Monod nonlinear kinetic

For those pesticides which are utilized as microbial growth substrates, sigmoidal rates of biodegradation are frequentiy observed (see Fig. 2). Sigmoidal data are more difficult to summarize than exponential (first-order) data because of their inherent nonlinearity. Sigmoidal rates of pesticide metabohsm can be described using microbial growth kinetics (Monod) however, four kinetics constants are required. Consequentiy, it is more difficult to predict the persistence of these pesticides in the environment. 

Each of the two enzymes thus behaves as phosphofructokinase in the model considered for glycolytic oscillations (chapter 2). To limit the study to temporal organization phenomena, the system is considered here as spatially homogeneous, as in the case of experiments on glycolytic oscillations (Hess et ai, 1969). In the case where the kinetics of the two enzymes obeys the concerted allosteric model (Monod et al, 1965), the time evolution of the model is governed by the kinetic equations (4.1), which take the form of three nonlinear, ordinary differential equations ... 

Equations 3.95a,b and 3.96a,b form a set of nonlinear differential equations that are difficult to solve analytically they are more readily solved by computer techniques. In special cases, however, the equations can be integrated, for example, when the amount of biomass formed by the reaction is small relative to the entering amount and the value of x is nearly constant over the reaction length (Xa e)- Thus, integration of Equ. 3.95a is possible, yielding the following expression with Monod kinetics... 

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