The Michaelis-Menten reaction

According to the hypothesis one can neglect c in the equation including the mass balance 

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In B, only the kinetics of simple irreversible reactions is shown. More complicated cases, such as reaction with three or more reversible steps, can usually be broken down into first-order or second-order partial reactions and described using the corresponding equations (for an example, see the Michaelis-Menten reaction, p. 92). 

Determine the kinetic parameters of the Michaelis-Menten reaction for the ACE reaction without the inhibitor. 

Horvath and ENGASSER<58) point out that, whilst the curves are superficially similar to those produced by the Michaelis-Menten reaction scheme, or Monod kinetics in the case of micro-organisms, the functional relationship with the surface concentration is different. This difference may be most marked when the Eadie-Hof-stee type plot is considered, as shown in Fig. 5.54. This time the curves obtained for the cases where 0 is not zero have a sigmoidal shape, even for low values of 0. 

The mathematics for the Michaelis-Menten reaction resembles that of the Langmuir14 adsorption isotherm presented in Section 4.23. 

Here to illustrate the procedure for non-linear systems, we work out the chemical master equation for the Michaelis-Menten reaction of Equation (11.19). We let p(m, n, t) be the probability that m, S, and n ES molecules occur in the enzyme reaction system at time t. The probability p(m, n, t) satisfies the CME... 

When an enzyme is immobilized on a smface, there may be a mass transfer resistance that limits the concetration of the reacting species on the surface. The following problem (from Shuler, 1988) finds the concentration of substrate on the surface when there is a reaction accompanied by mass transfer resistance. The Michaelis-Menten reaction on a surface is governed by... 

The next example is a reaction-diffusion problem in a spherical domain. The reaction rate expression is a nonlinear function of concentration, of a type that is appropriate for the Michaelis-Menten reaction in biological systems. The nondimensional form of the problem is in Eq. (9.25), and it is solved for a = 5, X = 2. 

The DNA elongation process Elongation reactions along the DNA template (step 2 of curve A in Fig. 4) were initiated by addition of complementary monomers (dNTP) after formation of the DNA/KF complex on the QCM. The elongation process is expressed simply by the Michaelis-Menten reaction between the DNA/KF complex and added monomers (Eqs. 6-8) ... 

The dependence on concentration derived above corresponds to the relationship of the Michaelis-Menten reaction, which was given in Section 2.5.1.2. 

Aranyi Toth (1977) have investigated the Michaelis-Menten reaction... 

Fig. 5.3 Time course of the Michaelis-Menten reaction, 1. Deter-...

Aranyi, P. Toth, J. (1977). A full stochastic description of the Michaelis-Menten reaction for small systems. Acta Biochim. Biophys. Acad. Sci. Hung., 12, 375-88. 

Fig. 1 Multi-parameter-analysis (MPA) of an experimental curve according to the Michaelis Menten reaction type.

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