Figure 2

Simulation and analysis of deterministic models of intrinsic apoptosis pathway. (A) Simulations of the Fussenegger ODE model of intrinsic apoptosis pathway show that the time courses of caspase 3 (CEA) starting from various initial conditions all converge to single steady state. (B) Bifurcation analysis of the Fussenegger model. Plot of steady-state CEA versus input signal Cytochrome C (CC) shows that the model is monostable. (C) Simulations of our ODE model modified based on Fussenegger model show that the time courses of CEA can converge either to a high steady state, if the input signal is high (solid line), or to a near-zero steady state, if the input signal is low (dashed line). (D) Bifurcation analysis of our model confirms that CEA has two stable steady states (upper and lower branches of black solid lines) and an unstable steady state (middle branch of dashed line). The bifurcation diagram has two saddle-node (SN) bifurcation points at CC = 0.08 μ M (SN1) and CC = 0.83 μ M (SN2). CEA jumps from one sable steady state to the other stable steady state if CC shifts below SN1 or above SN2 as illustrated by the red arrows. Therefore, the modified apoptosis model is bistable, and the bistability domain between SN1 and SN2 allows the system to resist against mild input perturbation.