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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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How the reflection of a receptor near a membrane is modeled. The value ∂ΩN2 is the reflecting boundary of the membrane; r and r′ are the position of the receptor at its actual position and at its mirrored position. The values ΔS and ΔS′ represent the distance between the Ca2+ ion and the actual position of the receptor and the position of the mirrored one.
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fig4: How the reflection of a receptor near a membrane is modeled. The value ∂ΩN2 is the reflecting boundary of the membrane; r and r′ are the position of the receptor at its actual position and at its mirrored position. The values ΔS and ΔS′ represent the distance between the Ca2+ ion and the actual position of the receptor and the position of the mirrored one.

Mentions: The reflecting property of a membrane increases the expected concentration of a nearby Ca2+ ion. A receptor at or close to the membrane will therefore experience a higher concentration from a single Ca2+ ion and hence a larger probability of binding. The increase was included by mirroring the location of a receptor close to a membrane, to the opposite side, as illustrated in Fig. 4. The probability of binding was then calculated for this mirrored position and added to the initial probability,(31)\documentclass[10pt]{article}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{pmc}\usepackage[Euler]{upgreek}\pagestyle{empty}\oddsidemargin -1.0in\begin{document}\begin{equation*}P^{\prime}_{{\mathrm{B}}}=1-[1-P_{{\mathrm{B}}}({\Delta}S)][1-P_{{\mathrm{B}}}({\Delta}S^{\prime})]{\simeq}P_{{\mathrm{B}}}({\Delta}S)+P_{{\mathrm{B}}}({\Delta}S^{\prime}).\end{equation*}\end{document}Here, ΔS is the distance between the Ca2+ ion and the actual position of the receptor and ΔS′ is the distance between the ion and the mirrored receptor. The approximation in Eq. 31 holds for probabilities ≪1. If the receptor is situated at the membrane, we have ΔS = ΔS′. For simplicity, we mirrored all buffers in the upper part of the cleft to the opposite side of the SR membrane and all buffers in the lower part of the cleft to the opposite side of the TT membrane.


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

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

How the reflection of a receptor near a membrane is modeled. The value ∂ΩN2 is the reflecting boundary of the membrane; r and r′ are the position of the receptor at its actual position and at its mirrored position. The values ΔS and ΔS′ represent the distance between the Ca2+ ion and the actual position of the receptor and the position of the mirrored one.
© Copyright Policy
Related In: Results  -  Collection

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

fig4: How the reflection of a receptor near a membrane is modeled. The value ∂ΩN2 is the reflecting boundary of the membrane; r and r′ are the position of the receptor at its actual position and at its mirrored position. The values ΔS and ΔS′ represent the distance between the Ca2+ ion and the actual position of the receptor and the position of the mirrored one.
Mentions: The reflecting property of a membrane increases the expected concentration of a nearby Ca2+ ion. A receptor at or close to the membrane will therefore experience a higher concentration from a single Ca2+ ion and hence a larger probability of binding. The increase was included by mirroring the location of a receptor close to a membrane, to the opposite side, as illustrated in Fig. 4. The probability of binding was then calculated for this mirrored position and added to the initial probability,(31)\documentclass[10pt]{article}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{pmc}\usepackage[Euler]{upgreek}\pagestyle{empty}\oddsidemargin -1.0in\begin{document}\begin{equation*}P^{\prime}_{{\mathrm{B}}}=1-[1-P_{{\mathrm{B}}}({\Delta}S)][1-P_{{\mathrm{B}}}({\Delta}S^{\prime})]{\simeq}P_{{\mathrm{B}}}({\Delta}S)+P_{{\mathrm{B}}}({\Delta}S^{\prime}).\end{equation*}\end{document}Here, ΔS is the distance between the Ca2+ ion and the actual position of the receptor and ΔS′ is the distance between the ion and the mirrored receptor. The approximation in Eq. 31 holds for probabilities ≪1. If the receptor is situated at the membrane, we have ΔS = ΔS′. For simplicity, we mirrored all buffers in the upper part of the cleft to the opposite side of the SR membrane and all buffers in the lower part of the cleft to the opposite side of the TT membrane.

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