Nonlinear dynamic modeling of 2-dimensional interdependent calcium and inositol 1,4,5-trisphosphate in cardiac myocyte

Calcium (Ca$^{2+}$) and inositol 1,4,5-trisphosphate (IP$_3$) is critically important parameters for a vast array of cellular functions. One of the main functions is communication in all parts of the body which is achieved through cell signaling. Abnormalities in Ca$^{2+}$ signaling have been implicated in clinically important conditions such as heart failure and cardiac arrhythmias. We propose a mathematical model which systematically investigates complex Ca$^{2+}$ and IP$_3$ dynamics in cardiac myocyte. This two dimensional model is based on calcium-induced calcium release via inositol 1,4,5-trisphosphate receptors and includes calcium modulation of IP$_3$ levels through feedback regulation of degradation and production. Forward-Time Center-Space method has been used to solve the coupled equations. We were able to reproduce the observed oscillatory patterns in Ca$^{2+}$ as well as IP$_3$ signals. The model predicts that calcium-dependent production and degradation of IP$_3$ is a key mechanism for complex calcium oscillations in cardiac myocyte. The impact and sensitivity of source, leak, diffusion coefficients on both Ca$^{2+}$ and IP$_3$ dynamics have been investigated. The results show that the relationship between Ca$^{2+}$ and IP$_3$ dynamics is nonlinear.