Simple One-Substrate Enzyme Kinetics

One-substrate enzyme kinetics are applied to many reactions that require water as a cosubstrate, that is, the hydrolases (such as esterases and proteases), since aqueous solutions have a water concentration of 55.6 M. The kinetic model is based on the initial formation of the enzyme-substrate complex, with the rate constants as shown in Eq. 2.11. 

From this model, the dissociation constant of the enzyme substrate complex, K, will be equal to k jk, which is equal to [E][S]/[E S], 

The mathematical derivation of the expression for the reaction rate is based upon the initial rate of the reaction. We will assume that, almost immediately after the reaction begins, the rate of change of concentration of the enzyme-substrate complex is zero that is, a steady-state [E S] value is achieved. The rate of change of [E S] with time, d[E S]/df, may be expressed as in Eq. 2.12  

The enzyme exists in solution as either E or E S, so that at any time, the total enzyme concentration is equal to the sum of these concentrations, or [E]0 = [E] + [E S]. Using this expression to substitute for [E] in Eq. 2.12 yields 

Equation 2.15 can now be used to find the initial rate of formation of product, as given in Eq. 2.16  

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