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

Janine Vierheller,Martin Falcke,Stephen H Gilbert,Wilhelm Neubert,Nagaiah Chamakuri

doi:10.3389/fphys.2015.00255

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 Ca2+ content within tens of seconds. Our concept for a multiscale mathematical model of Ca2+ -induced Ca2+ 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 Ca2+ and Ca2+-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 Ca2+-concentration profiles using three previously published RyR-channel Markov schemes.

Highlights

Cardiomyocyte muscle filament shortening and lengthening is a Ca2+ dependent process
In order to employ the two state ryanodine receptor channels (RyRs)-models by Cannell et al (2013) and Walker et al (2014) we found it necessary to introduce a form of Ca2+buffering in the dyadic space
We showed on a level of proof-of-concept that multiscale modeling of cardiomyocyte ECC from sub-dyadic scales to many z-discs using full partial differential equations is possible

Summary

Introduction

Cardiomyocyte muscle filament shortening and lengthening is a Ca2+ dependent process. The timing of contraction is controlled through electrical excitation via a process known as excitationcontraction-coupling (ECC). ECC is mediated through Ca2+, and is facilitated through an amplification process known as Ca2+-induced Ca2+ release (CICR). CICR is controlled locally by the colocalization of L-type Ca2+-channels (LCCs) in the T-tubule membrane on the one side of a dyadic cleft [aka Ca2+ release unit (CRU)] and ryanodine receptor channels (RyRs) in the junctional sarcoplasmic reticulum (jSR) membrane on the other side. Depolarization of the plasma membrane leads to the activation of LCCs, which causes Ca2+ entry from the extracellular space into the dyadic space. The influx of Ca2+ activates RyRs, which release Ca2+ from the sarcoplasmic reticulum (SR) (Fabiato and Fabiato, 1975).

Results

Discussion

Conclusion