The Stochastic Effects of Ca2+ Oscillations on Activation of Glycogen Phosphorylase

Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations based on discrete particle are more accurate. Unfortunately, there are no general rules for determining which method should be employed for a specific problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system by calcium oscillation transmission signals. Used stochastic effects of calcium oscillations on glycogen phosphorylase activation in hepatocytes as an example, we attempted to solve the problem of simulation and modeling in the biochemical system with small number of molecules by stochastic differential equation. The possible role of Ca2+ released from the inositol 1, 4, 5-trisphosphate (IP3) receptor channel in the regulation of the phosphorylation-dephosphorylation cycle process involved in glycogen degradation by glycogen phosphorylase have theoretically investigated using stochastic the Li-Rinzel model for cytosolic Ca2+ oscillations. The results show that the fraction of active phosphorylase is decreased with the total number of receptor channel IP3R increasing and for the small concentration of IP3 with appearance of coherence resonance.