Calcium Sparks and Homeostasis in a Minimal Model of Local and Global Calcium Responses in Quiescent Ventricular Myocytes

Hartman, Jana M.; Sobie, Eric A.; Smith, Gregory D.

doi:10.1016/j.bpj.2009.12.585

Cited by 4 publications

(5 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To overcome this problem, stochastic models that account for the heterogeneous dyadic subspace and junctional SR [Ca 2ϩ ] have been developed (19,22,39). Similar to the Langevin model that is the focus of this article, these local control models include a large number of CaRUs.…”

Section: Discussionmentioning

confidence: 99%

Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release

Wang

Weinberg

Hao

et al. 2015

American Journal of Physiology-Heart and Circulatory Physiology

Self Cite

View full text Add to dashboard Cite

Mechanistic models of ER/SR Ca 2ϩ release often represent the stochastic gating of Ca 2ϩ channels using Monte Carlo methods. When these approaches are applied to cardiac myocytes, voltage-gated L-type Ca 2ϩ channel(s) interact with a cluster of RyRs through changes in [Ca 2ϩ ] in small "dyadic subspaces" between the sarcolemmal and SR membranes. These models also sometimes consider depletion of junctional SR [Ca 2ϩ ] that may influence Ca 2ϩ spark termination and refractoriness (31,32,35). Realistic global (cell-wide) SR Ca 2ϩ release can be reproduced by Monte Carlo simulation of the stochastic triggering of sparks from hundreds to thousands of CaRUs (19,20,29,32). However, such simulations of local control of excitation-contraction coupling are computationally demanding, especially when each CaRU is composed of interacting Markov chain models of individual RyRs (e.g., see Ref. 23).Population density approaches are an alternative to Monte Carlo simulations that produce realistic and computationally efficient models by using a master equation to represent heterogeneous local Ca 2ϩ signals in dyadic subspaces and junctional SR domains (37). This approach involves the numerical solution of advection-reaction equations for the time-dependent bivariate probability density of subspace and junctional SR [Ca 2ϩ ] conditioned on CaRU state, coupled to ordinary differential equations (ODEs) for the bulk myoplasmic and network SR [Ca 2ϩ ]. This methodology was validated in prior work (37) and an associated moment-based approach to simulating the probability distribution of junctional SR [Ca 2ϩ ] was benchmarked to be several orders of magnitude faster than conventional Monte Carlo simulation of the dynamics of local Ca 2ϩ associated with a physiological number of CaRUs (38). One disadvantage of the population density approaches to modeling local control is that their run times (computational efficiency) are proportional to the number of CaRU states. When realistically modeled as the collective gating of identical

show abstract

Section: Discussionmentioning

confidence: 99%

Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release

Wang

Weinberg

Hao

et al. 2015

American Journal of Physiology-Heart and Circulatory Physiology

Self Cite

View full text Add to dashboard Cite

show abstract

“…1). Similar to previous work by Hartman and colleagues [28], this minimal whole cell model considers both local and global Ca 2+ responses to the stochastic gating of Ca 2+ channels. Further, release and reuptake fluxes are balanced in this model.…”

Section: A Minimal Whole Cell Modelmentioning

confidence: 96%

“…Following previous work [28] by Hartman and colleagues, our model formulation assumes a permeabilized cell, and the plasma membrane flux J pm is…”

Section: Concentration Balance Equations For the Bulk Cytosol And Ermentioning

confidence: 99%

“…7) of the sensitization process. On the other hand, the parameters of the regular or "unsensitized" Ca 2+ activation were chosen to be consistent with the parameters in [28], where many puff/spark statistics of a group of 10 two-state Ca 2+ -activated channels were studied. The number of Ca 2+ release sites is assumed to be large so that the distribution of release site states can be well approximated by π(t) (solved from Eq.…”

Section: Reducing Ca 2+ Release Site Models That Are Composed Of Fourmentioning

confidence: 99%

See 1 more Smart Citation

Reduction of calcium release site models via optimized state aggregation

Hao

2016

EPJ Nonlinear Biomed Phys

View full text Add to dashboard Cite

Background: Markov chain models of calcium release sites in living cells exhibit stochastic dynamics reminiscent of the experimentally observed phenomenon of calcium puffs and sparks. Such models often take the form of stochastic automata networks in which the transition probabilities for each of a large number of intercellular channel models depend on the local calcium concentration and thus the state of nearby channels. The state-space size in such compositionally defined calcium release site models increases exponentially as the number of channels increases, which is referred to as "state-space explosion". Methods: In order to overcome the state-space explosion problem, we utilized the idea of "coarse graining" and implemented an automated procedure that reduces the state space by aggregating and lumping states of the full release site model. For a given state aggregation scheme, the transition rates between reduced states are chosen consistent with the conditional probability distribution among states within each group. A genetic algorithm-based approach is then applied to select the state aggregation schemes that lead to reduced models that approximate the observable behaviors of the full model. Results: The genetic algorithm-based approach is implemented in Matlab® and applied to two different release site models. The approach found reduced models that approximate the full model in the number of open channels, spark statistics, and the jump probability matrix as a function of time. Conclusions: A novel automated genetic algorithm-based searching technique is implemented to find reduced calcium release site models that approximate observable behaviors of the full Markov chain models that possess intractable state-spaces. As compared to the full model, the reduced models produce quantitatively similar results using significantly less computational resources.

show abstract

“…In these definitions, c myo Because the experimental observations that are of primary relevance to this report involve permeabilized cells (52), the plasma membrane flux (J pm) was chosen to be as follows: (22) where k pm was chosen to be large enough to "clamp" the bulk myoplasmic [Ca 2ϩ ] (cmyo) at the level of the extracellular bath (cext ϭ 0.1 M in the standard parameter set). Even so, the total myoplasmic …”

Section: Model Formulationmentioning

confidence: 99%

Spontaneous Ca²⁺ sparks and Ca²⁺ homeostasis in a minimal model of permeabilized ventricular myocytes

Hartman

Sobie

Smith

2010

American Journal of Physiology-Heart and Circulatory Physiology

Self Cite

View full text Add to dashboard Cite

] in the myoplasm or SR can influence the frequency, amplitude, and kinetics of local events. In ventricular myocytes, for instance, propagating Ca 2ϩ waves emerge when spontaneous Ca 2ϩ sparks trigger additional sparks in a regenerative fashion (5). Similarly, changes in channel gating at the level of individual RyRs can immediately affect the production of local events and, over time, influence bulk myoplasmic and SR [Ca 2ϩ ]. An increase in RyR opening will cause a gradual decrease in SR [Ca 2ϩ ] (46), whereas inhibition of RyR opening, over time, will lead to elevated SR [Ca 2ϩ ] (21). This principle has been elegantly demonstrated by Lukyanenko and coworkers (35) in quiescent rat ventricular myocytes treated with caffeine (to sensitize RyRs) or tetracaine (to inhibit RyRs).In heart cells, changes in Ca 2ϩ signaling due to altered RyR activity are currently receiving considerable attention because of close links to disease (13, 48). In particular, catecholaminergic polymorphic ventricular tachycardia (CPVT), an inherited disorder associated with a dramatic increase in arrhythmia risk, results from mutations in either RyRs or calsequestrin, a SR Ca 2ϩ buffer protein that associates with and modulates RyRs (20,33). Experiments in vitro have shown that CPVT-causing mutations usually increase the open probability of the RyR, resulting in a hyperactive or "leaky" channel (12,28,31). Studies (1, 36) have also suggested that leaky RyRs are characteristic of several experimental heart failure models. Thus, a quantitative understanding of how changes in RyR gating influence local and global Ca 2ϩ responses can provide insights into disease pathophysiology and can potentially suggest novel therapies.The difference in spatial scales between local and global Ca 2ϩ signals, however, creates significant challenges for the development of mechanistic mathematical models. In particular, gating of RyRs depends on both myoplasmic and SR [Ca 2ϩ ] (30), and concentrations within clusters during local events can be dramatically different from the bulk concentrations. In addition, because of the relatively small number of RyRs responsible for Ca 2ϩ sparks (6), the stochastic gating of these channels must be considered when simulating local events. Previous studies (9,27,42,44) have used Monte Carlo simulation methods to investigate the stochastic triggering of Ca 2ϩ sparks, but these have generally treated myoplasmic and bulk SR [Ca 2ϩ ] as fixed boundary conditions. Conversely, modeling studies (4, 10, 40) focusing on cellular Ca 2ϩ transients have usually used representations of SR Ca 2ϩ release that do not account for the stochastic nature of the local events. Attempting to simulate Ca 2ϩ signaling at both spatial scales simultaneously is a daunting prospect because the stochastic behavior of thousands of local events must be considered to determine the effects on the bulk concentrations. As a result, only a few studies (16, 17, 49, 50) have attempted to capture both phenomena.

show abstract

Calcium Sparks and Homeostasis in a Minimal Model of Local and Global Calcium Responses in Quiescent Ventricular Myocytes

Cited by 4 publications

References 0 publications

Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release

Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release

Reduction of calcium release site models via optimized state aggregation

Spontaneous Ca²⁺ sparks and Ca²⁺ homeostasis in a minimal model of permeabilized ventricular myocytes

Contact Info

Product

Resources

About

Calcium Sparks and Homeostasis in a Minimal Model of Local and Global Calcium Responses in Quiescent Ventricular Myocytes

Cited by 4 publications

References 0 publications

Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release

Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release

Reduction of calcium release site models via optimized state aggregation

Spontaneous Ca2+ sparks and Ca2+ homeostasis in a minimal model of permeabilized ventricular myocytes

Contact Info

Product

Resources

About

Spontaneous Ca²⁺ sparks and Ca²⁺ homeostasis in a minimal model of permeabilized ventricular myocytes