Colored noises and time delay induced periodic square calcium wave

Abstract

Intracellular calcium oscillation with colored noises and same time delay \(\tau \) in active and passive transport processes of intracellular Ca\(^{2+}\) is investigated by the means of second-order algorithm for stochastic simulation colored noises. By simulating time series, stationary probability distribution and average of intracellular Ca\(^{2+}\) concentrations, we obtain the results which indicate that is anti-synchronous between calcium store and cytosol and the critical phenomenon of time delay with critical value \(\tau _{c}\simeq 0.1\) s, appears. As \(\tau \rightarrow \) 0.1 s or as correlation time \(\tau _{1}\) of colored noises increases, the stability of system is strengthened. Especially, the long \(\tau \) and \(\tau _{1}\) induce periodically square calcium wave. Additionally, as \(\tau _{1}\) prolongs, the average of Ca\(^{2+}\) concentrations of cytosol and calcium store respectively always increases and maintains a constant value.