Enzymes Catalyzed Reactions
Many enzyme catalyzed reactions follow a complex rate equation that can be written in terms of the total amount of enzyme and the total amount of substrate in the reaction system.
Many rate equations that are more complex than first and second order equations and are encountered in chemical rate studies. Such rate equations can be illustrated by considering reactions that occur in biological systems, or at least are affected by enzymes occurring in such systems.
The effect of enzymes on the rate with which chemical reactions move toward their equilibrium position provides one of the most dramatic catalytic effects. Much of the current interest in the subject is centered on the details of the action between the enzyme, which is the catalyst, and the material, known as substrate, whose reaction it effects. It is important to understand how an enzyme catalyzed reaction proceeds in time and how the catalytic activity of the enzyme substrate pair is evaluated from the measurement of the progress of such reactions.
The experimental data for enzyme catalyzed reactions show a variety of forms that depend on the enzyme, the substrate, the temperature, the presence of interfering substances, and so forth. Many of the behaviors that are found can be looked on as variations from the ideal curve. It is such rate curves for which we now develop a rate equation in a form that is conviently related to the quantities measured in enzymes studies.
Inspection of the curve shows that at high substrate concentrations the rate of the reaction is independent of the substrate concentration. It is, the however, proportional to the total amount of the enzyme. At low substrate concentrations the rate, as shown by the initial straight line section of the curves, is proportional to the substrate concentration. The rate would be found to be proportional to the total enzyme concentration. These features also be found to be proportional by a rate of equation, where R denotes the rate of the reaction, of the form:
R = (const) [E_{tot} ] [ S ] / const’ + [S]
To anticipate the notion introduced when the mechanism of enzyme catalyzed reactions is dealt with, we introduce the symbols k_{2} and K_{M} for the two constants and thus write the equation in the form:
R = k_{2} [E_{tot}] [S]/const’ + [S]
To anticipate the notion when the mechanism of enzyme catalyzed reactions is dealt with, we introduce the symbols k_{2} and K_{M} for the two constants and thus write the rate equation in the form:
R = k_{2} [E_{tot}] [S]/KM + [S]
Although the parameters k_{2} and K_{M} could be determined so that a function corresponding to the experimental more convenient procedure can be found. The initial rate is often obtained by measuring [S] after a time t at which only a small fraction of the substance has been consumed. If [S_{0}] is the initial substrate concentration, we can express the initial rate as [S_{0}] – [S]/t. then becomes:
[S_{0}] – [S] = k_{2} [E_{tot}] [S_{0}]/K_{M} + [S_{0}] × t
The “constants” k2 [E_{tot}] and K_{M} can be evaluated from measurements of the initial rate of reaction. This rate, R_{init}, is approximately [S_{0}] – [S]/t, where [S] is the concentration after a small time interval t.
Values of R_{init} can be obtained for various values of [S0]. A convenient procedure for obtaining the constants is based on the reciprocal of this equation. We write:
1/R_{init} = 1/k_{2} [E_{tot}] + K_{M}/k_{2}[E_{tot}] × 1/[S_{0}]
Thus, if a plot of 1/R_{init} versus 1/S_{0} gives a straight line, the intercept and slope can be used to obtain k_{2} [E_{tot}] and K_{M}/k_{2} [E_{tot}]. From these quantities the value of K_{M} can be calculated. Separation of the factors k_{2} and [E_{tot}] requires studies of systems with various amounts of enzyme.
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