Rapid Equilibrium Ordered bisubstrate

As a mle, an uncompetitive inhibition occurs only if there are more than one substrate or product (Huang, 1990). For example, an uncompetitive inhibition will take place in a Rapid Equilibrium Order bisubstrate reaction, when an inhibitor competes with B while A is the variable substrate. Thus, the equilibria shown below describe an ordered bisubstrate system in which an inhibitor competes with B but does not bind to free enzyme. 

Figure 3. Uncompetitive inhibition. Rapid Equilibrium Ordered bisubstrate s em with an inhibitor uncompetitive with A. Graphical presentation of Eq. (5-i7) B as a constant and A as a variable substrate.

Dead-end Inhibition in a Rapid Equilibrium Ordered Bisubstrate System... 

In Section 5.4, a case of a dead-end inhibition in a Rapid Equilibrium Ordered bisubstrate system was described. One can compare this system with the following example. 

This rate equation is identical to that for a rapid equilibrium ordered addition bisubstrate mechanism (/.c., a scheme where substrate A rapidly binds prior to the addition of the second substrate B). Huang has presented the theoretical basis for mechanisms giving rise to... 

The Rapid Equilibrium Ordered Bi Bi system (Section 8.2) is a limiting case of the more realistic Steady-State Ordered Bi Bi system (Section 9.2). In bisubstrate mechanisms, the two approaches yield different velocity equations. As described... 

However, the primary double reciprocal plots of some rapid equilibrium systems are identical. In rapid equilibrium systems, in the presence of the products of reaction, the primary reciprocal plots are very characteristic and depend on the number and type of enzyme-substrate and enzyme-product complexes that can form. Therefore, in order to distinguish between different t5q>es, one must revert to product inhibition patterns that can easily distinguish between aU types of rapid equilibrium bisubstrate systems (Plowman, 1972 Segel, 1975) (Table 2). 

This example clearly shows that completely randomized steady-state bisubstrate reactions wiU produce extremely complex rate equations which are, in most cases, unmanageable and almost useless for practical purposes. Thus, for example, the rate equation for an Ordered Bi Bi mechanism has 12 terms in the denominator (compare Eq. (9.8)). A completely Random Bi Bi mechanism yields an even more comphcated rate equation with 37 new terms in the denominator. Eor this reason, and in such cases, we shah usuahy revert to simplifying assumptions, usually introducing the rapid equilibrium segments in the mechanism in order to reduce the rate equations to manageable forms. 

The intersecting pattern for an Ordered bisubstrate mechanism in Fig. 1 (left) will also be obtained with a Rapid Equilibrium bisubstrate mechanism in each case, an intersecting point may be above, below, or on the axis. 

In an ordered bisubstrate mechanism one must vary the second substrate, B, and determine V/JSTb, regardless of whether the label is in A or B, since ly AwiU not show an isotope effect. For a random mechanism one must vary both A and B, since one may see different isotope effects on VfK and V/Aa, a distinction that may help to characterize the mechanism. The effects onV/K and V/Aa shouldbe different when one or both substrates are sticky, that is, dissociate more slowly from the enzyme than they react to give products. The substrate with the lower V7A is the sticky one. Larger effects on Vthan on either V7A show that both substrates are sticky smaller ones show that a slow step follows release of the first product. A rapid equilibrium random mechanism will show equal isotope effects on V, V/Ab, and F/Aa, aU larger than unity. 

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