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A multiscale computational model of spatially resolved calcium cycling in cardiac myocytes: from detailed cleft dynamics to the whole cell concentration profiles.

Vierheller J, Neubert W, Falcke M, Gilbert SH, Chamakuri N - Front Physiol (2015)

Bottom Line: Mathematical modeling of excitation-contraction coupling (ECC) in ventricular cardiac myocytes is a multiscale problem, and it is therefore difficult to develop spatially detailed simulation tools.Our concept for a multiscale mathematical model of Ca(2+) -induced Ca(2+) release (CICR) and whole cardiomyocyte electrophysiology incorporates stochastic simulation of individual LC- and RyR-channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca(2+) and Ca(2+)-binding molecules in the bulk of the cell.We developed a novel computational approach to resolve the concentration gradients from dyadic space to cell level by using a quasistatic approximation within the dyad and finite element methods for integrating the partial differential equations.

View Article: PubMed Central - PubMed

Affiliation: Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine Berlin, Germany.

ABSTRACT
Mathematical modeling of excitation-contraction coupling (ECC) in ventricular cardiac myocytes is a multiscale problem, and it is therefore difficult to develop spatially detailed simulation tools. ECC involves gradients on the length scale of 100 nm in dyadic spaces and concentration profiles along the 100 μm of the whole cell, as well as the sub-millisecond time scale of local concentration changes and the change of lumenal Ca(2+) content within tens of seconds. Our concept for a multiscale mathematical model of Ca(2+) -induced Ca(2+) release (CICR) and whole cardiomyocyte electrophysiology incorporates stochastic simulation of individual LC- and RyR-channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca(2+) and Ca(2+)-binding molecules in the bulk of the cell. We developed a novel computational approach to resolve the concentration gradients from dyadic space to cell level by using a quasistatic approximation within the dyad and finite element methods for integrating the partial differential equations. We show whole cell Ca(2+)-concentration profiles using three previously published RyR-channel Markov schemes.

No MeSH data available.


Related in: MedlinePlus

The modules of the model and their interaction. The mathematical model comprises a set of partial differential equations (PDEs) for the bulk concentrations of cytosolic and sarcoplasmic free Ca2+, cytosolic and sarcoplasmic mobile buffers and a cytosolic stationary buffer. The Nc Ca2+ release units (CRUs) are simulated all individually and are source terms in the bulk concentration dynamics PDEs. The state dynamics of each of their LC- or RyR-channels is a continuous time Markov chain. The concentration profile in the dyadic space is modeled in spatial detail with a quasistationary approximation, the dynamics of the concentrations of free Ca2+ and buffer in the jSR are determined by release into the cleft and refilling from the network SR (nSR). The electrophysiology model has been developed by Mahajan et al. (2008a). The LCC current in the CRUs and the Na+/Ca2+-exchanger flux couple the membrane potential dynamics directly to the concentration dynamics.
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Figure 1: The modules of the model and their interaction. The mathematical model comprises a set of partial differential equations (PDEs) for the bulk concentrations of cytosolic and sarcoplasmic free Ca2+, cytosolic and sarcoplasmic mobile buffers and a cytosolic stationary buffer. The Nc Ca2+ release units (CRUs) are simulated all individually and are source terms in the bulk concentration dynamics PDEs. The state dynamics of each of their LC- or RyR-channels is a continuous time Markov chain. The concentration profile in the dyadic space is modeled in spatial detail with a quasistationary approximation, the dynamics of the concentrations of free Ca2+ and buffer in the jSR are determined by release into the cleft and refilling from the network SR (nSR). The electrophysiology model has been developed by Mahajan et al. (2008a). The LCC current in the CRUs and the Na+/Ca2+-exchanger flux couple the membrane potential dynamics directly to the concentration dynamics.

Mentions: The mathematical model comprises a system of partial differential equations for the cytosolic and sarcoplasmic concentration dynamics, Nc models for the individual CRUs and a system of ordinary differential equations for the electrophysiology (see Figure 1). We present the individual modules first and then describe their coupling to a whole cell model. All parameter values are listed in Tables 1–5.


A multiscale computational model of spatially resolved calcium cycling in cardiac myocytes: from detailed cleft dynamics to the whole cell concentration profiles.

Vierheller J, Neubert W, Falcke M, Gilbert SH, Chamakuri N - Front Physiol (2015)

The modules of the model and their interaction. The mathematical model comprises a set of partial differential equations (PDEs) for the bulk concentrations of cytosolic and sarcoplasmic free Ca2+, cytosolic and sarcoplasmic mobile buffers and a cytosolic stationary buffer. The Nc Ca2+ release units (CRUs) are simulated all individually and are source terms in the bulk concentration dynamics PDEs. The state dynamics of each of their LC- or RyR-channels is a continuous time Markov chain. The concentration profile in the dyadic space is modeled in spatial detail with a quasistationary approximation, the dynamics of the concentrations of free Ca2+ and buffer in the jSR are determined by release into the cleft and refilling from the network SR (nSR). The electrophysiology model has been developed by Mahajan et al. (2008a). The LCC current in the CRUs and the Na+/Ca2+-exchanger flux couple the membrane potential dynamics directly to the concentration dynamics.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4585174&req=5

Figure 1: The modules of the model and their interaction. The mathematical model comprises a set of partial differential equations (PDEs) for the bulk concentrations of cytosolic and sarcoplasmic free Ca2+, cytosolic and sarcoplasmic mobile buffers and a cytosolic stationary buffer. The Nc Ca2+ release units (CRUs) are simulated all individually and are source terms in the bulk concentration dynamics PDEs. The state dynamics of each of their LC- or RyR-channels is a continuous time Markov chain. The concentration profile in the dyadic space is modeled in spatial detail with a quasistationary approximation, the dynamics of the concentrations of free Ca2+ and buffer in the jSR are determined by release into the cleft and refilling from the network SR (nSR). The electrophysiology model has been developed by Mahajan et al. (2008a). The LCC current in the CRUs and the Na+/Ca2+-exchanger flux couple the membrane potential dynamics directly to the concentration dynamics.
Mentions: The mathematical model comprises a system of partial differential equations for the cytosolic and sarcoplasmic concentration dynamics, Nc models for the individual CRUs and a system of ordinary differential equations for the electrophysiology (see Figure 1). We present the individual modules first and then describe their coupling to a whole cell model. All parameter values are listed in Tables 1–5.

Bottom Line: Mathematical modeling of excitation-contraction coupling (ECC) in ventricular cardiac myocytes is a multiscale problem, and it is therefore difficult to develop spatially detailed simulation tools.Our concept for a multiscale mathematical model of Ca(2+) -induced Ca(2+) release (CICR) and whole cardiomyocyte electrophysiology incorporates stochastic simulation of individual LC- and RyR-channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca(2+) and Ca(2+)-binding molecules in the bulk of the cell.We developed a novel computational approach to resolve the concentration gradients from dyadic space to cell level by using a quasistatic approximation within the dyad and finite element methods for integrating the partial differential equations.

View Article: PubMed Central - PubMed

Affiliation: Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine Berlin, Germany.

ABSTRACT
Mathematical modeling of excitation-contraction coupling (ECC) in ventricular cardiac myocytes is a multiscale problem, and it is therefore difficult to develop spatially detailed simulation tools. ECC involves gradients on the length scale of 100 nm in dyadic spaces and concentration profiles along the 100 μm of the whole cell, as well as the sub-millisecond time scale of local concentration changes and the change of lumenal Ca(2+) content within tens of seconds. Our concept for a multiscale mathematical model of Ca(2+) -induced Ca(2+) release (CICR) and whole cardiomyocyte electrophysiology incorporates stochastic simulation of individual LC- and RyR-channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca(2+) and Ca(2+)-binding molecules in the bulk of the cell. We developed a novel computational approach to resolve the concentration gradients from dyadic space to cell level by using a quasistatic approximation within the dyad and finite element methods for integrating the partial differential equations. We show whole cell Ca(2+)-concentration profiles using three previously published RyR-channel Markov schemes.

No MeSH data available.


Related in: MedlinePlus