1 / 15

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

libby
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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!

More Related