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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

Free [Ca2+]i and SR free [Ca2+] at 70.0 ms after activation, using the Walker et al. (2014)-RyR-model. (A) Myoplasm [Ca2+]i. (B) nSR [Ca2+] for the 8th z-disc numbered from the bottom in Figure 7. The concentration is color-coded according to the color scale shown. There are 320 CRU per z-disc, with an average of 50 RyR and 12.5 LCC per CRU. See Supplementary Movies 1, 2 for the evolution of [Ca2+]i and nSR [Ca2+] through an AP.
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Figure 6: Free [Ca2+]i and SR free [Ca2+] at 70.0 ms after activation, using the Walker et al. (2014)-RyR-model. (A) Myoplasm [Ca2+]i. (B) nSR [Ca2+] for the 8th z-disc numbered from the bottom in Figure 7. The concentration is color-coded according to the color scale shown. There are 320 CRU per z-disc, with an average of 50 RyR and 12.5 LCC per CRU. See Supplementary Movies 1, 2 for the evolution of [Ca2+]i and nSR [Ca2+] through an AP.

Mentions: We simulated 16 z-discs, each with 320 CRUs, and the Ca2+ dynamics for this sub-cellular region (~30% of the cardiomyocyte) were coupled to the whole-cell electrophysiology ODE model. It took 64.2 h to solve a single action potential on 848 Intel Xeon E5-2650 v2 2.60 GHz CPUs (central processing units). The Ca2+ concentration profile 70.0 ms after stimulus at a single z-disc is shown in Figure 6. The local Ca2+ dynamics and corresponding whole cell electrophysiology are shown in Figure 7A and in Supplementary Movie 1. The SR free [Ca2+] is visualized in Figure 7B and in Supplementary Movie 2. Currents are shown in Figure 8.


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)

Free [Ca2+]i and SR free [Ca2+] at 70.0 ms after activation, using the Walker et al. (2014)-RyR-model. (A) Myoplasm [Ca2+]i. (B) nSR [Ca2+] for the 8th z-disc numbered from the bottom in Figure 7. The concentration is color-coded according to the color scale shown. There are 320 CRU per z-disc, with an average of 50 RyR and 12.5 LCC per CRU. See Supplementary Movies 1, 2 for the evolution of [Ca2+]i and nSR [Ca2+] through an AP.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 6: Free [Ca2+]i and SR free [Ca2+] at 70.0 ms after activation, using the Walker et al. (2014)-RyR-model. (A) Myoplasm [Ca2+]i. (B) nSR [Ca2+] for the 8th z-disc numbered from the bottom in Figure 7. The concentration is color-coded according to the color scale shown. There are 320 CRU per z-disc, with an average of 50 RyR and 12.5 LCC per CRU. See Supplementary Movies 1, 2 for the evolution of [Ca2+]i and nSR [Ca2+] through an AP.
Mentions: We simulated 16 z-discs, each with 320 CRUs, and the Ca2+ dynamics for this sub-cellular region (~30% of the cardiomyocyte) were coupled to the whole-cell electrophysiology ODE model. It took 64.2 h to solve a single action potential on 848 Intel Xeon E5-2650 v2 2.60 GHz CPUs (central processing units). The Ca2+ concentration profile 70.0 ms after stimulus at a single z-disc is shown in Figure 6. The local Ca2+ dynamics and corresponding whole cell electrophysiology are shown in Figure 7A and in Supplementary Movie 1. The SR free [Ca2+] is visualized in Figure 7B and in Supplementary Movie 2. Currents are shown in Figure 8.

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