Systematical bifurcation analysis of an intracellular calcium oscillation model

As a very important second messenger, Ca(2+) plays the role of adjusting various cellular physiological processes through calcium oscillations. In this paper, a further theoretical study is conducted to explore the kinetic behavior of the calcium signals based on a mathematical model. At first, the causes behind the appearance and disappearance of calcium oscillations are strictly verified from the theoretical level and a comparative analysis between the improved model and the original model is also made. Then, it is found that with the increase of relaxation time, the second bifurcation point of the system moves towards the increasing direction of the stimulus intensity and the oscillation interval displays gradual increase. It is also found that under given stimulus intensity, with the relaxation time getting longer, both the peak value and the period of the calcium oscillations display significant increase. Combining the results from the comparative analysis between the improved model and the original model with the results from the analysis of the relaxation time, it shows that the calcium pump activity exerts a direct impact on the calcium oscillation interval. Finally, the calcium leakage item is introduced into the improved model and it is found that as the calcium leakage increases, the two Hopf bifurcation points of the system both move towards the decreasing direction of the stimulus intensity and the oscillation interval gradually narrows down. The study also shows that under given stimulus intensity, as the calcium leakage increases, the peak value of the calcium oscillations displays slow increase and the oscillation period displays gradual decline.