A Stochastic Spatiotemporal Model of Rat Ventricular Myocyte Calcium Dynamics Demonstrated Necessary Features for Calcium Wave Propagation

Abstract

Calcium (Ca2+) plays a central role in the excitation and contraction of cardiac myocytes. Experiments have indicated that calcium release is stochastic and regulated locally suggesting the possibility of spatially heterogeneous calcium levels in the cells. This spatial heterogeneity might be important in mediating different signaling pathways. During more than 50 years of computational cell biology, the computational models have been advanced to incorporate more ionic currents, going from deterministic models to stochastic models. While periodic increases in cytoplasmic Ca2+ concentration drive cardiac contraction, aberrant Ca2+ release can underly cardiac arrhythmia. However, the study of the spatial role of calcium ions has been limited due to the computational expense of using a three-dimensional stochastic computational model. In this paper, we introduce a three-dimensional stochastic computational model for rat ventricular myocytes at the whole-cell level that incorporate detailed calcium dynamics, with (1) non-uniform release site placement, (2) non-uniform membrane ionic currents and membrane buffers, (3) stochastic calcium-leak dynamics and (4) non-junctional or rogue ryanodine receptors. The model simulates spark-induced spark activation and spark-induced Ca2+ wave initiation and propagation that occur under conditions of calcium overload at the closed-cell condition, but not when Ca2+ levels are normal. This is considered important since the presence of Ca2+ waves contribute to the activation of arrhythmogenic currents.

Multi-Scale Computational Modeling of Spatial Calcium Handling From Nanodomain to Whole-Heart: Overview and Perspectives

“…This model also indicated the importance of realistic (and variable) dyad distribution on the specific dynamics of both CaT alternans and SCRE, providing spatial constraints on the randomness of both. These results are further supported by the recent sub-micron, type 1 model of Hoang-Trong et al (2021) which included experimentally influenced spatial distributions of multiple Ca 2+ -flux channels, explicit modeling of transverse- and axial-tubules, and Ca 2+ -CaM interactions. This study highlighted the importance of CRU distribution and the presence of rogue (non-junctional or orphaned) RyRs on Ca 2+ -spark propagation and wave dynamics.…”

“…It is worth highlighting that the models of single nanodomains do not reproduce well experimentally measured values for the full width half maximum (FWHM) of Ca 2+ , generally resulting in values of ∼1 μm which are below the 1.8–2.2 μm in experiment. Hoang-Trong et al (2021) for example did simulate a realistic feature of 1.85 μm, but this required using a large RyR cluster combined with two smaller satellite clusters. However, due to spatio-temporal limits on the resolution of functional imaging experiments, sparks smaller than given sizes are not detected experimentally with any given accuracy.…”

“…Spatial coupling is solved using FDM [equation (40)] on regular structured grids or using the more complex finite element method (FEM) on structured or unstructured meshes. They can be discretized at different choices of resolution, generally between 0.05 and 0.2 μm ( Nivala et al, 2012a , 2015 ; Colman et al, 2017b ; Marchena and Echebarria, 2018 , 2020 ; Hoang-Trong et al, 2021 ), although there are other intermediary approaches, such as Sutanto et al (2018) which uses the CRU-grid approach in the transverse direction but is discretized at half-CRU distance in the longitudinal direction.…”

Critical Requirements for the Initiation of a Cardiac Arrhythmia in Rat Ventricle: How Many Myocytes?

“…This study integrated our previous local-control model of excitation–contraction coupling rat ventricular myocytes into a network of myocytes to describe ventricular tissue [ 11 , 19 ]. Local-control is the feature that excitation–contraction coupling is modulated locally at the release site level.…”

“…The model used in this paper has several important features, some of which were introduced in [ 11 , 19 , 20 , 21 ], such as a spark model well-constrained by experimental data and a thermodynamically and biochemically constrained model for SERCA2a (sarco- and endoplasmic reticulum Ca 2+ ATPase isoform 2a) pump [ 22 ]. Other changes include using (1) explicit buffer dynamics in the subspace, (2) a different L-type Ca 2+ channel that incorporate Ca 2+ -bound calmodulin-dependent inactivation and updated parameters based on newer experimental data from rat ventricular myocyte [ 23 ].…”