Bisubstrate enzyme mechanisms complexes

Determining balanced conditions for a single substrate enzyme reaction is usually straightforward one simply performs a substrate titration of reaction velocity, as described in Chapter 2, and sets the substrate concentration at the thus determined Ku value. For bisubstrate and more complex reaction mechanism, however, the determination of balanced conditions can be more complicated. 

Fromm and Rudolph have discussed the practical limitations on interpreting product inhibition experiments. The table below illustrates the distinctive kinetic patterns observed with bisubstrate enzymes in the absence or presence of abortive complex formation. It should also be noted that the random mechanisms in this table (and in similar tables in other texts) are usually for rapid equilibrium random mechanism schemes. Steady-state random mechanisms will contain squared terms in the product concentrations in the overall rate expression. The presence of these terms would predict nonhnearity in product inhibition studies. This nonlin-earity might not be obvious under standard initial rate protocols, but products that would be competitive in rapid equilibrium systems might appear to be noncompetitive in steady-state random schemes , depending on the relative magnitude of those squared terms. See Abortive Complex... 

In the literature, literally dozens of kinetic mechanisms have been proposed for bisubstrate enzymes (Alberty, 1958 Alberty Hammes, 1958 Teller Alberty, 1959 Wong Hanes, 1962 Fromm, 1967 Dalziel, 1969 Hurst, 1969 Rudolph Fromm, 1969, 1971, 1973). However, only those pathways that are either weU documented, or seem to be a logical extension of established mechanisms, will be presented in this and the following chapters. Thus, we shall divide the rapid equilibrium bisubstrate reactions into the following major types, according to the type and number of enzyme-substrate or enzyme-product complexes that can form (Alberty, 1953 Cleland, 1970, 1977 Fromm, 1979 Engel, 1996 Purich Allison, 2000) ... 

Why product inhibition occurs. The products of reaction are formed at the active site of enzyme and are the substrates for the reverse reaction. Consequently, a product may act as an inhibitor by occupying the same site as the substrate from which it is derived. In the Rapid Equilibrium Random bisubstrate mechanism, most ligand dissociations are very rapid compared to the interconversion of EAB and EPQ. Thus, the levels of EP and EQ are essmtiaUy zero in the absence of added P and Q. In the presence of only one of the products, the reverse reaction can be neglected, as the concentration of the other product is essentially zero during the early part of the reaction. Nevertheless, the forward reaction will be inhibited because finite P (or Q) ties up some of the enzyme. The type of this product inhibition depends on the number and type of enzyme-product complexes that can form. Consequently, product inhibition studies can be very valuable in the diagnostics of kinetic mechanisms (Rudolph, 1979). 

Many other multisubstrate examples abound in metabolism. In effect, these situations are managed by realizing that the interaction of the enzyme with its many substrates can be treated as a series of uni- or bisubstrate steps in a multi-step reaction pathway. Thus, the complex mechanism of a multisubstrate reaction is resolved into a sequence of steps, each of which obeys the single- and double-displacement patterns just discussed. 

In this chapter we described the thermodynamics of enzyme-inhibitor interactions and defined three potential modes of reversible binding of inhibitors to enzyme molecules. Competitive inhibitors bind to the free enzyme form in direct competition with substrate molecules. Noncompetitive inhibitors bind to both the free enzyme and to the ES complex or subsequent enzyme forms that are populated during catalysis. Uncompetitive inhibitors bind exclusively to the ES complex or to subsequent enzyme forms. We saw that one can distinguish among these inhibition modes by their effects on the apparent values of the steady state kinetic parameters Umax, Km, and VmdX/KM. We further saw that for bisubstrate reactions, the inhibition modality depends on the reaction mechanism used by the enzyme. Finally, we described how one may use the dissociation constant for inhibition (Kh o.K or both) to best evaluate the relative affinity of different inhibitors for ones target enzyme, and thus drive compound optimization through medicinal chemistry efforts. 

FIGURE 6-13 Common mechanisms for enzyme-catalyzed bisubstrate reactions, (a) The enzyme and both substrates come together to form a ternary complex. In ordered binding, substrate 1 must bind before substrate 2 can bind productively. In random binding, the substrates can bind in either order. 

In the sequential mechanism, all substrates must bind to the enzyme before any product is released. Consequently, in a bisubstrate reaction, a ternary complex of the enzyme and both substrates forms. Sequential mechanisms are of two... 

While developed as possible therapeutics, bisubstrate analogs have found great utility in the dissection and characterization of enzyme structure and mechanism. As discussed below, bisubstrate analogs have been used extensively in structural studies, where the use of natural substrates would result in catalysis, to investigate the architecture of the active site at the Michaelis complex, and to define structural changes at the active site produced by allosteric effectors. In some cases, bisubstrate analogs that are formed during the reaction (a type of mechanism-based inhibitor) can help to support or eliminate proposed chemical mechanisms. 

There are two possible bisubstrate systems that combine the enzyme feature of the Ping Pong sequence with the hit-and-mn feature of the Theorell-Chance mechanism. These are in fact the hmiting cases of the common Ping Pong Bi Bi system, in which one of two central complexes has extremely short life. The reaction sequences are shown below ... 

Distribution equations for bisubstrate reactions in the steady state are often very complex expressions (Chapter 9). However, in the chemical equilibrium, the distribution equations for all enzyme forms are usually less complex. Consider an Ordered Bi Bi mechanism in reaction (16.12) with a single central complex ... 

It is important to note that commitment factors may depend on the level of other reactants present, and this variation can be used to determine the kinetic mechanism. For an ordered bisubstrate mechanism, the commitment of B (the second substrate to add) is independent of A (the first substrate to add), and depends only on how fast B is released from the enzyme relative to the forward rate constant for the bond-breaking step. Conversely, the commitment for A varies from infinity at saturating B to the value for B at near zero B, and thus the actual rate constant for release of A from the EA complex does not affect the commitment of B, even if it is quite small. 

An experimental protocol in Fig. 8 is shown for an ordered bisubstrate mechanism. A small volume of enzyme is incubated with sufficient labeled substrate. A, to convert most or all of the enzyme into a binary complex, EA. This solution is then diluted into a large volume containing the unlabeled substrate. A, plus variable amounts of cosubstrate, B. After several seconds, add is added to stop the enzymatic reaction, and labeled product, Q, is determined analytically. A blank is then run with the labeled reactant already diluted in the large solution, plus only the enzyme present in the small volume. The experiment is then repeated at different levels of the second substrate B, and a reciprocal plot is made of the amount of labeled product, Q, as a function of the reciprocal of the substrate B concentration thus, by extrapolation, the maximum amount of labeled product formed, Q a. is obtained. 

---