Haldane relation

The approximate kinetic formats discussed above face inherent difficulties to account for fundamental physicochemical properties of biochemical reactions, such as the Haldane relation discussed in Section III.C.4 a major drawback when aiming to formulate thermodynamically consistent models. 

The starting point is the generic reaction equation (47), already discussed in Section III.C.5. The equation is rewritten using the Haldane relation... 

Applying the Haldane relation to obtain an equilibrium constant from initial rate kinetics. Because of the inherently greater uncertainty in determinations of rate parameters, this method often proves to be unreliable ... 

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 ... 

Rigorous adherence of enzymes to the Haldane relation is well illustrated by the case of wild-type and Glu -to-Asp triose-phosphate isomerases. These enzymes differ only with respect to a single methylene in the side-chain carboxyl group of residue 165. The steady-state parameters for the wild-type enzyme are kcat,forward, 430 s" ... 

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... 

Alberty first proposed the use of Haldane relations to distinguish among the ordered Bi Bi, the ordered Bi Bi Theorell-Chance, and the rapid equilibrium random Bi Bi mechanisms. Nordlie and Fromm used Haldane relationships to rule out certain mechanisms for ribitol dehydrogenase. 

In order to derive a thermodynamic Haldane relation for this mechanism, the true dissociation constants for B (i.e., kjks) and for P (i.e., k lkd) are needed. From the definitions for the various kinetic parameters (See Ordered Bi Bi Mechanism) it is readily seen that... 

Kinetic Haldane relations use a ratio of apparent rate constants in the forward and reverse directions, if the substrate concentrations are very low. For an ordered Bi Bi reaction, the apparent rate constant for the second step is Emax,f/ b (where K, is the Michaelis constant for B) and, in the reverse reaction, V ax,v/Kp. Each of these is multiplied by the reciprocal of the dissociation constant of A and Q, respectively. The forward product is then divided by the reverse product. Hence, the kinetic Haldane relationship for the ordered Bi Bi reaction is Keq = KiO V eJKp)l Kiq V eJKp) = y ,ax.f pKiq/ (yranx,rKmKif). For Completely random mechanisms, thermodynamic and kinetic Haldane relationships are equivalent. 

In ping pong reactions, Haldane relations can also be written for the individual half-reactions. In such cases, Haldane expressions assist in analyzing isotope exchange studies involving these partial reactions. 

Excluded volume effects in cytoplasm, MOLECULAR CROWDING Excluding kinetic reaction mechanisms, HALDANE RELATION EXERGONIC EXOCYTOSIS EXOENZYME EXOERGIC Exo-j8-f ru ctosi d ase,... 

COMPUTER ALGORITHMS SOFTWARE HABER-WEISS REACTION HALDANE RELATION... 

TRIOSE-PHOSPHATE ISOMERASE AFFINITY LABELING HALDANE RELATION ENZYME ENERGETICS (The Case of Proline Racemase)... 

One of the important predictions from Equation (4.10) is the Haldane relation, which states that... 

The equilibrium constant of the overall catalyzed reaction is related to kinetic coefficients for the forward and reverse reactions by the Haldane relation (5,6)... 

The Haldane relation, Eq. (9), common to all the mechanisms considered in Section II,B, is reasonably well satisfied by data for very many dehydrogenases, in some cases over a range of pH, especially when the difficulty of estimating < pq is taken into account. For the Theorell-Chance mechanism there is a second Haldane relation (S), but this derives from the two limiting maximum rate relations which can be tested separately with greater precision. 

This difference in the magnitude of the buffer effect in equilibrium studies versus initial rate studies could be accounted for by at least three possibilities. The first is that under equilibrium and initial rate conditions, BCA exhibits different mechanisms. This is an unattractive hypothesis, and is inconsistent with the well characterized adherence of BCA catalysis to Michaelis-Menten kinetics and to the Haldane relation under initial rate conditions. 

Equations (3.3.27) and (3.3.28) are referred to as the Haldane relations in recognition of the original derivation by Haldane (1930). It can readily be shown that the overall equilibrium constant of a consecutive reaction is the... 

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... 

---