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

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

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

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  1. Stochastic modeling of calcium-regulated calcium influx and discrete calcium ions Seth Weinberg Acknowledgements: Xiao Wang, Yan Hao, Gregory Smith

  2. Motivation • Calcium plays a key role in regulating cell signaling processes, such as myocyte contraction and synaptic transmission • Due to the small number of channels in a release site (~20 – 100), stochastic fluctuations can influence overall dynamics • Resting concentrations 100 nM and subspace volumes on the order of 10-17– 10-16 L • ~0.6 – 6 calcium ions • Hypothesis: Fluctuations due to small number of ions can also influence dynamics, perhaps induce sparks

  3. Model formulation • Markov chain model of a calcium-regulated calcium channel • Calcium modeled by a continuous differential equation

  4. Including discrete calcium ions • Elementary reactions • Calcium-binding to the closed channel opens the channel • Calcium fluxes into and out of volume

  5. Langevin formulation • Differential equations:

  6. Integration and evaluation • Euler-Maruyama method, fixed time step • Spark score statistics

  7. Deterministic system • Spontaneous activity • Not a triggered response • No sparks in the deterministic system

  8. Stochastic system vrel = 0.1 ms-1 Score

  9. Stochastic system vrel = 0.2 ms-1 Score

  10. Stochastic System vrel= 0.1 ms-1 0.15 ms-1 0.2 ms-1 0.3 ms-1

  11. Implications/conclusions • Calcium fluctuations • Can “induce” calcium sparks under conditions of small calcium release • Can “suppress” calcium sparks under conditions of greater calcium release • Necessary to include the effects of the discrete calcium ions • Continuous description of calcium inaccurate

  12. Future goals • Incorporate more biophysically detailed channel models • Calcium-activation, -inactivation; calsequestrin, calmodulin regulation • Spatial coupling between small volumes (10,000 dyadic subspaces) • Multiscale modeling – brings a new set of challenges

  13. Moving towards multiscale modeling • Langevin formulation • Computationally fast, compared with SSA, tau-leaping • Slow, compared with deterministic • Appropriate algorithm depends on time-step, propensity function • Langevin inappropriate in some cases, unnecessary in others Gillespie, 2007

  14. Adaptive modeling • Propensity functions vary throughout the simulation • Recall Ca2+ concentration ranges from 0.1 – 100 uM • Ideally, algorithm could vary depending current state • Further, could make time-step as large as possible • Future work in multiscale modeling can utilizing these efficient algorithms Partition-leaping (Harris, 2006)

  15. Thank you!

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