Velocity vs. substrate concentration

ADH CD 3D HEThDP Mes nh PAC PDC PDCS.c. PDCS.u. PDCZ.w. So.5 ThDP v/S v max wt alcohol dehydrogenase circular dichroism three-dimensional 2-(hydroxyethyl)thiamine diphosphate 4-morpholineethanesulfonsaure Hill-coefficient phenylacetyl carbinol pyruvate decarboxylase PDC from Saccharomyces cerevisiae PDC from Saccharomyces uvarum PDC from Zymomonas mobilis substrate concentration necessary for half-maximal velocity thiamine diphosphate velocity vs substrate concentration maximal velocity wild-type... 

FIGURE 5.21 Yield-velocity vs. substrate concentration for an enzyme-catalyzed reaction. 

The fact that so many transport systems (cf. Figs. 1-3) display the same characteristic form for the dependence of velocity on substrate concentration as do enzyme systems strongly suggests that a formal analysis of transport kinetics along the lines of that of enzyme kinetics might be valuable. The simple Michaelis-Menten or hyperbolic velocity vs. substrate concentration curve for enzymes has traditionally been interpreted as arising from the combination between enzyme and substrate, with the subsequent breakdown of this complex to product and free enzyme. One writes... 

FIGURE 6. Plot of substrate/velocity vs. substrate concentration SI V vs. S) for data from Fig. 8. 

Figure 1. Idealized (A) velocity vs. substrate concentration and (B) double reciprocal plots (Lineweaver-Burk) for enzymes demonstrating (a) hyperbolic (classical Michaelis-Menten) behavior (b) positive cooperativity (c) negative cooperativity.

Plotting the velocity expressed as optical density per minute vs. substrate concentrations in the absence and presence of the three inhibitors yields the results shown in Figure 17.5. 

Figure 22 Examples of enzyme kinetic plots used for determination of Km and Vmax for a normal and an allosteric enzyme Direct plot [(substrate) vs. initial rate of product formation] and various transformations of the direct plot (i.e., Eadie-Hofstee, Lineweaver-Burk, and/or Hill plots) are depicted for an enzyme exhibiting traditional Michaelis-Menten kinetics (coumarin 7-hydroxylation by CYP2A6) and one exhibiting allosteric substrate activation (testosterone 6(3-hydroxylation by CYP3A4/5). The latter exhibits an S-shaped direct plot and a hook -shaped Eadie-Hofstee plot such plots are frequently observed with CYP3A4 substrates. Km and Vmax are Michaelis-Menten kinetic constants for enzymes. K is a constant that incorporates the interaction with the two (or more) binding sites but that is not equal to the substrate concentration that results in half-maximal velocity, and the symbol n (the Hill coefficient) theoretically refers to the number of binding sites. See the sec. III.C.3 for additional details.

Figure 11.34 illustrates how heteroallosteric control of an enzyme affects the shape of a V-vs-[S] curve. Note that shifts toward the R state (activators) increase the velocity for a given substrate concentration. 

Lineweaver-Burk plots provide a good illustration of competitive inhibition and pure noncompetitive inhibition (Fig. 9.18). In competitive inhibition, plots of 1/v vs 1/[S] at a series of inhibitor concentrations intersect on the ordinate. Thus, at infinite substrate concentration, or 1/[S] = 0, there is no effect of the inhibitor. In pure noncompetitive inhibition, the inhibitor decreases the velocity even when [S] has been extrapolated to an infinite concentration. However, if the inhibitor has no effect on the binding of the substrate, the is the same for every concentration of inhibitor, and the lines intersect on the abcissa. 

Figure 15.12 Evolution of the threshold temperature as a function of velocity Vs and solid content.In this experiment, the solid content of the dispersion was adjusted between 0.25% and 1%, whereas the concentration of the solutes in the continuous phase was set to 25% of the original concentration [by appropriate dilution and centrifugation steps). The substrate velocity was varied from 0.5 to 5 nm.s . ...

A commonly used test for competitive inhibition is to plot 1 / v vs 1 / [S] (Eq. 9-61), both in the absence of inhibitor and in the presence of one or more fixed concentrations of I. The result, in each case, is a family of lines of varying slope (Fig. 9-10) that converge on one of the axes at the value 1/Vmax. We see that the maximum velocity is unchanged by the presence of inhibitor. If sufficient substrate is added, the enzyme will be saturated with substrate and the inhibitor cannot bind. The value of Kt can be calculated using Eq. 9-61 from the change in slope caused by addition of inhibitor. 

Rates of substrate hydrolysis (Subheading 3.3.1.) are plotted vs concentration of inhibitors. Typically, the average of the eight control (uninhibited) rates in each fit is used (data from column 12 of a full microtiter plate). The uninhibited velocity is a limiting value, and it is useful to have several values averaged to define it. This value is particularly important when using Eq. 4 in which the uninhibited rate is used to normalize all values (see step 4). 

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