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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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Statistical data for binding events that are registered from Random Walk simulations. The Ca2+ source was passive diffusion from the cytosol during diastole, i.e., the resulting [Ca2+] was, on average, 0.1 μM. The binding events are registered at four different RyRs, positioned at 10, 30, 50, and 70 nm from the center of the cleft. The binding events were collected from 100 simulation runs. The total time simulated was 20 s. (A) Box-plot of the number of binding events from the runs at each receptor, together with a 95% confidence interval for the true means (red horizontal lines). The blue solid circles represent the expected number of binding events predicted by the continuous model. These values were computed on the basis of the fixed [Ca2+] at each receptor. (For an explanation of the box-plot, see the legend of Fig. 8.) (B1–B4) Inter-event intervals from all runs presented in scaled histogram plots, corresponding to the receptor at positions 10, 30, 50, and 70 nm from the center of the cleft. (For an explanation of the histogram, see the legend of Fig. 8.)
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fig9: Statistical data for binding events that are registered from Random Walk simulations. The Ca2+ source was passive diffusion from the cytosol during diastole, i.e., the resulting [Ca2+] was, on average, 0.1 μM. The binding events are registered at four different RyRs, positioned at 10, 30, 50, and 70 nm from the center of the cleft. The binding events were collected from 100 simulation runs. The total time simulated was 20 s. (A) Box-plot of the number of binding events from the runs at each receptor, together with a 95% confidence interval for the true means (red horizontal lines). The blue solid circles represent the expected number of binding events predicted by the continuous model. These values were computed on the basis of the fixed [Ca2+] at each receptor. (For an explanation of the box-plot, see the legend of Fig. 8.) (B1–B4) Inter-event intervals from all runs presented in scaled histogram plots, corresponding to the receptor at positions 10, 30, 50, and 70 nm from the center of the cleft. (For an explanation of the histogram, see the legend of Fig. 8.)

Mentions: As mentioned in the Introduction, we considered the event of a single Ca2+ ion binding to a receptor to be the stochastic event that determines the functional properties of the dyadic cleft. We tested how well the continuous model fits the equivalent binding events registered from the RW model. We used four tentative RyRs, positioned from the center of the cleft to the rim, to test whether the radial position of single receptors had any effect on the event registrations. We performed three different set of simulations, in which binding events were registered under different physiological conditions. These conditions were as follows: 1), steady-state [Ca2+] response due to one open LCC; 2), uniform [Ca2+] due to passive diffusion from cytosol, using very low diastolic [Ca2+] = 0.1 μM; and 3), transient [Ca2+] response from three different LCCs, which alternated between closed and open during the simulations. The statistical results from these three sets of simulations are presented in Figs. 8–10.


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

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

Statistical data for binding events that are registered from Random Walk simulations. The Ca2+ source was passive diffusion from the cytosol during diastole, i.e., the resulting [Ca2+] was, on average, 0.1 μM. The binding events are registered at four different RyRs, positioned at 10, 30, 50, and 70 nm from the center of the cleft. The binding events were collected from 100 simulation runs. The total time simulated was 20 s. (A) Box-plot of the number of binding events from the runs at each receptor, together with a 95% confidence interval for the true means (red horizontal lines). The blue solid circles represent the expected number of binding events predicted by the continuous model. These values were computed on the basis of the fixed [Ca2+] at each receptor. (For an explanation of the box-plot, see the legend of Fig. 8.) (B1–B4) Inter-event intervals from all runs presented in scaled histogram plots, corresponding to the receptor at positions 10, 30, 50, and 70 nm from the center of the cleft. (For an explanation of the histogram, see the legend of Fig. 8.)
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
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fig9: Statistical data for binding events that are registered from Random Walk simulations. The Ca2+ source was passive diffusion from the cytosol during diastole, i.e., the resulting [Ca2+] was, on average, 0.1 μM. The binding events are registered at four different RyRs, positioned at 10, 30, 50, and 70 nm from the center of the cleft. The binding events were collected from 100 simulation runs. The total time simulated was 20 s. (A) Box-plot of the number of binding events from the runs at each receptor, together with a 95% confidence interval for the true means (red horizontal lines). The blue solid circles represent the expected number of binding events predicted by the continuous model. These values were computed on the basis of the fixed [Ca2+] at each receptor. (For an explanation of the box-plot, see the legend of Fig. 8.) (B1–B4) Inter-event intervals from all runs presented in scaled histogram plots, corresponding to the receptor at positions 10, 30, 50, and 70 nm from the center of the cleft. (For an explanation of the histogram, see the legend of Fig. 8.)
Mentions: As mentioned in the Introduction, we considered the event of a single Ca2+ ion binding to a receptor to be the stochastic event that determines the functional properties of the dyadic cleft. We tested how well the continuous model fits the equivalent binding events registered from the RW model. We used four tentative RyRs, positioned from the center of the cleft to the rim, to test whether the radial position of single receptors had any effect on the event registrations. We performed three different set of simulations, in which binding events were registered under different physiological conditions. These conditions were as follows: 1), steady-state [Ca2+] response due to one open LCC; 2), uniform [Ca2+] due to passive diffusion from cytosol, using very low diastolic [Ca2+] = 0.1 μM; and 3), transient [Ca2+] response from three different LCCs, which alternated between closed and open during the simulations. The statistical results from these three sets of simulations are presented in Figs. 8–10.

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