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Stochastic binding of Ca2+ ions in the dyadic cleft; continuous versus random walk description of diffusion.

Hake J, Lines GT - Biophys. J. (2008)

Bottom Line: With these results we demonstrate that the stochasticity and discreteness of the Ca(2+) signaling in the dyadic cleft, determined by single binding events, can be described using a deterministic model of Ca(2+) diffusion together with a stochastic model of the binding events, for a specific range of physiological relevant parameters.Time-consuming RW simulations can thus be avoided.We also present a new analytical model of bimolecular binding probabilities, which we use in the RW simulations and the statistical analysis.

View Article: PubMed Central - PubMed

Affiliation: Simula Research Laboratory, Lysaker, Norway. hake@simula.no

ABSTRACT
Ca(2+) signaling in the dyadic cleft in ventricular myocytes is fundamentally discrete and stochastic. We study the stochastic binding of single Ca(2+) ions to receptors in the cleft using two different models of diffusion: a stochastic and discrete Random Walk (RW) model, and a deterministic continuous model. We investigate whether the latter model, together with a stochastic receptor model, can reproduce binding events registered in fully stochastic RW simulations. By evaluating the continuous model goodness-of-fit for a large range of parameters, we present evidence that it can. Further, we show that the large fluctuations in binding rate observed at the level of single time-steps are integrated and smoothed at the larger timescale of binding events, which explains the continuous model goodness-of-fit. With these results we demonstrate that the stochasticity and discreteness of the Ca(2+) signaling in the dyadic cleft, determined by single binding events, can be described using a deterministic model of Ca(2+) diffusion together with a stochastic model of the binding events, for a specific range of physiological relevant parameters. Time-consuming RW simulations can thus be avoided. We also present a new analytical model of bimolecular binding probabilities, which we use in the RW simulations and the statistical analysis.

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Time-step in the RW algorithm. The upper part, above the dashed line, shows the reaction loop and the lower part shows the diffusion loop. The reaction loop is simulated with a coarser time-step, Dt = 125 ns, than the diffusion loop, dt = 5 ns.
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fig5: Time-step in the RW algorithm. The upper part, above the dashed line, shows the reaction loop and the lower part shows the diffusion loop. The reaction loop is simulated with a coarser time-step, Dt = 125 ns, than the diffusion loop, dt = 5 ns.

Mentions: A full step in our RW algorithm is presented schematically in Fig. 5. First, any Ca2+ that is scheduled to enter the cleft at this time-step is added to the variable that keeps track of all Ca2+ ions. After that, we check whether any Ca2+ ions were bound to mobile or stationary buffers or to the included RyRs, using the precomputed binding probabilities from Eq. 24. Then, we update the mobile buffers and the Ca2+ ions with new positions, using the Monte Carlo method presented above. The first procedure (the reaction loop) operated on a larger timescale than the second (the diffusion loop). A single step in the reaction loop took much longer and the accuracy was not so sensitive to the time-step, which allowed us to simulate this procedure at a larger timescale. The sampling of new displacement in the diffusion loop was cheap, but the escape rate of the Ca2+ ions leaving the cleft by the absorbing boundary ∂ΩD, was underestimated (41). This error was time-step dependent and was therefore minimized by using smaller time-steps in this loop.


Stochastic binding of Ca2+ ions in the dyadic cleft; continuous versus random walk description of diffusion.

Hake J, Lines GT - Biophys. J. (2008)

Time-step in the RW algorithm. The upper part, above the dashed line, shows the reaction loop and the lower part shows the diffusion loop. The reaction loop is simulated with a coarser time-step, Dt = 125 ns, than the diffusion loop, dt = 5 ns.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2480677&req=5

fig5: Time-step in the RW algorithm. The upper part, above the dashed line, shows the reaction loop and the lower part shows the diffusion loop. The reaction loop is simulated with a coarser time-step, Dt = 125 ns, than the diffusion loop, dt = 5 ns.
Mentions: A full step in our RW algorithm is presented schematically in Fig. 5. First, any Ca2+ that is scheduled to enter the cleft at this time-step is added to the variable that keeps track of all Ca2+ ions. After that, we check whether any Ca2+ ions were bound to mobile or stationary buffers or to the included RyRs, using the precomputed binding probabilities from Eq. 24. Then, we update the mobile buffers and the Ca2+ ions with new positions, using the Monte Carlo method presented above. The first procedure (the reaction loop) operated on a larger timescale than the second (the diffusion loop). A single step in the reaction loop took much longer and the accuracy was not so sensitive to the time-step, which allowed us to simulate this procedure at a larger timescale. The sampling of new displacement in the diffusion loop was cheap, but the escape rate of the Ca2+ ions leaving the cleft by the absorbing boundary ∂ΩD, was underestimated (41). This error was time-step dependent and was therefore minimized by using smaller time-steps in this loop.

Bottom Line: With these results we demonstrate that the stochasticity and discreteness of the Ca(2+) signaling in the dyadic cleft, determined by single binding events, can be described using a deterministic model of Ca(2+) diffusion together with a stochastic model of the binding events, for a specific range of physiological relevant parameters.Time-consuming RW simulations can thus be avoided.We also present a new analytical model of bimolecular binding probabilities, which we use in the RW simulations and the statistical analysis.

View Article: PubMed Central - PubMed

Affiliation: Simula Research Laboratory, Lysaker, Norway. hake@simula.no

ABSTRACT
Ca(2+) signaling in the dyadic cleft in ventricular myocytes is fundamentally discrete and stochastic. We study the stochastic binding of single Ca(2+) ions to receptors in the cleft using two different models of diffusion: a stochastic and discrete Random Walk (RW) model, and a deterministic continuous model. We investigate whether the latter model, together with a stochastic receptor model, can reproduce binding events registered in fully stochastic RW simulations. By evaluating the continuous model goodness-of-fit for a large range of parameters, we present evidence that it can. Further, we show that the large fluctuations in binding rate observed at the level of single time-steps are integrated and smoothed at the larger timescale of binding events, which explains the continuous model goodness-of-fit. With these results we demonstrate that the stochasticity and discreteness of the Ca(2+) signaling in the dyadic cleft, determined by single binding events, can be described using a deterministic model of Ca(2+) diffusion together with a stochastic model of the binding events, for a specific range of physiological relevant parameters. Time-consuming RW simulations can thus be avoided. We also present a new analytical model of bimolecular binding probabilities, which we use in the RW simulations and the statistical analysis.

Show MeSH
Related in: MedlinePlus