Rate Accelerations

Links between Enzyme Reaction Performance Parameters 2.3.3.1 Rate Acceleration 

The data provides clear guidance that the biggest improvement in enzyme catalysts can be achieved for reactions with very low chemical background rate constants and not by optimizing rate constants or specificities which are already fairly high. 

2 Ratio between Catalytic Constant rcat and Deactivation Rate Constant lrd 

In Chapter 17, Section 17.4, we will encounter the rate equation for a deactivating enzyme in a batch reactor [Eq. (2.31)]. 

The influence of deactivation depends linearly on the dimensionless ratio kat/kd, which might serve as a ratio to assess quickly the potential of a deactivating enzyme for synthesis. 

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Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

Page, M. L., Jencks, W. P. Entropic contributions to rate accelerations in enzymic and intramolecular interactions and the chelate effect. Proc. Natl. Acad. Sci. USA 68 (1971) 1678-1683... 

Dramatic rate accelerations of [4 + 2]cycloadditions were observed in an inert, extremely polar solvent, namely in5 M solutions oflithium perchlorate in diethyl ether(s 532 g LiC104 per litre ). Diels-Alder additions requiring several days, 10—20 kbar of pressure, and/ or elevated temperatures in apolar solvents are achieved in high yields in some hours at ambient pressure and temperature in this solvent (P.A. Grieco, 1990). Also several other reactions, e.g, allylic rearrangements and Michael additions, can be drastically accelerated by this magic solvent. The diastereoselectivities of the reactions in apolar solvents and in LiClO EtjO are often different or even complementary and become thus steerable. 

CuClO, and copper(II) perchlorate [13770-18-8] Cu(Cl04)2, form a number of complexes with ammonia, pyridine, and organic derivatives of these compounds. The copper perchlorate is an effective bum-rate accelerator for soHd propellants (39). 

Dry potassium cyanide in sealed containers is stable for many years. An aqueous solution of potassium cyanide is slowly converted to ammonia and potassium formate the decomposition rate accelerates with increasing temperature. However, at comparable temperatures the rate of conversion is far lower than that for sodium cyanide only about 25% as great. 

Here o is the stress, A and n are creep constants and Q is the activation energy for creep. Most engineering design against creep is based on this equation. Finally, the creep rate accelerates again into tertiary creep and fracture. 

The extent of the corrosion depends on the amount of nickel and chromium in the alloy. The oxide films become porous and nonprotective, which increases the oxidation rate (accelerated oxidation). 

Substitution reactions by the ionization mechanism proceed very slowly on a-halo derivatives of ketones, aldehydes, acids, esters, nitriles, and related compounds. As discussed on p. 284, such substituents destabilize a carbocation intermediate. Substitution by the direct displacement mechanism, however, proceed especially readily in these systems. Table S.IS indicates some representative relative rate accelerations. Steric effects be responsible for part of the observed acceleration, since an sfp- caibon, such as in a carbonyl group, will provide less steric resistance to tiie incoming nucleophile than an alkyl group. The major effect is believed to be electronic. The adjacent n-LUMO of the carbonyl group can interact with the electnai density that is built up at the pentacoordinate carbon. This can be described in resonance terminology as a contribution flom an enolate-like stmeture to tiie transition state. In MO terminology,.the low-lying LUMO has a... 

Evidently, since there is no appreciable rate acceleration, this participatimi is not very strong at the transition state. Nevertheless, the participation is strong enough to control stereochemistry. When mote nucleophilic solvents are used (e.g., acetic acid), participation is not observed, and the product is 100% of inverted configuration. 

There are many reactions in which the products formed often act as catalysts for the reaction. The reaction rate accelerates as the reaction continues, and this process is referred to as autocatalysis. The reaction rate is proportional to a product concentration raised to a positive exponent for an autocatalytic reaction. Examples of this type of reaction are the hydrolysis of several esters. This is because the acids formed by the reaction give rise to hydrogen ions that act as catalysts for subsequent reactions. The fermentation reaction that involves the action of a micro-organism on an organic feedstock is a significant autocatalytic reaction. 

Thus, the enzymatic rate acceleration is approximately equal to the ratio of the dissociation constants of the enzyme-substrate and enzyme-transition-state complexes, at least when E is saturated with S. 

Enzymes are powerful catalysts. Enzyme-catalyzed reactions are typically 10 to times faster than their uncatalyzed counterparts (Table 16.1). (There is even a report of a rate acceleration of >10 for the alkaline phosphatase-catalyzed hydrolysis of methylphosphate )... 

These large rate accelerations correspond to substantial changes in the free energy of activation for the reaction in question. The urease reaction, for example. 

Any or all of these mechanisms may contribute to the net rate acceleration of an enzyme-catalyzed reaction relative to the uncatalyzed reaction. A thorough understanding of any enzyme would require that the net acceleration be accounted for in terms of contributions from one or (usually) more of these mechanisms. Each of these will be discussed in detail in this chapter, but first it is important to appreciate how the formation of the enzyme-substrate (ES) complex makes all these mechanisms possible. 

When a substrate enters the active site, charged groups may be forced to interact (unfavorably) with charges of like sign, resulting in electrostatic destabilization (Figure 16.6). The reaction pathway acts in part to remove this stress. If the charge on the substrate is diminished or lost in the course of reaction, electrostatic destabilization can result in rate acceleration. 

Some enzyme reactions derive much of their rate acceleration from the formation of covalent bonds between enzyme and substrate. Consider the reaction ... 

FIGURE 16.15 Orientation effects in intramolecular reactions can be dramatic. Steric crowding by methyl groups provides a rate acceleration of 2.5 X 10 for the lower reaction compared to the upper reaction. (Adaptedfrom Milstien,. S., and Cohen, L. A., 1972. Stereopopnlation control I. Rate enhancements in the laetonization of o-hyelroxyhyeJroeinnamie acid. Journal of the American Chemical Society 94 9158-9165.)... 

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. 

On the basis of the above, the rate acceleration afforded by lysozyme appears to be due to (a) general acid catalysis by Glu (b) distortion of the sugar ring at the D site, which may stabilize the carbonium ion and the transition state) and (c) electrostatic stabilization of the carbonium ion by nearby Asp. The overall for lysozyme is about 0.5/sec, which is quite slow (Table... 

The use of 1 M HBF4 in TFA/thioanisole was found to give significant rate accelerations during cleavage of the Mtr group. Sulfuric acid at 90° has also been used to cleave the Mtr group. ... 

In these equations, Dmax is the larger of the summed values of STERIMOL parameters, Bj, for the opposite pair 68). It expresses the maximum total width of substituents. The coefficients of the ct° terms in Eqs. 37 to 39 were virtually equal to that in Eq. 40. This means that the a° terms essentially represent the hydrolytic reactivity of an ester itself and are virtually independent of cyclodextrin catalysis. The catalytic effect of cyclodextrin is only involved in the Dmax term. Interestingly, the coefficient of Draax was negative in Eq. 37 and positive in Eq. 38. This fact indicates that bulky substituents at the meta position are favorable, while those at the para position unfavorable, for the rate acceleration in the (S-cyclodextrin catalysis. Similar results have been obtained for a-cyclodextrin catalysis, but not for (S-cyclodextrin catalysis, by Silipo and Hansch described above. Equation 39 suggests the existence of an optimum diameter for the proper fit of m-substituents in the cavity of a-cyclodextrin. The optimum Dmax value was estimated from Eq. 39 as 4.4 A, which is approximately equivalent to the diameter of the a-cyclodextrin cavity. The situation is shown in Fig. 8. A similar parabolic relationship would be obtained for (5-cyclodextrin catalysis, too, if the correlation analysis involved phenyl acetates with such bulky substituents that they cannot be included within the (5-cyclodextrin cavity. 

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