Copyright © 2000-2010 Mark Brandt, Ph.D. 79Inhibition kinetics Structure-based enzyme mechanism studies are extremely useful for understanding the mechanism used by an inhibitor. However, for many proteins, structural information is not available. In addition, even if structural information is available for the enzyme, information may not be available for the inhibitor/enzyme complex. Finally, enzyme-inhibitor binding affinity is very difficult to measure using the structural information alone. In many cases, therefore, full understanding of the inhibition of a given enzyme requires performing kinetic analyses of the system. Kinetic studies will yield information regarding the mechanism; however, kinetics cannot prove a given mechanism. Kinetic studies can only either refute the proposed mechanism, or provide supporting evidence for it. Competitive inhibition In one common type of inhibition, the inhibitor acts as though it competes with the substrate for binding to the enzyme. This is called competitive inhibition: kinetically, the enzyme behaves as though the binding of the substrate and inhibitor are mutually exclusive. This adds an additional term to the reaction scheme that we have already discussed (shown below). Note that the Ki (the equilibrium dissociation constant for the inhibitor) is an equilibrium constant (i.e. a ratio of rate constants). The Ki can be expressed as a function of the inhibitor concentration, free enzyme concentration, and enzyme-inhibitor complex concentration as shown in the equation below: E + S ES E + P+EIaIKi Kia=[E][I][EI] This reaction scheme requires the addition of a new term to the possible states of the enzyme: [E]total = [E]free + [ES] + [EI] Taking the additional term in the reaction into account results in a modification to the Michaelis-Menten equation: v =Vmax[S]Km1 +[I]Kia       + [S]Copyright © 2000-2010 Mark Brandt, Ph.D. 80This additional term also appears in the slope of the Lineweaver-Burk equation: 1v= 1 +[I]Kia       KmVmax1[S]+1Vmax y = m x + b The usual method of determining the Ki is to perform Km determinations at several different inhibitor concentrations. (Look at the equation. What do you expect to happen to the apparent Km and Vmax as the result of a competitive inhibitor?) In competitive inhibition, the apparent Km increases as a result of the inhibitor. The effect of the inhibitor is to raise the concentration of substrate required for a given velocity. In contrast, the apparent Vmax is unaffected by a competitive inhibitor. This is because once substrate binds, the reaction proceeds normally, and therefore Vmax depends only on the maximum possible ES complex concentration (and on the kcat, but kcat is unaffected by a competitive inhibitor), and the maximum ES concentration depends only on the total amount of enzyme present. Each line in the Lineweaver-Burk plot corresponds to a set of data obtained at a single inhibitor concentration. The fact that the Vmax does not change is immediately obvious, because the lines all intersect at the same point on the y-axis. !!!"#$"%$&'&()")"#$$%*+,-./0*1&"%$!2"#% Note that, in competitive inhibition the true values of the Km and Vmax do not change. The enzyme either binds the inhibitor, and does nothing, or binds the substrate and behaves normally. The measured values of Km in the presence of the inhibitor are altered, and are called the apparent Km. The apparent Km varies depending on the inhibitor concentration involved.Copyright © 2000-2010 Mark Brandt, Ph.D. 81Mixed Inhibition The other major type of inhibition occurs when the inhibitor is capable of binding to both the free enzyme and to the enzyme-substrate complex. This adds an additional term to the reaction scheme. Note that the dissociation constant for binding the free enzyme may differ from the dissociation constant for binding the ES complex. E + S ES E + P++EI ESIabIIKiKi + S Kia=[E][I][EI] Kib=[ES][I][ESI] The result of the inhibitor binding is a somewhat different alteration to the Michaelis-Menten equation. v =Vmax[S]Km1 +[I]Kia       + [S] 1 +[I]Kib       This results in an altered Lineweaver-Burk equation. 1v= 1 +[I]Kia       KmVmax1[S]+1 +[I]Kib       Vmax y = m x + b !!!"#$"%$&'&()")"#$$%*+,-./0*1&"%$!2"#%!2"#%#$$Copyright © 2000-2010 Mark Brandt, Ph.D. 82In the case of mixed inhibition, the apparent Vmax changes, because the inhibitor is capable of preventing catalysis regardless of whether the substrate is bound to the enzyme. With mixed inhibitors, the change in apparent Km varies, depending on the relative values of Kia (the Ki for binding to the free enzyme) and Kib (the Ki for binding to the ES complex). Note that, depending on the relative values of the Ki, the apparent Km may decrease. In the special case where the two Ki values are the same, the apparent Km will be unchanged. This special case is called non-competitive inhibition. In non-competitive inhibition, all of the lines of a Lineweaver-Burk plot intersect at the same point on the x-axis. Uncompetitive Inhibition One more special case for inhibitor kinetics is occasionally observed, primarily with multisubstrate enzymes. This final type of inhibition, which is really another special case for mixed inhibition, occurs when the inhibitor only binds to the ES complex. For this type of inhibition, the altered Michaelis-Menten and Lineweaver-Burk equations are: v =Vmax[S]Km+ [S] 1 +[I]Kib       1v=KmVmax1[S]+1 +[I]Kib       Vmax y = m x + b Uncompetitive inhibition results in parallel lines on a Lineweaver-Burk plot: !!!"#$%*+,-./0*1&"%$!2"#%)")"#$$!2"#%#$$"%$&'&(Copyright © 2000-2010 Mark Brandt, Ph.D. 83Summary The binding of molecules to enzymes may alter the activity of the enzyme. If this alteration is a decrease in activity, the compound is called an inhibitor. Inhibitors that bind only the free enzyme are called competitive