Enzyme entropy effect

There are several processes that account for the enhancement of reaction rates by enzymes. The major mechanisms are proximity-entropy effects, substrate strain, covalent catalysis, and acid-base catalysis. 

Exact determination of entropy effects in enzymatic reactions is not an easy task even nowadays when sophisticated Monte Carlo and molecular dynamics methods are available for calculations (Warshel, 1991 Aqvist and Warshel, 1993). One way to examine the importance of entropy is to analyse the configuration space available to the system in its ground and transition states, both in the enzyme and in solution. The entropic contribution to the catalytic effect, relative to the uncatalysed solution can be expressed as... 

There are no single explanations for enzyme activity. Different enzymes catalyze their reactions in different ways, and one approach can describe more closely the mechanism for one than for another. The main idea underneath is the necessity to build a model as close to reality as possible, including an environmental and chemical effect that modulates both reactants and TSs. The catalytic power has to be measured relative to a reference state, and a careful inspection of the reaction coordinate, including solvent and entropy effects, is necessary for its accurate determination.18,19 The reference state allows the definition of the proficiency of the enzyme as a quantitative measure of its catalytic power. For a generic catalytic reaction... 

The enzyme binds the substrate(s) (and cofactor) in such a way that the susceptible bonds are (a) in close proximity to the catalytic group on the active side (called the entropy effect) and (b) so oriented in relation to the catalytic group that the transition state is readily formed (orbital steering). 

In case a) deacylation is faster by a factor of 3540 since the carbonyl group is immobilized by insertion of the bulky N-acetyl-L-tyrosyl group into a hydrophobic pocket on the enzyme (Fig. 2.14a) at the correct distance from the attacking nucleophilic OH ion derived from water (cf. 2.4.2.S). In case b) the immobilization of the small acetyl group is not possible (Fig. 2.14b) so that the difference between the ground and transition states is very large. The closer the ground state is to the transition state, the more positive will be the entropy of the transition state, AS a fact that as mentioned before can lead to a considerable increase in reaction rate. The thermodynamic data in Table 2.7 show that the difference in reaction rates depends, above all, on an entropy effect the enthalpies of the transition states scarcely differ. 

The driving force for this exergonic reaction is the generation of the carbonyl bond. The metabolic reaction is catalyzed by chorismate mutase. The enzyme increases the rate by a factor of a million. The enzyme mechanism has been extensively studied, and it appears that the enzyme stabilizes the transition state in the conformation required for catalysis. Thus, it might well be that the enzyme increases the reaction rate mostly by an entropy effect. 

Both types of mutations have been made in T4 lysozyme. The chosen mutations were Gly 77-Ala, which caused an increase in Tm of 1 °C, and Ala 82-Pro, which increased Tm by 2 °C. The three-dimensional structures of these mutant enzymes were also determined the Ala 82-Pro mutant had a structure essentially identical to the wild type except for the side chain of residue 82 this strongly indicates that the effect on Tm of Ala 82-Pro is indeed due to entropy changes. Such effects are expected to be additive, so even though each mutation makes only a small contribution to increased stability, the combined effect of a number of such mutations should significantly increase a protein s stability. 

FIGURE 16.2 The intrinsic binding energy of the enzyme-snbstrate (ES) complex (AGi ) is compensated to some extent by entropy loss dne to the binding of E and S (TAS) and by destabilization of ES (AGt) by strain, distortion, desolvation, and similar effects. If AGi, were not compensated by TAS and AG, the formation of ES would follow the dashed line. 

Clearly, proximity and orientation play a role in enzyme catalysis, but there is a problem with each of the above comparisons. In both cases, it is impossible to separate true proximity and orientation effects from the effects of entropy loss when molecules are brought together (described the Section 16.4). The actual rate accelerations afforded by proximity and orientation effects in Figures 16.14 and 16.15, respectively, are much smaller than the values given in these figures. Simple theories based on probability and nearest-neighbor models, for example, predict that proximity effects may actually provide rate increases of only 5- to 10-fold. For any real case of enzymatic catalysis, it is nonetheless important to remember that proximity and orientation effects are significant. 

The entropic hypothesis seems at first sight to gain strong support from experiments with model compounds of the type listed in Table 9.1. These compounds show a huge rate acceleration when the number of degrees of freedom (i.e., rotation around different bonds) is restricted. Such model compounds have been used repeatedly in attempts to estimate entropic effects in enzyme catalysis. Unfortunately, the information from the available model compounds is not directly transferable to the relevant enzymatic reaction since the observed changes in rate constant reflect interrelated factors (e.g., strain and entropy), which cannot be separated in a unique way by simple experiments. Apparently, model compounds do provide very useful means for verification and calibration of reaction-potential surfaces... 

It is noteworthy that the value of this substrate is smaller by one order compared to non-cyclic compounds. According to the discussions proposed above, this is considered to be due to its conformation already being fixed to the one that fits to the binding site of the enzyme. This estimation was demonstrated to be true by the examination of the effect of temperature on the kinetic parameters. Arrhenius plots of the rate constants of indane dicarboxylic acid and phenyl-malonic acid showed that the activation entropies of these substrates are —27.6 and —38.5 calmol K , respectively. The smaller activation entropy for the cyclic compound demonstrates that the 5yn-periplanar conformation of the substrate resembles the one of the transition state. 

---