Limits...
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

Two examples for channel placement in the CRU model. For 30 RyRs and 8 LCCs (left) and 16 RyRs and 5 LCCs (right). The number of RyR channels per CRU obeys an exponential distribution with an average of 50 across all CRUs.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4585174&req=5

Figure 2: Two examples for channel placement in the CRU model. For 30 RyRs and 8 LCCs (left) and 16 RyRs and 5 LCCs (right). The number of RyR channels per CRU obeys an exponential distribution with an average of 50 across all CRUs.

Mentions: The CRU model was based on a model previously developed by Schendel et al. (2012). We adapted it in a few key points to properly interact with the PDE model described above. We omit the index numbering the CRUs in this section for simpler notation. The dyadic space is modeled as a cylinder of variable radius and a height of 15 nm containing LCCs and RyRs, which are placed in regular arrays at the bottom and top of the cylinder (see Figure 2). The number of RyRs in each CRU was randomly determined using an exponential distribution with mean 50. For each four RyRs there was one LCC. The diameter of the cylinder was determined for each CRU such that there was a margin of 60 nm between the outermost channel and the boundary of the cleft.


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)

Two examples for channel placement in the CRU model. For 30 RyRs and 8 LCCs (left) and 16 RyRs and 5 LCCs (right). The number of RyR channels per CRU obeys an exponential distribution with an average of 50 across all CRUs.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 2: Two examples for channel placement in the CRU model. For 30 RyRs and 8 LCCs (left) and 16 RyRs and 5 LCCs (right). The number of RyR channels per CRU obeys an exponential distribution with an average of 50 across all CRUs.
Mentions: The CRU model was based on a model previously developed by Schendel et al. (2012). We adapted it in a few key points to properly interact with the PDE model described above. We omit the index numbering the CRUs in this section for simpler notation. The dyadic space is modeled as a cylinder of variable radius and a height of 15 nm containing LCCs and RyRs, which are placed in regular arrays at the bottom and top of the cylinder (see Figure 2). The number of RyRs in each CRU was randomly determined using an exponential distribution with mean 50. For each four RyRs there was one LCC. The diameter of the cylinder was determined for each CRU such that there was a margin of 60 nm between the outermost channel and the boundary of the cleft.

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