Stochastic modeling of alginate production by Azotobacter Vinelandii - C. Gallardo (Revista Mexicana de Física, 2006)
A stochastic description of the effects of internal fluctuations on the biomass growth of A. vinelandii in a bioreactor, is given in terms of a nonlinear master equation (M E). We use van Kampen’s systematic expansion method to obtain an approximate but analytic solution of the M E. We predict the time behavior of the average values of the concentrations of biomass, alginate and sucrose, as well as the fluctuations of biomass around its average value, for different values of dissolved oxygen tension (DOT ). We optimize the values of some of the parameters involved in the stochastic and dynamic equations, so that the statistical average error between theoretical and experimental results for both, average and fluctuations, is a minimum. We compare our analytical results for these quantities with those reported experimental measurements for A. vinelandii. We find that the total quadratic average error varies between 0.17 − 0.29. We close the paper by discussing the scope, advantages and limitations of our approach.