Michaelis–Menten model

The following concept is used in the Michaelis–Menten model of enzyme catalysis:

The enzyme which is denoted by E combines with its substrate that is denoted by S to form an enzyme–substrate complex that is denoted by ES.  The  ES  complex  can  dissociate  again  to  form  E + S,  or  can go on chemically to form E and the product P. The rate constants k1, k2 and the k3 defines the rates related with each and every step of the catalytic procedure. It is supposed that there is no signi?cant rate for the backward reaction of enzyme and product (E + P) being converted to ES complex.  [ES] leftovers approximately constant.

                                  Figure: The effect of (a) temperature and (b) pH on enzyme activity.

until closely all the substrate is used, therefore the rate of synthesis of ES equals its rate of consumption  over most of the course of the reaction;  which is, ES maintains a steady state. From the observation  of the properties  of several enzymes it was  known  in which  the  initial  velocity  (V₀)  at  low  substrate   concentrations   is straightly  proportional  to [S] although at high substrate  concentrations  the velocity tends  towards  a maximum  value,  which is the rate becomes  independent  of [S]. This maximum velocity is known as Vmax the units of μmol min. The initial velocity (V0) is the velocity measured experimentally before more than approximately 10 percent of the substrate has been converted to product in order to minimize like complicating factors as the effects of reversible reactions inhibition of the enzyme through product and progressive inactivation of the enzyme.

Michaelis and Menten define an equation to describe these observations the Michaelis–Menten equation is given below:

This equation elaborates a hyperbolic curve of the kind described for the experimental data in Figure. In deriving the equation, Michaelis and Menten described Km a new constant the Michaelis constant units Molar instance for per mole.

K_m is a measure of the stability of the ES complex being equal to the sum of the rates of breakdown of ES over its rate of formation.  For several enzymes k₂ is much greater than k₃. In Under these circumstances  Km becomes a measure of the af?nity  of an enzyme  for its substrate  because  its value  depends  on the relative values  of k₁,  k₂   for ES dissociation and formation,  correspondingly.  A high  Km denotes  weak substrate  binding  k₂   predominant  over k₁, a low K_m denotes strong substrate binding k₁  predominant  over k₂. Km can be determined experimentally through the fact in which its value is equivalent to the substrate concentration at that the velocity is equal to half of V_max.