Enzyme kinetics Monod equation

Microbial Biotransformation. Microbial population growth and substrate utilization can be described via Monod s (35) analogy with Michaelis-Menten enzyme kinetics (36). The growth of a microbial population in an unlimiting environment is described by dN/dt = u N, where u is called the "specific growth rate and N is microbial biomass or population size. The Monod equation modifies this by recognizing that consumption of resources in a finite environment must at some point curtail the rate of increase (dN/dt) of the population ... 

The graphical significance of the constants in the Monod equation are identical to the corresponding constants in the Michaelis-Menten relationship for enzyme kinetics (see Section 5.4.4). The specific growth rate initially increases with increas-... 

Substrate Concentration One of the most widely employed expressions for the effect of substrate concentration on jj. is the Monod equation, which is an empirical expression based on the form of equation normally associated with enzyme kinetics or gas adsorption 1... 

The Monod kinetic parameters, and Ks, cannot be estimated with a series of batch runs as easily as the Michaelis-Menten parameters for an enzyme reaction. In the case of an enzyme reaction, the initial rate of reaction can be measured as a function of substrate concentration in batch runs. However, in the case of cell cultivation, the initial rate of reaction in a batch run is always zero due to the presence of a lag phase, during which Monod kinetics does not apply. It should be noted that even though the Monod equation has the same form as the Michaelis-Menten equation, the rate equation is different. In the Michaelis-Menten equation,... 

The mathematical function to be chosen as the model is not of the purely numerical form but is taken from analogies. Analogy means that known mathematical functions, generally from conventional mechanistic work with a similar phenomenology, are selected (e.g., the Monod equation as an analogy to enzyme kinetics). 

This short presentation of integral solution techniques for biokinetic equations shows that integration of the function incorporating the hypothesis works only in the simplest cases. In addition, the integrated form lacks much of the flexibility desired for fitting data there is an immediate tendency to resort to descriptive polynomial functions. One also tries to use simplified forms of enzyme kinetics such as Monod kinetics, and this involves power law -type equations (cf. type 1 in Fig. 4.12 or Equ. 2.2a). 

In most cases of inhibition, the formal kinetic model equations are, like Monod s relationship, derived from theories of the inhibition of single enzymes. The equations are, however, only hypotheses they may be replaced by any other adequate model. 

Lineweaver-Burk plot A double-reciprocal plot used to determine the two constants featured in simple enzyme kinetic equations such as Michaelis-Menten kinetics, Monod kinetics, and in similar adsorption isotherm models such as the Langmuir adsorption isotherm. The constants are determined from the intercept with the y-axis and the gradient (see Fig. 26). It was devised and published in 1934 by American chemist Hans Lineweaver (1907-2009) and American biochemist Dean Burk (1904-1988). 

The Monod equation has the same form as the Michaelis-Menten[29] equation for enzyme kinetics, but differs in that it is empirical while the latter is based on theoretical considerations. For the simple enzyme reaction given below, the Michaelis-Menten equations are provided below. 

An understanding of the influence of environmental conditions on the kinetics of enzyme reactions is essential for the design of processes based upon the use of these materials as catalysts. Their growth kinetics are also governed by similar kinetic equations (c.f. Monod growth equations, Section S.9). 

Assuming that the local rate of enzyme reaction follows Michaelis-Menten kinetics, or that the microbe film follows Monod kinetics regardless of immobilisation, then equation 5.86 becomes ... 

The experimental and mathematical models were divided into two hierarchical steps, as seen in Fig. 5. First, hydrolysis experiments were conducted, and the hydrolysis time profile was matched to hydrolysis rate equations. A separate hydrolysis-only model was used to match the hydrolysis data to Michaelis-Menten based kinetics and to solve for unknown parameters. Second, SSF experiments were conducted using identical enzyme loading, and these datasets were matched to a complete SSF model. The SSF model incorporated the hydrolysis parameters from the first step and was used to solve for the unknown fermentation parameters using Monod-based kinetics. 

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 ... 

The interactions of the subunits (protomers) of the enzyme with substrate, coenzyme, activator and inhibitor molecules lead to far more complicated kinetic equations, quite outside the scope of this chapter. The experimenter interested in such work is advised to take it up only with the help of an experienced enzymol-ogist The interested reader can profitably obtain further information by consulting the articles or reviews of Bernhard (1968), Changeux (1965). Mahler and Cordes (1966). Monod et al. (1965). Segel (1968) and Stadtman (19 ). 

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