Michaelis-Menten formula

The mathematical expressions relating reaction rate and inhibitor concentration are often rather complicated, but there are four simple equations that are extensions of the Michaelis-Menten formula. These merit special consideration because the kinetics of many enzymes can be satisfactorily described by them. In the equations in Table 9.1, [I] denotes the inhibitor concentration and K and K are inhibition constants, the units of which are those of a dissociation equilibrium constant (mmolL-1). Mechanisms that are consistent with these equations are described in Sect. 9.10. 

Relative recovery can be mathematically expressed by Fick s law of diffusion as modified by Jacobson (Jacobson et al., 1985). In this relationship, recovery is the ratio of the concentration in the perfusate to the concentration extracellular. For the mass recovery, an expression similar to a Michaelis-Menten formula for enzymatic reactions was derived (Ekblom et al., 1992). A number of other mathematical models for quantitative microdialysis have been proposed and are reviewed elsewhere (Justice 1993 Kehr, 1993b). 

The formal structure of various types of mathematical models has been summarized by Frederickson, Ramkrishna, and Tsuchiya (I) and Weiss (2). The various biological assumptions that are implicit in many simple models, such as the Michaelis-Menten formula, are discussed, and generalized approaches are suggested. Few specific actual examples... 

Analysis was based on the derived Michaelis Menten formula ... 

In the ground-breaking scientific paper that presented their work, Menten and Michaelis also derived an important mathematical formula. This formula describes the rate at which enzymes break down their substrates. It correlates the speed of the enzyme reaction with the concentrations of the enzyme and the substrate. Called the Michaelis-Menten equation, it remains fundamental to our understanding of how enzymes catalyze reactions. 

Analogous to the above ordinary Michaelis-Menten kinetics, substitution of Equation (11.56) in Equation (11.21) yields a formula which allows straightforward calculation of the residence time required for a specific conversion ... 

By analogy to Michaelis and Menten enzymatic kinetics, Monod (1949) proposed the formula shown in Equation 15 that represents the cell growth rate as a function of cell and substrate concentrations. 

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