Briggs-Haldane equation

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

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... 

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 ... 

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 ... 

In the Briggs-Haldane derivation of the Michaelis-Menten equation, the concentration of ES is assumed to be at steady state, i.e., its rate of production [Eq. (3.12)] is exactly counterbalanced by its rate of dissociation [Eq. (3.13)]. Since the rate of formation of ES from E -(- P is vanishingly small, it is neglected. Equating the two equations and rearranging yields Eq. (3.14), where KM replaces (k2 + h)/k and is known as the Michaelis-Menten... 

Finally, introduction of the commonly used symbols Vmax and Km yields the Briggs-Haldane rate equation for enzymatic reactions (compare with Equation 11.6)... 

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 ... 

An enzyme is said to obey Michaelis-Menten kinetics, if a plot of the initial reaction rate (in which the substrate concentration is in great excess over the total enzyme concentration) versus substrate concentration(s) produces a hyperbolic curve. There should be no cooperativity apparent in the rate-saturation process, and the initial rate behavior should comply with the Michaelis-Menten equation, v = Emax[A]/(7 a + [A]), where v is the initial velocity, [A] is the initial substrate concentration, Umax is the maximum velocity, and is the dissociation constant for the substrate. A, binding to the free enzyme. The original formulation of the Michaelis-Menten treatment assumed a rapid pre-equilibrium of E and S with the central complex EX. However, the steady-state or Briggs-Haldane derivation yields an equation that is iso-... 

This expression by Briggs-Haldane is similar to Equation 3.28, obtained by the Michaelis-Menten approach, except that is equal to (Ar i -F These... 

The result of equation 3.39 for nonproductive binding is quite general. It applies to cases in which intermediates occur on the reaction pathway as well as in the nonproductive modes. For example, in equation 3.19 for the action of chy-motrypsin on esters with accumulation of an acylenzyme, it is seen from the ratios of equations 3.21 and 3.22 that kQJKM = k2IKs. This relationship clearly breaks down for the Briggs-Haldane mechanism in which the enzyme-substrate complex is not in thermodynamic equilibrium with the free enzyme and substrates. It should be borne in mind that KM might be a complex function when there are several enzyme-bound intermediates in rapid equilibrium, as in equation 3.16. Here kcJKM is a function of all the bound species. 

For most enzymes, the rate of reaction can be described by the Michaelis-Menten equation which was originally derived in 1913 by Michaelis and MENTEN 21 . Its derivation can be achieved by making one of two assumptions, one of which is a special case of the more general Briggs-Haldane scheme, whilst the alternative is the rapid-equilibrium method given in Appendix 5.3(2 ). 

Derive the rate equation by employing (a) the Michaelis-Menten and (b) the Briggs-Haldane approach. Explain when the rate equation derived by the Briggs-Haldane approach can be simplified to that derived by the Michaelis-Menten approach. 

To derive a rate equation, let s follow the Briggs-Haldane approach as explained in Chapter 2, which assumes that the change of the... 

This is an important question that has been addressed by many enzyme kineticists over the years. For the correct application of the Briggs-Haldane steady-state analysis, in a closed system, [S]0 must be >[E](), where the > sign implies a factor of at least 1,000. M. F. Chaplin in 1981 noted that the expression v0= V max[S]c/(Km + [S]0 + [E]0) yields, for example, only a 1 percent error in the estimate of v() for [S]0 = 10 x [E]0 and [S]0 = 0.1 Km the expression thus applies under much less stringent conditions than does the simple Michaelis-Menten equation. In open systems [S]0 can approximate [E]0 and a steady state of enzyme-substrate complexes can pertain computer simulation of both types of system is the best way to gain insight into the conditions necessary for a steady state of the complex. 

The one-plus rate equation 8.22 is of the same algebraic form as the Michaelis-Menten equation 8.18, only the physical significance of the coefficients is different [instead of the constant K, the expression kAX /(k + kXP) now appears]. Accordingly, the behavior is the same as for Michaelis-Menten kinetics, and that name is often used for Briggs-Haldane kinetics as well. 

A common feature of all single-cycle kinetics discussed so far is a one-plus rate behavior with reaction order between zero and one with respect to the reactant, A (and for a possible reverse rate, with respect to the product, P). The Michaelis-Menten and Briggs-Haldane rate equations 8.18 and 8.22 have the same algebraic form, and so has the initial rate in the reversible cycle, that is, eqn 8.24 with terms involving CP still being insignificant. This common one-plus form can be rearranged ... 

In addition to the preceding assumptions, there are three different approaches to derive the rate equation Michaelis-Menten approach [10], Briggs-Haldane approach [11], and numerical solution. 

If we adopt the Briggs-Haldane steady-state assumption and substitute from Eqn. lb rather than Eqn. la, we obtain an equation of exactly the same form except that AT now is not k, //c, but (A , +... 

As shown above, the equilibrium assumption leads to a version of the Michaelis-Menten equation in which the Michaelis constant is equivalent to the dissociation constant for the enzyme-substrate complex EA. This unfortunately encourages many biochemists to assume that Michaelis constants can always be so equated. The misleading statement that K, reflects an enzyme s affinity for its substrate is often encountered. Even if we consider only 1-substrate enzymes, the Briggs-Haldane version of will only approximate to k /k if However, if, for instance, /c2 = 10/c, then is 11 times greater than the dissociation constant for EA. If kj k, then = k2/k rather than k /k. ... 

In order to solve Equation (8.3), expressions for [E] and [ES] are required that are obtained by applying Briggs-Haldane steady state principles. According to these principles, biocatalysis rapidly attains a condition of stasis under which all biocatalyst species are at a constant equilibrium concentration. In other words [E] and [ES] are constant with time. Stasis is reflected by... 

In this section, we shall begin to see how the Briggs-Haldane steady state approach can be enlarged to derive steady state kinetics equations appropriate to more complex kinetic schemes. In doing this, there will be some pleasant surprises in that the form of these new steady state kinetic equations will follow the form of Michaelis-Menten equation (8.8) with a few adaptations not unlike those seen in the Uni Uni steady state kinetic scheme adapted to fit the presence of inhibitors (see Section 8.2.4). 

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