Rapid Equilibrium Ordered

This muscle phosphotransferase (EC 2.132) catalyzes the reversible rephosphorylation of ADP to form ATP (/.c., T eq = [ATP][Creatine]/([Creatine phosphate] [ADP]) = 30). In resting muscle, creatine phosphate is synthesized at the expense of abundant stores of ATP intracellular creatine phosphate stores often reach 50-60 mM. If ATP is suddenly depleted by muscle contraction, its product ADP is immediately converted back into ATP by the reverse of the creatine kinase reaction. Depending on the pH at which the enzyme is studied, the kinetic reaction can be either rapid equilibrium random or rapid equilibrium ordered. A-Ethylglycocyamine can also act as a substrate. 

A potential limitation encountered when one seeks to characterize the kinetic binding order of certain rapid equilibrium enzyme-catalyzed reactions containing specific abortive complexes. Frieden pointed out that initial rate kinetics alone were limited in the ability to distinguish a rapid equilibrium random Bi Bi mechanism from a rapid equilibrium ordered Bi Bi mechanism if the ordered mechanism could also form the EB and EP abortive complexes. Isotope exchange at equilibrium experiments would also be ineffective. However, such a dilemma would be a problem only for those rapid equilibrium enzymes having fccat values less than 30-50 sec h For those rapid equilibrium systems in which kcat is small, Frieden s dilemma necessitates the use of procedures other than standard initial rate kinetics. 

A] at different constant concentrations of B, a series of straight lines will be obtained having a common intersection point. The intersection point will always be in the second quadrant. A double-reciprocal plot of 1/v vs. 1/[B] at different constant concentrations of A will consist of a series of straight lines all intersecting on the vertical axis. This observation is characteristic of the rapid equilibrium ordered system but not of the steady-state scheme. 

Unconsumed substrates are treated as substrates or essential activators in deriving rate equations and studying detailed mechanisms. Nonetheless, one must indicate whether an unconsumed substrate (U) remains bound to the enzyme or not (in this case, U also becomes an unaltered product) in the reaction scheme. In practice, unconsumed substrates are likely to be involved in all the typical multisubstrate kinetic mechanisms Only one case is illustrated here, namely that the unconsumed substrate Su activates catalysis when bound in a rapid-equilibrium ordered mechanism ... 

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... 

How do the reciprocal plots for a rapid equilibrium ordered bireactant system differ from those of a steady-state ordered bireactant system ... 

Figure 5.4 Patterns of double reciprocal plots for two substrate reactions, (a) Ping-pong. The double reciprocal plots for one substrate in the presence of fixed concentrations of the other are parallel, no matter which substrate reacts first, (b) Rapid equilibrium random, (c) Rapid equilibrium ordered, first binding substrate only.

The velocity equation has now the same form as that for the total Rapid Equilibrium Ordered Bi Bi mechanism (Eq. (8.12)), except that the constants associated with B and P are the Michaelis constants and the constants associated with A and Q are the dissociation constants. 

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.

In rapid equilibrium systems, the relative concentration of any particular enzyme form is given by a single denominator term in the velocity equation. For example, in the rapid equilibrium ordered bireactant system (Section 8.2), the velocity Eq. (8.2) is... 

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. 

Rapid Equilibrium Ordered system occurs when the substrates A and B combine with the enzyme in an ordered manner, that is, when B can bind only to the EA complex and EB complex is not formed ... 

PRODUCT INHIBITION IN A RAPID EQUILIBRIUM ORDERED BI BI SYSTEM... 

General rate equation. Let us examine the product inhibition in the Rapid Equilibrium Ordered Bi Bi system, in the presence of products P or Q. Both substrates and both products of reaction are binding in an ordered fashion. 

Figure 5. Product inhibition by Q in the Rapid Equilibrium Ordered Bi Bi stem. Graphical presentation of Eq. (8.15), with A as a constant and B as a variable substrate.

In rapid equilibrium systems, the Haldane relationship can be obtained directly from rate equations. In equilibrium, the rate equation for the Rapid Equilibrium Ordered Bi Bi system (Eq. (8.12)), becomes... 

Thus, for the Rapid Equilibrium Ordered Bi Bi system, the Haldane relationship is... 

Rapid Equilibrium Ordered with a dead-end EB complex. Rate constants 6 and kg are absent. 

Reduction of Steady-State Ordered to Rapid Equilibrium Ordered Bi Bi System... 

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... 

The Steady-State Ordered Bi Bi system reduces to a Rapid Equilibrium Ordered system when ks VJEo. In this case, Ka reduces to zero and the other kinetic constants reduce to dissociation constants. Let us write out again the definition of some kinetic constants in the Steady-State Ordered system (Eq. 9.9) ... 

Thus, when the rate constant for the dissociation of A is greater than the maximal velocity in the forward direction (fc2 V,/Ko), the Ka term is eliminated from the denominator of the velocity equation, but the Ka term and other terms remain. Consequently, the velocity equation for the Steady-State Ordered Bi Bi system (Eq. (9.15)) reduces to the velocity equation for the Rapid Equilibrium Ordered Bi Bi system (Eq. (8.2)). 

If the value of is very fast with respect to k B at any concentration of B used, the mechanism approximates rapid equilibrium order addition of A. Under these conditions, the isotope effect will be constant, that is, whatever substrate is varied at any concentration of the fixed substrate. 

Based on isotope effects only, it is not possible to distinguish the Rapid Equilibrium Ordered from the Rapid Equilibrium Random mechanism. However, the first mechanism gives a distinctive initial velocity pattern that intersects on the ordinate with B as the varied substrate. To teU the difference between the Rapid Equilibrium Random and the Steady-State Random mechanism will require other methods, such as the isotope trapping method (Rose et al, 1974), or isotopic exchange. 

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