Perturbation and Truncation of Probability Generating Function Methods for Stiff Chemical Reactions

Figure 1

Comparison of mean, standard deviation and marginal probability for the enzyme-substrate model. In the three figures, we assume that , , and . (a) shows the comparison of exact values and approximate values obtained from the PPGF method for mean and mean standard deviations () of and (b) shows the comparison of the exact probability and the approximate probability obtained from the PPGF method. In the figure, denotes the probability that the number of the substrate is . The exact probability, mean, and variance are obtained by rewriting (15) into the linear ODE system under the given initial condition and then solving it by MATLAB.

(a)

(b)