Haldane relationships systems

As in any other chemical reaction, there is a relationship between the rate constants for forward and reverse enzyme-catalyzed reactions and the equilibrium constant. This relationship, first derived by the British kineticist J. B. S. Haldane and proposed in his book Enzymes41 in 1930, is known as the Haldane relationship. It is obtained by setting v( = vr for the condition that product and substrate concentrations are those at equilibrium. For a single substrate-single product system it is given by Eq. 9-42. 

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... 

The Haldane relationship is identical for all rapid equilibrium random systems (Haldane, 1930 Cleland, 1982). Thus, from Eq. (8.37), one also obtains... 

The general rate equations for the steady-state sequential mechanisms, in the presence of products, are developed in the following sections. The rate equations in the absence of products can be written down directly from the general rate equations, simply by omitting the terms in the denominator and the numerator that contain the concentration terms for products P, Q, and R, and eliminating the JKeq with the aid of Haldane relationships. In all trisubstrate systems, the inhibition constants will always represent tme dissociation constants. 

In the treatments discussed so far, it has been assumed that the back reaction could be neglected. The reactions catalysed by many enzymes are essentially irreversible or the products are immediately subject to further reaction, so that the assumption of irreversibility is valid. However, if the reaction is reversible, the Michaelis equation must be modified. Haldane suggested a notation in which V, and V, are the maximal velocities in the forward and reverse directions, and and K ,p are the Michaelis constants for the substrate and product. The Haldane relationship for a system with a single substrate and single product is then = V,K pA, K s. 

The Haldane Relationship. Another of the properties of enzyme systems frequently measured is the equilibrium constant of the over-all reaction. This is the means for determining a fundamental thermodynamic property, the free enei (F) of a reaction. Free energy will be discussed later. At this point a relation between enz3uue kinetics and equilibrium is of interest. The equilibrium constant for a reaction... 

There can be many reasons why a reaction does not proceed to equilibrium. The standard free energy, then, does not define the amount of work that will be obtained from a reaction it is the maximum energy available under defined conditions. When the standard free energy is known, it can be used to determine the equilibrium constant of a reaction. This, it must be remembered, measures the extent to which a reaction may proceed, but it does not indicate the speed of a reaction or even that a reaction will occur at all. AF is related indirectly to the relative rates of enzyme-catalyzed reactions by the Haldane relationship (p. 12), but the absolute rate of reaction is determined by the amount of enzyme and substrate in a given system. 

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See also in sourсe #XX -- [ ]

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