Stochastic modeling of calcium-regulated calcium influx and discrete calcium ions

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Stochastic modeling of calcium-regulated calcium influx and discrete calcium ions. Seth Weinberg Acknowledgements: Xiao Wang, Yan Hao , Gregory Smith. Motivation. Calcium plays a key role in regulating cell signaling processes, such as myocyte contraction and synaptic transmission - PowerPoint PPT Presentation

Text of Stochastic modeling of calcium-regulated calcium influx and discrete calcium ions

Stochastic modeling of discrete ions in a calcium release site

Stochastic modeling of calcium-regulated calcium influx and discrete calcium ionsSeth Weinberg

Acknowledgements: Xiao Wang, Yan Hao, Gregory SmithMotivationCalcium plays a key role in regulating cell signaling processes, such as myocyte contraction and synaptic transmissionDue to the small number of channels in a release site (~20 100), stochastic fluctuations can influence overall dynamicsResting concentrations 100 nM and subspace volumes on the order of 10-17 10-16 L~0.6 6 calcium ionsHypothesis: Fluctuations due to small number of ions can also influence dynamics, perhaps induce sparks

Model formulationMarkov chain model of a calcium-regulated calcium channel

Calcium modeled by a continuous differential equation

Complications using Markov chainsFor N channels and M states per channel

b(20, 2) = 21b(20, 3) = 231b(20, 4) = 1771b(20, 12) = 5.7e8

Chemical Langevin EquationGeneral equation for M reactions

Two-state channel fraction of open channels

Including discrete calcium ionsElementary reactionsCalcium-binding to the closed channel opens the channel

Calcium fluxes into and out of volume

Langevin formulationStochastic differential equations:

Integration techniquesNot so simple to integrate stochastic differential equations!Ito vs Stratonovich calculus different assumptions regarding Riemman integrals, leads to different integration techniques, not equivalentEuler method is simple

Other methods, complex to implement

Sample problemAnalytical solution

Matlab simulationEuler, Milstein, stochastic RK4

Sample simulation

N = 20 channels, Wds = 10-17 LCalcium spark scoresParameter space for one set of parameters