A mathematical model for interdependent calcium and inositol 1,4,5-trisphosphate in cardiac myocyte

Abstract

Calcium ($${\text {Ca}}^{2+}$$) signaling is the secondary signaling processes which have been one of the most vital intracellular signaling mechanisms. Over recent decades, this signaling process has been studied a lot in various cells to understand its mechanisms and also cure of various health hazards. In this paper, an attempt has been made to propose a model for coupled dynamics of $${\text {Ca}}^{2+}$$ and inositol 1,4,5-trisphosphate ($${\text {IP}}_3$$) in cardiac myocyte for a better understanding of the dependence of $${\text {Ca}}^{2+}$$ signaling on other chemical ions such as $${\text {IP}}_3$$ ions. The parameters such as influx, outflux, diffusion coefficient, SERCA pump, and Leak have been incorporated into the model and the finite differences scheme has been employed for the solution of the problem. The numerical results have been used to study the interdependence of $${\text {Ca}}^{2+}$$ and $${\text {IP}}_3$$ in the cardiac myocyte. It is observed that this interdependence is quite significantly affected by all these parameters except Leak. Also, the relationship between $${\text {Ca}}^{2+}$$ and $${\text {IP}}_3$$ dynamics is found to be non-linear. Such realistic models can be useful to generate the information of these dynamics in cardiac cells which can be useful for developing protocols for diagnosis and treatment of heart diseases like abnormal calcium signaling due to mutation of calsequestrin which results in sudden cardiac death and cardiomyopathy that affects the squeezing of the heart muscle.