Computation of Steady-State Probability Distributions in Stochastic Models of Cellular Networks
Figure 3
Calculating steady-state distributions for a simple birth-death process.
Calculating the steady-state distribution of a (A) simple birth-death process; A is expressed in terms of molecule number for all distributions. (B) Simulated distribution using the Gillespie algorithm (histogram) as compared with the analytical solution (blue line) from the CME, which is a Poisson distribution. (C) Final distributions from this systems with extrinsic noise were generated by taking ks/kd∼Γ(20,1) (green in C) or ks/kd∼Γ(10,2) (green in D); best-fit distributions based on convolution with a Gaussian (red; standard deviations 4.4 for C and 6.1 for D) and the intrinsic-noise-only distribution (blue) are shown as well. (The shift to lower molecule numbers arising from extrinsic noise in the parameter-distribution representation is equivalent to changing the base parameter set in the convolution representation; the “base” parameter set is less well defined in the parameter-distribution representation).