Fig. 5: A hybrid method combining the SSA and Holimap.

a SSA+Holimap serves as a highly efficient strategy to approximately solve the dynamics of complex stochastic gene networks. First, the SSA is used to generate a relatively small number of trajectories of the nonlinear network from which the steady-state or time-dependent sample moments are estimated. The low-order sample moments are then used to approximately compute the effective parameters of the linear network. Finally, the protein distributions follow directly by solving the dynamics of the linear network using FSP. b Comparison of the CPU times and the accuracy (measured by HDs at t = 30) for different methods. All methods were used to simulate the time-dependent protein distributions shown in Fig. 4d. The HD represents the Hellinger distance between the actual and approximate protein distributions. Here a proxy for the ground truth distribution is computed using the SSA with 10⁵ trajectories rather than FSP since the latter is computationally infeasible (see Supplementary Note 6 for the estimation procedure for the CPU time required by FSP). c An illustration of a random M-node gene network, where each pair of nodes has a probability of 2/M to be connected. There are on average 2M directed edges for the network, each having an equal probability to be positive or negative regulation. d Comparison of the CPU times and the accuracy (measured by HDs averaged over ten-time points and overall proteins) against the number of nodes M for SSA+2HM and the SSA with the same number of trajectories. Here the number of trajectories needed for both SSA+2HM and SSA is chosen as N = 2000. Both methods were used to simulate the time-dependent distributions for a random network. Data are presented as mean values +/− standard deviations for five different random networks. See “Methods” for the technical details. In (b) and (d), all simulations were performed on an Intel Core i9-9900K processor (3.60 GHz).