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

Abstract

Regulation of intracellular calcium is a critical component of cardiac electrophysiology and excitation-contraction coupling. The calcium spark, the fundamental element of the intracellular calcium transient, is initiated in specialized nanodomains which co-locate the ryanodine receptors and L-type calcium channels. However, calcium homeostasis is ultimately regulated at the cellular scale, by the interaction of spatially separated but diffusively coupled nanodomains with other sub-cellular and surface-membrane calcium transport channels with strong non-linear interactions; and cardiac electrophysiology and arrhythmia mechanisms are ultimately tissue-scale phenomena, regulated by the interaction of a heterogeneous population of coupled myocytes. Recent advances in imaging modalities and image-analysis are enabling the super-resolution reconstruction of the structures responsible for regulating calcium homeostasis, including the internal structure of nanodomains themselves. Extrapolating functional and imaging data from the nanodomain to the whole-heart is non-trivial, yet essential for translational insight into disease mechanisms. Computational modeling has important roles to play in relating structural and functional data at the sub-cellular scale and translating data across the scales. This review covers recent methodological advances that enable image-based modeling of the single nanodomain and whole cardiomyocyte, as well as the development of multi-scale simulation approaches to integrate data from nanometer to whole-heart. Firstly, methods to overcome the computational challenges of simulating spatial calcium dynamics in the nanodomain are discussed, including image-based modeling at this scale. Then, recent whole-cell models, capable of capturing a range of different structures (such as the T-system and mitochondria) and cellular heterogeneity/variability are discussed at two different levels of discretization. Novel methods to integrate the models and data across the scales and simulate stochastic dynamics in tissue-scale models are then discussed, enabling elucidation of the mechanisms by which nanodomain remodeling underlies arrhythmia and contractile dysfunction. Perspectives on model differences and future directions are provided throughout.

Models of the cardiac L‐type calcium current: A quantitative review

“…Modelers of the cardiac AP have accounted for these local phenomena by dividing the cell into smaller‐volume “subspaces” in which calcium ions, carried in by or released from the SR, can cause to transiently rise to much higher levels than those seen in the bulk cytosolic space (Colman et al, 2022). Figure 3 shows three commonly used subspace configurations.…”

Modeling Calcium Cycling in the Heart: Progress, Pitfalls, and Challenges

“…These same sequences of dynamics were demonstrated in experiments of ventricular myocytes [ 57 ]. Most of the 3D whole-cell models are similar but differ somewhat in spatial resolution and structural details, e.g., some with structural complexities between those in Figure 3 A–C (see Colman et al for a detailed review [ 4 ]). Although the CRU network models lack the realistic structures of the TT and the SR networks as the real one in Figure 3 A, or even as the complex one in Figure 3 B, they are much more computationally convenient, and can be easily modified to simulate different subcellular structures, different cell types, and diseased conditions [ 68 , 72 ].…”

“…The heart is probably the most intensively and accurately modeled biological system compared to other organs [ 1 , 2 , 3 , 4 , 5 ]. So far, more than 100 action potential models (or modified versions) have been developed for different types of myocytes and species.…”

Models of the cardiac L-type calcium current: a quantitative review

“…Modellers of the cardiac AP have accounted for these local phenomena by dividing the cell into smaller-volume ‘subspaces’ in which calcium ions, carried in by I CaL or released from the SR, can cause [Ca 2+ ] to transiently rise to much higher levels than those seen in the bulk cytosolic space (Colman et al, 2022). Figure 3 shows three commonly used subspace configurations.…”