Haldane-relationship

These relationships are identical to Haldane relationships, but unlike the latter, their validity does not derive from a proposed reaction scheme, but merely from the observed hyperbolic dependence of transport rates upon substrate concentration. Krupka showed that these relationships were not obeyed by the set of data previously used by Lieb [64] to reject the simple asymmetric carrier model for glucose transport. Such data therefore cannot be used either to confirm or refute the model. 

For reversible enzymatic reactions, the Haldane relationship relates the equilibrium constant KeqsNith the kinetic parameters of a reaction. The equilibrium constant Keq for the reversible Michaelis Menten scheme shown above is given as... 

The importance of the Haldane relationship Eq. (42) relates to the fact that the kinetic parameters of a reversible enzymatic reaction are not independent but are constraint by the equilibrium constant of the overall reaction [157]. 

The use of Haldane relationships to verify the magnitude of the equilibrium constant or, conversely, to determine (or verify) one of the kinetic parameters requires that aU constants be measured under the same experimental conditions (eg., temperature, pH, buffer species, ionic strength, free metal ion concentrations, etc) If not, the Haldane relationship has no meaning. In addition, kinetic data are often limited in precision, unlike equilibrium measurements. For multisubstrate reactions, there are at least two different Haldane relationships. Thus,... 

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. 

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. 

Haldane relationships can also be useful in characterizing isozymes or the same enzyme isolated from a different source. Reactions catalyzed by isozymes must have identical equilibrium constants, but the magnitudes of their kinetic parameters are usually different (e.g., the case of yeast and mammalian brain hexokinase ). Note that the Haldane relationship for the ordered Bi Bi mechanism is = Hmax,f p i iq/(f max.r ia b)- This same... 

Haldane is also valid for the ordered Bi Bi Theorell-Chance mechanism and the rapid equilibrium random Bi Bi mechanism. The reverse reaction of the yeast enzyme is easily studied an observation not true for the brain enzyme, even though both enzymes catalyze the exact same reaction. A crucial difference between the two enzymes is the dissociation constant (i iq) for Q (in this case, glucose 6-phosphate). For the yeast enzyme, this value is about 5 mM whereas for the brain enzyme the value is 1 tM. Hence, in order for Keq to remain constant (and assuming Kp, and are all approximately the same for both enzymes) the Hmax,f/f max,r ratio for the brain enzyme must be considerably larger than the corresponding ratio for the yeast enzyme. In fact, the differences between the two ratios is more than a thousandfold. Hence, the Haldane relationship helps to explain how one enzyme appears to be more kmeticaUy reversible than another catalyzing the same reaction. 

Haldane relationships based on the ratio of apparent rate constants for both the forward and reverse directions. Every enzyme mechanism has at least one kinetic Haldane relationship. For a Uni Uni mechanism the kinetic Haldane relationship is K q = (Vn. rlK, a)I (Umax,r/ m,p)- 66 Haldane Relationships Thermodynamic Haldane Relationships W. W. Cleland (1982) Meth. Enzymol. 87, 366. 

In Scheme 1, the rate parameters Vmax,f and Emax,r are the maximum velocities in the forward and reverse direction, respectively (such that Emax,f = [Etotai] and Emax,r = ki [Etotai]), a is the Michaelis constant for substrate A (Xa = (/c2 + ksykb), and Xeq is the equihbrium constant (equal to kikslk2k, and having the Haldane relationships... 

MICROTUBULE ASSEMBLY KINETICS KINETIC ELECTROLYTE EFFECT IONIC STRENGTH KINETIC EQUIVALENCE KINETIC AMBIGUITY KINETIC HALDANE RELATIONSHIPS HALDANE RELATIONSHIPS... 

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. 

For the bimolecular reaction that we have considered, there are two Haldane relationships ... 

Cleland, W. W. An analysis of Haldane relationships. Methods Enzymol 1982, 87 366-369. 

HALDANE RELATIONSHIP BETWEEN KINETIC CONSTANTS AND EQUILIBRIUM CONSTANT... 

Haldane relationships are relationships between the equilibrium constant and the various kinetic constants defined for a given mechanism. They exist because we define for each mechanism more kinetic parameters than there are independently determinable parameters. They are of two types, kinetic and thermodynamic, and every mechanism has at least one of each. Thermodynamic Haldanes consist of the cross product of reciprocal dissociation constants for the substrates and dissociation constants for the products (i.e., the product of equilibrium constants for each step in the mechanism). For mechanisms with at least three substrates, the Cleland notation defines dissociation constants as K, values (i.e., /fia, ib, K c, etc.), but for Ordered Uni Bi and Bi Bi mechanisms, Cleland defined the dissociation constants of the inner substrates differently (4). The dissociation constants for A and Q were and /(jq, but that for B was... 

The kinetic Haldane is the ratio of the apparent rate constants in forward and reverse directions when reactant concentrations are very low. With only one substrate, the apparent rate constant is the VIK value, but with more than one substrate the VIK value for the last substrate to add is multiplied by the reciprocal dissociation constants of all substrates that have previously added to the enzyme. The kinetic Haldane relationships for several sequential mechanisms are given as... 

A , is the rate constant for combination of A with the free enzyme E. However, = ( 4 6 + 4 7 + k k-j)/k k kj. This involves 5 rate constants Aj, A4, Aj, Ag and kj all of which involve both A and B or, in the case of Ag and k-, both corresponding products. Thus is unlikely to be independent of the nature of A for this mechanism. Clearly this criterion will distinguish between two mechanisms shown in Schemes 5 and 8, and in fact the prediction is unique to the ping-pong mechanism. Another distinctive test of the ping-pong mechanism is the Haldane relationship. Haldane pointed out that from the initial rate kinetic parameters for the forward and reverse directions of a reversible enzyme-catalysed-reaction it was possible to obtain an expression for the overall equilibrium constant [66]. 

This Haldane relationship for the ping-pong mechanism is not shared by any of the other 2-substrate mechanisms. 

This mechanism, moreover, has its own unique Haldane relationship in addition to Eqn. 22 ... 

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