Calcium Ion Fluctuations Alter Channel Gating in a Stochastic Luminal Calcium Release Site Model

Ji, Hao; Li, Yaohang; Weinberg, Seth H.

doi:10.1109/tcbb.2015.2498552

Cited by 6 publications

(5 citation statements)

References 29 publications

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“…In particular, our model does not account for the detailed kinetics of the transmembrane potential and ion channel gating 59,60 and neglects stochastic aspects of subcellular Ca release, such as Ca sparks and microdomain Ca fluctuations. 61–64 Stochasticity may be particularly important to account for in future work, as Sato et al showed that Ca fluctuations can govern the phase of Ca alternans, which in turn may lead to the formation of SD alternans. 8 Ma and Xiao showed that Ca fluctuations can alter alternans formation and lead to chaotic or disordered dynamics in a single cell-coupled map.…”

Section: Discussionmentioning

confidence: 99%

Impaired Sarcoplasmic Reticulum Calcium Uptake and Release Promote Electromechanically and Spatially Discordant Alternans: A Computational Study

Weinberg

2016

Clin Med Insights Cardiol

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Cardiac electrical dynamics are governed by cellular-level properties, such as action potential duration (APD) restitution and intracellular calcium (Ca) handling, and tissue-level properties, including conduction velocity restitution and cell–cell coupling. Irregular dynamics at the cellular level can lead to instabilities in cardiac tissue, including alternans, a beat-to-beat alternation in the action potential and/or the intracellular Ca transient. In this study, we incorporate a detailed single cell coupled map model of Ca cycling and bidirectional APD-Ca coupling into a spatially extended tissue model to investigate the influence of sarcoplasmic reticulum (SR) Ca uptake and release properties on alternans and conduction block. We find that an intermediate SR Ca uptake rate and larger SR Ca release resulted in the widest range of stimulus periods that promoted alternans. However, both reduced SR Ca uptake and release promote arrhythmogenic spatially and electromechanically discordant alternans, suggesting a complex interaction between SR Ca handling and alternans characteristics at the cellular and tissue level.

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Section: Discussionmentioning

confidence: 99%

Impaired Sarcoplasmic Reticulum Calcium Uptake and Release Promote Electromechanically and Spatially Discordant Alternans: A Computational Study

Weinberg

2016

Clin Med Insights Cardiol

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“…In this paper, we have reported a novel application of a particlebased spatial algorithm for diffusion to investigate the influence of diffusive noise on the dynamics of intracellular calcium release. Particle number noise in calcium microdomains has attracted interest in recent studies [22,55,56,32], also for L-type and RyR calcium channels [34,49,28], and it is important to clarify whether calcium diffusion as an additional noise source needs to be incorporated to obtain a better understanding of sub-cellular calcium signals.…”

Section: Discussionmentioning

confidence: 99%

Particle-Based Multiscale Modeling of Calcium Puff Dynamics

Dobramysl¹,

Rüdiger²,

Erban³

2016

Multiscale Model. Simul.

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Abstract. Intracellular calcium is regulated in part by the release of Ca 2+ ions from the endoplasmic reticulum via inositol-4,5-triphosphate receptor (IP 3 R) channels (among other possibilities such as RyR and L-type calcium channels). The resulting dynamics are highly diverse and lead to local calcium "puffs" as well as global waves propagating through cells, as observed in Xenopus oocytes, neurons, and other cell types. Local fluctuations in the number of calcium ions play a crucial role in the onset of these features. Previous modeling studies of calcium puff dynamics stemming from IP 3 R channels have predominantly focused on stochastic channel models coupled to deterministic diffusion of ions, thereby neglecting local fluctuations of the ion number. Tracking of individual ions is computationally difficult due to the scale separation in the Ca 2+ concentration when channels are in the open or closed states. In this paper, a spatial multiscale model for investigating of the dynamics of puffs is presented. It couples Brownian motion (diffusion) of ions with a stochastic channel gating model. The model is used to analyze calcium puff statistics. Concentration time traces as well as channel state information are studied. We identify the regime in which puffs can be found and develop a mean-field theory to extract the boundary of this regime. Puffs are possible only when the time scale of channel inhibition is sufficiently large. Implications for the understanding of puff generation and termination are discussed.

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“…Numerical results. In this section, we present numerical results on the calculation of the stationary distribution of a Markov chain model of a stochastic lumincal calcium release site [6]. See [6] for details of the model.…”

Section: Stopping Criteriamentioning

confidence: 99%

“…In this section, we present numerical results on the calculation of the stationary distribution of a Markov chain model of a stochastic lumincal calcium release site [6]. See [6] for details of the model. The calcium release site model consists of N calcium-regulated calcium ion channels, in which each channel is represented by a four-state model (i.e., closed, inactivated, closed-inactivated, and open states).…”

Section: Stopping Criteriamentioning

confidence: 99%

“…The Markov chain representing the complete calcium release site is composed of all possible calcium channel state configurations and possible values for the discrete number of calcium ions present at the release site. We have previously used this model to show that fluctuations in calcium ion concentration can alter the stationary properties of calcium release site channel opening and closing [6]. Depending on the number of calcium ion channels and model parameters, the corresponding Markov chain transition matrices vary in sizes and relative eigenvalue magnitudes, which provides nice scenarios with different patterns to analyze the convergence of the simple power method, the block power method, and the sliding window scheme.…”

Section: Stopping Criteriamentioning

confidence: 99%

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A Revisit of Block Power Methods for Finite State Markov Chain Applications

Ji,

Weinberg,

2016

Preprint

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According to the fundamental theory of Markov chains, under a simple connectedness condition, iteration of a Markov transition matrix P , on any random initial state probability vector, will converge to a unique stationary distribution, whose probability vector corresponds to the left eigenvector associated with the dominant eigenvalue λ 1 = 1. The corresponding convergence speed is governed by the magnitude of the second dominant eigenvalue λ 2 of P . Due to the simplicity to implement, this approach by using power iterations to approximate the dominant eigenpair, known as the power method, is often applied to estimate the stationary distributions of finite state Markov chains in many applications.In this paper, we revisit the generalized block power methods for approximating the eigenvector associated with λ 1 = 1 of a Markov chain transition matrix. Our analysis of the block power method shows that when s linearly independent probability vectors are used as the initial block, the convergence of the block power method to the stationary distribution depends on the magnitude of the (s+1)th dominant eigenvalue λ s+1 of P instead of that of λ 2 in the power method. Therefore, the block power method with block size s is particularly effective for transition matrices where |λ s+1 | is well separated from λ 1 = 1 but |λ 2 | is not. This approach is particularly useful when visiting the elements of a large transition matrix is the main computational bottleneck over matrix-vector multiplications, where the block power method can effectively reduce the total number of times to pass over the matrix. To further reduce the overall computational cost, we combine the block power method with a sliding window scheme, taking advantage of the subsequent vectors of the latest s iterations to assemble the block matrix. The sliding window scheme correlates vectors in the sliding window to quickly remove the influences from the eigenvalues whose magnitudes are smaller than |λs| to reduce the overall number of matrix-vector multiplications to reach convergence. Finally, we compare the effectiveness of these methods in a Markov chain model representing a stochastic luminal calcium release site.

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Calcium Ion Fluctuations Alter Channel Gating in a Stochastic Luminal Calcium Release Site Model

Cited by 6 publications

References 29 publications

Impaired Sarcoplasmic Reticulum Calcium Uptake and Release Promote Electromechanically and Spatially Discordant Alternans: A Computational Study

Impaired Sarcoplasmic Reticulum Calcium Uptake and Release Promote Electromechanically and Spatially Discordant Alternans: A Computational Study

Particle-Based Multiscale Modeling of Calcium Puff Dynamics

A Revisit of Block Power Methods for Finite State Markov Chain Applications

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