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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

A schematic illustrating the basic steps for a single iteration. Orange marks all values produced and all work done by the CRU-Model. The work and results of the PDE-Model are marked in red, everything involved with the Electrophysiology ODE-Model (Electrophys. in the diagram) is marked in brown. A superscript t marks the value of a given quantity at time t, while a superscript t + τ denotes the predicted value of that quantity at time t + τ, e.g., the prediction step for the PDE-Model uses the flux values from the CRU and ODE-Model at time t. The CRU Transition Prediction step uses both the current values at time t and the predicted values at time t + τ from the PDE- and ODE-model.
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Figure 4: A schematic illustrating the basic steps for a single iteration. Orange marks all values produced and all work done by the CRU-Model. The work and results of the PDE-Model are marked in red, everything involved with the Electrophysiology ODE-Model (Electrophys. in the diagram) is marked in brown. A superscript t marks the value of a given quantity at time t, while a superscript t + τ denotes the predicted value of that quantity at time t + τ, e.g., the prediction step for the PDE-Model uses the flux values from the CRU and ODE-Model at time t. The CRU Transition Prediction step uses both the current values at time t and the predicted values at time t + τ from the PDE- and ODE-model.

Mentions: The bulk calcium cycling PDE model and the electrophysiology model are integrated from t to t + τdet, where τdet is the accepted deterministic timestep of the PDE solver. Then, the stochastic channel transitions are predicted from t to t + τdet. Suppose there were Ns conductance changing stochastic events at times t + τi where i = 1…Ns, τi ≤ τdet and 0 ≤ Ns ≤ Nc. Here, the time of the stochastic event is τi for the ith CRU. In case that there is no stochastic event for a CRU, τi is set to τi = τdet. The stochastic timestep τstoc is determined from the τi as the time by which a maximum number of acceptable transitions is reached. The maximum number has been determined empirically to be sufficiently small with 0.1 Ns to cause no essential difference to simulations with τstoc sufficiently small to guarantee Ns = 1. Now all the occurring events in the CRUs up to t + τstoc are set to take place at time t + τstoc. By doing so, we avoid time steps which are too small for acceptable simulation time. A schematic illustrating a single iteration and how the time steps are determined can be found in Figure 4.


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)

A schematic illustrating the basic steps for a single iteration. Orange marks all values produced and all work done by the CRU-Model. The work and results of the PDE-Model are marked in red, everything involved with the Electrophysiology ODE-Model (Electrophys. in the diagram) is marked in brown. A superscript t marks the value of a given quantity at time t, while a superscript t + τ denotes the predicted value of that quantity at time t + τ, e.g., the prediction step for the PDE-Model uses the flux values from the CRU and ODE-Model at time t. The CRU Transition Prediction step uses both the current values at time t and the predicted values at time t + τ from the PDE- and ODE-model.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 4: A schematic illustrating the basic steps for a single iteration. Orange marks all values produced and all work done by the CRU-Model. The work and results of the PDE-Model are marked in red, everything involved with the Electrophysiology ODE-Model (Electrophys. in the diagram) is marked in brown. A superscript t marks the value of a given quantity at time t, while a superscript t + τ denotes the predicted value of that quantity at time t + τ, e.g., the prediction step for the PDE-Model uses the flux values from the CRU and ODE-Model at time t. The CRU Transition Prediction step uses both the current values at time t and the predicted values at time t + τ from the PDE- and ODE-model.
Mentions: The bulk calcium cycling PDE model and the electrophysiology model are integrated from t to t + τdet, where τdet is the accepted deterministic timestep of the PDE solver. Then, the stochastic channel transitions are predicted from t to t + τdet. Suppose there were Ns conductance changing stochastic events at times t + τi where i = 1…Ns, τi ≤ τdet and 0 ≤ Ns ≤ Nc. Here, the time of the stochastic event is τi for the ith CRU. In case that there is no stochastic event for a CRU, τi is set to τi = τdet. The stochastic timestep τstoc is determined from the τi as the time by which a maximum number of acceptable transitions is reached. The maximum number has been determined empirically to be sufficiently small with 0.1 Ns to cause no essential difference to simulations with τstoc sufficiently small to guarantee Ns = 1. Now all the occurring events in the CRUs up to t + τstoc are set to take place at time t + τstoc. By doing so, we avoid time steps which are too small for acceptable simulation time. A schematic illustrating a single iteration and how the time steps are determined can be found in Figure 4.

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