Figure 4.

Generalization of protein system and understand numerical limitations. (A) The dominating eigenvalue for the protein production-degradation system is shown to be a ratio of the production rate over the degradation rate times some constant. The simulations of different ratios match the analytic solution. (B) The second eigenvalues for the protein production and degradation rate are nonzero during simulation because of the limitation of the physical system itself. At steady state, the average number of proteins is 100 proteins, which means that the smallest shift for probability to calculate the finite derivatives is one protein (1% of the average number), which gives a nonzero eigenvalue. To see this figure in color, go online.