Enzyme Kinetics as an Approach to Understanding Mechanism:- Substrate Concentration Affects the Rate of Enzyme-Catalyzed Reactions

A key factor affecting the rate of a reaction catalyzed by an enzyme is the concentration of substrate, [S]. However, studying the effects of substrate concentration is complicated by the fact that [S] changes during the course of an in vitro reaction as substrate is con verted to product. One simplifying approach in kinetics experiments is to measure the initial rate (or initial velocity), designated V₀, when [S] is much greater than the concentration of enzyme, [E]. In a typical reaction, the enzyme may be present in nanomolar quantities, whereas [S] may be five or six orders of magnitude higher. If only the beginning of the reaction is monitored (often the first 60 seconds or less), changes in [S] can be limited to a few percent, and [S] can be regarded as constant. V0can then be explored as a function of [S], which is adjusted by the investigator. The effect on V0 of varying [S] when the enzyme concentration is held constant is shown in Figure 6–11. At relatively low concentrations of substrate, V₀ increases almost linearly its substrate to form an enzyme-substrate complex in a relatively fast reversible step:

The ES complex then breaks down in a slower second step to yield the free enzyme and the reaction product P:

Because the slower second reaction (Eqn 6–8) must limit the rate of the overall reaction, the overall rate must be proportional to the concentration of the species that reacts in the second step, that is, ES. At any given instant in an enzyme-catalyzed reaction, the enzyme exists in two forms, the free or un combined form E and the combined form ES. At low [S], most of the enzyme is in the uncombined form E. Here, the rate is proportional to [S] because the equilibrium of Equation 6–7 is pushed toward formation of more ES as [S] increases. The maximum initial rate of the cat, alyzed reaction (Vmax) is observed when virtually all the enzyme is present as the ES complex and [E] is vanishingly small. Under these conditions, the enzyme is “saturated” with its substrate, so that further increases in [S] have no effect on rate. This condition exists when [S] is sufficiently high that essentially all the free en zyme has been converted to the ES form. After the ES complex breaks down to yield the product P, the en zyme is free to catalyze reaction of another molecule of substrate. The saturation effect is a distinguishing characteristic of enzymatic catalysts and is responsible for the plateau observed in Figure 6–11. The pattern seen in Figure 6–11 is sometimes referred to as saturation kinetics.

When the enzyme is first mixed with a large excess of substrate, there is an initial period, the pre–steady state, during which the concentration of ES builds up. This period is usually too short to be easily observed, lasting just microseconds. The reaction quickly achieves a steady state in which [ES] (and the concentrations of any other intermediates) remains approximately con stant over time. The concept of a steady state was introduced by G. E. Briggs and Haldane in 1925. The measured V0 generally reflects the steady state, even though V0 is limited to the early part of the reaction, and analysis of these initial rates is referred to as steady-state kinetics.

FIGURE 6–11 Effect of substrate concentration on the initial velocity of an enzyme-catalyzed reaction. V_max is extrapolated from the plot, because V₀ approaches but never quite reaches V_max. The substrate concentration at which V₀ is half maximal is K_m, the Michaelis constant. The concentration of enzyme in an experiment such as this is generally so low that [S]>>[E] even when [S] is described as low or relatively low. The units shown are typical for enzyme-catalyzed reactions and are given only to help illustrate the meaning of V0 and [S]. (Note that the curve describes part of a rectangular hyperbola, with one asymptote at Vmax. If the curve were continued below [S]= 0, it would approach a vertical asymptote at [S]=- Km.)

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