Trisubstrate mechanisms

Three substrates can combine with an enzyme to produce two or three products of reaction, in a wide variety of ways. If aU the binding steps are much faster than the catalytic step, which is the rate-limiting, then aU forms of enzyme are in a rapid equilibrium, and aU kinetic constants are true dissociation constants of respective enzyme-substrate complexes. If the catalytic step is not the slowest step in the kinetic mechanism, aU forms of enzyme attain a steady-state concentration shortly after the mixing of enzyme with substrates. AH kinetic mechanisms of steady-state reactions fall into only two major groups. Those in which all reactants must combine with the enzyme before reaction can take place and any product can be released, are called sequential. Mechanisms in which one or more products are released before aU substrates have added are called Ping Pong (Cleland, 1963). 

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Figure 2. "Hie King-Altmaii patterns for major bisubstrate and trisubstrate mechanisms.

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. 

The general property of all above mechanisms is their adherence to the Michaelis-Menten kinetics. In the absence of products, the double reciprocal plots for aU bisubstrate mechanisms represent a family of straight lines with a common intersection point, if one substrate is varied while the other substrate is held at different fixed concentrations. Similarly, the double reciprocal plots for all trisubstrate mechanisms represent a family of straight lines with a common intersection point, if one substrate is varied while the second substrate is held at different fixed concentrations, and the third substrate is held at a fixed concentration. This, however, is tme only if each substrate adds just once if one of them adds twice in sequential fashion, the reciprocal plots will be parabolic. 

We shall start the analysis of trisubstrate mechanisms by examining the form of the rate equation, proceed with the mechanistic interpretation of the absence of various terms from the general rate equation, and conclude with experimental methods for establishing the presence or absence of such terms. 

Several simple mles can be formulated for sequential trisubstrate mechanisms with the aid of reaction (12.3). 

In this section, we shall reviewthe rate equations forthe majortypes of trisubstrate mechanisms, written in the absence of products (Cleland, 1963 Plowman, 1972 Fromm, 1975,1979). All trisubstrate mechanisms in the rapid equilibrium category are relatively rare and the steady-state mechanisms are more common. However, the derivation of rate equations for rapid equilibrium mechanisms, in the absence of products, is less demanding, as it requires only the rapid equilibrium assumptions and, therefore, the resulting rate equations are relatively simple. 

In Sections 12.2.1 and 12.2.2, we shall divide the rapid equilibrium trisubstrate mechanisms into the following major t)q)es ... 

Although each trisubstrate mechanism has a unique general rate equation, the rate equations in the absence of the products of reaction sometimes have identical forms for several Ter Bi and Ter Ter mechanisms. Therefore, in order to identify unequivocally the mechanism, we must revert to the product inhibition analysis and the use of dead-end inhibitors. 

Therefore, in order to simplify the product analysis of trisubstrate reactions, and for a proper interpretation of product inhibition patterns, we shall need a suitable comparative overview of trisubstrate mechanisms. Table 5 lists the product inhibition patterns for the major Ter Bi and Ter Ter mechanisms. Table 5 shows that, ultimately, each mechanism can be identified unequivocally on the basis of its unique product inhibition patterns. Product inhibition analysis is also able to identify unequivocally each substrate in a given mechanism (Plowman, 1972 Fromm, 1975, 1995). 

In all rapid equilibrium systems, aU Michaehs constants are always true dissociation constants of the complexes that dissociate. In aU trisubstrate mechanisms, aU inhibition constants are also always tme dissociation constants of the corresponding complexes. The temperature dependence of the equilibrium constants can be treated as described in Section 152.1 for a monosubstrate reaction. 

Trisubstrate reactions (Chapter 72). In trisubstrate reactions, initially, one is trying to detect the absence of particular term(s) from the general rate equation for trisubstrate mechanisms by graphical methods, simply by trying the proper combinations of aU three substrates in double reciprocd plots (Section 12.1). When the kinetic mechanism is established in this way, the rate data are fitted to an appropriate rate equation by computer. 

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