Most Enzymecatalyzed Reactions Involve Two Or More Substrates

While many enzymes have a single substrate, many others have two—and sometimes more than two—substrates and products. The fundamental principles discussed above, while illustrated for single-substrate enzymes, apply also to multisubstrate enzymes. The mathematical expressions used to evaluate multisubstrate reactions are, however, complex. While detailed kinetic analysis of multisubstrate reactions exceeds the scope of this chapter, two-substrate, two-product reactions (termed "Bi-Bi" reactions) are considered below.

Sequential or Single Displacement Reactions

In sequential reactions, both substrates must combine with the enzyme to form a ternary complex before catalysis can proceed (Figure 8—11, top). Sequential reactions are sometimes referred to as single displacement

E EA EAB-EPQ EQ E

E EA EAB-EPQ EQ E

EP QP

EA-FP

FB-EQ

Figure 8-11. Representations of three classes of Bi-Bi reaction mechanisms. Horizontal lines represent the enzyme. Arrows indicate the addition of substrates and departure of products. Top: An ordered Bi-Bi reaction, characteristic of many NAD(P)H-dependent oxidore-ductases. Center: A random Bi-Bi reaction, characteristic of many kinases and some dehydrogenases. Bottom: A ping-pong reaction, characteristic of aminotransferases and serine proteases.

reactions because the group undergoing transfer is usually passed directly, in a single step, from one substrate to the other. Sequential Bi-Bi reactions can be further distinguished based on whether the two substrates add in a random or in a compulsory order. For random-order reactions, either substrate A or substrate B may combine first with the enzyme to form an EA or an EB complex (Figure 8—11, center). For compulsory-order reactions, A must first combine with E before B can combine with the EA complex. One explanation for a compulsory-order mechanism is that the addition of A induces a conformational change in the enzyme that aligns residues which recognize and bind B.

Ping-Pong Reactions

The term "ping-pong" applies to mechanisms in which one or more products are released from the enzyme before all the substrates have been added. Ping-pong reactions involve covalent catalysis and a transient, modified form of the enzyme (Figure 7-4). Ping-pong Bi-Bi reactions are double displacement reactions. The group undergoing transfer is first displaced from substrate A by the enzyme to form product

Increasing [Sal

Increasing [Sal

Figure 8-12. Lineweaver-Burk plot for a two-substrate ping-pong reaction. An increase in concentration of one substrate (S1) while that of the other substrate (S2) is maintained constant changes both the x and y intercepts, but not the slope.

P and a modified form of the enzyme (F). The subsequent group transfer from F to the second substrate B, forming product Q and regenerating E, constitutes the second displacement (Figure 8—11, bottom).

Most Bi-Bi Reactions Conform to Michaelis-Menten Kinetics

Most Bi-Bi reactions conform to a somewhat more complex form of Michaelis-Menten kinetics in which Vmax refers to the reaction rate attained when both substrates are present at saturating levels. Each substrate has its own characteristic Km value which corresponds to the concentration that yields half-maximal velocity when the second substrate is present at saturating levels. As for single-substrate reactions, double-reciprocal plots can be used to determine Vmax and Km. v; is measured as a function of the concentration of one substrate (the variable substrate) while the concentration of the other substrate (the fixed substrate) is maintained constant. If the lines obtained for several fixed-substrate concentrations are plotted on the same graph, it is possible to distinguish between a ping-pong enzyme, which yields parallel lines, and a sequential mechanism, which yields a pattern of intersecting lines (Figure 8-12).

Product inhibition studies are used to complement kinetic analyses and to distinguish between ordered and random Bi-Bi reactions. For example, in a random-order Bi-Bi reaction, each product will be a competitive inhibitor regardless of which substrate is designated the variable substrate. However, for a sequential mechanism (Figure 8-11, bottom), only product Q will give the pattern indicative of competitive inhibition when A is the variable substrate, while only product P will produce this pattern with B as the variable substrate. The other combinations of product inhibitor and variable substrate will produce forms of complex noncompeti-tive inhibition.

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Diabetes 2

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