Enzyme reactions Haldane relations

A mathematical equation indicating how the equilibrium constant of an enzyme-catalyzed reaction (or half-reaction in the case of so-called ping pong reaction mechanisms) is related to the various kinetic parameters for the reaction mechanism. In the Briggs-Haldane steady-state treatment of a Uni Uni reaction mechanism, the Haldane relation can be written as follows ... 

Fromm and Cleland provide valuable discussions of the utility of Haldane relations in excluding certain kinetic reaction mechanisms based on a numerical evaluation of the constants on each side of the equal sign in the Haldane relation. If the equality is maintained, the candidate mechanism is consistent with the observed rate parameter data. Obviously, one must be concerned about the quality of experimentally derived estimates of rate parameters, because chemists have frequently observed that thermodynamic data (such as equilibrium constants) are often more accurate and precise than kinetically derived parameters. See Haldane Relations for Multisubstrate Enzymes... 

This is exactly what the Haldane relations demonstrate for the sequence of intermediates in enzyme reactions. They are useful criteria when changing Michaelis parameters are compared to the equilibrium constant for an enzyme catalysed reaction. We shall return to this problem in section 5.1, when we discuss how transient kinetic analysis can be used to determine the equilibrium constants of individual steps. In this connection the equations which express the concentrations of the intermediates in terms of the fraction of total amount of enzyme in the reaction mixture will turn out to be useful. Many enzyme reactions can be studied in both directions and the two sets of parameters for the reactions starting on either side (with S or P as the substrate) - Kh, and - give further insight. 

In chapter S the phenomenon of on enzyme equilibria is discussed with examples. This refers to the fact that the equilibrium between enzyme-substrate and enzyme-product complexes is often near unity, even if the overall equilibrium constant for the interconversion of free substrate to free product is a large number. This does not contradict the statement that enzymes (or catalysts in general) do not affect equilibrium constants of reactions. It has to be remembered that this definition of catalysis only applies to the equilibrium between free substrates and products. An example, which illustrates this in terms of the Haldane relation, is heart lactate dehydrogenase. By the methods discussed in section 5.1 it was shown that the equilibrium constant for the two complexes... 

If we consider the back reaction Fj Fq + P. where k4 is not zero in the reactions of the enzyme-substrate system, modify the Michaelis-Menten kinetics. Show that when equilibrium is established, after a very long time, equilibrium concentrations of substrate and product are related by the following Haldane s relation... 

A model for enzyme kinetics that has found wide applicability was proposed by Michaelis and Menten in 1913 and later modified by Briggs and Haldane. The Michaelis-Menten equation relates the initial rate of an enzyme-catalyzed reaction to the substrate concentration and to a ratio of rate constants. This equation is a rate equation,... 

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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