Hierarchic Stochastic Modelling Applied to Intracellular Ca2+ Signals

Moenke, Gregor; Falcke, Martin; Thurley, Keven

doi:10.1371/journal.pone.0051178

Cited by 18 publications

(12 citation statements)

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“…For a general computational approach which accounts for the detailed structure of the RyR cluster, and which can be applied to more complex Markovian models, see Ref. [26]. To proceed, we follow Lindenberg et al [44] who show that in the high barrier regime, which corresponds to case I & II here, then the FPD can be well approximated by an exponential distribution.where is the inverse of the MFPT for the CRU.…”

Section: Resultsmentioning

confidence: 99%

“…In this paper we will apply numerical and analytic approaches to address these questions. Our approach builds on the work of several authors, in particular Hinch [19] and Thul et al [20] (see also [17], [21]–[26] for similar approaches), who have applied the theory of stochastic processes to describe subcellular Ca signaling. As a starting point we will first determine the timing statistics of spontaneous Ca sparks within a single isolated CRU at a fixed SR Ca load.…”

Section: Introductionmentioning

confidence: 99%

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The Timing Statistics of Spontaneous Calcium Release in Cardiac Myocytes

2013

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A variety of cardiac arrhythmias are initiated by a focal excitation that disrupts the regular beating of the heart. In some cases it is known that these excitations are due to calcium (Ca) release from the sarcoplasmic reticulum (SR) via propagating subcellular Ca waves. However, it is not understood what are the physiological factors that determine the timing of these excitations at both the subcellular and tissue level. In this paper we apply analytic and numerical approaches to determine the timing statistics of spontaneous Ca release (SCR) in a simplified model of a cardiac myocyte. In particular, we compute the mean first passage time (MFPT) to SCR, in the case where SCR is initiated by spontaneous Ca sparks, and demonstrate that this quantity exhibits either an algebraic or exponential dependence on system parameters. Based on this analysis we identify the necessary requirements so that SCR occurs on a time scale comparable to the cardiac cycle. Finally, we study how SCR is synchronized across many cells in cardiac tissue, and identify a quantitative measure that determines the relative timing of SCR in an ensemble of cells. Using this approach we identify the physiological conditions so that cell-to-cell variations in the timing of SCR is small compared to the typical duration of an SCR event. We argue further that under these conditions inward currents due to SCR can summate and generate arrhythmogenic triggered excitations in cardiac tissue.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Timing Statistics of Spontaneous Calcium Release in Cardiac Myocytes

2013

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“…However, running the model can be computationally demanding and in practice, the spatio-temporal dimensions of realistic models are limited. An alternative modeling strategy is represented by hybrid algorithms that treat nonlinear system components stochastically and bulk reactions deterministically (11,19,38,(53)(54)(55). In terms of Ca 2þ signaling, hybrid approaches explicitly ignore Ca 2þ noise.…”

Section: Discussionmentioning

confidence: 99%

Exact Stochastic Simulation of a Calcium Microdomain Reveals the Impact of Ca2+ Fluctuations on IP3R Gating

Wieder

Fink

Wegner

2015

Biophysical Journal

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In this study, we numerically analyzed the nonlinear Ca(2+)-dependent gating dynamics of a single, nonconducting inositol 1,4,5-trisphosphate receptor (IP₃R) channel, using an exact and fully stochastic simulation algorithm that includes channel gating, Ca(2+) buffering, and Ca(2+) diffusion. The IP₃R is a ubiquitous intracellular Ca(2+) release channel that plays an important role in the formation of complex spatiotemporal Ca(2+) signals such as waves and oscillations. Dynamic subfemtoliter Ca(2+) microdomains reveal low copy numbers of Ca(2+) ions, buffer molecules, and IP₃Rs, and stochastic fluctuations arising from molecular interactions and diffusion do not average out. In contrast to models treating calcium dynamics deterministically, the stochastic approach accounts for this molecular noise. We varied Ca(2+) diffusion coefficients and buffer reaction rates to tune the autocorrelation properties of Ca(2+) noise and found a distinct relation between the autocorrelation time τac, the mean channel open and close times, and the resulting IP₃R open probability PO. We observed an increased PO for shorter noise autocorrelation times, caused by increasing channel open times and decreasing close times. In a pure diffusion model the effects become apparent at elevated calcium concentrations, e.g., at [Ca(2+)] = 25 μM, τac = 0.082 ms, the IP₃R open probability increased by ≈20% and mean open times increased by ≈4 ms, compared to a zero noise model. We identified the inactivating Ca(2+) binding site of IP₃R subunits as the primarily noise-susceptible element of the De Young and Keizer model. Short Ca(2+) noise autocorrelation times decrease the probability of Ca(2+) association and consequently increase IPvR activity. These results suggest a functional role of local calcium noise properties on calcium-regulated target molecules such as the ubiquitous IP₃R. This finding may stimulate novel experimental approaches analyzing the role of calcium noise properties on microdomain behavior.

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“…In this context, our approach can be seen as a generalized and applicable method to predict mesoscopic behavior from underlying complex microscopic dynamics, which was for instance explicitly approximated for clustered IP 3 receptors (Higgins et al, 2009). A slightly different approach for characterizing the dynamics of such a mesoscopic system was recently developed that is based on waiting time distributions of observable mesoscopic variables (Moenke et al, 2012). Due to the non-Markovian character of the mesoscopic dynamics, the considered waiting-time probabilities are non-exponential making calculations of the statistical moments of the dynamics based on Laplace transformation potentially problematic.…”

Section: Discussionmentioning

confidence: 99%

“…The time evolution of microstates is guided by the standard "master equation", that is in turn ruled by the elementary Markovian transition probabilities between pairs of microstates, while the time evolution of mesostates is driven by non-Markovian equations resulting from summing over the microstates defining each one of the mesostates. Applications and the further development of this approach have been reviewed in Ball et al (2000) and have been applied in a variant in Moenke et al (2012). A notable difference of our method, compared to other approaches, is that it provides an efficient way to compute the first statistical moments of the observable mesoscopic process for an underlying arbitrarily complex microscopic dynamics, as it avoids inversion of the often extremely large transition probability matrices encoding the elementary underlying Markov processes, by breaking them down into smaller sub-matrices.…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels

Christian¹,

Skupin²,

Morante³

et al. 2014

Journal of Theoretical Biology

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A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation of mesoscopic properties from the knowledge of microscopic Markovian transition probabilities. We show how exact analytic formulae for the first and second moments of resident time distributions in mesostates can be derived from microscopic resident times and transition probabilities even for systems with a large number of microstates. We apply our formalism to models of the inositol trisphosphate receptor, which plays a key role in generating calcium signals triggering a wide variety of cellular responses. We demonstrate how experimentally accessible quantities, such as opening and closing times and the coefficient of variation of inter-spike intervals, and other, more elaborated, quantities can be analytically calculated from the underlying microscopic Markovian dynamics. A virtue of our approach is that we do not need to follow the detailed time evolution of the whole system, as we derive the relevant properties of its steady state without having to take into account the often extremely complicated transient features. We emphasize that our formulae fully agree with results obtained by stochastic simulations and approaches based on a full determination of the microscopic system's time evolution. We also illustrate how experiments can be devised to discriminate between alternative molecular models of the inositol trisphosphate receptor. The developed approach is applicable to any system described by a Markov process and, owing to the analytic nature of the resulting formulae, provides an easy way to characterize also rare events that are of particular importance to understand the intermittency properties of complex dynamic systems.

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Hierarchic Stochastic Modelling Applied to Intracellular Ca2+ Signals

Cited by 18 publications

References 58 publications

The Timing Statistics of Spontaneous Calcium Release in Cardiac Myocytes

The Timing Statistics of Spontaneous Calcium Release in Cardiac Myocytes

Exact Stochastic Simulation of a Calcium Microdomain Reveals the Impact of Ca2+ Fluctuations on IP3R Gating

Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels

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