System size and simulation performance. (A) Cost of network-free simulation vs. cost of on-the-fly simulation. The CPU time required to perform the simulation specified in the BioNetGen input file of Supplemental Archive File 1, but without equilibration, was determined for the on-the-fly stochastic simulation algorithm (SSA) implemented in BioNetGen and also for the network-free stochastic simulation algorithm implemented in NFsim. Equilibration was not performed so that the initial condition would encompass a minimal number of populated species. Thus, in these simulations, all proteins were free and unphosphorylated at time t = 0. As can be seen, the computational cost for on-the-fly simulation increases exponentially as a function of time, whereas the computational cost of network-free simulation increases linearly as a function of time. There are no data points for t ≥ 1.5 s for the on-the-fly algorithm because the cost of network generation made simulating the model beyond this time impractical. (B) On-the-fly stochastic simulation of the model with BioNetGen (see Methods). The simulation results demonstrate that a large number of chemical species are populated in the ERBB receptor signaling network.