Mathematical models of calcium signalling in the context of cardiac hypertrophy

Abstract

Throughout the average human lifespan, our hearts beat over 2 billion times. With each beat, calcium floods the cytoplasm of every heart cell, causing it to contract until calcium re-uptake allows the heart to relax, ready for the next beat. However, calcium is known to be critical in other cell functions, including growth. Calcium plays a central role in mediating hypertrophic signalling in ventricular cardiomyocytes on top of its contractile function. How intracellular calcium can encode several different, specific signals at once is not well understood.

In heart cells, calcium release from ryanodine receptors (RyRs) triggers contraction. Under hypertrophic stimulation, calcium release from inositol 1,4,5-trisphosphate receptor (IP3R) channels modifies the calcium contraction signal, triggering dephosphorylation and nuclear import of the transcription factor nuclear factor of activated T cells (NFAT), with resulting gene expression linked to cell growth.

Several hypotheses have been proposed as to how the modified cytosolic calcium contraction signal transmits the hypertrophic signal to downstream signalling proteins, including changes to amplitude, duration, duty cycle, and signal localisation. We investigate the form of these signals within the cardiac myocyte using mathematical modelling. Using a compartmental heart cell model, we show that the effect of calcium channel interaction on the global calcium signal supports the idea that increased calcium duty cycle is a plausible mechanism for IP3-dependent hypertrophic signalling in cardiomyocytes.

A corresponding calcium signal within the nucleus must be present to maintain NFAT in the nucleus and thus allow NFAT to alter gene expression, initiating hypertrophic remodelling. Yet the nuclear membrane is permeable to calcium and this must all occur on a background of rising and falling calcium with each heartbeat. The mechanisms shaping calcium dynamics within the nucleus remain unclear.

We use a spatial model of calcium diffusion into the nucleus to determine the effects of buffers and cytosolic transient shape on nuclear calcium dynamics. Using experimental data, we estimate the diffusion coefficient and the effects of buffers on nuclear [Ca2+]. Additionally, we explore the effects of altered cytosolic calcium transients and calcium release on nuclear calcium. To approximate experimental measurements of nuclear calcium, we find that there must be perinuclear Ca2+ release and nonlinear diffusion. Comparisons of 1D and 3D models of calcium in the nucleus suggest that spatial variation in calcium concentration within the nucleus will not have a large effect on calcium-mediated gene regulation.

This work brings us closer to understanding the signalling pathway that leads to pathological hypertrophic cardiac remodelling.