Intramolecular catalysis effective concentrations

The relative importance of the potential catalytic mechanisms depends on pH, which also determines the concentration of the other participating species such as water, hydronium ion, and hydroxide ion. At low pH, the general acid catalysis mechanism dominates, and comparison with analogous systems in which the intramolecular proton transfer is not available suggests that the intramolecular catalysis results in a 25- to 100-fold rate enhancement At neutral pH, the intramolecular general base catalysis mechanism begins to operate. It is estimated that the catalytic effect for this mechanism is a factor of about 10. Although the nucleophilic catalysis mechanism was not observed in the parent compound, it occurred in certain substituted derivatives. 

The intermolecular general-base catalysis of the hydrolysis may also be measured. Comparing the rate constants for this with those of the intramolecular reaction shows that a 13-M solution of an external base is required to give the same first-order rate as the intramolecular reaction has.12 The effective concentration of the carboxylate ion in aspirin is therefore 13 M. This is a typical value for intramolecular general-acid-base catalysis. 

The high effective concentration of intramolecular groups is one of the most important reasons for the efficiency of enzyme catalysis. This can be explained theoretically by using transition state theory and examining the entropy term in the rate equation (2.7). It will be seen that effective concentrations may be calculated by substituting certain entropy contributions into the exp (AS /R) term of equation 2.7. 

The lower effective concentrations found in intramolecular base catalysis are due to the loose transition states of these reactions. In nucleophilic reactions, the nucleophile and the electrophile are fairly rigidly aligned so that there is a large entropy loss. In general-base or -acid catalysis, there is considerable spatial freedom in the transition state. The position of the catalyst is not as closely defined as in nucleophilic catalysis. There is consequently a smaller loss in entropy in general-base catalysis, so that the intramolecular reactions are not favored as much as their nucleophilic counterparts. 

Attempts have been made to account for the rate enhancements in intramolecular catalysis on the basis of an effective concentration of 55 M combined with the requirement of very precise alignment of the electronic orbitals of the reacting atoms orbital steering. Although this treatment does have the merit of emphasizing the importance of correct orientation in the enzyme-substrate complex, it overestimates this importance, because, as we now know, the value of 55 M is an extreme underestimate of the contribution of translational entropy to effective concentration. The consensus is that although there are requirements for the satisfactory overlap of orbitals in the transition state, these amount to an accuracy of only 10° or so.23-24 The distortion of even a fully formed carbon-carbon bond... 

Intramolecular catalysis The effective concentration of a group on an enzyme... 

Important milestones in the rationalization of enzyme catalysis were the lock-and-key concept (Fischer, 1894), Pauling s postulate (1944) and induced fit (Koshland, 1958). Pauling s postulate claims that enzymes derive their catalytic power from transition-state stabilization the postulate can be derived from transition state theory and the idea of a thermodynamic cycle. The Kurz equation, kaJkunat Ks/Kt, is regarded as the mathematical form of Pauling s postulate and states that transition states in the case of successful catalysis must bind much more tightly to the enzyme than ground states. Consequences of the Kurz equation include the concepts of effective concentration for intramolecular reactions, coopera-tivity of numerous interactions between enzyme side chains and substrate molecules, and diffusional control as the upper bound for an enzymatic rate. 

The rates at the extremities pH < 2 and pH > 9 are proportional to [H ] and [ OH], respectively, and represent the specific proton-catalyzed and hydroxide-catalyzed mechanisms. In the absence of an intramolecular catalytic mechanisms, the H+- and OH-catalyzed reactions would decrease in proportion to the concentration of the catalytic species and intersect at a minimum value representing the uncatalyzed water hydrolysis. An estimate of the effectiveness of the intramolecular mechanisms can be made by extrapolating the lines that are proportional to [H+] and [ OHj. The extent to which the actual rate lies above these extrapolated lines in the pH range 2-8 represents the contribution from the intramolecular catalysis. The region at pH 2-4 is the area where intramolecular general acid catalysis operates. Comparison with similar systems where intramolecular proton transfer is not available suggests a 25-100 fold rate enhancement. At pH 6-8 the intramolecular general base catalysis mechanism is... 

An example of a proton-transfer reaction occurring by the stepwise trapping mechanism (Ch. 7, Section 2.1) is the general base-catalysed aminolysis of benzyl-penicillin. Amines react with penicillin to form an unstable tetrahedral intermediate which may be trapped by a diffusion-controlled encounter with a strong base as shown in Eqn. 8. Diamines also undergo this reaction but at a much faster rate than monoamines of the same basicity which is attributed to intramolecular general base catalysis i.e. the second amino group acts as a proton acceptor (V). However, the effect of intramolecularity itself is small and the effective concentration (Ch. 1)... 

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