Optimization and Validation of a CA1 Pyramidal Cell Model with Glutaminergic Synapses

EONS – Elementary Objects of the Nervous System – Modeling at the synaptic level

NEURON Simulation Environment – Compartmental modeling of the neuron

The Ideal Model•Accurate - reproduces observed data precisely•Global (not ad hoc) – model interpolates and extrapolates to data or situations beyond what was originally used to describe the model• Interpretable – describes causal relationships in the system to answer scientific questions of how mechanistic processes give rise to function

Strategy - a reductionist and integrative approach

• A parametric model describes the large scale interactions of a system’s elementary components. • EONS/NEURON framework integrates cellular and synaptic interactions at

the molecular level

All elementary models were optimized using a large number of experimental results with multiple levels of complexityHowever, no optimization had yet been conducted for the entire framework.

Experimental ProtocolRoom temperature: 25-27CEPSC voltage clamp: -80mVEPSP current clamp: -246.3pA20uM picrotoxin to block inhibitory GABAA channels

Results – Initial vs current efforts

Optimization Objectives• Accurate dendritic integration of synaptic inputs to the soma• Spatial summation• Temporal summation

• Spiking behavior – Threshold, AP amplitude and half-width• After-potentials• Fast AHP• After depolarization • Medium AHP• Slow AHP

• Synaptic nonlinearities • Presynaptic nonlinearities• NT release and residual calcium hypothesis• NMDA/AMPA• Paired pulse facilitation and depression

Summary of optimization efforts

• Synapse placement• Experimental evidence through immunogold staining (Megias 2001)

• Synapse count• Do we need to accurately replicate the number of active synapses present in the

experimental setup?

• Effects of temperature• Parts of the model is generated at room temperature (25C) while other parts at body

temperature (37C). • How big of a role does temperature play in the results? • How to model temperature dependency?

Summary of optimization efforts• Explored multiple CA1 models• Jarsky 2005 • Inherited from Sushmita• Limited variety of channel types • Experimental validation: backpropagation (Golding 2001)• Very low spike threshold (-62mV)

•Migliore 2004• Inherited from Sushmita • Limited variety of channel types• Validation data only exists for elementary models• Spikes prematurely due to dendritic spikes

CA1 Channel Types Source: The Hippocampus Book

• Multiple CA1 models, continued…• Poirazi-Mel 2003/2013

• Comprehensive variety of channels. • Validated prediction: Spatial summation, validated by Losonczy 2006 • Validation: Spike train attenuation• Validation: Backpropagation attenuation• Low spike threshold (-57mV)?• Q10 temperature dependence in most biophysics components

Summary of optimization efforts

Ca2+ ICaR

Summary of optimization efforts•Hand tuned channel conductances of Poirazi 2013 to

optimize spike threshold and amplitude, and after-potentials• Evolutionary Optimization of conductances - planned

•NMDA-8 model – temporal nonlinearities• Optimization of parameters to EMOO with multiple objectives

•Presynaptic mechanisms – temporal nonlinearities• Deconvolution of EPSC• P/Q Calcium Channel• Diffusion model - planned• NT Release model - planned

Synapse placementDistribution of synapses imaged through immunogold staining of synapses. (Megias 2001)6.9 : 2.3 : 0.04 ratio distribution forDistal : medial : proximal radiatum, respectively.

For 30 synapses, 22:7:1 synapse count in the distal:medial:proximal radiatum, respectively.

• Exact synapse placement may not matter• Distance-dependent conductance scaling

(Magee and Cook, 2000) shows increased conductance as a function of distance from the soma that compensates for distance attenuation.

Synapse count• Reduction of many synapses to a few strong ones?• Valid if dendritic spikes are generated or not generated appropriately

• Synapses sum sigmoidally as shown by Losonczy et al. 2006 • Sigmoidal summation is due to strong local depolarization

causing dendritic spikes. Thus at subthresholds, synaptic scaling would be similar to linear summation of synapses.

Forward Propagating Dendritic Spikes: in vivo/in vitro

• Strong synchronous input• Dendritic spikes can be generated with ~50 synapses spread over 100µm and

activated within 3msec. (Gasparini 2004)• Conjectured to only occur in slow wave sleep by Poirazi and Mel, 2011

• Schaffer Collateral stimulation is very synchronous, but does it activate enough synapses to elicit dendritic spikes?

CA Pyramidal Cell Model – Poirazi 2013

Spatial Summation

•Sigmoidal nonlinear summation within branch

•Linear summation between branches

Sidiropoulou et al. “Inside the brain of a neuron” 2006

Mechanisms of Sigmoidal Summation Characteristics

• Multiple inputs in ‘within branch’ oblique dendrites generates sodium spikes due to strong local depolarization

• Between branch inputs insufficient to generate sodium spike

Losonczy, A, Magee, J, “Integrative Properties of Radial Oblique Dendrites in Hippocampal CA1 Pyramidal Neurons” 2006

Temperature

• Varied temperature conditions in data• Room temp ~ 24C• Body temp – 37C

• Influences• Spike threshold• Resting potential• Rise and fall rates of channel currents• Afterpotentials• Conductance

• Modeling in active channels• Voltage dependency

• Boltzmann equations (Ca2+ channels, and Ka)• Q10 temperature coefficient (some K+ channels)

• Time dependency – Q10 (only Ka)

Poirazi CA1 model - 34°C

95AMPA/60NMDA

Poirazi CA1 model - 25°C

95AMPA/60NMDA

Poirazi CA1 model - 34°C

Increased input strength to spiking

105AMPA/71NMDA

Temperature on CA1 Pyramidal Neuron – in vitro

Source: Vitro, Thompson, Temperature Dependence of Intrinsic Membrane Properties and Synaptic Potentials in Hippocampal CA1 Neurons, 1985

Temp on Voltage Dependency - Model• Boltzmann equations describe the activation and inactivation steady state

voltage dependencies of active channels. Po=P(open), Pc=P(closed)

W=potential, zeE=potential(p(0.5)),

K=Boltzmann constant, T=temp in kelvin

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Modeling temp with Q10 - Model

•Modeled with Q10 coefficients• For voltage dependency• q10*exp((1e-3)*zettax*(v-vhalfx)*kT))

• For time dependency • qt=q10^((Celsius-24)/10)• Taun=betn(v)/(qt*a0n*1+a))

Temp modeling - which channels?• Boltzmann voltage dependency

• cal• calH• can• car• cat• hha-Hodgkin Huxley Na+ channels, only in s attenuation system• kadist, kaprox

• Q10 voltage dependency • Kct• kdBG• km

• Q10 time dependency• kadist, kaprox

• No temperature dependency• pas• Na+, Nap+• Kdr • Kd• Kap• kahp• h

Spike Threshold and Resting Potential

• According to "The Hippocampus Book," the action potential threshold of CA1 pyramidal cells is -45mV (pg 165). • 20mV subthreshold window on experimental cell at 24°C (Shane’s

data)• Resting membrane potential @ 27°C -60.0±7.4 n=14 (Thompson

1985)• Spike threshold higher in dendrites than soma

Optimizing Channel Conductances – Experimental Limitations - Examples• To measure ion channel density, drugs are used to block all but the

one ion channel. It's uncertain if all the necessary drugs are used to block all but that one channel. (Catterall, 1995)• Experience-dependent dendritic plasticity shows distribution of K+

channel concentrates change with experience (Makara, Magee, 2009)• It's unknown if the CA1 pyramidal neuron is the strong

backpropagating or weak backpropagating type. (Golding, 2001)

Weak Propagating

Strong Propagating

Optimizing Channel Conductances - Strategy• Na+ conductance: spike amplitude• Na+/K+ permeability ratio: spike threshold and

afterdepolarization potential time course and amplitude• Ca2+ T-type and R-type conductance:

afterdepolarization potential time course and amplitude• Hyperpolarization current conductance: passive

channel pulls potential to resting. Attenuates subthreshold temporal summation and strengthens EPSP repolarization at potentials approaching spike threshold.• Ca2+ dependent K+ conductance: After

hyperpolarization potential amplitude

Optimizing Channel Conductances – Preliminary Results

Optimizing Channel Conductances – Future Plans• Optimization with EMOO• Objective: I-V plots

• Objective: Effects of blocking various channels on synaptic summation(Cash and Yuste 1999)• In thin branches• In apical trunk

Optimizing Channel Conductances – Future Plans – cellular temporal nonlinearities• Objective: Effects of blocking Na+ and K+ on temporal summation

(Margulis et al. 1998)• Objective: Effects of blocking Ih on temporal summation (Magee

2000)

Margulis, Tang 1998. “Temporal Integration Can Readily Switch Between Sublinear and Supralinear Summation”Magee J, 2000, “Dendritic Integration of Excitatory Synaptic Input,” Nature Reviews

• Objective (if able to obtain data) – Use two photon microscopy to perform dual somato-dendritic recordings with glutamate uncaging as the input.• Optimize afterpotentials• Florescent imaging to match model morphology with experimental• Glutamate uncaging to know synapse location which will be useful to optimize

the non-uniform channel conductances

Optimizing Channel Conductances – Future Plans

NMDA-R Model – 15 statesIt was not possible to optimize the AMPA/NMDAR ratio to match the EPSP shape. NMDAR persistently appeared much slower than the experimental data. A revisit to the NMDAR-15 model reveals that it is indeed much slower than experimental data.

NMDA-R Model – 8 states

• Fixed slowness problem as AMPAR/NMDAR ratio can be optimized to a count of 80/55, in range of physiological recordings (Takumi et al., 1999; Matsuzaki et al., 2001). • However, problems with desensitization

NMDA-R Optimization with EMOO

• Optimization to additional objectives that account for desensitization.• Objective: Paired pulse• Objective: Long step input

Temporal Nonlinearities – quantifying the disparity

Interval(ms) Experimental(V2/V1) Simulation(V2/V1)56ms .68(to AP threshold), 1.27(to ADP peak) 0.2284ms .80 .57

Presynaptic contribution to nonlinearities• According to Song 2007, presynaptic mechanisms account for an

overwhelming majority of the temporal nonlinearities• Residual Calcium Hypothesis

• To test this, I deconvolved the EPSC to extract the presynaptic nonlinearities in addition to a smaller component of AMPA nonlinearities. This provided an impulse amplitude that corresponds to the NT release strength.

EPSC Deconvolution Results

Subthreshold NRMSE = 10%

Temporal nonlinearities significantly restored

• Reasons?• Presynaptic nonlinearities• No NMDA with overly strong

desensitization

EPSC Deconvolution Results – A longer timespan

Presynaptic mechanisms - Planned

• P/Q VDCC (Bischofberger 2002) - implemented• Ca2+ Diffusion model (Sikora 2005) – prior model• NT release model (Nadkarni et al 2010) - planned

PQ VDCC EONS Implementation

Activation Curve IV Curve