Initial velocity patterns

A number of initial velocity studies have been made with yeast hexokinase. All results to date indicate an intersecting initial velocity pattern in... 

Initial velocity patterns obtained for the reduction of NAD by dihy-droplipoamide give a series of parallel lines (reciprocal plots). The K ... 

A third study of the kinetics of lipoamide dehydrogenase has utilized the enzyme isolated from rat liver (95). At 25°, the temperature of the two previous studies, when dihydrolipoamide was varied at fixed levels of NAD, the double reciprocal plots were concave down. At 37° this behavior was not observed. The detailed studies were carried out at the higher temperature. Rates were measured in both directions at pH 8.0, the pH optimum for the reduction of NAD. Under these conditions, initial velocity patterns for the forward and reverse reactions were a series of parallel lines. The Km for NAD was 0.52 mM, for dihydrolipoamide was 0.49 mAf, for NADH was 0.062 mM, and for lipoamide was... 

Enzyme kinetics is an important tool for assaying enzyme activities and for determining enzyme mechanisms. Although other techniques can provide useful information on enzyme mechanisms, the kinetics has to be the ultimate arbiter because it looks at the reaction while it is taking place. Initial velocity patterns, inhibition patterns, patterns of isotopic exchange, pH profiles, and isotope effects are all kinetic tools that allow one to determine kinetic mechanisms, chemical mechanisms, and transition state structures. 

The approach outlined above is sufficient when there is only one substrate or in an assay where one varies only the concentration of one substrate. However, where two or more substrates exist and one wants to know the order of their combination with the enzyme, one needs to determine an initial velocity pattern. One varies the concentrations of one substrate at several different levels of a second substrate and determines the initial velocities for the different reaction mixtures. It is, of course, necessary to have the same enzyme level in each reaction or correct the rates to constant enzyme concentration. 

Three initial velocity patterns are commonly observed. When both substrates have to add to the enzyme before any products... 

Equation 6 describes an intersecting initial velocity pattern where 1/v is plotted versus 1/A at different values of B, whereas Equation 6 describes the pattern where 1/v is plotted versus 1/B at different values of A (Fig. 1). Both the slopes and the intercepts of the reciprocal plots are functions of the other substrate concentration, and replots of slopes or intercepts versus the reciprocal of the other substrate concentration allow determination of all kinetic constants. 

Figure 1 Reciprocal plots with A varied at different levels of B (intersecting initial velocity pattern) or different levels of I (noncompetitive inhibition pattern).

The constant term is missing, which leads to a parallel initial velocity pattern (Fig. 2) regardless of which substrate concentration is varied ... 

The third type of initial velocity pattern results from a mechanism in which 1) the substrates add in obligatory order and 2) the off-rate constant for the first substrate to bind exceeds the turnover number (V/Et or kcat) sufficiently that its binding is at equilibrium, which is called an equilibrium ordered initial velocity pattern (Fig. 3). The rate equation is... 

The determination of kinetic mechanisms requires more than just initial velocity patterns, and inhibition studies are usually required. Several types of inhibitors are useful. The products are substrates in the reverse reaction and thus have some affinity for the enzyme and will give inhibition unless their inhibition constants exceed their solubility. Dead-end inhibitors are molecules that play musical chairs with the substrates for open portions of the active site but do not react. Substrates may act as dead-end inhibitors by combining at points in the mechanism where they are not intended and thus cause substrate inhibition. The inhibition patterns caused by these inhibitors are useful in distinguishing between different kinetic mechanisms. 

The compulsory ordered mechanism arrived at through isotopic exchange rates is basically in agreement with mechanisms postulated on the basis of initial velocity studies. Heyde and Ainsworth showed that for beef heart m-MDH the initial velocity pattern in the absence of products and the product inhibition pattern are consistent with an ordered mechanism (77). Raval and Wolfe obtained similar results with pig heart m-MDH data obtained by initial velocity studies in both directions are in agreement with a compulsory ordered mechanism (78,79). Substrate inhibition by oxaloacetate also occurs with pig heart m-MDH (80). Similar initial velocity studies on beef heart s-MDH did... 

The initial velocity patterns for two-substrate cases were dealt with in Volume... 

Not many terreactant mechanisms have had full initial velocity patterns determined, but because of the many possible mechanisms that can be distinguished, this type of kinetic study gives much information, and should be more widely used. In particular, the altered patterns when a slow alternate substrate (or altered mutant enzyme) are used can give much information on the kinetic mechanism. 

This may change the initial velocity pattern, as in the case of fructose-6-sulfate, which is a slow substrate for phosphofructokinase. This substrate has lost sufficient affinity for the enzyme that it binds only when MgATP is present, and thus the mechanism changes from a random one with both substrates sticky with fructose 6-phosphate (fructose-6-P) to an equilibrium ordered one with MgATP adding first (19). Slow alternate substrates give cleaner and more easily interpreted pH profiles, and isotope effects are often (but not always) more fully expressed (see Sections VII,A and VII,B below). 

Because the denominator is factored, this equation is particularly easy to fit, and this is one of the better ways to get accurate dissociation constants, especially if the substrates are at all sticky so that correct values are not obtained from initial velocity patterns. Equation (61) becomes... 

Table 1. Types of initial velocity patterns in the primaiy double reciprocal graphs in rapid equUtbrium systems in the absence of products...

We shall distinguish three types of initial velocity patterns ... 

Thus, the initial velocity pattern will be intersecting regardless of whether A and B, A and C, or B and C are the variable and changing fixed substrates. In each case, the third substrate would be held at constant concentration for the entire pattern. If substrate B is truly saturating, however, the reversible sequence is broken and the A-C initial velocity pattern becomes a parallel one. In practice, the slope effect becomes smaller and smaller as fi is raised, but unless B is raised to over 100 times the Michaelis constant, a parallel pattern will not be seen. The A-B and B-C initial velocity patterns will always be intersecting, regardless of the level of the other substrate. Tfie same pattern seen for the ordered mechanism is seen for one where A and B have to be added in that order, but C can be added randomly. Such mechanisms are known (Viola Cleland, 1982). 

While an ordered trisubstrate mechanism shows a parallel initial velocity pattern when substrate B is saturating, a completely random mechanism shows intersecting patterns at all times. If one substrate must be added first, but the other two can be added randomly (Section 123), parallel initial velocity pattern wiU be obtained when either B or C is saturating. This is easily understood if one remembers that the saturation with B leads to addition in order A, B, and C, while saturation with C causes the order to be A, C, and B, that is, saturation at the branch point diverts aU reaction flux through one path or the other. 

Note that the case (5) is a subcase of (4). Cases (4)-(6) cannot be distinguished easily, because in each case the initial velocity patterns will be intersecting and look very much like the ordered mechanism. Only the equilibrium ordered mechanism will give different initial velocity patterns. 

In the absence of products, aU initial velocity patterns are parallel, in the same way as in the Ping Pong Bi Bi mechanism. However, the product inhibition patterns are different, and may serve to distinguish between the different systems (Table 6). 

When there are three substrates for an enzymatic reaction, the number of possible initial velocity patterns is large, and interpretation of the patterns is not as straightforward as when only two substrates are involved. 

This means a Ping Pong type of mechanism. AU Ping Pong types of mechanisms lack the constant term, as is evident from Tables 3 and 4 in addition to the constant term, the A and B terms are also missing. The Hexa Uni Ping Pong mechanism lacks not only the constant, but also the A, B, and C terms, and aU initial velocity patterns (A-B, B-C, andA-C)are paraUel. 

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