A Rationale for Monod′s Biochemical Growth Kinetics

ion of complex systems in various ways. Thus the subject of lumping of multicomponent, multireaction systems in petrochemical reaction engineering sought to find component clumps whose concentrations would serve to define their rates of change and to see the circumstances under which such simplifications would emerge. Naturally, linear reaction systems could be dealt with more elegance as, for example, in the publication of Wei and Kuo. Several other papers exist on the concept of lumping of nonlinear reaction systems. Metabolism involves a very complicated reaction network with multitudes of reactions enabled by the catalytic activities of a great many enzymes. It involves the catabolic breakdown of substrates into diverse intracellular metabolites that are recruited into the synthesis of biomass and many fermentation products that are released into the abiotic environment. That such a complex process can find a reasonable description with a model that can at best be compared to a single reaction catalyzed by an enzyme deserves reflection toward providing some insight into the extent of success that it has enjoyed. It is fair to warn that an explanation of this kind cannot be unique but insofar as it is based on the many insights that have become available in treating metabolism, it has all the attributes of a reasonable argument. The treatment begins with a short prologue on Monod kinetics, followed by a stoichiometric formulation of metabolism, its decomposition into so-called elementary modes, the pseudostate assumption for intracellular metabolites, and finally toward the formulation of Monod kinetics by determining the Michaelis constant and the growth rate of the organism that would fit in the expression. 2. Monod Kinetics The kinetic expression due to Monod applies to the straitjacketing of metabolism into the following single step B+ Sf (1+ Y)B+ · · · (1) Thus the foregoing reaction simply describes the yield of Y mass units of biomass from (a carbon, rate limiting) substrate of course, however, with the aid of existing biomass. The Monod kinetic expression is designed to address the rate at which transformation (1) occurs without regard to the actual mechanism by which metabolism functions to accomplish the same. The specific growth rate (i.e., the rate of synthesis of biomass per cell) is given by