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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

Simulation of a typical Ca2+ gradient in a CRU. The stationary dyadic [Ca2+] profile of a single open RyR is shown.
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Figure 5: Simulation of a typical Ca2+ gradient in a CRU. The stationary dyadic [Ca2+] profile of a single open RyR is shown.

Mentions: Our main result is the fully coupled simulation tool. Our motivation was to be able to take stochastic channel state dynamics for each channel in each CRU and the concentration profile within CRUs into account while executing the simulation of (partial) differential equations for other state variables. Figure 5 shows such a concentration profile inside the dyadic space calculated with Equation (17) for a typical RyR current. Gradients are substantial such that distant RyRs and LCCs experience much smaller concentrations and Ca2+-dependent transition rates than channels close to an open one.


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)

Simulation of a typical Ca2+ gradient in a CRU. The stationary dyadic [Ca2+] profile of a single open RyR is shown.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 5: Simulation of a typical Ca2+ gradient in a CRU. The stationary dyadic [Ca2+] profile of a single open RyR is shown.
Mentions: Our main result is the fully coupled simulation tool. Our motivation was to be able to take stochastic channel state dynamics for each channel in each CRU and the concentration profile within CRUs into account while executing the simulation of (partial) differential equations for other state variables. Figure 5 shows such a concentration profile inside the dyadic space calculated with Equation (17) for a typical RyR current. Gradients are substantial such that distant RyRs and LCCs experience much smaller concentrations and Ca2+-dependent transition rates than channels close to an open one.

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