Haldane equation

BRIGGS-HALDANE EQUATION STEADY-STATE ASSUMPTION ENZYME KINETICS UNI-UNI MECHANISM Bromohydroxyacetone phosphate,... 

Theoretically, all chemical reactions are reversible and, in the presence of enzymes, a dynamic equihbrium state will be reached rather than a total transformation of substrate molecules to product molecules. The dynamic equilibrium could be characterized by the Haldane equation ... 

The binding of carbon monoxide to hemoglobin is described by the Haldane equation ... 

This relationship is known as the Haldane equation, after J. B. S. Haldane.9... 

The Haldane equation does not relate the equilibrium constant between ES and EP to that between S and P in solution. The equilibrium constant for the enzyme-bound reagents is often very different from that in solution for several reasons ... 

Hence, by the principle of microscopic reversibility, the reverse reaction (the hydrolysis of peptides by the acylenzyme mechanism) must also occur. The question is whether or not this reaction is rapid enough to account for the observed hydrolysis rate. This can be answered by measuring (kcJKM)s for the synthesis of a peptide by the acylenzyme route, and for the hydrolysis of the peptide (kcJKM)u for the hydrolytic reaction can then be calculated from the Haldane equation,... 

There is one further consideration. The value of kcJKM cannot be at the diffusion-controlled limit for a reaction that is thermodynamically unfavorable. This point stems from the Haldane equation (Chapter 3, section H), which states that the equilibrium constant for a reaction in solution is given by the ratio of the values of kctA/KM for the forward and reverse reactions. Clearly, kcat/KM for an unfavorable reaction cannot be at the diffusion-controlled limit, since kQ.JKM for the favorable reverse reaction would have to be greater than the diffusion-controlled limit to balance the Haldane equation. The value of kcM/KM for an unfavorable reaction is limited by the diffusion-controlled limit multiplied by the unfavorable equilibrium constant for the reaction. 

The final proof of the acylenzyme route comes from calculating the rate constant for the hydrolytic reaction from the rate constant for the reverse reaction (the synthesis of the substrate by the acylenzyme route) and the Haldane equation (Chapter 3, section H). It is found that amines will react with the acylenzyme to produce amides and peptides. 

With this expression for [ES] we can follow the same procedure that led to equation (18), this time arriving at the Briggs-Haldane equation for the reaction velocity. 

Significance of the Specificity Constant, kcat/Km. Under physiological conditions, enzymes usually do not operate at saturating substrate concentrations. More typically, the ratio of the substrate concentration to the Km is in the range of 0.01-1.0. If [S] is much smaller than Km, the denominator of the Briggs-Haldane equation [equation (25)] is approximately equal to Km, so that the velocity of the reaction becomes... 

Faraci and Walsh263 studied the substrate and solvent deuterium isotope effects of the reactions catalyzed by alanine racemases of S. typhimurium (DadB and Air enzymes) and B. stearothermophilus. Although the kinetic constants for all three alanine racemases obey the Haldane equation, i.e., Keq= 1 (this confirms that the enzymes are true racemases), the individual Micaelis-Menten parameters in both directions show marked difference in the binding of each isomer. This suggests a structural asymmetry at the active sites of these enzymes. The asymmetry in the recognition and turnover of substrate enantiomer was also clearly seen in the results of isotope effect experiment with DadB enzyme. In the d-... 

Equation 8.23 is the most general rate equation for a trace-level catalyst cycle A <— P with one intermediate. It reduces to the Briggs-Haldane equation 8.21 if fcPX - 0 or CP = 0, that is, if the second step is irreversible or only the initial rate is considered. It reduces further to the Michaelis-Menten equation 8.18 if, in addition, kxr A xa, that is, if the first step is in quasi-equilibrium. 

With lumping of X, X2, and X3 into a single pseudo-species XL (shown in box), the reduced cycle now has only two members cat and X. The Briggs-Haldane equation 8.21 applies, without restriction to initial rate and with index X replaced by L ... 

This relation, representing the ratio of the rate constants of the first order kinetics is known as the Haldane equation . Haldane equations can be formulated for every kinetic model describing an equilibrium reaction, just by setting the numerator to zero. 

A Haldane equation can be formulated by setting the numerator to zero, resulting in a relation for the equilibrium constant (Eq. (43)) ... 

This rate equation is called Michaelis-Menten double substrate kinetics . It is a formal multiplication of two Michaelis-Menten models for both substrates A and B. This model can be used to describe rate kinetics of two substrate reactions in the absence of the product(s). The kinetic measurements have to be performed by varying the concentration of one substrate keeping the concentration of the second substrate at a constant value well above the Km value. The model cannot be used if back reactions occur and an equilibrium has to be described by an appropriate Haldane equation. 

As described above, the rate equation can be set to zero yielding the equilibrium condition of the reaction (Haldane equation). Using the kinetic data, fQ,q is calculated to be 12.2 mol L 1. 

The various kinetic constants for any bisubstrate or trisubstrate steady-state mechanism are related to the thermodynamic equilibrium constant by Haldane equations of the general type ... 

Briggs-Haldane equation as an alternative with a different interpretation of the value. 

If a steady-state approximation for [ES] is used (see Section 2.2) instead of the rapid-equilibrium assumption, then one obtains Eq. (8.4), known as the Briggs-Haldane equation ... 

Experimental verification of this relationship was found when iiC was calculated from F .x and Km values at different pH values. In experiments carried out in various concentrations of phosphate and at varying pH values, the ratio Fm.x fumarate/Fm x malate varied by a factor of 65, but the Aeq calculated by using the Haldane equation was found to be remarkably constant, averaging 4.4 at 25°C. 

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