Henri-Michaelis-Menten equation

Equation (18) is the Henri-Michaelis-Menten equation, which relates the reaction velocity to the maximum velocity, the substrate concentration, and the dissociation constant for the enzyme-substrate complex. Usually substrate is present in much higher molar concentration than enzyme, and the initial period of the reaction is examined so that the free substrate concentration [S] is approximately equal to the total substrate added to the reaction mixture. 

The constant Km defined in equation (23) is called the Michaelis constant and is one of the key parameters in enzyme kinetics. It is a simple matter to proceed from this point to an expression comparable to the Henri-Michaelis-Menten equation (18), but with Km in place of Ks. First, rearranging equation (23) gives... 

Let s assume that the rate constant kcat for the formation of products on either subunit is the same, whether only that site or both catalytic sites are occupied. Suppose also that ES, SE, and SES are in equilibrium with the free enzyme and substrate. By following the same procedure that led to the Henri-Michaelis-Menten equation in chapter 7, we can derive an expression for the rate of the enzymatic reaction in terms of [S], AT], and K2. Here we just give the result. 

Michaelis-Menten equation (also knov/n as the Henri-Michaelis-Menten equation). An equation relating the reaction velocity to the substrate concentration of an enzyme. 

The Michaelis constant, KM, can be obtained from measurements conducted at a constant enzyme concentration and different substrate concentrations. Under conditions in which the substrate concentration [S] is significantly higher than the enzyme concentration and the substrate consumption is below 20%, the initial enzymatic velocity v0 can be approximated by the Henri-Michaelis-Menten equation ... 

Thus, Kn, the Michaelis constant, is a dynamic or pseudo-equilibrium constant expressing the relationship between the actual steady-state concentrations, rather than the equilibrium.concentrations. If Aj, is very small compared to A-i, reduces to K. A steady-state treatment of the more realistic reaction sequence E+ S ES EP E + P yields the same final velocity equation although now Km is a more complex function, composed of the rate constants of all the steps. Thus, the physical significance of K cannot be stated with any certainty in the absence of other data concerning the relative magnitudes of the various rate constants. Nevertheless, represents a valuable constant that relates the velocity of an enzyme-catalyzed reaction to the substrate concentration. Inspection of the Henri-Michaelis-Menten equation shows that Km is equivalent to the substrate concentration that yields half-maximal velocity ... 

Under the usual assay conditions, velocities are measured very early in the reaction before the product concentration has increased to a significant level. For the reaction sequence shown above, we can calculate the initial velocity for the reaction in either direction from the appropriate Henri-Michaelis-Menten equations. 

The Henri-Michaelis-Menten equation describes the curve obtained when initial velocity is plotted versus substrate concentration. The curve shown in Figure 4-7 is a right rectangular hyperbola with limits of and - K . The curvature is fixed regardless of the values of and V mxx- Consequently, the ratio of substrate concentrations for any two fractions of Vj m is constant for all enzymes that obey Henri-Michaelis-Menten kinetics. For example, the ratio of substrate required for 90% of Vmat to the substrate required for... 

Any other set of data should give the same answer if the enzyme obeys the Henri-Michaelis-Menten equation. 

The linear relationship between v and [S] when [S] K can be derived from the Henri-Michaelis-Menten equation. 

This plot is based on the rearrangement of the Henri-Michaelis-Menten equation into a linear y = mx + fr) form ... 

If the Henri-Michaelis-Menten equation is rearranged as described above for the li versus u/[S] plot, we obtain ... 

Calculate Uob over a wide range of substrate concentrations, for example, [S] = 0.1 to [S] = 25. Plot 1/Vob. versus 1/[S], Uobs/[S] versus i/ob., and so on. All the plots are linear if only one enzyme is present. If more than one enzyme is present, the plots will deviate from linearity. Figures 4-16a and b show two of the plots. The Vobi/[S] versus u bi obviously provides the better indication that the data do not conform to a single Henri-Michaelis-Menten equation. (The plot is curved over a wider range of points.) The Vob. versus Wob /[S] and [SJ/Vob, versus [S] plots are also better than the 1/Vom versus l/[6] plot for detecting multiple enzymes that catalyze the same reaction. 

The constant K in the above equation no longer equals the substrate concentration that yields half-maximal velocity (except when n = 1, when the equation reduces to the Henri-Michaelis-Menten equation). 

An equation equivalent to the Michaelis-Menten rate law has been derived earlier by Henri (1902,1903) indeed, Michaelis and Menten in their original publication in 1913 honored the contribution of Henri. Therefore, in appreciation of the work of Henri, it is often also referred to as the Henri-Michaelis-Menten equation. 

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