Sardar Vallabhbhai National Institute of Technology, Ichchhanath, Surat, Gujarat, India

Abstract. Calcium (Ca²⁺) and inositol 1,4,5-trisphosphate (IP₃) is critically important actors for a vast array of cellular processes. The most significant of the functions is One of the main functions is communication in all parts of the body which is achieved through cell signaling. Abnormalities in Ca²⁺ signaling have been implicated in clinically important conditions such as heart failure and cardiac arrhythmias. We propose a mathematical model which systematically investigates complex Ca²⁺ and IP₃ 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 IP₃ levels through feedback regulation of degradation and production. Forward-Time Centered-Space method has been used to solve the coupled equations. We were able to reproduce the observed oscillatory patterns in Ca²⁺ as well as IP₃ signals. The model predicts that calcium-dependent production and degradation of IP₃ is a key mechanism for complex calcium oscillations in cardiac myocyte. The impact and sensitivity of source, leak, diffusion coefficients on both Ca²⁺ and IP₃ dynamics have been investigated. The results show that the relationship between Ca²⁺ and IP₃ dynamics is nonlinear.

Key words: calcium and inositol 1,4,5-trisphosphate, signaling, cardiac myocyte,  finite difference method, nonlinear coupled dynamics.