.

T-Type Calcium Channels

For LVA or T-type Ca2+ channels, kinetics are largely described by the same set of equations as with the HVA orL-type channels. Key differences are in the current ICaT , and equations describing αm, βm, and τm:

ICaT = gCaT· m2 · h ·

0.001mM0.001mM + [Ca2+]i

· ghk(V, [Ca2+]i, [Ca2+]o) (2.26)

For the T-type Ca2+ channels, the activation gating variable m was given as above. Current through these channelsis also dependent on an inactivation gating variable h, which was described by:

ht+dt = ht +(1 − e−dt/τh

)·( αh(V)αh(V) + βh(V)

− ht

)(2.27)

Forward and reverse rate constants for the activation and inactivation gating variables were given by:

αm(V) = −0.196 ·V − 19.88

e−(V−19.88)/10 − 1(2.28)

αh(V) = 0.00016 · e−(V+57)/19 (2.29)

βm(V) = 0.046 · e−V/22.73 (2.30)

βh(V) =1

e−(V−15)/10 + 1(2.31)

τm(V) =1

αm(V) + βm(V)(2.32)

τh(V) =1

0.68 · (αh(V) + βh(V))(2.33)

The parameters V and dt are as above in the case of L-type channels. Note that the inactivation gating variable inthe T-type channels ensures that there is no current flow through the channel in the absence of a hyperpolarization

27

Methods

to “de-inactivate” the T-type channel.

T-type Ca2+ channels are given a maximal conductance of gCaT= 7.6 mS/cm2 in the normal conductance

condition, and a maximal conductance of gCaT∗= 3.8 mS/cm2 in the low conductance condition. Poirazi et

al. (2003) gave conductance values for T-type channels in different sections in a multicompartment model whichreflected increasing channel conductance with distance from the soma. The section in our model was large enoughsuch that the conductance for T-type channels from Poirazi et al. (2003) did not have a significant effect on the[Ca2+]i. As a first pass T-type channels were given equal conductance values to L-type channels to observe therelative effects on Ca2+ influx via these two mechanisms. Secondary experiments were conducted with loweredT-type channel conductance to reflect the differences in L- and T-type channel distribution in dendritic cellularcompartments as described in Catterall (2005) [14]. Experiments were run in four Ca2+ channel conditions:

Table 2.1: Ca2+ Channel Conductance Values Used in STDP Induction Experiments

Condition Conductance Value(s) (mS/cm2)

L-type Channels only gCaL= 7.6 gCaT

= 0.0T-type Channels only gCaL

= 0.0 gCaT= 7.6

Low conductance T-type Channels only gCaL= 0.0 gCaT

= 3.8L- and T-type Channels together gCaL

= 7.6 gCaT= 7.6

Calcium Accumulation and Decay

Changes in [Ca2+]i were managed by a mechanism designed by Poirazi et al. (2003), modified from the originalwhich was presented in Destexhe et al. (1994) [23, 81]. The kinetic equations are given by:

d[Ca2+]i

dt= D +

10−4mM − [Ca2+]i

1.4S(2.34)

D =

− fe ·( ICaTotal

0.2·F)

if ICaTotal ≤ 0

0 otherwise(2.35)

Where F is the Faraday constant, and D is the drive for Ca2+ into the cell, controlling the level of [Ca2+]i accu-mulation. ICaTotal is the sum of ICaL and ICaT . The term fe is a factor controlling the rate of Ca2+ entry into the cell,set to 555.6 based on Poirazi et al. (2003) [81]. Notice that when the drive for Ca2+ is D ≤ 0, the drive is set to0 to prevent pumping of Ca2+ out of the cell via this mechanism. Ca2+ decay is given by the second term in theequation. Ca2+ channel parameters are summarized in Table E.5 in the Appendix.

KCC2 Transporter

For the computational model, detailed kinetic schemes of KCC2 regulation in the cell and transport function weredesigned. Full details and derivations of key equations governing these functions are given in Appendix A.

KCC2 Regulation

A detailed kinetic scheme was designed to characterize the changes in KCC2 distribution between its cytoplasmic,membrane unphosphorylated, and membrane phosphorylated states. As the stability of KCC2 in the membrane is

28

Methods

[KI] [MKA]

[C] [PA][M][KA] [KA][MP][PA]

[MPPA] [PI]

α

β

vIK vAKr11

r12

rMP

vIPvAPr22

r21rM

Figure 2.1: Kinetic Scheme of KCC2 Distribution in the Cell. KCC2 can be cytoplasmic [C], unphosphorylated inthe membrane [M], or phosphorylated in the membrane [MP]. Active and inactive states of kinase ([KA] and [KI])and phosphatase ([PA] and [PI]) are shown either bound ([MKA]) or unbound ([M][KA]) from KCC2. Similarlybound and unbound phosphatase-KCC2 are given as [MPPA] and [MP][PA], respectively. rx give rate constantsof binding and unbinding. vAK and vIK give rates of kinase activation and inactivation; similarly vAP and vIP

give rates of phosphatase activation and inactivation. Rates of membrane insertion and endocytosis are given byparameters α and β, respectively.

determined by its phosphorylation state, and therefore by the relative activity of the acting kinase and phosphatase,this scheme must also include dynamics of kinase and phosphatase activity. This kinetic scheme is presented inFigure 2.1. This kinetic scheme can be summarized by the set of differential equations:

d[C]dt

= β[M] − α[C] (2.36)

d[M]dt

= α[C] − (β + RMP[KA])[M] + RM[MP][PA] (2.37)

d[MP]dt

= −RM[MP][PA] + RMP[M][KA] (2.38)

d[KA]dt

= vAK[KI] − vIK[KA] (2.39)

d[PA]dt

= vAP[PI] − vIP[PA] (2.40)

d[KI]dt

= vIK[KA] − vAK[KI] (2.41)

d[PI]dt

= vIP[PA] − vAP[PI] (2.42)

Where RMP and RM are the rates of phosphorylation and dephosphorylation, respectively. RMP and RM are givenby:

RMP =r11rMP

(r12 + rMP)and RM =

r22rM

(r21 + rM)

Full derivations for these equations, based on Michaelis-Menten principles of reaction dynamics are given inAppendix B. The terms ri, j are rate constants for the binding and unbinding of enzyme and substrate (see Figure2.1 above and Table E.7, Appendix E). [C], [M], and [MP] represent the proportion of KCC2 in each of its possiblestates: in the cytoplasm ([C]), unphosphorylated in the membrane ([M]), and phosphorylated in the membrane

29

Methods

([MP]). Consequently, we require that:

[C] + [M] + [MP] = 1 (2.43)

The proportion of kinase in its active and inactive states is given by [KA] and [KI], respectively. Similarly, [PA]and [PI] represent the proportion of phosphatase in its active and inactive states. Hence we also require that:

[KA] + [KI] = 1 (2.44)

[PA] + [PI] = 1 (2.45)

Summaries of variable definitions are given in Table D.1.

The rates of kinase and phosphatase activation (vAK and vAP) are Ca2+-dependent functions described by theHill function (equation (82), Appendix A):

vAK =VAK[Ca2+]hK

RhKK + [Ca2+]hK

(2.46)

vAP =VAP[Ca2+]hP

RhPP + [Ca2+]hP

(2.47)

We assume rates of inactivation (vIK and vIP) are constant.

It has been shown that kinetic properties of PKCs vary among isozymes [53]. Specific parameters for theconventional isozymes PKCα, PKCβ and PKCγ are given in Table E.8. As all of the members of the conven-tional PKC subfamily are found in brain tissue (see [72]), the average of each of these parameters was taken forsimulations. That is, rates of inactivation (vIK) and maximal activation (VAK) were set to 32.1/s and to 390/s,respectively [53]. The half-maximal [Ca2+]i for kinase activation was set 2.37 µM, and the Hill coefficient forcooperativity of Ca2+ binding was set to 1.5 [53].

Experimentally supported kinetic parameters for calcineurin activity were not all available. Half-maximal[Ca2+]i for phosphatase activation was set to 0.7943 µM, and the Hill coefficient for cooperativity of Ca2+ bindingwas set to 2.9 as an average of the range (2.8-3.0) given by Stemmer & Klee (1994) [102]. However, ratesfor the inactivation and maximal activation of phosphatase could not be found in the literature. It is importantto note that the ratio between activation and inactivation is critical for characterizing phosphatase activity (seeequation (2.47)). To this end, we set the rate of phosphatase inactivation arbitrarily to 10/s, and performed multipleexperiments at different ratios of inactivation to maximal activation. We refer to this ratio as Q = VAK/vIK (for“quotient”). In order to ensure physiologically realistic levels of KCC2 in the membrane, we fit the rate parametersfor KCC2 phosphorylation (RMP) and dephosphorylation (RM) based on each Q value in order to match themodel’s steady-state behaviour to experimentally determined levels of KCC2 in the membrane. A more detaileddiscussion of this parameter fitting is given in section 2.3.2. Parameters are summarized in Table E.9 in theAppendix.

While we choose RM, RMP, and Q to maintain steady state levels of [C], [M], and [MP], these valueshave important consequences for the transition of KCC2 among these states with changing levels of [Ca2+]i.Critically, changes in [MP] ultimately allow for changes in the level of available transporter in the membrane, as

30

Methods

dephosphorylated KCC2 can be endocytosed back to the [C] state. Our model tracks total level of membraneassociated KCC2 ([M] + [MP]), and only KCC2 in this pool is used for Cl− transport. Consequently, reductionsin [MP] ultimately lead to diminished Cl− transport from the cell. The precise dynamics of Cl− transport arediscussed in more detail below.

KCC2 Transport

Ion transport via KCC2 in its active, membrane-bound state can be described by the following kinetic scheme:

[TCl−][K+]

[T ][Cl−][K+] [TCl−K+] [P]

[T K+][Cl−]

r1

r2

r1

r2

r1

r2

r1

r2

rT

Figure 2.2: Kinetic Scheme of Cl− Transport via Membrane-Bound, Active KCC2 ([T]). Unbound KCC2 ([T])binds Cl− and K+ at a fixed rate (r1). Transporter may be bound to K+, Cl−, or both ([TK+], [TCl−], and [TK+Cl−],respectively). Ions may spontaneously unbind from the transporter at a fixed rate (r2). Only when bound to bothions ([TK+Cl−]) can KCC2 transport Cl− out of the cell. rT gives the rate of ion transport from the cell, while [P]represents the end product (i.e. unbound transporter with extruded Cl−).

Where [K+] and [Cl−] are the cytosolic concentrations of free K+ and Cl−, respectively, and [T] is theproportion of KCC2 which is in a state conducive to active transport. Since KCC2 is only able to transport whenit is in the membrane, we have:

[T ] = [M] + [MP] (2.48)

The rate at which the transporter [T] extrudes Cl−, is given by:

v =VT [K+][Cl−]

(RT + [K+])(RT + [Cl−])(2.49)

Where RT is the Michaelis constant for Cl− transport through KCC2, set as 5 mM by hand to approximatephysiological rates of Cl− extrusion. (Future work will attempt to determine this value experimentally.) VT isthe maximal rate of transport of Cl− across the membrane via KCC2 given by:

VT = rT [T ] (2.50)

T is the amount of KCC2 in the membrane-bound, actively transporting state and rT is the rate constant of transportacross the membrane once K+ and Cl− are both bound to the transporter, set as 10/s by hand to approximaterealistic Cl− extrusion behaviour. Full derivations of these equations are given in Appendix C.

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Methods

The driving force for the transport of Cl− via KCC2 is given by:

DCl =RTF·(log

[K+]i

[K+]o+ log

[Cl−]i

[Cl−]o

)(2.51)

That is, functional KCC2 will stop transport when [Cl−]i reaches its equilibrium value, i.e.

[Cl−]i =[K+]o

([K+]i[Cl−]o)(2.52)

The explicit flux of Cl− across the membrane is given by:

dCl−

dt= (1 × 104)

[Cl−]i · d · πF

+ (1 × 10−3)ϕ(z) · π · d2

4+ (1 × 104)

Itonic · π · dF

(2.53)

The first term in this expression describes the Cl− current from GABA inputs, discussed in greater detail below.The second term describes the Cl− transport via KCC2, while the third term describes the tonic GABA current(Itonic). The coefficients in front of each term are unit scaling factors for the relative contribution of each sourceof Cl− to the overall flux to ensure consistent units in each term. Here d is the compartment diameter, and thefunction ϕ(z) is the transport function, determining the direction of KCC2 transport across the membrane as afunction of [Cl−]i. ϕ(z) is given by:

ϕ(z) =

vT if DCl ≤ 0

−vT if DCl > 0(2.54)

The tonic GABA current is given by:

Itonic = gtonic · (VM − ECl) (2.55)

Here gtonic is the tonic conductance, set as 0.01 S/cm2 by hand to approximate realistic behaviour. VM and ECl arethe membrane voltage and Cl− reversal potential, as above.

The diffusion of Cl− within each compartment (DiffC) of the cell is given by:

DiffC =dCl−

dt·π · d2

4(2.56)

And the longitudinal diffusion of Cl− between adjacent compartments (DiffL) is given by:

DiffL = axDCl · DiffC (2.57)

Where axDCl is the axial diffusion coefficient for Cl−, set to 10 µm2/ms to produce rapid diffusion of Cl− through-out all segments, effectively rendering the cell a single compartment for Cl−. Future work will examine morerealistic Cl− diffusion simulations.

32

Methods

2.1.5 Synaptic Inputs

GABAergic inputs were designed as custom point processes driven by NEURON’s NetStim objects. De-signing GABAergic synapses in this fashion allowed for multiple point process to be stimulated repeatedly at aspecified frequency, which is not possible with point processes alone. NetStim objects are given a frequencyfor input activation. For custom point processes such as our GABAA receptors, NetStim information is re-ceived in a NET RECEIVE block of code in the mod file (for more information, see NEURON documentation atwww.neuron.yale.edu/neuron/docs). In contrast to distributed mechanisms such as the channels and transportersoutlined above, point processes are present at specific locations on the cell.

Synaptic Distribution

The insertion of multiple identical point processes throughout the cell required a rule for their distributionover the membrane. In our model, inputs are distributed uniformly along the length of the compartment. Theirposition is determined by a user defined seed for a pseudo-random number generator which assigns inputs. Thedensity of the synapses (ρ) is by default set to ρ = 0.01/µm2. At this density, simulations were run with 3GABAergic synapses uniformly distributed over the membrane.

GABAA Receptors

GABAergic synaptic inputs are simulated in NEURON using a model of synaptic Cl− and HCO−3 currentsbased originally on the work of Staley & Proctor (1999) [99]. Kinetics of synaptic conductance are based onpreviously developed models of synapse dynamics

(see Destexhe et al. (1994) and Mainen & Sejnowski (1998)

),

wherein it is assumed that:

• A presynaptic spike releases neurotransmitter into the synaptic cleft with a fixed increase in concentration,C = 1 mM

• Each neurotransmitter release lasts for a fixed amount of time, tD = 1 ms

• GABAA receptors saturate at the maximum conductance level, gGABA = 0.003 µS

Current through the GABAA receptor is given by:

ICl = g · PCl · (VM − ECl) (2.58)

IHCO3 = g · PHCO3 · (VM − EHCO3 ) (2.59)

Where PCl is a scaling factor representing the permeability of the receptor to Cl−. Similarly, PHCO3 is the receptorpermeability of HCO−3 . In our model, PCl = 0.9 and PHCO3 = 0.1. This is to reflect that the GABAAR has a relativepermeability of Cl−:HCO−3 of 9:1, similar to values given in Kaila (1994) [46]. VM, ECl, and EHCO3 are membranevoltage, Cl− reversal potential, and HCO−3 reversal potential, respectively. The conductance g of the GABAR isgiven by:

g = g · (ron + roff) (2.60)

33

Methods

Where g is the maximal conductance and ron and roff are functions giving a measure of GABAAR conductance.ron and roff amount to the number of active and inactive GABAARs in the membrane, respectively, and are scaledby g for the actual conductance (equation (2.60)). These are given by:

ron =G · r∞

rτ− e−t/rτ (2.61)

roff = e−βGABA t (2.62)

Here G is a Boolean variable representing the presence or absence of GABA in the synapse, such that:

G =

1 ron → r∞ with time constant rτ

0 ron == roff

This variable allows the GABAA point processes to manage receiving multiple events less than tD ms apart – i.e.while a signal is being processed, n successive inputs may be received and are processed as transmitter continuingto remain in the synapse for a duration of (n · tD) ms. The above expressions indicate that while neurotransmitterremains in the synapse, ron tends towards an upper bound of r∞. Furthermore, if there is no transmitter present inthe synapse, ron takes the most recent value of roff so that if not all channels have been inactivated, the conductancevalue increases from this point rather than from zero.

In the above expressions, the variable r∞ is the maximal number of open channels, given by:

r∞ =C · αGABA

(C · αGABA ) + βGABA

(2.63)

Where αGABA is the rate of GABA binding to the GABAAR (set as αGABA = 5/ms) and βGABA is the rate of GABAunbinding (set as αGABA = 0.18/ms). C is the maximal neurotransmitter concentration released into the synapticcleft (set as C = 1mM). That is, r∞ is the maximal number of activated GABAARs.

In equation (2.61) rτ is the time constant for transmitter binding to the receptor, given by:

rτ =1

(C · αGABA ) + βGABA

(2.64)

Presynaptic spikes are delivered from NetStim objects to the GABAA point processes as a representation ofneurotransmitter in the synapse, which lasts for a fixed duration (tD = 1 ms). When the neurotransmitter is nolonger present in the cell, the proportion of open channels decreases by the function rδ, given by:

rδ =1

1 − e−tD/rτ(2.65)

Derivations for these equations are given in full in Destexhe et al. (1994) and Mainen & Sejnowski (1998) [24, 62].

2.1.6 Current Clamp

For the STDP protocol, a simulated current clamp was used to initiate postsynaptic spiking. The currentclamp was a custom made point process driven by NetStim objects in a similar fashion to the GABAergic synapses.

34

Methods

However, the current clamp required only one NetStim object to drive a single point process with a set frequency.

The current clamp was inserted in the center compartment of the model. The amplitude of the currentwas set to 2nA with a duration of 2ms, to reflect the experimental conditions we wished to compare resultsagainst [3, 111]. Frequency of inputs to the current clamp was given by NetStim objects in a similar fashion toGABAergic synaptic inputs. During the STDP protocol, 150 current clamp pulses occurred 200 ms apart. Tomaintain a consistent spike timing interval, the initiation time of current clamp events was determined by theinitiation time of GABAergic inputs and the spike timing interval specified by the STDP protocol (see below).Therefore, as GABAergic inputs were initiated at 10050ms after beginning the simulation run to ensure steadystate values for all variables had been reached, current clamp events were initiated at (10050 + ∆t)ms. Currentclamp parameters are summarized in Table E.12, Appendix E.

2.1.7 Spike Timing Dependent Plasticity (STDP) Induction Protocol

Details of the STDP induction protocol were meant to reflect as closely as possible the experimental con-ditions of Woodin et al. (2003) (see Figure 1.4), which was the first experimental demonstration of inhibitorySTDP [111]. For each set of Ca2+ channel conductance conditions (see Table 2.1) and each Q condition (seeTable 3.1), 201 plasticity induction experiments were conducted. These 201 simulation runs varied spike timingintervals (∆t values) from -100 ms to +100 ms with 1 ms steps. In the following sections, a single simulation runis the 100000 ms over which the STDP protocol is run for a given set of Ca2+ channel conditions, Q value, andfixed ∆t value. The STDP protocol began 10000 ms after the initiation of the simulation run to allow all variablesto reach steady state. The protocol lasted 30000 ms at 5Hz to mimic relevant experimental work [3, 111]. Presy-naptic spikes were given as GABAA point process driven by NetStim objects, as outlined above. Spikes weregenerated 200 ms apart. For each presynaptic input, all GABAA point processes were stimulated simultaneously.Postsynaptic spiking was generated by input from the current clamp point process. As a fixed spike timing intervalwas maintained for each simulation run, postsynaptic spikes were also generated 200 ms apart. A sample voltagetrace for an STDP protocol with ∆t = +75 ms is provided in Figure 2.3 (see also Figure 1.5, panel 1). Followingplasticity induction, simulation recordings ran for an additional 60000 ms to observe the return of variables tosteady state levels.

For each simulation run, minimum, maximum, and average values over the course of plasticity induction(10000 < t < 40000), and final value (at t = 40000) for each of the following variables was recorded:

• Intracellular Ca2+ concentration ([Ca2+]i) • Proportion of KCC2 in:• Proportion of kinase in the active state([KA]) – Cytoplasmic state ([C])• Proportion of phosphatase in the active state([PA]) – Membrane (unphosphorylated) state ([M])

– Membrane phosphorylated state ([MP])

Recordings from STDP protocols were made in the NEURON simulation environment and analyzed withcustom code in Python, outlined in greater detail in the Results (see §3.3). These data were used to generate STDPcurves in a similar manner to those presented in Figures 1.3 and 1.4. Rather than measures of the postsynapticcurrent, STDP curves are plotted as the percentage change in membrane phosphorylated KCC2 over the courseof the induction protocol, as a function of spike timing interval (see for example Figure 3.6, below). This wasdone to assess how the percentage of phosphorylated KCC2 changed as a function of ∆t. We assert that if theproposed mechanism for inhibitory STDP is correct, then coincident activity (-20 ms < ∆t < +20 ms) should

35

Methods

Figure 2.3: Example Voltage Trace from the Postsynaptic Cell for STDP Protocol for a Single Simulation Runwith ∆t = +75 ms. Stimulation was carried out for 30000 ms at a frequency of 5Hz. Note hyperpolarizationresulting from presynaptic inputs, followed ∆t ms later by the depolarization from postsynaptic activation.

produce significant dephosphorylation of KCC2, but non-coincident activity (-100 ms < ∆t < -50 ms, +50 ms <∆t < +100 ms) should not.

Changes in ECl during plasticity induction were also measured for specific ∆t values representative of co-incident and non-coincident spike timing intervals. Coincident spike timing intervals were taken to be -20 ms< ∆t < +20 ms, and non-coincident spike timing intervals as -100 ms < ∆t < -50 ms ∪ +50 ms < ∆t < +100ms. Changes in ECl in plasticity induction protocols using coincident and non-coincident spike timing intervalswas compared against data from conditions with pre- or post-synaptic firing alone. Spike timing intervals of ±5ms were taken as representative of coincident activation, and intervals of ±75 ms were taken as representative ofnon-coincident activation. It should be noted, however, that many of our parameters for the extrusion of KCC2-mediated Cl− extrusion were set by hand to create qualitatively realistic behaviour (as described in §2.1.4, KCC2Transport, above). As such, whereas our measurements of changes in KCC2 phosphorylation state are based onparameters grounded in experimental data, changes in ECl were dependent on hand-tuned parameters. It is impor-tant to note, therefore, that the values for ECl changes given in the results must be taken with caution, and do notnecessarily reflect realistic measurements. Future work will use experimental data to determine the parametersfor Cl− extrusion in the model, and examine the effects of different ∆t values on ECl anew.

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Methods

2.2 Experimental Data

Experimental work was performed by Jessica Pressey and Vivek Mahadevan in the lab of Dr. Melanie A.Woodin in the Department of Cell and Systems Biology at the University of Toronto. These experiments weredone in order to estimate rate constants for the insertion and removal of KCC2 to and from the membrane.

2.2.1 Total Internal Reflection Fluorescence (TIRF) Microscopy

To determine the rate of KCC2 insertion into the membrane, tagged KCC2 in the membrane was imagedusing TIRF microscopy under conditions of pharmacological blockade of PKC activity.

Transfection and cDNA constructs

Transfection was carried out using full length murine KCC2 which contained three copies of the influenzahemaglutinin (HA) epitope tag (23), and a GluK2 construct containing a myc-tag (GluR6a-myc). Transfectionwas done in COS 7 cells 24 hours prior to running the experiment with 0.6 g KCC2-HA alone, or 0.25 g KCC2-HA with 0.5 g GluK2. To verify equal KCC2 expression with these concentrations, Western blots were performed.COS 7 cells were transfected using Transfectin Lipid reagent (BioRad), and neurons were transfected with cDNAusing Lipofectamine 2000 (Life Technologies) as per the manufacturers recommendations.

Live immunohistochemistry on COS 7 cells using TIRF Microscopy

COS 7 cells were transfected with KCC2-HA, outlined above. Dishes were washed in PBS, 24 hrs aftertransfection and prior to incubation with mouse monoclonal anti-HA antibody (1/350) at 37 C for 20 minutes.Cells were washed in PBS and incubated in secondary (Alexa Fluor 555 goat anti-mouse secondary, 1/350) for 10minutes. Live images were acquired using a Total Internal Reflection Fluorescence (TIRF) Microscope (Olympus)with an Olympus IX81 inverted microscope using a 60x 1.49NA oil immersion objective with 561 nm excitationwavelengths at a penetration depth of 100nm. Images were acquired using a Hamamatsu C9100-13 EM-CCDcamera. Volocity (Perkin Elmer) was used for both image acquisition and analysis. Anti-HA immunofluores-cence was identified using the spots identification tool in Volocity software. Both cellular transfection and TIRFmicroscopy was performed by Jessica Pressey.

2.2.2 Biotinylation & Western Blot Analysis

To determine steady state levels of KCC2 in the membrane in both phosphorylated and dephosphorylatedstates, biotinylation and Western blot studies were carried out.

Biotinylation

300µm coronal slices from age-matched (postnatal day 30 - 40) male wild-type and GluK1/2-null littermatemice (n=5) were cut using a Leica Vibratome in modified ACSF solution (180 mM sucrose, 25 mM sodium bicar-

37

Methods

bonate, 25 mM glucose, 2.5 mM KCl, 1.25 mM sodium phosphate, 2 mM MgCl2, 1 mM CaCl2, 0.4 mM sodiumascorbate, and 3 mM sodium pyruvate, and saturated with 95% O2/5% CO2 (pH 7.4. osmolarity 295mOsm) toimprove cellular viability. Twelve slices from each genotype were recovered in a 50:50 mix of modified ACSFand normal ACSF solution (125 mM NaCl, 25 mM sodium bicarbonate, 25 mM glucose, 2.5 mM KCl, 1.25 mMsodium phosphate, 1 mM MgCl2, 2 mM CaCl2 (pH 7.4. osmolarity 295mOsm and saturated with 95% O2/5%CO2) for 30 minutes. This was followed by a second recovery in normal ACSF for another 30 minutes at roomtemperature. Slices were incubated in 5 ml of cold-ACSF containing 500 µg/ml EZ-Link Sulfo-NHS-SS-Biotin(21328, Thermo Scientific) bubbled in 95% O2 5% CO2, with gentle agitation for 2 hours at 4C. The reactionwas stopped by quenching excess biotin in cold-ACSF containing 100mM Tris and slices were washed twice incold-ACSF, once in cold-modified ACSF and snap-frozen immediately on dry ice. Entire cortex region was dis-sected under dissecting microscope (Olympus), lysed immediately in modified radioimmunoprecipitation assay(RIPA) buffer [50 mM TrisHCl, pH 7.4, 150 mM NaCl, 1 mM EDTA, 1% Nonidet P-40, 0.1% sodium dodecylsulfate (SDS), 0.5% DOC, protease inhibitors and phosphatase inhibitor mixture (Roche)] and incubated on icefor 30 minutes. After thoroughly homogenizing, the samples was centrifuged, supernatant was collected, andquantified using the BioRad protein quantification kit. 50 µg of total protein in a total volume of 300 µl (made upusing modified RIPA) was mixed with 200 µl of 50% slurry of Neutravidin beads (29201, Thermo Scientific) androtated for 2 hours at 4C. The beads were harvested by centrifugation and the supernatant corresponding to ∼5µg of unbound fraction was aliquoted (to measure the internal, unbiotinylated fraction of surface proteins). Thebeads were subsequently washed three times in modified RIPA buffer. After the last wash all solution was thor-oughly removed from beads, and the biotin-bound and unbound fractions were denatured in 6XSDS sample buffercontaining the reducing agent dithiothreitol (DTT) at 37C for hr before resolving them on onto polyacrylamidegel (6% acrylamide) to perform SDS polyacrylamide gel electrophoresis (PAGE).

Immunoblot Analysis

Protein samples were resolved on denaturing SDS-PAGE gels using standard methods. Samples were incu-bated with the appropriate volume of 6X sample buffer (60% glycerol, 375 mM Tris/HCl [pH 6.8], 0.3% bromo-phenol blue, and 12% SDS), and incubated at 37C for 30 minutes to an hour to prevent aggregation of KCC2proteins. Subsequently samples were loaded on the gel (5% or 7% TrisHCl gels for KCC2), and electrophoresedin SDS-PAGE running buffer (192 mM glycine, 25mM Tris/HCl [pH 8.3], and 0.1% SDS) for 90 - 120 minutes at110 V. Protein samples separated on the gel were transferred onto Hybond-C Extra nitrocellulose membranes (GEHealthcare) at 40 V in transfer buffer (192 mM glycine, 25 mM Tris/HCl [pH 8.3], and 20% methanol). Followingtransfer (overnight/25V/4C, or 2hrs/60V/4C) membranes were briefly stained with Ponceau S solution (0.1%(w/v) Ponceau S, 5% acetic acid) to verify efficient protein transfer and to cut the membranes for probing with dif-ferent antibodies. Subsequently, membranes were rinsed with double distilled water to remove the Ponceau stain,and were then blocked for 30 minutes at room temperature with 5% skim milk powder dissolved in 1X-TBS-T(150mM, 2.5 mM KCl, 50mM Tris/HCl, 0.05% Tween-20, [pH 7.6]), followed by overnight incubation at 4Cwith primary antibody. Membranes were washed four times with TBS-T (10 minutes per wash) and incubated.Biotinylation and immunoblot analysis experiments were performed by Vivek Mahadevan.

38

Methods

2.3 Simulation Analysis

All simulations were performed and analyzed using a custom built PC running Linux Ubuntu 14.04 with anIntel Core i7-3770 CPU with 3.40GHz x 8 processor, and a 2013 Asus Zenbook running a Windows 7 operatingsystem.

2.3.1 Simulation Analysis and Software

The model was developed and run using the NEURON Simulation Environment (version 7.3) (www.neuron.y-ale.edu) [35]. Simulations were analyzed using iPython version 2.7 [78], using Numpy and Pandas packages andcustom code for reading in data generated by NEURON.

2.3.2 Establishing Parameters for KCC2 State Dynamics

Setting Kinetic Parameters of Phosphatase Activation

Parameter setting for phosphatase activation was conducted by generating Ca2+ dose response curves (DRCs) forsteady state [PA] (see equation (2.40)). The steady-state value for [PA] for different values of [Ca2+]i was solvedanalytically in Python, varying [Ca2+]i from 0-0.01 mM in increments 0.1 nM (1×10−7mM). The maximal valuefor Ca2+ in this dose response protocol is two orders of magnitude larger than the resting [Ca2+]i, which was set at1.082×10−4 mM. DRCs were generated in this manner for Q values (see §2.1.4, KCC2 Regulation) varying from0.1 to 250.0 in increments of 1.0. These DRCs were then compared to an analogous Ca2+ dose response for [KA].

VaryingQ gave rise to changes in the relative steady state levels of active kinase and phosphatase in responseto different levels of [Ca2+]i. It was found that there were four distinct regimes for the relative dose responsecurves for active kinase and phosphatase. Details are given below in the Results (see §3.1.2). These regimes andassociated range of Q values are outlined below in Table 3.1. The boundaries of these four different regimes weredetermined by observation of Ca2+ dose response curves generated by Python.

For all STDP experiments, vIP was arbitrarily chosen as vIP = 10/s. Changes inQwere made by varying VAP

in NEURON and Python code. The STDP protocol was performed at 5 different Q values. For each of the fourregimes described in Table 3.1, the midpoint value was taken. Sufficiently lowQ values were shown to give rise tosubstantially different dynamics in response to changes in [Ca2+]i, hence Q = 0.1 was also taken for comparativepurposes.

Fitting Rates of Phosphorylation and Dephosphorylation

The amount of KCC2 in the [MP] state at steady state is dependent on the relative levels of activation of kinaseand phosphatase for a given level of [Ca2+]i. Thus, a change in the value of Q would lead to a change in thevalue steady-state values for [C], [M] and [MP]. However, based on experimental data from the Woodin lab (seeResults, §3.1.1), we estimated that approximately 20% of KCC2 was embedded in the membrane at steady state.Consequently, the rates of phosphorylation (RMP) and dephosphorylation (RM) had to be recalculated for each Qvalue to preserve the distribution of KCC2 among states [C]:[M]:[MP] calculated from experimental data, which

39

Methods

was 0.8:0.1372:0.0628 (see §3.1.1). Similarly to VAP and vIP, we aim to fit the ratio between RM and RMP. Atsteady state, from equation (2.38) we have :

RMP[M][KA] = RM[MP][PA]

=⇒RMP

RM=

( x[M]

− 1) [PA][KA]

(2.66)

Where x is the membrane fraction of KCC2, i.e. x = [M] + [MP] (the full derivation of this expression is givenin the Appendix, §B.4, Solving for RMP and RM). At steady state, [KA] can be determined by equations (2.39)and (2.46). [PA] was recalculated from equations (2.40) and (2.47) for each Q value. RMP, and RM were thenrecalculated for each Q value from equation (2.66) in order to preserve the relationship between [C]:[M]:[MP] atsteady state.

2.3.3 Measures of Plasticity Induction

In order to observe whether the STDP induction protocol did indeed lead to activity-dependent dephosphory-lation of KCC2 in the membrane, we plotted changes in the proportion of phosphorylated KCC2 in the membrane([MP]), as well as changes in intracellular Ca2+ concentration, and changes in Cl− reversal potential. Changesin [MP] were calculated as the difference between the maximal and minimal [MP] values reached during the in-duction protocol, i.e. 10000 ms < t < 40000 ms, as the distribution of KCC2 between [C], [M], and [MP] tendsback toward steady state values when synaptic inputs are no longer present (see Figure 2.4 A). Importantly, thisindicates the necessity for additional downstream mechanisms to maintain changes in the phosphorylation stateof KCC2 in a more permanent manner for the long-term effects of inhibitory synaptic plasticity seen experimen-tally. One potential mechanism mediating such long-lasting effects is oligomerization of KCC2 proteins in themembrane, further increasing their stability in the membrane and decreasing the probability of endocytosis [9, 44].

Changes in [Ca2+]i were also measured as the difference between maximal and minimal values reachedduring the course of plasticity induction. Given the strength of Ca2+ homeostatic mechanisms, the minimumvalue of [Ca2+]i achieved is its steady state value of 1.082×10−4mM. Hence, measures of the difference in [Ca2+]i

could also be taken over the entire course of the simulation run and yield identical results (see Figure 2.4 B).Finally, changes in ECl were measured as the difference between maximal and minimal values achieved from1000 ms < t < 100000 ms. 1000 ms after the initiation of the simulation run was given to allow ECl to reach itsappropriate steady state value (see Figure 2.4 C).

40

Methods

Figure 2.4: Measures of Plasticity Induction with ∆t = +1 ms, in a cell using L-type Ca2+ Channels Only and Q= 7.4. (A) Changes in proportion of KCC2 in the membrane phosphorylated state are measured at t = 40000 ms,immediately following completion of the plasticity induction protocol. After the induction protocol is complete,[MP] tends back toward steady state levels, indicating the necessity of additional mechanisms to confer long-termstability to changes in KCC2 distribution among cellular states. (B) Changes in Ca2+ levels are measured at t= 40000 ms. After the induction protocol is complete, there is no longer any source of Ca2+ influx, and [Ca2+]iquickly returns to basal levels. (C) Change in Cl− reversal potential is measured upon completion of the simulationrun (t = 100000 ms), as it takes several hundred ms to return to baseline.

41

Results

3.1 Parameter Fitting

The ultimate goal of the thesis was to describe how KCC2 is regulated in the cell – that is, how activity-dependent Ca2+ influx leads to changes in the phosphorylation state of the transporter, ultimately altering its dis-tribution among its cytoplasmic ([C]), membrane unphosphorylated ([M]), and membrane phosphorylated ([MP])states in the cell. The above kinetic scheme in Figure 2.1 describes, theoretically, the transitions of KCC2 through-out the cell. In this scheme, cytoplasmic KCC2 is inserted in the membrane with a fixed rate, α. As phosphory-lation of KCC2 is assumed to occur only in the membrane-associated, unphosphorylated pool of the transporter([M]), all KCC2 leaving the [C] state may only enter the [M] state or remain in [C]. [M] KCC2 can be removedfrom the membrane via endocytosis and returned to the cytoplasmic pool with a fixed rate β. [M] KCC2 state mayalso associate with the active form of kinase ([KA]). The resulting phosphorylation reaction occurs with a rate ofRMP, converting [M] KCC2 to [MP] KCC2. Similarly, [MP] KCC2 can associate with active-state phosphatase([PA]), which catalyzes a dephosphorylation reaction with a rate of RM, returning KCC2 to its [M] state. Conver-sion of kinase and phosphatase from their active to inactive states occurs with fixed rates vIK and vIP, respectively.Rates of activation of both kinase and phosphatase are described by Ca2+-dependent functions vAK and vAP (givenby equations (2.46) and (2.47)). A schematic diagram for this process is given below in Figure 3.1. In orderto model KCC2 transitions throughout these states, we required measures of basal distribution of KCC2 amongstates and rate constants for the transitions between states.

KCC2 Distribution Among Cellular States Under Basal Conditions

Biotinylation experiments in combination with immunoblot analysis were performed by Vivek Mahadevanof the Woodin lab to determine the fraction of KCC2 present in the membrane of neurons. It was found that 20%of KCC2 was present in the membrane fraction, while the remaining 80% was present in the cytosol. That is, [C]= 0.8 while [M] + [MP] = 0.2 under basal conditions. In order to determine the proportion of KCC2 in each ofthe [M] and [MP] states, we solved equation (2.36) at steady state. That is:

[M] =α[C]β

(3.67)

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Results

Figure 3.1: Schematic Diagram of Ca2+-Dependent KCC2 Regulation in the Model. Ca2+-influx via VGCCs leadsto activation of the Ca2+-sensitive kinases and phosphatases which target membrane-associated KCC2 ([M] and[MP). Ca2+-dependent activation of kinase and phosphatase occurs with rates vAK and vAP, respectively. Activestate kinase ([KA]) and phosphatase ([PA]) are returned to their inactive states ([KI] and [PI]) with fixed ratesvIK and vIP. Binding of [KA] to membrane unphosphorylated ([M]) KCC2 leads to phosphorylation with a rateof RMP. Binding of [PA] to membrane phosphorylated ([MP]) KCC2 leads to dephosphorylation with a rate ofRM. [M] KCC2 is endocytosed to the cytoplasmic pool ([C]) with a fixed rate, β. [C] KCC2 is inserted into themembrane with a fixed rate, α.

43

Results

3.1.1 Rates of Membrane Insertion and Removal of KCC2

The parameters α and β were determined by live immunohistochemistry with COS7 cells transfected withHA-tagged KCC2. TIRF analysis was performed to determine a parameter value for α, while β was calculatedfrom equation (2.36) at steady state using values for [C] and [M] in COS7 cells. The proportion of KCC2 inthe cytoplasm ([C]) was determined by treatment of COS7 cells for 12-14 hours with the PKC inhibitor Go6983.Surface biotinylation showed that in these preparations, 30% of total KCC2 was present in the membrane (i.e. [M]+ [MP] = 0.3) and hence the remaining 70% was in the cytoplasmic fraction (i.e. [C] = 0.7). As it is known thatPKC typically requires the presence of phospholipid components for activation, phosphorylation of KCC2 wasassumed to occur only in the membrane [53]. A growing body of evidence suggests that phosphorylated KCC2 isstabilized in the membrane, and hence less likely to undergo endocytosis [17, 57]. For the purposes of this thesis,we assumed that KCC2 in the [MP] pool was to be stable in the membrane and resistant to endocytosis. Hence weassume that no phosphorylated KCC2 is present in the cytoplasmic fraction after 12-14 hours of PKC inhibition.

To determine the total amount of phosphorylated KCC2 ([MP]), hippocampal cells were treated with Go6983for 4 hours to block further phosphorylation of membrane-associated KCC2 over the duration of the treatment. Itwas found that approximately 18% of total KCC2 was phosphorylated under these conditions. Consequently, wetake this to mean that under basal conditions, membrane unphosphorylated KCC2 makes up 12% of the total pool(i.e. [M] = 0.12).

The rate of KCC2 insertion into the membrane, α, was determined by TIRF microscopy examining themovement of flourescent puncta in the membrane of COS7 cells treated with the PKC inhibitor Go6983 anddynasore, an inhibitor of endocytosis. As above, treatment with Go6983 prevented phosphorylation of KCC2during the course of treatment, allowing for a baseline measure for [M]. Subsequent treatment of cells with bothGo6983 and dynasore, an inhibitor of endocytosis, gave the number of KCC2 puncta in the membrane when nonewere removed by endocytosis during the time of treatment. Over the course of 10 minutes, an average of 38 punctawere inserted into the membrane (n = 4). It is assumed that KCC2 exists as tetramers in the membrane [9, 16], andhence each puncta represents 4 separate KCC2 proteins. Hence the rate of insertion of KCC2 into the membraneis ∼15.2/minute or:

α = 0.2533/s (3.68)

The rate of removal of KCC2 from the membrane is calculated from equation (2.36) at steady state as:

β =α[C][M]

=(0.2533)(0.7)

0.12= 1.4776/s (3.69)

Given these values for α and β, we then calculated the proportion of KCC2 in the membrane at steady state fromequation (3.67):

[M] =(0.2533)(0.8)

1.477= 0.1372 (3.70)

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Results

Since at steady state [M] + [MP] = 0.2 this implies that:

[MP] = 0.2 − 0.1372

= 0.0628 (3.71)

We used these values to fit the parameters RMP and RM. Specifically, as described above, RMP and RM weretuned to ensure that the steady-state values of [C], [M] and [Mp] are 0.8, 0.1372 and 0.0628, respectively, when[Ca2+]i is at basal levels.

Changes in KCC2 Distribution Among Cellular States in Response to Increases in [Ca2+]i

In order to determine the dynamics of KCC2 regulation between its cytoplasmic [C], membrane unphospho-rylated [M], and membrane phosphorylated [MP] states in the cell, the remainder of the variables and parametersoutlined in the kinetic scheme (Figure 2.1) had to be explicitly determined. Values for [KA] were calculatedusing parameters found in relevant literature [53]. Values for [PA] were calculated for each Q value used (see§2.1.4, KCC2 Regulation). RM, and RMP were fit using the estimates of steady state [C], [M], and [MP] given byexperimental data as described above. Details of these calculations are summarized below.

To determine the relative proportion of active and inactive kinase, equations for [KA] and [KI] (2.39, 2.41)were solved at steady state:

[KA] =vAK

vAK + vIK[KI] =

vIK

vAK + vIK(3.72)

Derivations of these equations are available in the Appendix (§B.4). Recall that vAK is given by the Hill function(equation (2.46)) such that:

vAK =VAK[Ca2+]hK

RhKK + [Ca2+]hK

=390/s · [Ca2+]1.5

(2.37 × 10−3mM)1.5 + [Ca2+]1.5 (3.73)

Under basal conditions (i.e. for resting levels of [Ca2+]i = 1.082×10−4 mM), we have from equations (3.72) and(3.73):

[KA] =3.7676

3.7676 + 32.1= 0.105

[KI] =32.1

3.7676 + 32.1= 0.895

Using equation (3.73), analytically determined steady state [KA]:[KI] for different fixed levels of [Ca2+]i wereplotted as a dose response curve with custom code in Python in to determine the effect of changes in [Ca2+]i onkinase activation.

45

Results

3.1.2 Rates of Phosphatase Activation and Inactivation

In contrast to the calculation of [KA] and [KI], values for [PA] and [PI] had to be derived from hand-tuned pa-rameters, as experimentally determined values for VAP and vIP were not available in the literature. The proportionof active or inactive phosphatase is chiefly determined by the ratio between maximal activation and inactivation,and hence we varied this ratio in order to fit parameters for phosphatase activation and inactivation. As describedabove, we called this parameterQ = VAP

vIP. As with the calculation of steady state proportions of active and inactive

kinase, steady state phosphatase was found by solving equations (2.40) and (2.42):

[PA] =vAP

vAP + vIP[PI] =

vIP

vAP + vIP(3.74)

The rate of activation, vAP is given by:

vAP =VAP[Ca2+]hP

RhPP + [Ca2+]hP

(3.75)

=VAP · [Ca2+]2.9

(7.943 × 10−4mM)2.9 + [Ca2+]2.9 (3.76)

From equations (3.74) and (3.76) we see that establishing values for the steady state levels of [PA] and [PI] aredependent on our choice of the values for VAP and vIP. As the specific values for VAP and vIP are unknown, weformulated expressions for [PA] and [PI] in terms of Q. From equations (3.74) and (3.76) we have:

[PA] =Q · [Ca2+]hP

RhPP +

(Q + 1

)[Ca2+]hP

[PI] =RhP

P + [Ca2+]hP

RhPP +

(Q + 1

)[Ca2+]hP

(3.77)

Derivations for these equations are provided in the Appendix (§B.4, Calculating [PA] in Terms of Q). From theseequations, Ca2+ dose response curves were created for the proportion of phosphatase in the active state at steadystate with varying Q, and compared against the analogous dose response curves created for steady state [KA] (seeFigure 3.2). Ultimately, the distribution of KCC2 among states [C], [M] and [MP] was dependent on the relativesteady-state levels of [KA] and [PA] for a given [Ca2+]i. Figure 3.2 shows the relative levels of [KA] and [PA]reached at steady state with increasing [Ca2+]i for various Q values.

For sufficiently low values of Q, the steady state values of reached by [PA] were lower than that of [KA] forall possible values of Ca2+. This suggests that for a cell with low Q, there is a bias towards phosphorylation ofKCC2 with sustained elevated levels of [Ca2+]i (see Figure F.1), leading to the establishment of a new steady statedistribution of [C], [M], and [MP] (the particulars of which are discussed in more detail below, see §3.3.2). Forsufficiently high values of Q, the steady state level of active kinase is lower than that of active phosphatase forall Ca2+, leading to a bias towards dephosphorylation (see Figure F.5). That is, when the maximal activation ofphosphatase is much larger than its inactivation rate, the system tends towards activation of phosphatase for anyvalue of Ca2+, and hence decreased proportion of KCC2 in the [MP] state.

Between these two extremes, the relative behaviour of [KA] and [PA] in response to changing [Ca2+]i is morenuanced. Observation of individual dose response curves forQ values varying from 0.1 to 250.0 showed that thereare four distinct regimes for the kinase-phosphatase steady state response to changing levels of intracellular Ca2+.The boundaries of these regimes were determined by observation of Ca2+ dose response curves for [KA] and [PA]at several Q values. It was found that boundaries points for these regimes were at Q = 3.9, 10.9, 46.0. Example

46

Results

Figure 3.2: Proportion of Kinase and Phosphatase in Active States with Varying Ca2+ and Q Values. Ca2+ doseresponse curves for both kinase and phosphatase were generated for Q values ranging from 0 to 60. Q values inthe upper range (60 < Q < 250) were excluded from the surface plot in order to provide better visualizationof switch between regimes at Q = 3.9, 10.9, 46.0. Lines at which the two surfaces cross indicate a shift indominance between kinase and phosphatase at steady state for particular values of Ca2+.

dose response curves of [KA] and [PA] plotted against changing [Ca2+]i forQ values representative of each regimeare included in Appendix F.

Since neither VAP nor vIP may take negative values, necessarilyQ > 0. Furthermore, while it is theoreticallypossible for Q → ∞, sufficiently large values indicate a maximal rate of activation in far excess of the rate ofinactivation for phosphatase, and at some point must be considered physiologically unrealistic. Q = 250 waschosen as the upper bound, since nearly all phosphatase was found to be in the [PA] pool (> 99%) at steady statefor Ca2+ values reached during the plasticity induction protocol. This information is summarized below in Table3.1.

For each of these regimes, the midpoint value was chosen as representative for our STDP simulation ex-periments. STDP induction was performed with each of these Q values to determine which gave rise to changesin KCC2 and hence Cl− regulation which were physiologically realistic. It was also observed that the relativesteady state values reached by [KA] and [PA] showed different behaviour in the Ca2+ dose response curve for verylow values of Q. Consequently, experiments were also conducted with Q = 0.1. In particular, plotting differ-ence curves between [KA] and [PA] reached at steady state against Ca2+ for these Q values (illustrating the netprobability of phosphorylation at steady state for each [Ca2+]i value) shows that Q = 0.1 gives rise to a mono-

47

Results

Table 3.1: Four Distinct Regimes for Kinase and Phosphatase Activation in Response to Changing Q Values

Q Range Regime RepresentativeValue

1 0 < Q < 3.9There are no critical points for which dominance betweenactive kinase and active phosphatase switches.For all [Ca2+]i, [PA] < [KA] at steady state.

0.1, 1.9

2 3.9 < Q < 10.9

There are two critical points ([Ca2+]* and [Ca2+]**)1 wheredominance between kinase and phosphatase switches.For [Ca2+]i < [Ca2+]*, [PA] < [KA] at steady state.For [Ca2+]* < [Ca2+]i < [Ca2+]**, [KA] < [PA] at steady stateFor [Ca2+]** < [Ca2+]i, again [PA] < [KA] at steady state.

7.4

3 10.9 < Q < 46.0There is one critical point ([Ca2+]*) where dominance switches.For [Ca2+]i < [Ca2+]*, [PA] < [KA] at steady stateFor [Ca2+]* < [Ca2+]i, [KA] < [PA] at steady state.

28.45

4 46.0 < Q < 250.0There are no critical points.For all [Ca2+]i, [KA] < [PA] at steady state. 148.0

1 Values for critical points [Ca2+]* and [Ca2+]** are dependent on particular choice of Q value

tonically increasing difference between [KA] and [PA]. This describes a one-to-one relationship between [Ca2+]i

and enzyme activation, suggesting that phosphorylation does not have a dynamic response to changing Ca2+ lev-els. While this is likely unphysiological, simulations were run with this value for comparative purposes. Curvesshowing the difference between [KA] and [PA] for changing levels of [Ca2+]i are plotted in Figure 3.3, below.

Q values from each of these four regimes were chosen to observe the response of the kinetic system tochanges in [Ca2+]i. If Ca2+-dependent dephosphorylation of KCC2 is a plausible mechanism for the depolarizingshift in EGABA seen in inhibitory STDP, then it stands to reason that degree of change of [Ca2+]i via postsynapticVGCCs must be such that it may alter the balance between active kinase and phosphatase. As discussed previ-ously, for sufficiently lowQ values (as in Regime 1), the net response to Ca2+ is a higher steady state level of [KA]than [PA] for all values of Ca2+, resulting in a push toward the [MP] state by the Law of Mass Action. Similarly,for large Q values, [PA] reaches a higher steady state level than [KA] for all values of Ca2+, indicating a push inthe direction of [MPPA]→ [M][PA].

3.1.3 Rates of Phosphorylation and Dephosphorylation

In order to maintain steady state levels of [C]:[M]:[MP] consistent with our experimental findings outlinedabove (see §3.1.1, equations (3.70) and (3.71)), we calculated rates of phosphorylation and dephosphorylationfor each Q value. As mentioned above, the values of RMP and RM were such that the steady state distribution ofKCC2 among states [C], [M], and [MP] was maintained at experimentally observed levels. As Q value (reflectingthe sensitivity of phosphatase activation to changes in [Ca2+]i) increased, the relative rates of phosphorylation anddephosphorylation were adjusted so that increasing Q did not affect the steady state distribution of KCC2 amongstates of [C]:[M]:[MP] = 0.8:0.1372:0.0628 (see §3.1.1). As in the case with VAP and vIP, we aimed to fit the ratiobetween RM and RMP rather than their specific values. Derivations for these equations are given in the Appendix(§B.4, Solving for RMP and RM).

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Results

At steady state, from equation (2.38):

RMP[M][KA] = RM[MP][PA] (3.78)

It was experimentally determined that under basal conditions, KCC2 in the membrane made up 20% of totalKCC2, i.e. [M] + [MP] = 0.2. Hence [MP] = 0.2 - [M] and equation (3.78) becomes:

RMP

RM=

(0.2[M]

− 1)(

[PA][KA]

)(3.79)

From equation (2.43) we know that [C] = 0.8. From 2.36 we get:

[M] =α[C]β

=(0.2533)(0.8)

1.477= 0.1372

Then equation (3.79) becomes:

RMP

RM= 0.4577

[PA][KA]

(3.80)

At steady state, [KA] = 0.105 (from equation (3.72)). The value of [PA] changed as we varied Q, changingthe ratio RM:RMP in order to preserve the relationship between [C]:[M]:[MP] at steady state. The calculated valuesfor RM and [PA] with their associated Q values is given below in Figure 3.4.

Figure 3.3: Net Phosphorylation Activity Calcium Dose Response Curves for Varying Q Values. There are fourdistinct regimes of relative activity of kinase and phosphatase in response to intracellular Ca2+, outlined in Table3.1. Q = 0.1 (yellow trace) is a special case of Regime 1, in which steady state [KA] is greater than [PA] forall values of Ca2+, yet differs significantly in that the difference curve is a monotonically increasing functionindicating a one-to-one relationship between Ca2+ level and net phosphorylation activity. Since it is thought thatkinase and phosphatase activity should have a dynamic response to changes in [Ca2+]i, this is considered to bephysiologically unrealistic but is taken for comparative purposes.

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Results

Figure 3.4: Effects of Q Value on Steady State Active phosphatase and Net Phosphorylation Rate. The steadystate proportion of phosphatase in the active state (—) increases as a nonlinear function of the Q value. To main-tain experimentally determined levels of net phosphorylation, this required that the the ratio between the rates ofphosphorylation (RMP) and dephosphorylation (RM) (- -), was recalculated for each Q value. As sensitivity ofphosphatase to changes in [Ca2+]i increases, the rate of dephosphorylation slows relative to the rate of phospho-rylation in order to preserve the steady state distribution of KCC2 among states [C], [M], and [MP].

3.2 Ca2+-Dependent Kinase and Phosphatase Activity Effectively Regu-lates KCC2 State

Once basal values for the variables [C], [M], and [MP] were established and rate constants were set and fitappropriately, it was important to verify that the NEURON model generated the results that were predicted byanalytical solutions before implementing the STDP protocol in the model. To do so, we compared NEURON-generated data with the analytical solutions to our differential equations. In particular, it was important to verifythat the NEURON model appropriately responded to changes in [Ca2+]i within the range of values producedduring spiking activity (up to ∼ 2.5 µM). To check the response of the model to different levels of Ca2+, thedifferential equations were solved at steady state over varying [Ca2+]i using a fixed Q value of 4.89. A series ofNEURON simulations were run with changing resting levels of [Ca2+]i, with both GABAergic inputs and currentclamp generated spiking absent to allow the model to reach steady state. The simulation ran until steady state wasachieved, and the values for the proportion of KCC2 in [C], [M], and [MP] states, as well as proportion of kinaseand phosphatase in the [KA] and [PA] states were recorded. For these simulations we assume that at [Ca2+]i = 0,all KCC2 is in the membrane phosphorylated state. Figure 3.5 shows that NEURON-generated steady state valuesfor different Ca2+concentrations agreed extremely well with the analytical solutions to our differential equations.

Ca2+ dose response curves generated from analytical solutions alone are provided for our five representativeQ values as a supplemental figure (see Figure F.6, Appendix F). These results indicated that the NEURON modelappropriately responded to changes in [Ca2+]i, which is crucial to the mechanisms proposed to regulate phospho-rylation state of KCC2 and consequently its extrusion capacity. Therefore, our model was able to represent thekey features of our proposed mechanism accurately and was suitable for testing the effects of sustained repetitiveGABAergic inputs paired with postsynaptic spiking in a STDP protocol.

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Figure 3.5: Calcium Dose Response Curve. Analytical solutions to differential equations (—) together withNEURON-generated numerical integration data () for Q = 4.89 (A) Net Phosphorylation - difference betweenactive kinase and active phosphatase in response to different levels of [Ca2+]i. (B-D) Proportion of KCC2 incytoplasmic (B), in membrane unphosphorylated (C), and in membrane phosphorylated state (D) in response todifferent levels of [Ca2+]i.

3.3 KCC2 is Dephosphorylated Following STDP Protocol

STDP protocols were simulated for each of the five representativeQ values (see Table 3.1) in order to observethe effects of different kinetic parameters for phosphatase activation on plasticity induction. Furthermore, STDPprotocols were simulated for each of the four Ca2+channel conditions (see Table 2.1) to observe the effects ofdifferent sources of Ca2+ influx on plasticity induction. Hence, twenty different conditions were tested to observethe effects of both phosphatase activation/inactivation rates and Ca2+influx dynamics on plasticity induction inour model cell. The STDP protocol (outlined above in §2.1.7) consisted of pre- and post-synaptic spike pairsseparated by ∆t ms, run for 30s at 5Hz. Each pre-post spike pair led to Ca2+ influx, triggering activation of kinaseand phosphatase which ultimately changed the distribution of KCC2 among its [C], [M] and [MP] states (seeFigures F.7 and F.8, Appendix F).

Following the induction protocol, changes in the proportion of KCC2 in the [MP] state were measured foreach Q regime (example trace given in Figure 2.4 A, for ∆t = 1ms in a cell with L-type Ca2+channels and Q= 7.4). The magnitude, polarity, and timing of these changes varied among conditions. Changes in [MP] wereused as a measurement of plasticity as this value was dependent solely on parameter values that had been sourced

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from the literature or been determined experimentally. Changes in ECl were also measured (see Figures 2.4C,3.9, 3.10), although these values were dependent on some parameters which had been hand tuned and thereforeprovided a less reliable measurement of the plasticity we are interested in. These results are summarized below inFigure 3.6.

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Figure 3.6: Percent Change in Membrane Phosphorylated KCC2 Following Spike Timing-Dependent PlasticityInduction Protocol for Different Phosphatase Activation Regimes. Across Q values, Ca2+ influx mediated byL-type Ca2+ channels led to dephosphorylation of KCC2 regardless of spike timing interval (blue trace) whileT-type channel-mediated Ca2+ influx facilitated changes in [MP] KCC2 in a temporally-dependent manner (greentraces). Simulations using only low conductance T-type channels showed similar qualitative changes to simula-tions where higher conductance T-type channels were used, though the magnitude of these changes was reduceddue to diminished Ca2+ influx. In simulations where both L- and T-type Ca2+channels were present, STDP curves(dotted red line) closely resembled those for the L-type Ca2+channels alone. The magnitude of dephosphorylationof KCC2 was dependent on the phosphatase activation regime (Q value).

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3.3.1 Ca2+ Influx Source Determines Changes in [MP] KCC2

The results of plasticity induction experiments summarized in Figure 3.6 importantly showed the followingkey points: (1) that Ca2+ influx mediated by L-type Ca2+ channels could lead to dephosphorylation of KCC2regardless of spike timing interval; (2) that T-type channel-mediated Ca2+ influx could give rise to temporally-dependent dephosphorylation of KCC2 consistent with experimental findings, with coincident activity causingdephosphorylation and non-coincident activity leaving KCC2 phosphorylation relatively unaffected, consistentwith our hypothesized mechanisms for inhibitory STDP; and (3) while Ca2+ influx triggered by activation of L-and T-type channels together was significantly larger than via L-type channels alone, this was not able to generatesignificant differences in dephosphorylation of KCC2. The maximal level of Ca2+ influx over each STDP protocolis provided in Figure 3.7.

Figure 3.7: Maximum Ca2+Reached During Plasticity Induction for Q = 7.4. Activation of L-type Ca2+ channelsled to significant increases in [Ca2+]i for both coincident and non-coincident spike timing intervals. T-type Ca2+

channels led to small increases in [Ca2+]i for negative non-coincident spike timing intervals (-100 ms < ∆t < -50ms), and moderate increases for negative coincident and positive non-coincident spike timing intervals. Notably,Ca2+ influx is greater via T-type channels for positive coincident spike timing intervals. In conditions with L-and T-type Ca2+ channels together, Ca2+ influx is increased above levels seen for L-type channels alone, thoughremains less than the sum of Ca2+ influx from L- and T-type channels separately.

L-Type Ca2+ Channels Led to KCC2 Dephosphorylation Regardless of Spike Timing Interval

L-type Ca2+ channels were activated with each postsynaptic depolarization initiated by current clamp inputs.Hence for each STDP protocol, postsynaptic spiking – regardless of presynaptic input – led to Ca2+ influx and

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subsequent activation of Ca2+-sensitive kinases and phosphatases. The level of Ca2+ influx varied with VGCCtype and over ∆t values (see Figure 3.7), but was invariant under changing Q values. Different Q values arein essence differences in the responsiveness of kinase and phosphatase to changes in [Ca2+]i achieved over thecourse of plasticity induction, but do not contribute to the dynamics of Ca2+ influx via VGCCs. Hence while Ca2+

influx via L-type channels led to more or less uniform changes in [MP] KCC2, the magnitude of this change wasdependent on Q value.

For Q = 0.1, a general homogeneous reduction in [MP] KCC2 of 42.25±0.96% was seen over all ∆t valuesfor this condition. For -5 ms < ∆t +5 ms, small fluctuations in the degree of dephosphorylation can be seen (see toppanel, Figure 3.6). For this Q value, phosphatase remained relatively insensitive to changes in [Ca2+]i, and moresignificant levels of change of [PA] were seen when Ca2+ fluctuations were large (see Figure F.9). However, theratio RMP:RM forQ = 0.1 was such that the rate of dephosphorylation was relatively high (see Figure 3.4). Hence,small amounts of [PA] led to proportionally large changes in the phosphorylation state of KCC2. Increasing Q to1.9 rendered phosphatase sensitive enough to changes in [Ca2+]i (Figure 3.7, blue trace) such that 91.24±0.09%of [MP] KCC2 was dephosphorylated. In a similar fashion, Q = 7.4 led to a 82.86±0.029% reduction, whileQ = 28.45 led to a 53.91±0.29% reduction in phosphorylated KCC2 in the membrane. Interestingly, for Q =

148.0, there were not significant changes in [MP] KCC2. It should be noted that some effects of spike timinginterval could be observed for -100 ms < ∆t < -50 ms. Namely, [MP] KCC2 was increased slightly (2.51±1.76%)following plasticity induction for spike timing intervals over this range. Spike timing intervals of -50 ms < ∆t< +100 ms yielded negligible reductions (0.02±0.002%) in the phosphorylation of [MP] KCC2 in this regime.The reason for this change was not resolved, and should be investigated in greater detail in future work. WhileCa2+ influx via L-type Ca2+ channels led to nearly uniform changes in KCC2 phosphorylation, changes in [Ca2+]i

mediated by T-type channels allow for timing-dependent alterations to KCC2 distribution among cellular states.

Temporally-Dependent Dephosphorylation of KCC2 is Mediated by T-type Ca2+ Channels

When Ca2+ currents were mediated by T-type Ca2+ channels, dephosphorylation of KCC2 occurred prin-cipally for positive coincident spike timing intervals. For 0 < ∆t < +20 ms, activation of the presynaptic cellprovided the necessary hyperpolarization to remove the T-type channel from its inactivated state and be primedfor activation by the subsequent depolarization of the postsynaptic cell. In the non-coincident and negative co-incident conditions, the necessary temporal separation of hyperpolarization and depolarization was not presentto allow for T-type channel activation and hence the Ca2+ influx necessary for enzyme activation. Hence, high-and low-conductance T-type channels produced qualitatively similar patterns of Ca2+ influx over spike timingintervals, though the magnitude was reduced for low conductance T-type channels.

For Q = 0.1 changes in [MP] KCC2 following plasticity induction were minimal. For non-coincident spiketiming intervals, high conductance T-type channels led to a 0.63±0.0003% change in [MP] KCC2 for both pos-itive and negative ∆t values. Negative coincident intervals gave rise to a 0.734±0.53% reduction, while positivecoincident intervals caused a 3.79±2.91% reduction in [MP] KCC2 following plasticity induction. For positiveand negative non-coincident intervals, low conductance T-type channels led to a 0.138±0.0001% reduction, whilenegative coincident spike timing intervals led to a 0.17±0.16% reduction, and positive coincident intervals led toa 1.17±0.97% reduction in [MP] KCC2. Comparatively large changes in [MP] KCC2 during these positive coin-cident spike timing intervals is consistent with our expectations for T-type channel-mediated plasticity. However,at this Q value, phosphatase was relatively insensitive to changes in [Ca2+]i, and even high levels of Ca2+ influx

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did not lead to significant changes in the level of [PA]. Consequently, low levels of dephosphorylation are seenunder these conditions.

As Ca2+ influx is invariant under changing Q values, differences in levels of KCC2 dephosphorylation fol-lowing plasticity induction were reflective of changing sensitivity of phosphatase to the [Ca2+]i levels generatedby VGCC activation. IncreasingQ to 1.9 yielded significant differences in the level to which KCC2 is dephospho-rylated following the STDP protocol. For Q = 1.9, plasticity induction led to substantial reduction of [MP] KCC2for positive coincident and small negative coincident spike timing intervals (57.19±10.83% for -1 ms < ∆t < +10ms) in the case of high conductance T-type Ca2+ channels. For low conductance T-type channels, a reduction of26.13±7.90% was seen over the same interval. For high conductance T-type channels, most negative spike timingintervals (-100 ms < ∆t < -1 ms) and positive non-coincident intervals showed a 9.51±0.008% reduction in [MP]KCC2 (as compared with 2.21±0.002% reduction for low conductance channels).

Qualitatively, similar changes were observed for Q = 7.4 and 28.45. For these Q values, high levels of [PA]were achieved in response to Ca2+ influx (see Figures F.11 and F.12, green traces). For Q = 7.4, Ca2+ influx ledto higher levels of [PA] as compared with lower Q values, and a greater degree of KCC2 dephosphorylation overpositive coincident spike timing intervals. Interestingly, thoughQ led to higher levels of [PA] achieved for each ∆t([PA] > 0.9 for most values of [Ca2+]i, see Figures F.11 and F.12), lower levels of dephosphorylation were seen ascompared with Q = 7.4. However, similar levels of dephosphorylation were seen for non-coincident spike timingintervals as compared with Q = 7.4 (24.38±0.008% reduction in [MP] KCC2 for Q = 28.45, as compared with20.97±0.015% forQ = 7.4), as a result of scaling the dephosphorylation rate to eachQ value (see Figure 3.4). Dur-ing positive coincident intervals, differences in the magnitude of induced plasticity betweenQ regimes were againa result of both phosphatase responsiveness and scaling of RM:RMP. For Q = 7.4, positive coincident and smallnegative coincident (∆t > -2 ms) spike timing intervals led to reduction of [MP] KCC2 by 70.19±6.05% for highconductance and by 45.92±9.65% for low conductance T-type Ca2+ channels. For positive non-coincident andnegative spike timing intervals, [MP] KCC2 was reduced by 22.35±8.25% for high conductance and 5.68±2.30%for low conductance channels. For Q = 28.45, positive coincident and small negative coincident (∆t > -2 ms)spike timing intervals led to reduction of [MP] KCC2 by 59.37±3.14% for high conductance and by 44.43±6.86%for low conductance T-type Ca2+ channels. For non-coincident/negative coincident spike timing intervals, [MP]KCC2 was reduced by 24.55±2.91% for high conductance and 7.27±2.45% for low conductance channels.

Finally, for Q = 148.0 changes in [MP] showed only slight spike-timing dependence. In contrast to the pre-vious phosphatase activation regimes, STDP curves for conditions of high and low conductance T-type channelswere qualitatively different. While changes in [MP] over the spike timing window for low conductance T-typechannels resembles that of previous Q values, high conductance T-type channels give rise to variable changesin [MP] over positive coincident spike timing intervals. For high conductance T-type channel conditions, posi-tive and negative non-coincident spike timing intervals led to an 11.81±0.003% decrease in [MP]. This level ofchange was maintained for negative coincident spike timing intervals, wherein postsynaptic depolarization pre-cedes presynaptic hyperpolarizing inputs, leading to an 11.80±1.21% reduction in [MP]. Positive coincident spiketiming intervals caused a 12.18±4.44% reduction in [MP] KCC2, which did not differ significantly from negativecoincident or non-coincident spike timing intervals. Low conductance T-type channels led to less significant de-creases in [MP] KCC2 – 4.24±0.002% for non-coincident spike timing intervals, and 4.63±2.41% for negativecoincident spike timing intervals. Positive coincident intervals gave rise to a 12.53±4.50% decrease in [MP].Qualitative differences in STDP curves for high and low conductance T-type channels were the result of differentlevels of Ca2+ influx leading to different responsiveness of phosphatase at this Q value (see Figure F.5) Greater

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detail of differences between Q values is provided below in Section 3.3.2.

Ca2+ Influx via L- and T-type Ca2+ Channels Together Leads to Changes in [MP] KCC2 Similar to L-typeCa2+ Channels Alone

For all Q values, presence of L- and T-type Ca2+ channels of equal conductance yielded nearly identicalresults to that of the L-type channel only condition (see Figures 3.6, 3.8). This was reflective of the relativelystrong contribution of Ca2+ influx occurring through the L-type channels with postsynaptic depolarization, whicheclipsed the effects of Ca2+ influx via T-type channels. While there was a significant increase in [Ca2+]i whenL- and T-type channels are present together as compared with L-type channels alone (see Figure 3.7), this ad-ditional Ca2+ was unable to lead to greater phosphatase activation within a given Q regime. For example, forL-type Ca2+ channels, [Ca2+]i reached over the course of the STDP protocol ranged from 1.78 µM to 3.0 µM.Ca2+dose response curves (Figures 3.3, F.1-F.5) showed that for these levels of Ca2+, the maximal level of [PA]was reached at steady state. That is, further increases in [Ca2+]i, as with L- and T-type Ca2+ channel-mediatedCa2+ currents, could not lead to greater levels of [PA] being reached, and hence could not lead to greater levelsof dephosphorylation of KCC2. It should be noted that in the case of Q = 7.4, Ca2+ influx via L- and T-typechannels together provided sufficient [Ca2+]i to pass the second critical point after which [KA] > [PA] (see Table3.1), though barely within the dynamic range. Consequently, the level of dephosphorylation was diminished ascompared with conditions wherein Ca2+ influx was mediated solely by L-type channels, but the magnitude of thischange was small as [PA] values were becoming saturated for this level of [Ca2+]i (see Figure 3.8, inset).

3.3.2 Q Value Determines Magnitude of Changes in [MP] KCC2

Changes in [Ca2+]i described above for each type of VGCC configuration can have varied effects on KCC2phosphorylation state depending on the Q value, which in essence characterizes the sensitivity of phosphataseactivation to changes in intracellular Ca2+concentration. In particular, a given level of Ca2+ influx will leadto different relative levels of active kinase and phosphatase at steady state (see Figures 3.3, F.1-F.13), whichultimately affects the distribution of KCC2 among [C], [M], and [MP] states (see Figure F.6).

Q = 0.1

As outlined in Table 3.1, Q = 0.1 is representative of a regime wherein more active kinase than activephosphatase was present at steady state for all values of [Ca2+]i. For L-type Ca2+ channels, dephosphorylationof KCC2 was largely homogeneous across ∆t values, as Ca2+ influx in the range of 1.80-3.0 µM gave rise toconsistent low levels of [PA] across different ∆t values (see Figure F.9). Consequently, only marginal increasesin [PA] could be achieved with greater Ca2+ influx, as in the case of L- and T-type Ca2+ channels together.Fluctuations in the level of dephosphorylation for -5 ms < ∆t < +5 ms were due to fluctuations in the levelof maximal Ca2+ influx during STDP protocols with these spike timing intervals (see Figure 3.7). Ca2+ influxmediated by T-type channels alone achieved maximal [Ca2+]i levels between 0.53-1.95 µM. Within this range,low levels of [PA] were achieved at steady state, and relatively little dephosphorylation can occur (see Figures F.1,F.9). Small changes in maximal [PA] were observed for positive coincident spike timing intervals, yielding lowmagnitude reductions in [MP] KCC2 in a spike timing-dependent fashion.

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Figure 3.8: Percent Change in [MP] Following STDP Induction Protocol for Q = 7.4. Spike timing-dependentchanges in [MP] KCC2 occur with T-type channels as the primary mediator of Ca2+ currents, in positive coin-cident (+20 ms) spike timing intervals. L-type Ca2+ channel-mediated Ca2+ influx gave rise to high levels ofdephosphorylation regardless of spike timing interval. Inset: Spike timing windows for L-type only and L- andT-type Ca2+channel conditions. Presence of L- and T-type Ca2+ channels together allowed for sufficient Ca2+

influx to pass the second critical point of the regime, leading to reduced phosphorylation as compared with theL-type only condition.

Q = 1.9

Similarly to the previous condition, a value of Q = 1.9 is representative of a regime wherein there existsmore active kinase than active phosphatase at steady state for all values of [Ca2+]i. However, increasing thephosphatase activation ratio to 1.9 increases the dynamic range for [PA]. Figure 3.3 shows that for Q = 1.9,different values of [Ca2+]i can yield the same relative amounts of [KA] and [PA] at steady state (see also FigureF.2, Appendix F). Ca2+ influx via L-type Ca2+ channels (1.8-3.0 µM) led to moderate levels of [PA] (Figure F.10).However, the RM:RMP value for this regime was such that even moderate levels of active [PA] were sufficient fordephosphorylation of more than 90% of [MP] KCC2 (see Figures 3.6, F.2). While fluctuations in the level ofdephosphorylation were seen for -5 ms < ∆t < +5 ms when Q = 0.1, increasing the sensitivity of phosphataseactivation to 1.9 led to high [PA] levels even for relatively small increases in [Ca2+]i. Ca2+ influx through T-type Ca2+ channels led to lower overall increases in [Ca2+]i than in L-type Ca2+ channel conditions, such thatdifferences in steady state levels of [PA] were in the dynamic range and could be observed over this range of[Ca2+]i values. For positive coincident spike timing intervals, [Ca2+]i ranged from 1.2-1.95 µM. Over thesevalues, small variations in [Ca2+]i led to substantial differences in levels of [PA] and hence phosphorylation (seeFigure F.2).

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Q = 7.4

As outlined in Table 3.1, Q = 7.4 is representative of a phosphatase activation regime wherein there isproportionally more active kinase than active phosphatase at steady state for both high and low values of [Ca2+]i.For a range of [Ca2+]i values, steady state levels of active phosphatase exceed levels of active kinase (see alsoFigure F.3. For Q = 7.4, this range is 3.6072×10−4 mM < [Ca2+]i < 3.0831×10−3 mM. Changes in [Ca2+]i rangefrom 5.302×10−4mM (T-type Ca2+ channel-mediated influx, for ∆t ∈ -100, -82 ms) to 3.809×10−3 mM (Ca2+

influx via both L- and T- type Ca2+ channels together, for ∆t = 4 ms), providing values of [Ca2+]i spanning therange necessary to observe the highly dynamic responses in [PA] to changes in [Ca2+]i. This indicates that themaximal [Ca2+]i values reached during plasticity induction may either lead to more active kinase than phosphataseat steady state, or vice versa. Therefore, depending on the source of Ca2+ influx, [Ca2+]i may reach levels whereeither kinase or phosphatase dominates at steady state. Consequently, we explore the particulars of plasticityinduction in greater detail for this regime. These effects have been shown in Figure 3.8. Importantly, the maximallevel of [Ca2+]i achieved sits just above the critical value for the shift back to dominant [KA] at steady state (seeFigure F.3), consequently slightly less dephosphorylation is observed in this condition as compared with the L-type only condition (see Figure 3.8, inset). Greater levels of Ca2+ influx may be tested in future work to observethe effects of maximal [PA] activation on dephosphorylation of KCC2.

Q = 28.45

This value is within a regime where [KA] is greater than [PA] for [Ca2+]i below some critical value of[Ca2+]i, after which point active phosphatase outstrips active kinase. For Q = 28.45 this critical point occurs at1.335×10−4mM. As such, all VGCC-mediated changes in [Ca2+]i resulting from the STDP protocol exceeded thiscritical value and led to relatively higher levels of active phosphatase than kinase at steady state. T-type Ca2+

channel mediated changes in [Ca2+]i gave rise to similar STDP curves as for Q = 1.9 and 7.4. This was due to thefact that Ca2+ influx in the range given by T-type channels during positive coincident spike timing intervals wassuch that [PA] levels were in their dynamic range - i.e. saturating levels have not yet been reached. Consequently,small changes in intracellular Ca2+ could yield large changes in the level of active phosphatase (see Figure F.4).While L-type channel-mediated Ca2+ influx led to high levels of [PA], lower levels of dephosphorylation wereseen than for previous Q values. This is a consequence of the change in the ratio RM:RMP for Q = 28.45, whichcauses a reduced rate of dephosphorylation in this regime as compared to previous Q values (see Figures 3.4,F.12).

Q = 148.0

Q values in this regime are such that the level of active phosphatase reached at steady state exceeds that ofactive kinase for all values of [Ca2+]i. The level of [PA] reached at steady state approached 0.99 with increasing[Ca2+]i and reached its half-maximal value at [Ca2+]i = 1.38×10−4 mM. Given this sensitivity of phosphatase tochanges in [Ca2+]i, it might be expected that [MP] KCC2 was almost entirely removed during plasticity inductionwhen Ca2+ currents are mediated by L-type Ca2+ channels. Perhaps surprisingly, changes in [MP] following theSTDP protocol with this Q value were smaller in magnitude than for other phosphatase activation regimes (seeFigure 3.6). Though high levels of [PA](> 94% of phosphatase in active state) were achieved for all spike timingintervals (see Figure F.13, Appendix F), the ratio of RMP:RM at this Q value was such that phosphorylation of[M] KCC2 by [KA] was able to replenish some of the [MP] pool. In the case of T-type Ca2+ channels, qualitative

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differences in the shape of the STDP curve were reflective of the degree of Ca2+ influx via low versus highconductance channels. For low conductance T-type channels, relatively small increases in [Ca2+]i during positivecoincident spike timing intervals allowed for differential changes in level of [PA] achieved over different ∆t values(see Figure F.5). By contrast, high conductance T-type channels led to Ca2+ influx over positive coincident spiketiming intervals which led to near maximal [PA] activation. Small fluctuations in the level of dephosphorylationwith 0 ms < ∆t < +5 ms are due to differences in the maximal level of [Ca2+]i achieved with each of thesespike timing intervals. These differences in [Ca2+]i are sufficient to give rise to slightly different levels of activephosphatase at steady state, leading to differences in the level of dephosphorylation achieved.

3.3.3 Changes in ECl in Coincident Spike Timing Intervals Due To KCC2 Dephospho-rylation and Synaptic Cl− Loading

Finally, Figures 3.9 and 3.10 show the effect of different levels of dephosphorylation resulting from changingQ values on ECl (see also Figures F.14 and F.15, Appendix F). Small depolarizing shifts in ECl were observed inall conditions where presynaptic spiking occurred, a result of synaptic Cl− loading. Large depolarizing shifts inECl were observed for positive coincident spike timing intervals, as depolarization of the postsynaptic membraneduring GABAAR activation led to a significant driving force for Cl− through the receptor pore. Hence, thesechanges were primarily due to the effects of significant synaptic Cl− loading when postsynaptic depolarizationoccurred while the GABAAR was open and allowing Cl− flux across the membrane (i.e. ∆t = +1 ms). Differencesin the degree of change in ECl across Q values during positive coincident spike timing intervals reflected thedegree of dephosphorylation of KCC2 which occurred during each of these regimes.

As described above, the greatest reduction in [MP] KCC2 was seen for Q = 1.9 with L-type Ca2+ channels.For this reason, the greatest depolarizing shift in ECl was observed at this Q value (Figure 3.9). Less overalldephosphorylation of KCC2 was seen for Q = 0.1 and 148.0, and hence more KCC2 was available to counteractthe effects of synaptic Cl− loading in these cases. In the case of T-type channel-mediated Ca2+ influx, largestdepolarizing shifts in ECl were seen for Q = 7.4 (Figure 3.10). As L- and T-type channels together gave rise tolevels of dephosphorylation similar to L-type channels alone, changes in ECl did not differ significantly betweenthese two conditions (see Figure F.14). Changes in ECl resulting from low conductance T-type channel-mediatedCa2+ influx were significantly smaller than for other channel conditions (see Figure F.15), leading to a maximaldepolarizing shift of 0.78 mV as compared with 2.23 mV for T-type Ca2+ channels and 4.62 mV for L-type Ca2+

channels.

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Figure 3.9: Changes in ECl Following Plasticity Induction for L-type Ca2+Channels. For this plot, ∆t = ± 75 mswas used as representative of the non-coincident STDP protocols, and ∆t = ± 1 ms was used as representativeof the coincident STDP protocols. Large changes in ECl during the positive coincident spike timing intervalcondition as compared with non-coincident/negative coincident conditions are largely the result of synaptic Cl−

loading. The degree of these changes differs acrossQ values, reflective of the level of dephosphorylation of KCC2which occurred as a result of STDP.

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Figure 3.10: Changes in ECl Following Plasticity Induction for T-type Ca2+Channels. As in Figure 3.9, ∆t = ± 75ms was used as representative of the non-coincident STDP protocols, and ∆t = ± 1 ms was used as representativeof the coincident STDP protocols. Large changes in ECl during the positive coincident spike timing intervalcondition as compared with non-coincident/negative coincident conditions are largely the result of synaptic Cl−

loading. The degree of these changes differs acrossQ values, reflective of the level of dephosphorylation of KCC2which occurred as a result of STDP. The magnitude of these changes is diminished as compared with L-type Ca2+

channels, as the degree of dephosphorylation of KCC2 was less substantial in this condition as compared withL-type Ca2+ channels.

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4.1 Summary of Results

For this thesis, we designed and implemented a kinetic model of KCC2 regulation, wherein KCC2 could bedifferentially distributed between three cellular states: cytoplasmic ([C]), membrane bound while unphosphory-lated ([M]), and membrane bound and phosphorylated ([MP]). In a biophysically realistic neuron simulation, weused this kinetic model to test the plausibility of our hypothesis for the mechanism by which the depolarizingshift in EGABA occurs following plasticity induction. In particular, we developed this model to verify whetherCa2+-dependent dephosphorylation of KCC2 can account for spike timing-dependent changes in EGABA. We in-vestigated whether spike timing-dependent changes in KCC2 phosphorylation state, and hence Cl− extrusion ca-pacity, could be explained by T-type channel-mediated Ca2+ influx. Importantly, our results showed that this maybe a plausible mechanism by which plasticity is induced at inhibitory synapses. We found that T-type channel-mediated Ca2+ influx gave rise to spike timing-dependent dephosphorylation of KCC2 in our simulations. Inconditions with T-type channels alone mediating Ca2+ currents, coincident activity caused dephosphorylation ofKCC2 while non-coincident activity left KCC2 phosphorylation relatively unaffected, consistent with our hypoth-esized mechanisms for inhibitory STDP. Furthermore, our model showed that Ca2+ influx mediated by L-typeCa2+ channels could lead to dephosphorylation of KCC2 regardless of spike timing interval. Finally, though Ca2+

influx triggered by activation of L- and T-type channels together was significantly larger than via L-type chan-nels alone, this was not able to generate significant differences in dephosphorylation of KCC2 beyond those seenwhen L-type channels alone were present as this level of Ca2+ influx was outside of the dynamic range for [PA]activation.

In order to create the kinetic model described above, parameter values were sourced from relevant litera-ture, set using experimental data, or hand tuned by testing several values against qualitative experimental results.Experimental work to determine the rates of insertion and removal of KCC2 to and from the membrane werecrucial pieces in determining physiologically realistic behaviour of the model. Experimental evidence suggestedthat under basal conditions, endocytosis of KCC2 from the membrane occurs faster than transporter insertionto the membrane. Consequently, the majority of KCC2 is present in the cytosolic fraction at steady state. Thisdata allowed us to calculate estimates of the level of KCC2 in each of its membrane-associated states ([M] and[MP]); we found that 13.72% was unphosphorylated in the membrane, while the remaining 6.28% was phospho-rylated at steady state. However, several important caveats to these results should be highlighted. First, estimatesof the proportion of KCC2 in the cytosolic fraction were lower ([C] = 0.7) in COS7 cell preparations than inprevious biotinylation experiments which utilized brain tissue slices ([C] = 0.8), indicating differences in ratesaffecting KCC2 transitions among states between these two preparations. Furthermore, COS7 cells were treated

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Discussion

with Go6983 for 12-14 hours prior to TIRF microscopy experiments to observe the movement of puncta. Wemade the assumption that this treatment resulted in full inhibition of PKC activity, and hence all KCC2 in themembrane under these conditions was in the [M] state. Finally, it was assumed that the puncta observed by TIRFmicroscopy were reflective of KCC2 tetramers. Importantly, if puncta were not tetrameric KCC2 proteins or ifthere was variability among puncta in the number of KCC2 molecules present, this would have significant effectson our estimate for α, and therefore also for our calculated values of β, as well as steady state values of [M] and[MP].

As no experimentally determined parameters were available for the maximal rate of phosphatase activa-tion nor for rate of inactivation, simulations were carried out with varying values for the ratio between thesetwo parameters (Q), representative of the net activation rate of phosphatase in response to changing [Ca2+]i. Itwas found that by varying Q, four distinct patterns could be found for the relationship between [KA] and [PA]achieved at steady state for varying levels of [Ca2+]i. For Q < 3.9, active kinase is present in larger proportionsas compared with active phosphatase at steady state for all [Ca2+]i. However, we recalculated the ratio betweenphosphorylation and dephosphorylation for each Q value in order to maintain steady state distribution of KCC2.Consequently, though low values for Q showed relatively high levels of active kinase at steady state, KCC2 stillunderwent net dephosphorylation following plasticity induction, as the rate of phosphorylation was extremelylow compared with the rate of dephosphorylation. For the same reason, large values of Q (> 46.0) did not lead tototal dephosphorylation of [MP] KCC2 as the rate of phosphorylation was much greater than the rate of dephos-phorylation, replenishing the pool of [MP] KCC2. In essence, Q value reflects the sensitivity of phosphatase tochanges in [Ca2+]i, while the calculated ratio RM:RMP reflects the tendency of phosphatase in the active state tocatalyze the removal of the phosphate group from [MP] KCC2 (and conversely the tendency for kinase to catalyzephosphorylation).

While selection of Q impacted the degree of dephosphorylation of KCC2 following plasticity induction,plasticity induction simulations showed that the source of Ca2+ influx determined the spike timing-dependence ofinduced plasticity. In particular, T-type channel-mediated Ca2+ influx led to dephosphorylation in a spike timing-dependent manner, while L-type channel-mediated Ca2+ currents led to changes in [MP] KCC2 independent ofspike timing interval. This result makes sense, given the requirement of T-type channels for hyperpolarizatingdeinactivation preceding depolarizing activation. This feature makes the T-type Ca2+ channel an effective coinci-dence detector for the firing of both pre- and post-synaptic cells. Furthermore, Ca2+ influx via both L- and T-typechannels together was not able to generate significant changes in [MP] beyond those seen when Ca2+ influx oc-curred via L-type channels alone. For all sources of Ca2+ influx, fluctuations in the level of dephosphorylation ofKCC2 seen for small coincident spike timing intervals (-5 ms < ∆t < +5 ms) were due to fluctuations in the levelof Ca2+ entering the cell for these spike timing intervals. At these spike timing intervals, interaction between inputsources may cause changes in the membrane potential affecting the driving force for Ca2+ and hence the level ofinflux achieved. Though overall qualitative changes in the level of phosphorylation of KCC2 were seen whenCa2+ source was varied, the precise level of change in [MP] KCC2 was determined by Q value. Consequently, weconclude that T-type channel-mediated Ca2+ influx causing dephosphorylation of KCC2 can provide a plausiblemechanism for the plasticity observed in experimental preparations of this nature.

Experimental results show that activation of L-type Ca2+ channels is necessary but not sufficient for plasticityinduction at inhibitory synapses [111]. Given that L-type Ca2+ channel activation does not require presynapticinput for activation, it is perhaps unintuitive that these channels would play a role in induction of plasticity thatis dependent on the temporal separation between pre- and post-synaptic spikes. Indeed, model results show that

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Discussion

dephosphorylation of KCC2 following L-type channel-mediated Ca2+ influx is relatively homogeneous across ∆tvalues, with only small fluctuations in dephosphorylation where [Ca2+]i differs significantly enough to move activephosphatase into its dynamic range. For this reason, it is slightly mysterious as to why L-type Ca2+ channels arenecessary for plasticity induction at inhibitory synapses. One possible explanation is that L-type Ca2+ channelsallow for consistent changes in [Ca2+]i for all ∆t, while T-type channels mediate additional Ca2+ influx only duringpositive coincident spike timing intervals. It is possible that the presence of L- and T-type channels together allowsadditional elevation in [Ca2+]i during positive coincident spike timing intervals, which is necessary to move activephosphatase into its dynamic range. It is possible that our model did not capture this phenomenon for severalreasons. First, L-type channel conductance was such that active phosphatase reached saturation for nearly everyQ value for the level of Ca2+ influx via these channels. Hence, active phosphatase was not in a dynamic rangewhere additional Ca2+ influx via T-type channels could have any effect.

Second, it is also possible that we have not accurately captured the dynamics of phosphatase action on KCC2in this model. Our model operates under the assumption that our phosphatase is either the constitutively active PP1(inhibited at rest by Cdk5), or calcineurin, whose activity dually controlled by Ca2+ – directly via Ca2+ bindingto its regulatory domain, and indirectly via Ca2+ binding to CaM, which in turn binds calcineurin to modulate itsactivity [102]. Altering the kinetic model to reflect dual regulation of calcineurin by Ca2+ may affect its activityrelative to kinase and its dynamic range for activation, perhaps giving rise to different net activation regimes thanthose presented in Table 3.1 and Figure 3.3, and hence different responses to [Ca2+]i elevations during plasticityinduction.

It is important to note, however, that experimental quantification of plasticity induction was principally madefrom measures of changes in EGABA rather than explicit measures of changes in KCC2 phosphorylation. In orderfor the model to generate meaningful data for comparison, we must have physiologically realistic parameters forthe dynamics of Cl− extrusion. Our model-generated measures of ECl, taken to be a reasonable proxy for EGABA

considering the relative permeability of GABAA receptors to Cl− and HCO−3 . Our results showed that for non-coincident and negative coincident spike timing intervals, small depolarizing shifts in ECl were seen as a resultof synaptic Cl− loading, rather than changes in KCC2 extrusion efficacy per se. Consequently, no significantdifferences were observed across Q values in these conditions, as Cl− influx was independent of phosphatasesensitivity. However, substantial differences in the depolarizing shift in ECl were seen acrossQ values for positivecoincident spike timing intervals. The large depolarizing shifts as compared with other spike timing intervalswere again the result of synaptic Cl− loading; activation of GABAA receptors followed shortly by postsynapticspiking (∆t = +1ms) causes substantial levels of Cl− influx due to the large driving force for Cl− created bythe postsynaptic depolarization while GABAA receptors are open. Hence, while synaptic Cl− loading was moresubstantial for positive coincident intervals as compared with other spike timing intervals, the degree of change inECl was determined by the amount of KCC2 available for transport to counteract the effects of this Cl− loading.

Importantly, this result comes with a significant caveat: since ECl steady state is dependent on tonic GABAconductance and on the amount of Cl− loading from the GABAergic synapses, depolarizing shifts in ECl are thesum of several different factors. Moreover, this data is only meaningful given physiologically realistic valuesfor parameters describing basal levels of Cl− stress on the cell. Experiments to determine realistic parameters ofthese sources of Cl− stress on the cell have only recently been conducted, and have not yet been implemented inthe model. We note that the magnitude of these changes may not be accurate, and further experiments should beconducted to determine to what degree each of these sources affects changes in ECl following plasticity induction(discussed below).

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Discussion

4.2 Model Predictions

Given the above results, this model makes several important predictions about the nature of inhibitory STDPseen experimentally:

1. Inhibitory STDP requires Ca2+ influx mediated by T-type VGCCs. Positive coincident spike timing intervalsallow for the necessary hyperpolarization-depolarization coupling to activate T-type channels, resulting inthe Ca2+ influx for activation of the Ca2+-sensitive kinases and phosphatases which target KCC2. Thisdependence on spike timing interval is not seen when Ca2+ currents are mediated by L-type channels,which do not require preceding hyperpolarization and are hence insensitive to activity of the presynapticcell. Thus, we would predict that experimental manipulations of T-type VGCCs will have particularlypronounced effects on inhibitory STDP.

2. The inhibitory STDP curves observed in Woodin et al. (2003) involve separate mechanisms to generatedepolarizing shifts in positive and negative coincident spike timing intervals. Based on our results, wepredict that changes in GABAergic postsynaptic current (GPSC) seen for positive coincident spike timingintervals can be attributed to a depolarizing shift in EGABA resulting from KCC2 dephosphorylation. Con-versely, our model would suggest that changes in GPSC for negative coincident spike timing intervals arenot attributable to dephosphorylation of KCC2 via T-type channel-mediated Ca2+ influx (though the specificmechanism resulting in this change experimentally is not predicted by this model).

3. Presence of L- and T-type Ca2+ channels in compartments of different size and with varying conductanceswill give rise to different effects on EGABA in response to plasticity induction with varying spike timingintervals. Thus, given that the distribution of L-type and T-type VGCCs is varied throughout dendrites[15, 81], we would predict that the spatial location of inhibitory synapses on the postsynaptic neuron couldhave significant implications for the specifics of inhibitory STDP.

4.3 Limitations

Lack of experimentally determined parameter values for rates of inactivation and maximal activation ofphosphatase significantly hamper the ability to draw firm conclusions from model generated results. Changes inlevels of KCC2 phosphorylation and ECl following plasticity induction may only be interpreted relative to oneanother, with important caveats about the physiological realism of extreme values of Q (i.e. 0.1, 148.0). Indeed,given accurate values for these parameters (or for rates of phosphorylation and dephosphorylation, from whichQ could then be inferred) would allow for more realistic characterization of the kinetic system, and hence moreaccurate predictions of STDP mechanisms. Essentially, any parameter values in the model set by hand limit theability of the model to make predictions of experimental outcomes. Furthermore, defining the kinetic systemwith parameters whose values have been derived from a variety of experimental sources, each with separateconditions, assumptions, and caveats, necessarily gives rise to results which must be taken to inherently deviatefrom real world conditions to some degree.

By the same token, our model made great simplifications to phosphatase activation dynamics. In part thiswas in order to remain agnostic about whether the acting phosphatase in this system was PP1 or calcineurin, whichhave both been implicated in regulation of KCC2 phosphorylation state [16, 57, 93]. Activation of both PP1 and

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Discussion

calcineurin is more complex than was presented in this model, and our simplifications may impede both our abilityto draw meaningful conclusions about which of these two phosphatases is responsible for changes seen in KCC2phosphorylation state, and the way in which these changes may occur. Hence, we must be mindful that differencesin phosphatase activation dynamics may give rise to different levels of change in KCC2 phosphorylation statefollowing plasticity induction.

Importantly, this model is limited in its ability to quantify changes in ECl – and hence changes in strength ofinhibition – following plasticity induction. As mentioned above, meaningful interpretation of these results is onlypossible when basal levels of Cl− stress on the cell are known. Moreover, it is important to have accurate valuesfor the various sources of Cl− input to the cell in order to determine their relative contribution to ECl, and hence towhat degree the depolarizing shift may be attributed to changes in KCC2 phosphorylation as opposed to artifacts.In particular, it is important to resolve the relative contributions of tonic GABA current, synaptic Cl− loading, andchanges in KCC2 phosphorylation state leading to a depolarizing shift in ECl for coincident versus non-coincidentspike timing intervals.

Finally, this model is limited in its ability to draw conclusions about the effects of compartment size andsynaptic distribution on plasticity induction. While we aimed to design a model which did not reflect any specificcellular compartment, this also meant that we were unable to test effects in compartments of different size andspatial location. Furthermore, it is known that VGCC channel conductance varies with synaptic location ondendritic branches [15, 81]. This model lacks the ability to test different relative levels of L- and T-type channelconductance in multicompartment cells with realistic diffusion dynamics. Future modeling studies will hopefullybe able to investigate these dynamics in greater detail.

4.4 Future Studies and Experimental Predictions

As mentioned above, experiments to determine values for Cl− extrusion parameters have only recently beenconducted. The simulation experiments presented above should be recreated with accurate values for Cl− extru-sion parameters, in order to have a better idea of the actual changes in ECl resulting from plasticity induction inthis model.

Furthermore, translating the model presented in this thesis to a physiologically realistic multicompartmentmodel could provide valuable insights into how plasticity induction may affect KCC2 in a real cell. In particular,effects of variations of compartment size, relative levels of L- and T-type channel conductances, and synapticlocation could be observed. Furthermore, we may test the effects of coincident and non-coincident spike pairsin the same cell in different dendritic compartments in order to see if we may recreate plasticity effects seen inOrmond et al. (2011) showing synapse specific LTP [75].

Finally, future experiments may involve testing the effects of more subtle variations in Q values in order tofully explore the differences between phosphorylation activation regimes presented in Table 3.1. If this is to bedone, it should be noted that a more detailed model of phosphatase activation in which dual regulation by Ca2+ isappropriately captured should be created. As discussed above, present phosphatase activation parameters aim tocapture simplified activation dynamics general enough to apply to either PP1 or calcineurin. It may also be inter-esting to test the effects of more realistic phosphatase activation dynamics tailored to each of these phosphatasesseparately, to test their effects on plasticity induction.

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Ultimately, the goal of a modelling study such as this is to generate predictions about experimental findings.For practical reasons, it may be difficult to experimentally test many of the findings of this model. For exam-ple, there are currently no known T-type VGCC-specific blockers. However, we may make the following broadpredictions which may one day be testable with appropriate technical advances:

1. T-type VGCCs are necessary for induction of plasticity with positive coincident spike timing intervals, butnot for negative spike timing intervals

2. The relative distribution of T-type and L-type VGCCs throughout the dendrites of a neuron will determinethe shape of the STDP curve for inhibitory synapses

3. Changes in the phosphorylation state of KCC2 may be observed in the early phases of STDP, thoughsecondary mechanisms are required to confer long-lasting changes in synaptic strength resulting from co-incident activity.

In conclusion, this study found that the proposed mechanism for inhibitory STDP is plausible, though furtherresearch must be conducted to determine whether this mechanism actually operates in neurons.

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77

Appendix

A Enzyme Kinetics

A.1 The Michaelis-Menten Equation

Suppose we have the following enzymatic reaction:

[E][S ]rα

GGGGGBFGGGGG

rβ[ES ]

kpGGGGGGA[P]

Where [E] represents moles of enzyme, [S ] moles of substrate, and [P] moles of product; rα and rβ are the forwardand reverse rates of enzyme-substrate binding, respectively, and kp is the rate of product formation. In accordancewith Michaelis-Menten model for enzyme kinetics, we assume that the product formation reaction is irreversible.

The rate of chemical product formation, v is:

v = kp[ES ]

And the measure of maximal rate of chemical product formation, V , is:

V = kp[ETotal] Where [ETotal] = [EBound] + [EUnbound]

= kp([E] + [ES ]

)=⇒

vV

= kp[ES ]

kp([E] + [ES ]

)=

[ES ][E] + [ES ]

Define R =rβrα

=⇒ [ES ] =[E][S ]

R

=⇒vV

=[E][S ]

R([E] + [ES ]

)=

[E][S ]

R([E] + [E][S ]

R)

=[S ]

R + [S ]

=⇒ v =V[S ]

R + [S ](81)

This is the Michaelis-Menten model, one of the simple and most widely used models of enzyme kinetics.Here we want to think of v as a weighted form of V . The rate constants rα and rβ have units /s and mol/s,respectively. Hence the constant R =

rβrα

has units mol so if [S ] = R

=⇒ v =V2

78

Appendix

We can think of R as the “half-maximal” concentration of v.

Note that the Michaelis-Menten equation (81) makes use of the assumption that kp is the rate limiting stepand therefore kp <<< rβ. Omitting this assumption, the reaction kinetics are described by:

d[ES ]dt

= 0 = rα[E][S ] − rβ[ES ] − kp[ES ]

=⇒ (rβ + kp)[ES ] = rα[E][S ]

=⇒rβ + kp

rα=

[ES ][E][S ]

or [ES ] =rβ + kp

rα[E][S ]

This is the more general Briggs-Haldane equation.

A.2 The Hill Function

Activity of both kinase and phosphatase depends on the presenece of calcium (Ca2+), so we treat Ca2+ as thesubstrate in this case. The reaction velocity of the activation or inactivation for kinase or phosphatase can begiven by the general equation:

v =V[Ca2+]h

Rh + [Ca2+]h

if h = 1 then we have Michaelis-Menten

if h > 1 then we have faster than MM

if h < 1 then we have slower than MM

(82)

Where the variable h is a unitless measure of the “cooperativity of Ca2+ binding.” That is, if a Ca2+ ion binds to akinase or phosphatase, it alters the enzyme’s affinity for a second ion. Values of h > 1 indicate increased affinityfor a second ion binding and therefore faster reaction kinetics. Values < 1 indicate decreased affinity, and a valueof 1 indicates that binding of one ion has no effect on the second. For this equation the units are:

vmol/s

=

mol/s

V

mol

[Ca2+]h

Rh

mol+ [Ca2+]h

mol

79

Appendix

B Kinase & Phosphatase Dynamics

B.1 The Kinetic Scheme

Activity of kinase and phosphatase in the cell can be described by the following kinetic scheme:

[KI] [MKA]

[C] [PA][M][KA] [KA][MP][PA]

[MPPA] [PI]

α

β

vIK vAKr11

r12

rMP

vIPvAPr22

r21rM

B.2 Differential Equations

The above system can be described by the differential equations:

d[C]dt

= β[M] − α[C] (83)

d[M]dt

= r12[MKA] + α[C] − β[M] − r11[M][KA] + rM[MPPA] (84)

d[MP]dt

= r21[MPPA] − r22[MP][PA] + rMP[MKA] (85)

d[MKA]dt

= r11[M][KA] − (r12 + rMP)[MKA] (86)

d[MPPA]dt

= r22[MP][PA] − (r21 + rM)[MP][PA] (87)

d[KA]dt

= r12[MKA] − r11[M][KA] + vAK[KI] − vIK[KA] + rMP[MKA] (88)

d[PA]dt

= r21[MPPA] − r22[MP][PA] + vAP[PI] − vIP[PA] + rM[MPPA] (89)

d[KI]dt

= vIK[KA] − vAK[KI] (90)

d[PI]dt

= vIP[PA] − vAP[PI] (91)

where vIK and vIP are the rates of inactivation and vAK and vAP are the rates of activation of kinase and phosphataserespectively.

B.3 Assumptions and Simplifications

The Free Ligand Assumption

The total amount of kinase is given by[KA] + [KI] + [MKA] = 1

80

Appendix

Similarly, total phosphatase is given by

[PA] + [PI] + [MPKA] = 1

We assume that at any given point in time, the concentration of available enzyme far exceeds the concentration ofenzyme bound to its substrate, i.e.

[KA] + [KI] >>> [MKA] and [PA] + [PI] >>> [MPKA]

So that

[KA] + [KI] ≈ 1 (92)

[PA] + [PI] ≈ 1 (93)

Similarly, the total amount of transporter is given by

[C] + [M] + [MP] + [MKA] + [MPPA] = 1

Again we assume that at any given point in time, the concentration of the substrate-bound enzyme is much smallerthan the available substrate, i.e. We assume that at any given point in time, the amount of available enzyme farexceeds the amount of enzyme that is bound by its substrate, i.e.

[M] >>> [MKA] and [MP] >>> [MPKA]

So that

[C] + [M] + [MP] ≈ 1 (94)

The Briggs-Haldane Assumption

The Briggs-Haldane assumption allows us to assume that d[MKA]dt = d[MPPA]

dt = 0. Then:

r11[M][KA] = (r12 + rMP)[MKA]

=⇒ [MKA] =r11

(r12 + rMP)[M][KA] (95)

r22[MP][PA] = (r21 + rM)[MPPA]

=⇒ [MPPA] =r22

(r21 + rM)[MP][PA] (96)

81

Appendix

We define the constants RM and RMP to be:

RM =r22rM

(r21 + rM)and RMP =

r11rMP

(r12 + rMP)

Then:

d[M]dt

=r12r11

(r12 + rMP)[M][KA] + α[C] − β[M] − r11[M][KA] +

rMr22

(r21 + rM)[MP][PA]

=

(r12r11

(r12 + rMP)−

r11(r12 + rMP)(r12 + rMP)

)[M][KA] + α[C] − β[M] +

rMr22

(r21 + rM)[MP][PA]

= −r11rMP

(r12 + rMP)[M][KA] + α[C] − β[M] +

r22rM

(r21 + rM)[MP][PA]

= −RMP[M][KA] + α[C] − β[M] + RM[MP][PA]

d[MP]dt

=r21r22

(r21 + rM)[MP][PA] − r22[MP][PA] +

rMPr11

(r12 + rMP)[M][KA]

=

(r21r22

(r21 + rM)−

r22(r21 + rM)(r21 + rM)

)[MP][PA] +

rMPr11

(r12 + rMP)[M][KA]

= −r22rM

(r21 + rM)[MP][PA] +

r11rMP

(r12 + rMP)[M][KA]

= −RM[MP][PA] + RMP[M][KA]

d[KA]dt

= (r12 + rMP)[MKA] − r11[M][KA] + vAK[KI] − vIK[KA]

= r11[M][KA] − r11[M][KA] + vAK[KI] − vIK[KA]

= vAK[KI] − vIK[KA]

d[PA]dt

= (r21 + rM)[MPPA] − r22[MP][PA] + vAP[PI] − vIP[PA]

= r22[MP][PA] − r22[MP][PA] + vAP[PI] − vIP[PA]

= vAP[PI] − vIP[PA]

82

Appendix

The differential equations describing the kinetic system then simplify to:

d[C]dt

= β[M] − α[C] (97)

d[M]dt

= α[C] − (β + RMP[KA])[M] + RM[MP][PA] (98)

d[MP]dt

= −RM[MP][PA] + RMP[M][KA] (99)

d[KA]dt

= vAK[KI] − vIK[KA] (100)

d[PA]dt

= vAP[PI] − vIP[PA] (101)

d[KI]dt

= vIK[KA] − vAK[KI] (102)

d[PI]dt

= vIP[PA] − vAP[PI] (103)

Rate Constants

The rates of kinase and phosphatase activation (vAK and vAP, respectively) are described by the Hill function (82):

vAK =VAK[Ca2+]hK

RhKK + [Ca2+]hK

vAP =VAP[Ca2+]hP

RhPP + [Ca2+]hP

We assume rates of kinase and phosphatase inactivation (vIK and vIP, respectively) are constant. Rates of phos-phorylation (RMP) and dephosphorylation (RM) are fit to experimental data using expressions derived from steadystate solutions to (97 - 99). These solutions are outlined below (see §B.4, Solving for RMP and RM).

B.4 Steady-State Solutions

We address the system at steady state, i.e.

d[C]dt

=d[M]

dt=

d[Mp]dt

=d[KA]

dt=

d[PA]dt

=d[KI]

dt=

d[PI]dt

= 0

Kinase and Phosphatase Dynamics

From (100), with (92):

[KI] = 1 − [KA]

=⇒ vAK(1 − [KA]) − vIK[KA] = 0

=⇒ (vAK + vIK)[KA] = vAK

=⇒ [KA] =vAK

vAK + vIK(104)

83

Appendix

Similarly, from equations (101)-(103) we have:

[PA] =vAP

vAP + vIP(105)

[KI] =vIK

vAK + vIK(106)

[PI] =vIP

vAP + vIP(107)

Calculating [PA] in Terms of Q

Experimentally supported parameters for VAP and vIP were not available for our simulations, so the ratio Q =

VAP/vIP was used as a proxy to calculate [PA] and [PI]. Below are the derivations for expresions for [PA] and [PI]in terms of the ratio Q.

[PA] =

VAP[Ca2+]hP

RhPP +[Ca2+]hP

VAP[Ca2+]hP

RhPP +[Ca2+]hP

+ vIP

(108)

=

(VAP[Ca2+]hP

RhP

P + [Ca2+]hP

)·

(RhP

P + [Ca2+]hP

VAP[Ca2+]hP + vIP(RhP

P + [Ca2+]hP) ) (109)

=VAP

vIP·

[Ca2+]hP

( VAPvIP

)[Ca2+]hP + RhPP + [Ca2+]hP

(110)

=Q · [Ca2+]hP

[Ca2+]hP(Q + 1

)+ RhP

P

(111)

Hence:

[PI] =RhP

P + [Ca2+]hP

RhPP +

(Q + 1

)[Ca2+]hP

(112)

84

Appendix

KCC2 Dynamics

From (97) we have

d[C]dt

= β[M] − α[C] = 0

=⇒ [C] =β

α[M]

Then (98) gives

d[M]dt

= 0 = α[C] − β[M]= 0 (by 0.2.13)

−RMP[KA][M] + RM[MP][PA]

=⇒ RMP[KA][M] = RM[MP][PA]

=⇒ [M] =RMP[PA]RM[KA]

[MP] (113)

=⇒ [MP] =RM[KA]RMP[PA]

[M] (114)

From (94) we can write:

[C] + [M] + [MP] = 1

=⇒β

α[M] + [M] +

RM[KA]RMP[PA]

[M] = 1

=⇒

(β

α+ 1 +

RM[KA]RMP[PA]

)[M] = 1

=⇒

(βRMP[PA] + αRMP[PA] + αRM[KA]

αRMP[PA]

)[M] = 1

Hence:

[M] =αRM[PA]

(α + β)RM[PA] + αRMP[KA](115)

From (97) at steady state:

[C] =β

α·

(αRMP[PA]

βRMP[PA] + αRMP[PA] + αRM[KA]

)=

βRM[PA](α + β)RM[PA] + αRMP[KA]

(116)

And from (114) we get:

[MP] =RM[KA]RMP[PA]

·

(αRMP[PA]

βRMP[PA] + αRMP[PA] + αRM[KA]

)=

αRMP[KA](α + β)RM[PA] + αRMP[KA]

(117)

85

Appendix

Solving for RMP and RM

To determine an explicit relationship between RMP, RM , and the distribution of KCC2 among its three states, wesolved equation (99) at steady state. We describe the fraction of KCC2 in the membrane as x = [M] + [MP]. From(99) we have:

RMP[M][KA] = RM[MP][PA] (118)

From our expression for x we have that [MP] = x - [M] and so:

RMP

RM[M][KA] = (x − [M])[PA] (119)

=⇒RMP

RM[M][KA] = x[PA] − [M][PA] (120)

=⇒

(RMP

RM[KA] + [PA]

)[M] = x[PA] (121)

=⇒

(RMP[KA]RM[PA]

+ 1)

=x

[M](122)

=⇒RMP

RM=

(x

[M]− 1

)·

([PA][KA]

)(123)

From equation 2.43 we know that [C] = 0.8. From 2.36 we get:

[M] =α[C]β

=(0.2533)(0.8)

1.477= 0.1372

Then equation 3.79 becomes:

RMP

RM

[KA][PA]

=0.2

0.1372− 1 (124)

=⇒RMP

RM= 0.4577

[PA][KA]

(125)

86

Appendix

C Chloride Transport

C.1 The Kinetic Scheme

Activity of the K+-Cl− cotransporter KCC2 in its active, membrane-bound state can be described by the followingkinetic scheme:

[TCl−][K+]

[T ][Cl−][K+] [TCl−K+] [P]

[T K+][Cl−]

r1

r2

r1

r2

r1

r2

r1

r2

rT

So far we have two kinetic schemes:(A) A scheme representing transitions of KCC2 in the cell between cytoplasmic, membrane-bound phosphory-lated, and membrane-bound unphosphorylated states, with KCC2 bound or unbound to active kinase or phos-phatase.(B) A scheme representing the KCC2 transporter bound or unbound to chloride ions, potassium ions, or both.

For scheme (A) we assume the Briggs-Haldane conditions: that certain transitions in the scheme are irre-versible reactions, i.e.

[MKA] −→ [M][KA] [MPA] −→ [M][PA]

For scheme (B) we make the additional assumtion of the Michaelis-Menten condition, i.e.

rT <<< r1, r2

Let RT = r2r1

and vT = rT [T K+Cl−].With the Michaelis-Mention (MM) assumption we have:

[T K+Cl−] =[T ][K+][Cl−]

RT2 (126)

The Briggs-Haldane assumption is that we are at steady state, i.e.

d[T K+Cl−]dt

= 0 (127)

d[T K+]dt

= 0 (128)

d[TCl−]dt

= 0 (129)

87

Appendix

From (127) we have:

r1[T K+][Cl−] + r1[TCl−][K+] − 2r2[T K+Cl−] = 0 (130)

=⇒ [T K+Cl−] =r1([T K+][Cl−] + [TCl−][K+])

2r2(131)

=([T K+][Cl−] + [TCl−][K+])

2RT(132)

From (128) we have:

r1[T ][K+] + r2[T K+Cl−] − r2[T K+] − r1[T K+][Cl−] = 0 (133)

=⇒ [T K+] =r1[T ][K+] + r2[T K+Cl−]

r2 + r1[Cl−](134)

Similarly to (134) we get from (129):

r1[T ][Cl−] + r2[T K+Cl−] − r2[TCl−] − r1[TCl−][K+] = 0 (135)

=⇒ [TCl−] =r1[T ][Cl−] + r2[T K+Cl−]

r2 + r1[K+](136)

Substituting (134) and (136) into (132) we get:

r1[T ][K+]+r2[T K+Cl−]r2+r1[Cl−] [Cl−] + r1[T ][Cl−]+r2[T K+Cl−]

r2+r1[K+] [K+]

2RT

=[Cl−](r2 + r1[K+])(r1[T ][K+] + r2[T K+Cl−]) + [K+](r2 + r1[Cl−])(r1[T ][Cl−](r2[T K+Cl−])

2RT(r2 + r1[K+])(r2 + r1[Cl−])

Let A = 2RT(r2 + r1[K+])(r2 + r1[Cl−])Hence we have

(r2[Cl−] + r1[K+][Cl−])(r1[T ][K+] + r2[T K+Cl−]) + (r2[K+] + r1[Cl−][K+])(r1[T ][Cl−] + r2[T K+Cl−])A

=r1r2[T ][K+][Cl−] + r2

2[Cl−][T K+Cl−] + r21[T ][K+]2[Cl−] + r1r2[T K+Cl−][K+][Cl−]A

+r1r2[T ][K+][Cl−] + r2

2[K+][T K+Cl−] + r21[T ][K+][Cl−]2 + r1r2[T K+Cl−][K+][Cl−]A

=2r1r2[K+][Cl−]([T ] + [T K+Cl−]) + r2

1[T ][K+][Cl−]([K+] + [Cl−]) + r22[T K+Cl−]([K+] + [Cl−])

A

88

Appendix

From (126) then we have

[T K+Cl−] =r2

1[T ][K+][Cl−]([K+] + [Cl−]) + 2r1r2[K+][Cl−]([T ] + [T K+Cl−])A

+r2

2[T K+Cl−]([K+] + [Cl−])A

=r2

1[T ][K+][Cl−]([K+] + [Cl−]) + 2r1r2[T ][K+][Cl−]A

+2r1r2[T K+Cl−] + r2

2[T K+Cl−]([K+] + [Cl−])A

=r2

1[T ][K+][Cl−]([K+] + [Cl−]) + 2r1r2[T ][K+][Cl−] + [T K+Cl−](2r1r2 + r22([K+] + [Cl−]))

A

=⇒r2

1[T ][K+][Cl−]([K+] + [Cl−]) + 2r1r2[T ][K+][Cl−]A

= [T K+Cl−] −[T K+Cl−]

(2r1r2 + r2

2([K+] + [Cl−]))

A

= [T K+Cl−](A − 2r1r2[K+][Cl−] − r2

2([K+] + [Cl−])A

)

=⇒ [T K+Cl−] =[T ][K+][Cl−]

(r2

1([K+] + [Cl−]))

A − 2r1r2[K+][Cl−] − r22([K+] + [Cl−])

=[T ][K+][Cl−]

(r2

1([K+] + [Cl−]))

2RT(r2 + r1[K+])(r2 + r1[Cl−]) − 2r1r2[K+][Cl−] − r22([K+] + [Cl−])

=[T ][K+][Cl−]

(r2

1([K+] + [Cl−]))

2RTr21[K+][Cl−] + 2r1r2([K+] + [Cl−]) + 2RTr2

2 − 2r1r2[K+][Cl−] − r22([K+] + [Cl−])

=[T ][K+][Cl−]

(r2

1([K+] + [Cl−]))

2RTr21[K+][Cl−] + 2r1r2

(RT([K+] + [Cl−]) − [K+][Cl−]

)+ r2

2(2RT − ([K+] + [Cl−])

)Substituting RT = r2

r1we get

=[T ][K+][Cl−]

(r2

1([K+] + [Cl−]))

2r1r2[K+][Cl−] + 2r22([K+] + [Cl−]) − 2r1r2[K+][Cl−] +

r32

r1− r2

2([K+] + [Cl−])

=[T ][K+][Cl−]

(r2

1([K+] + [Cl−]))

2r22([K+] + [Cl−]) +

r32

r1− r2

2([K+] + [Cl−])

And substituting back r2r1

= RT we get

=r2

1[T ][K+][Cl−](([K+] + [Cl−]) + 2RT

)r2

2([K+] + [Cl−] + 2RT

)=

r21

r22

[T ][K+][Cl−](

[K+] + [Cl−] + 2RT)(

[K+] + [Cl−] + 2RT)

=[T ][K+][Cl−]

RT2

89

Appendix

Hence the total amount of bound transporter (by the MM assumption) is

[T K+Cl−] =[T ][K+][Cl−]

RT2 (137)

Then for the Michaelis-Menten equation,v = [T K+Cl−]rT (138)

By the above calculations,

v =[T ][K+][Cl−]rT

RT2 (139)

Since VT = rT [Ttotal],

VT = rT([T K+Cl−] + [T K+] + [TCl−] + [T ]

)= rT

( [T ][K+][Cl−]RT

2 +r1[T ][K+] + r2[T ][K+][Cl−]

RT2

r2 + r1[Cl−]+

r1[T ][K+] + r2[T ][K+][Cl−]RT

2

r2 + r1[K+]+ [T ]

)= rT

( [T ][K+][Cl−]RT

2 +[T ][K+]

RT r2 + r1[Cl−]

r2 + r1[Cl−]+

[T ][Cl−]RT

+ [T ])

=⇒ rT =VT

[T ][K+][Cl−]RT

2 + [T ][K+]RT

+ [T ][Cl−]RT

+ [T ]

Plugging this into (139) we have

v =VT [T ][K+][Cl−]

RT2( [T ][K+][Cl−]

RT2 + [T ][K+]

RT+ [T ][Cl−]

RT+ [T ]

)=

VT [T ][K+][Cl−][T ][K+][Cl−] + RT[T ][K+] + RT[T ][Cl−] + RT

2[T ]

=VT [K+][Cl−]

[K+][Cl−] + RT[K+] + RT[Cl−] + RT2

Hencev =

VT [K+][Cl−](RT + [K+])(RT + [Cl−])

(140)

90

Appendix

D Variables

Table D.1: KCC2 Regulation Kinetic Scheme Variables

Variable Description Units Equation[C] KCC2 in cytosolic state % 2.36[M] KCC2 in membrane unphosphorylated state % 2.37[MP] KCC2 in membrane phosphorylated state % 2.38

[MKA] Membrane unphosphorylated KCC2 bound to active kinase % 95[MPPA] Membrane phosphorylated KCC2 bound to active phosphatase % 96

[KA] Active kinase % 2.39[KI] Inactive kinase % 2.41vAK Rate of kinase activation mol/s 2.46[PA] Active phosphatase % 2.40[PI] Inactive phosphatase % 2.42vAP Rate of phosphatase activation mol/s 2.47

91

Appendix

E Parameters

Table E.1: Physical Constants

Parameter Description Value

R Universal Gas Constant 8.314 J·K−1·mol−1

F Faraday Constant 9.6485×104C·mol−1

Table E.2: Compartment Parameters

Parameter Description Value Reference

L Compartment Length 10 µm Set by hand

d Compartment Diameter 10 µm Set by hand

VM Membrane Voltage -70 mV Set by hand

celsius Temperature 36 C Set by hand

CM Membrane Capacitance 1µf/cm2 [31]

RA Axial Resistivity 35.4Ω [37]

gl Leak Channel Conductance 0.001 S/cm2 Set by hand

El Leak Reversal Potential -70 mV Set by hand

ρGABAA Density of GABAergic Synapses 0.01 /µm2 [51]

gGABA Maximal Conductance of GABAA receptors 0.025 µS [60]

Table E.3: Initial Ion Parameters


Potassium[K+]i Intracellular Concentration 140 mM [2]

[K+]o Extracellular Concentration 5 mM [2]

Sodium[Na+]i Intracellular Concentration 10 mM [2]

[Na+]o Extracellular Concentration 145 mM [2]

Chloride[Cl−]i Intracellular Concentration 4 mM [2]

[Cl−]o Extracellular Concentration 110 mM [2]

axDCl− Axial Diffusion Coefficient 10 µm2/ms Set by hand

Calcium[Ca2+]i Intracellular Concentration 1.082e-4 mM [32]

[Ca2+]o Extracellular Concentration 1.5 mM [2]

Bicarbonate[HCO−3 ]i Intracellular Concentration 24 mM [46]

[HCO−3 ]o Extracellular Concentration 25 mM [46]

92

Appendix

Table E.4: Hodgkin-Huxley Parameters


gNa Maximal Sodium Conductance 0.120 S/cm2 [90]

gK Maximal Potassium Conductance 0.005 S/cm2 [90]

Vtraub Hodgkin-Huxley channel voltage-dependence factor -60 mV Set by hand

Table E.5: Calcium Channel Parameters


T Absolute Temperature 309.15 K [35]

dt Time step size 0.025 ms [35]

gCaLMaximal L-Type Channel Conductance 7.6 mS/cm2 [81]

gCaTMaximal T-Type Channel Conductance 7.6 mS/cm2 Set by hand

gCaT∗

Maximal T-Type Channel Conductance (LowConductance Condition)

3.8 mS/cm2 Set by hand

Table E.6: Michaelis-Menten Parameters

Parameter Description

rα Forward rate of reaction; rate of substrate-enzyme binding

rβ Reverse rate of reaction; rate of substrate-enzyme dissociation

kp Rate of product formation

v Rate of production of product

Vx Maximal rate of production of chemical product in reaction x

R Ratio of forward and reverse rates of reaction x

h Cooperativity of ion binding

Table E.7: Kinase and Phosphatase Kinetic Scheme Rate Constants

Parameter Description

r11 Rate of binding of active kinase to membrane KCC2

r12 Rate of dissociation of active kinase from membrane KCC2

r21 Rate of binding of active phosphatase to phosphorylated membrane KCC2

r22 Rate of dissociation of active phosphatase from phosphorylated membrane KCC2

rMP Rate of formation of phosphorylated membrane KCC2

rM Rate of formation of unphosphorylated membrane KCC2

93

Appendix

Table E.8: Kinetic Parameters of PKC Isozymes α, β, and γ (From Kohout et al. (2002) [53])

Parameter PKCα PKCβ PKCγ Average

Maximal Activation Rate (VAK) 420±40 /s 310±30 /s 440±40 /s 390 /sInactivation Rate (vIK) 17.3±0.7 /s 57±40 /s 22±1 /s 32.1 /sHalf-Maximal [Ca2+]i for Activation (RK) 1.4±0.1 µM 5.0±0.2 µM 0.7±0.1 µM 2.37 µMHill Coefficient (hK) 1.3±0.1 1.8±0.1 1.4±0.1 1.5

Table E.9: Kinetic Parameters of Kinase and Phosphatase


α Rate of insertion of KCC2 into membrane 0.2533 /sec Equation 3.68

β Rate of removal of KCC2 from membrane 1.4776 /sec Equation 3.69

VAK Maximal rate of kinase activation 390.0 /sec [53]

vIK Rate of kinase inactivation 32.1 /sec [53]

VAP Maximal rate of phosphatase activation 1-2500.0 /sec 3.2

vIP Rate of phosphatase inactivation 10.0 /sec Figure 3.2

Q = VAPvIP

Phosphatase activation ratio 0.1-250.0 Figure 3.2

RK [Ca2+] for half-maximal PKC Activation 2.37 µM [53]

RP[Ca2+] for half-maximal calcineurinactivation

0.79 µM [84]

hKHill coefficient for Ca2+-dependentactivation of PKC

1.5 [53]

hPHill coefficient for Ca2+-dependentactivation of calcineurin by calmodulin

2.9 [102]

RMP Rate of KCC2 phosphorylation (0.00134–1.89) Equation (3.80)

RM Rate of KCC2 dephosphorylation 1 Equation (3.80)

Table E.10: KCC2 Ion Transport Parameters


r1 Rate of ion binding to transporter N/A N/A

r2 Rate of ion dissociation from transporter N/A N/A

rT Rate of ion transport 10 (/s) Set by hand

RT Michaelis constant for ion transport 5 (mM) Set by hand

94

Appendix

Table E.11: Synaptic Parameters


ρ Synaptic Density 0.01/µm2 [51]

gGABA Maximal GABAAR Conductance 0.03 µS [24]

CMaximal [GABA] released into synapticcleft

1 mM[24] see

GABAa.mod

DGABA Duration of GABA release (rising phase) 1 ms[24] see

GABAa.mod

αGABA Rate of GABA binding to GABAAR 5 /ms Set by hand

βGABA Rate of GABA unbinding from GABAAR 0.18 /ms Set by hand

PClScaling factor for GABAAR permeabilityto Cl−

0.9Modifiedfrom [46]

PHCO3

Scaling factor for GABAAR permeabilityto Cl−

0.1Modifiedfrom [46]

gtonic Tonic GABAAR conductance 0.01 S/cm2 Set by had

Table E.12: Current Clamp Parameters


amp Current Amplitude 2 (nA) [111]

dur Duration of Current Injection 2 (ms) [111]

num Number of Current Pulses 150 [111]

int Interval Between Current Pulses 200 (ms) [111]

start Initation Time of Current Pulses 10050 + ∆t (ms) [111]

95

Appendix

F Supplementary Figures

Figure F.1: Ca2+ Dose Response Curve for Q = 0.1


96

Appendix



97

Appendix


98

Appendix

Figure F.6: Ca2+ Dose Response Curves for Various Q Values

99

Appendix

Figure F.7: Example of Changes in KCC2 Distribution During Plasticity Induction for a Coincident Spike TimingInterval (∆t = 1), Q = 7.4. Traces show induction protocols with different Ca2+ channel types. L-type channelsonly (· · ·); T-type channels only (- -); L- and T-type channels together (—).

100

Appendix

Figure F.8: Example of Changes in KCC2 Distribution During Plasticity Induction for a Non-Coincident SpikeTiming Interval (∆t = 75), Q = 7.4. Traces show induction protocols with different Ca2+ channel types. L-typechannels only (· · ·); T-type channels only (- -); L- and T-type channels together (—).

101

Appendix

Figure F.9: Maximum [PA] Reached During Plasticity Induction for Q = 0.1


102

Appendix



103

Appendix

Figure F.13: Maximum [PA] Reached During Plasticity Induction for Q = 148.0. Note different scale than forprevious Q values.

104

Appendix

Figure F.14: Changes in ECl Following Plasticity Induction for L- and T-type Ca2+Channels Together.

105

Appendix

Figure F.15: Changes in ECl Following Plasticity Induction for Low Conductance T-type Ca2+Channels. Noticedifference of scale compared with ECl plots for different Ca2+channel type conditions.

106

Modeling Ca2 -Dependent Regulation of KCC2 ......I am thankful to have had the opportunity to work...

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