A New Kinetic Structured Model for Cell Cultivation in a Chemostat

level: advanced M athematically modeling the kinetics of batch and continuous cultivation allows you to not only calculate and evaluate the effects of process parameters, but also to forecast those parameters and duration of cultivation to develop a costeffective production process. Mathematical modeling microorganism cultivation was intensively developed in the second half of the last century. Monod proposed Equation 1 for batch processes in 1942 (1). In that equation, μ and μmax are the specific and maximum growth rates, respectively (h–1), S is the substrate concentration, (g/L), and KS denotes a Monod semisaturation constant (g/L). That model implies that yield Y is a constant value. For continuous-mode cultivation (e.g., chemostat), Y can be calculated using Equation 2, in which X is the biomass concentration (g/L), and S0 is the limiting substrate concentration in the input (g/L). For a continuous cultivation at f low rate D (h–1), combined solution of Equations 1 and 2 gives the equation called a Monod model for chemostat cultivation under full stirred conditions and substrate limitation. For the biomass, this is Equation 3, and for the limiting substrate it is Equation 4. In 1959, Luedeking and Piret (2) presented a model describing cell cultivation to produce valuable metabolites. Moser (3) in 1958 and Andrews (4) in 1968 both described models for continuous processes, taking into account substrate inhibition as an example of trying to resolve some limitations of the Monod theory. Their work is shown as Equations 5 and 6, in which K * denotes a new parameter not considered in Equation 1, provided that K * > 1, and Ki is the inhibition constant. The improved Monod equation and kinetic models on its base describe biomass growth and formation of target products gave rise to various stochastic, unstructured, and structured models, which Gormely reviewed in detail in 1973 (5). Pirt (6), Bailey and Ollis (7), and Terskov and Gurevich (12) presented the classification and critical analysis of the developed kinetic models. Some studies have linked process kinetics to the physiological state of cells and to the concentration of substrates consumed for biomass growth and maintenance of population viability (8–11, 13–24). (www.sxc.hu)