Michaelis-Menten enzyme kinetic

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 ... 

An exponential function that describes the increase in product during a first-order reaction looks a lot like a hyperbola that is used to describe Michaelis-Menten enzyme kinetics. It s not. Don t get them confused. If you can t keep them separated in your mind, then just forget all that you ve read, jump ship now, and just figure out the Michaelis-Menten description of the velocity of enzyme-catalyzed reaction—it s more important to the beginning biochemistry student anyway. 

Box 12.2 An Enzyme-Catalyzed Reaction (Michaelis-Menten Enzyme Kinetics)... 

In Box 12.2, a simple model for a special kind of catalyzed reaction, the Michaelis-Menten enzyme kinetics, is presented, which leads to the following kinetic expression ... 

KiMM is given the subscript, MM, to remind us that it reflects Michaelis-Menten enzyme kinetics as distinguished from KiM used above to model microbial growth kinetics (see Monod cases above). Note, is the same as KE in Box 12.2 when it s value represents the reciprocal of the equilibrium constant for the binding step. 

Figure 17.16 Relationships of biodegradation rate, v, to substrate concentration, [/], when Michaelis-Menten enzyme kinetics is appropriate (a) when plotted as hyperbolic relationship (Eq. 17-79 in text), or (b) when plotted as inverse equation, Vv =...

Example simulating Michaelis-Menten enzyme kinetics... 

Assuming again that the cycle kinetics are rapid and maintain enzyme and complex in a rapid quasi-steady state, we can obtain the steady state velocity for the reversible Michaelis-Menten enzyme kinetics ... 

A more cogent mathematical treatment of this problem was given in the 1970s by several mathematical biologists. For details see books by Lin and Segel [130] and Murray [146], Here we provide a brief account of this approach. The approach uses the somewhat advanced mathematical method of singular perturbation analysis, but does provides a deep appreciation of the Michaelis-Menten enzyme kinetics. 

Recall that in the standard Michaelis-Menten enzyme kinetics we approximate the kinetics of substrate and product using Equation (3.32) or (4.26) for the essentially irreversible case ... 

As in Michaelis-Menten enzyme kinetics, the steady-state assumption of ML is given by... 

The initial reaction rate of a catalyzed reaction versus the concentration of the substrate [>q (Eq. (9.39), where K, =k, /ki). The catalytic reaction could be homogeneous, heterogeneous or enzyme catalysis so long as it follows the simple catalytic mechanism. The substrate concentration, [X]. at a tate of half the maximum reaction rate, V, I2, defines in Michaelis-Menten enzyme kinetics. 

D2. Belkic, Cell surviving fractions after irradiation novel radiobiological models with the Michaelis-Menten enzyme kinetics and the Lambert W function, J. Math. Chem. 49 (2011) 1618. 

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