Avrama Blackwell George Mason University Modeling Calcium Concentration and Biochemical Reactions.
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Transcript of Avrama Blackwell George Mason University Modeling Calcium Concentration and Biochemical Reactions.
Avrama BlackwellGeorge Mason University
Modeling Calcium Concentration and
Biochemical Reactions
Objectives● Explain importance of and relation
between biochemical reactions and calcium dynamics
● Present equations describing biochemical reactions and calcium dynamics
● Describe mechanisms modulating calcium concentration
● Demonstrate dynamics using small simulations
Importance of Calcium
● Calcium influences channel behavior, and thereby spike dynamics– Short term influences on calcium
dependent potassium channels– Long term influences such as potentiation
and depression via kinases● Electrical activity influences calcium
concentration via ICa
Importance of Biochemical Reactions
● Some mechanisms of calcium dynamics are modeled as biochemical reactions
● Second messengers, .e.g Dopamine, modulate channel behavior
● Second messenger pathways are modeled as biochemical reactions
Biochemical Reactions
● Bimolecular Reactions– Stoichiometric interactions between
substrate molecules to form product molecule
● Formation of bond between the substrate molecules
● Stoichiometric implies that the reaction specifies the number of each molecule required for reaction
● Molecules are consumed in order to make product
Biochemical Reactions
● Bimolecular Reactions– Reaction order is the number of
simultaneously interacting molecules● First order reaction: single substrate becomes
product● Rate constants: rate (units of per sec) at which
substrate becomes product● Ratio of rate constants gives concentration of
substrates and products at equilibrium
When to Model Biochemical Reactions
● Metabotropic Receptors– Protein does not form channel– Protein is linked to GTP binding protein– Effect mediated by
● Activated G protein subunits● Down stream second messengers
Ionotropic vs Metabotropic
From Nicholls et al. Sinauer
Activation of GTP Binding Protein
From Nicholls et al. Sinauer
Direct Modulation of Channel via Active G Protein Subunits
From Nicholls et al. Sinauer
From Nicholls et al. Sinauer
From Nicholls et al. Sinauer
Importance of Calcium Dynamics
Control of Calcium Dynamics● Calcium Current● Pumps
– Smooth Endoplasmic Calcium ATPase (SERCA)
– Plasma Membrane Calcium ATPase (PMCA)– Sodium-Calcium exchanger
Control of Calcium Dynamics● Release from Intracellular Stores
– IP3 Receptor Channel (IP3R)
– Ryanodine Receptor Channel (RyR)● Buffers● Diffusion
Calcium Current
High Threshold, Persistent
Derivation of Diffusion Equation
● Diffusion in a cylinder– Derive equation by looking at fluxes in and
out of a slice of width x
Derivation of Diffusion Equation
● Flux into left side of slice is q(x,t)● Flux out of right side is q(x+x,t)
– Fluxes may be negative if flow is in direction opposite to arrows
● Area for diffusional flux is A
Radial and Axial Diffusion
From Koch and Segev, MIT PressChapter 6 by DeSchutter and Smolen
Calcium Release through IP3R
Levitan and Kaczmark, Oxford Press
Calcium Release
● Receptors are modeled as multi-state molecules– One state is the conducting state
– For IP3 Receptor state transitions depend
on calcium concentration and IP3
concentration– For Ryanodine Receptor, state transitions
depend on calcium concentration
Dynamics of Release Channels
● Both IP3R and RyR have two calcium
binding sites:– Binding to one site is fast, causes fast
channel opening– Binding to other site is slower, causes slow
channel closing
● IP3R has an additional binding site for
IP3
IP3 Receptor
● 8 state model of DeYoung and Keizer
● Figure from Li and Rinzel
Flow of calcium ions through release channels
Levitan and Kaczmark, Oxford Press
Dynamics of Release Channels
● Dynamics similar to sodium channel:– IP3 + low calcium produces small channel
opening– Channel opening increases calcium
concentration– Higher concentration causes larger
channel opening– Positive feed back produces calcium spike
Dynamics of Release Channels
● High calcium causes slower channel closing– Slow negative feedback– Channel inactivates– Inactivation analogous to sodium channel
inactivation● SERCA pumps calcium back into ER
– Calcium concentration returns to basal level
Calcium ATPase Pumps
● Plasma membrane (PMCA)– Extrudes calcium to extracellular space– Binds one calcium ion for each ATP– Affinity ~300 -600 nM
● Smooth Endoplasmic Reticulum (SERCA)– Sequesters calcium in SER– Binds two calcium ions for each ATP– Affinity ~100 nM
Sodium Calcium Exchange (NCX)
● Stoichiometry– 3 (maybe 4) sodium exchanged for 1
calcium● Charge transfer
– Unequal => electrogenic– One proton flows in for each transport cycle– Small current produces small depolarization
● Theoretical capacity ~50x greater than PMCA
Sodium Calcium Exchange (NCX)● Depolarization may reverse pump direction● Ion concentration change may reverse
direction● Increase in Naint or decrease in Naext
● Increase in Caext or decrease in Caint
GENESIS objects
● Compartment-like objects– Keep track of molecule quantities and
concentrations● Similar to compartment calculating voltage
– Requires geometry/morphology values● length● radius● area of outer surface● area of inner surface (can be zero)● area of side surface● volume
GENESIS objects● Keep track of molecule quantities and
concentrations– rxnpool (Chemesis)
● dC/dt = A - B C● A = change in quantity independent of present
quantity● B = rate of change● Receives messages with quantities A and B
from other objects (enzymes, reactions, also calcium influx)
GENESIS objects● Keep track of molecule quantities and
concentrations– conservepool (Chemesis)
● C = Ctot - Ci● Quantity is remainder after all other forms of
molecule accounted for.– pool (Kinetikit)
● dC/dt = A - B C ● Or C = Ctot - Ci(if flag is set to conserve)
● Can also implement stochastic reactions
GENESIS objects
● Calculate changes due to reactions– mmenz (Chemesis)
● Use if MM assumptions are met● Fields: Km and Vmax● Inputs: Enzyme, substrate concentration● Calculates Vmax times [Enzyme] times substrate
● Empirical feedback modification of enzyme activity can be added.
GENESIS objects
● Calculate changes due to reactions– Enzyme (Chemesis)
● Fields: Kcat, Kf, Kb● Inputs: enzyme, substrate quantity● Calculates amount of Enzyme-Substrate
complex● Calculates change in product, enzyme,
substrate
– Enz (kinetikit)● Fields: Kcat, Kf, Kb● Inputs: enzyme, substrate quantity● Can implement stochastic reactions
GENESIS objects
● Calculate changes due to reactions– reaction (Chemesis) or reac (kinetikit)
● Fields: kf, kb● Inputs: substrates and products● Calculates:
– forward rate constant times substrate molecules– backward rate constant times product molecules
Chemesis Objects● CICR implements calcium release
states– One element for each state– One of the elements may be conserved
● Parameters (Fields)– 'Forward' rate constants, – State vector, e.g. 001 for 1 Ca++ and 0 IP3
bound– Fraction of receptors in this state– Whether this element is conserved
Chemesis Objects● CICR (cont.)● Messages (Inputs) required:
– IP3 concentration
– Cytosolic Ca++ concentration– fraction of molecules in states that can
transition to this state – rate constant governing transition from
other states to this state ● Calculates
– Fraction of molecules in the state
Chemesis Objects● CICRFLUX implements calcium release● Messages (inputs) required:
– Calcium concentration of ER– Calcium concentration of Cytosol– Fraction of channels in open state, X
● Parameters (Fields)– Permeability, P– Number of independent subunits, q
● Calculates Ca flux = P*Xq (CaER-CaCyt)
Chemesis Objects
● Diffusion● Parameters (Fields)
– Diffusion constant, D● Messages (Inputs)
– Length, concentration, surface area from two reaction pools
● Calculates– Flux from one pool to another– D SA Conc / len
Chemesis Objects
● Implemented using CICRFLUX● Messages (inputs) required:
– Calcium of cytosol– Calcium of ER or EC space– Value of 1.0 instead of open state
● Parameters (Fields)– Maximal Permeability (PL)
– Hill coefficient (should be 1.0)
Chemesis objects
● MMPUMP used for SERCA or PMCA Pump● Fields
– Affinity– Power (exponent)– Maximum rate
● Messages (inputs)– Concentration
● Calculates flux due to pump
Integrating Calcium Mechanisms
● RXNPOOL takes flux messages from various calcium sources– VDCC sends message CURRENT, with fields
current and charge– Diffusion and release send message
RXN2MOLES or RXN2, with fields difflux1 and difflux2, or fluxconc1 and fluxconc2, respectively
– Mmpump sends message RXN0MOLES with field moles-out (to cytosol) or moles_in
– Reactions send messages RXN0 - RXN2
Genesis Calcium Objects
● Ca_concen– Simplest implementation of calcium– Fields
● Time constant of decay● Minimum calcium● B = 1 / (z F vol): volume to produce
'reasonable' calcium concentration
– Inputs● Calcium current
Genesis Calcium Objects
● Code of all the following is in src/concen
● Concpool– Calcium concentration without diffusion– Fields: Shape and size– Inputs:
● Buffer rate constants, bound and free● MMPump coefficients● Influx and outflux of stores
Genesis Calcium Objects
● difshell– concentration shell. Has ionic current flow,
one-dimensional diffusion, first order buffering and pumps, store influx
● fixbuffer– Non-diffusible buffer (use with difshell)
● Difbuffer– Diffusible buffer (use with difshell)
Morphology of Model Cell
Calcium Dynamics in Model Cell