Briggs-Haldane kinetics

Figure 8.1 Model energy diagrams for non-enzymic reactions (A), enzymic reaction following the rapid equilibrium mechanism (see Table 8.1) (B) and enzymic reaction following Briggs-Haldane kinetics (C). E represents the activation energy of transition and the positive and...

In the Briggs-Maldane mechanism, when k2 is much greater than k-i, kcJKM is equal to kx, the rate constant for the association of enzyme and substrate. It is shown in Chapter 4 that association rate constants should be on the order of 108 s l M l. This leads to a diagnostic test for the Briggs-Haldane mechanism the value of kaJKu is about 107 to 108 s-1 M-1. Catalase, acetylcholinesterase, carbonic anhydrase, crotonase, fumarase, and triosephosphate isomerase all exhibit Briggs-Haldane kinetics by this criterion (see Chapter 4, Table 4.4). 

Table 4.5 shows that for some efficient enzymes, kcJKM may be as high as 3 X 108 s-1 M l. In these cases, the rate-determining step for this parameter, which is the apparent second-order rate constant for the reaction of free enzyme with free substrate, is close to the diffusion-controlled encounter of the enzyme and the substrate. Briggs-Haldane kinetics holds for these enzymes (Chapter 3, section B3). 

Breakdown of the simple rules Briggs-Haldane kinetics and change of rate-determining step with pH Kinetic p/fa s4,6 8... 

The most-studied enzyme in this context is chymotrypsin. Besides being well characterized in both its structure and its catalytic mechanism, it has the advantage of a very broad specificity. Substrates may be chosen to obey the simple Michaelis-Menten mechanism, to accumulate intermediates, to show nonproductive binding, and to exhibit Briggs-Haldane kinetics with a change of rate-determining step with pH. 

As we discussed in Chapter 3, the KM for an enzymatic reaction is not always equal to the dissociation constant of the enzyme-substrate complex, but may be lower or higher depending on whether or not intermediates accumulate or Briggs-Haldane kinetics hold. Enzyme-substrate dissociation constants cannot be derived from steady state kinetics unless mechanistic assumptions are made or there is corroborative evidence. Pre-steady state kinetics are more powerful, since the chemical steps may often be separated from those for binding. 

It was pointed out in Chapter 3, section A3, that when kcJKM is at the diffusion-controlled limit, Briggs-Haldane rather than Michaelis-Menten kinetics are obeyed. Thus, the more advanced an enzyme is toward the evolution of maximum rate, the more important are Briggs-Haldane kinetics. 

One example in which specificity may be lost is when Briggs-Haldane kinetics are occurring (Chapter 3, section A3a). Under these conditions, kCdLl/KM is equal to the rate constant for the association of the enzyme and the substrate. Since it is usually found that the higher dissociation constants for smaller substrates arise from a higher rate of dissociation rather than from a lower rate of association, there will be a partial or complete loss of specificity. 

Not all aminoacyl-tRNA synthetases have editing sites. The cysteinyl- and tyrosyl-tRNA synthetases bind the correct substrates so much more tightly than their competitors that they do not need to edit.13,14 Similarly, since the accuracy of transcription of DNA by RNA polymerase is better than the overall observed error rate in protein synthesis at about 1 part in 104, RNA polymerases do not need to edit.15 The same should be true for codon-anticodon interactions on the ribosome. However, it is possible that accuracy has been sacrificed to achieve higher rates in this case, which is analogous to a change from Michaelis-Menten to Briggs-Haldane kinetics, and so an editing step is required.16... 

Breakdown of the simple rules Briggs-Haldane kinetics... 

Dissociation rate constants are much lower than the diffusion-controlled limit, since the forces responsible for the binding must be overcome in the dissociation step. In some cases, enzyme-substrate dissociation is slower than the subsequent chemical steps, and this gives rise to Briggs-Haldane kinetics. 

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. 

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