Enzymes rate accelerations

The simplest conclusion is then that tunneling occurs both in enzymic hydride-transfer reactions and in related non-enzymic (model) reactions. It remains to be seen whether enzymic rate acceleration has evolved simply to make the existing tunneling reaction much more efficient or instead to create new tunneling mechanisms distinct from those observed in model systems. 

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... 

Interestingly, at very low concentrations of micellised Qi(DS)2, the rate of the reaction of 5.1a with 5.2 was observed to be zero-order in 5.1 a and only depending on the concentration of Cu(DS)2 and 5.2. This is akin to the turn-over and saturation kinetics exhibited by enzymes. The acceleration relative to the reaction in organic media in the absence of catalyst, also approaches enzyme-like magnitudes compared to the process in acetonitrile (Chapter 2), Cu(DS)2 micelles accelerate the Diels-Alder reaction between 5.1a and 5.2 by a factor of 1.8710 . This extremely high catalytic efficiency shows how a combination of a beneficial aqueous solvent effect, Lewis-acid catalysis and micellar catalysis can lead to tremendous accelerations. 

In contrast to the situation in the absence of catalytically active Lewis acids, micelles of Cu(DS)2 induce rate enhancements up to a factor 1.8710 compared to the uncatalysed reaction in acetonitrile. These enzyme-like accelerations result from a very efficient complexation of the dienophile to the catalytically active copper ions, both species being concentrated at the micellar surface. Moreover, the higher affinity of 5.2 for Cu(DS)2 compared to SDS and CTAB (Psj = 96 versus 61 and 68, respectively) will diminish the inhibitory effect due to spatial separation of 5.1 and 5.2 as observed for SDS and CTAB. 

Many globular proteins are enzymes They accelerate the rates of chemical reactions m biological systems but the kinds of reactions that take place are the fundamental reactions of organic chemistry One way m which enzymes accelerate these reactions is by bringing reactive func tions together m the presence of catalytically active functions of the protein... 

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 )... 

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. 

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

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 rate acceleration achieved by enzymes is due to several factors. Particularly important is the ability of the enzyme to stabilize and thus lower the energy of the transition state(s). That is, it s not the ability of the enzyme to bind the substrate that matters but rather its ability to bind and thereby stabilize the transition state. Often, in fact, the enzyme binds the transition structure as much as 1012 times more tightly than it binds the substrate or products. As a result, the transition state is substantially lowered in energy. An energy diagram for an enzyme-catalyzed process might look like that in Figure 26.8. 

It has been frequently suggested that dynamical factors are important in enzyme catalysis (Ref. 9), implying that enzymes might accelerate reactions by utilizing special fluctuations which are not available for the corresponding reaction in solutions. This hypothesis, however, looks less appealing when one examines its feasibility by molecular simulations. That is, as demonstrated in Chapter 2, it is possible to express the rate constant as... 

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... 

As discussed in the early sections it seems that there are very few effective ways to stabilize the transition state and electrostatic energy appears to be the most effective one. In fact, it is quite likely that any enzymatic reaction which is characterized by a significant rate acceleration (a large AAgf +p) will involve a complimentarity between the electrostatic potential of the enzyme-active site and the change in charges during the reaction (Ref. 10). This point may be examined by the reader in any system he likes to study. 

Enzymes are proteins catalyzing all in vivo biological reactions. Enzymatic catalysis can also be utilized for in vitro reactions of not only natural substrates but some unnatural ones. Typical characteristics of enzyme catalysis are high catalytic activity, large rate acceleration of reactions under mild reaction conditions, high selectivities of substrates and reaction modes, and no formation of byproducts, in comparison with those of chemical catalysts. In the field of organic synthetic chemistry, enzymes have been powerful catalysts for stereo- and regioselective reactions to produce useful intermediates and end-products such as medicines and liquid crystals. ... 

Methylmalonyl-CoA mutase (MCM) catalyzes a radical-based transformation of methylmalonyl-CoA (MCA) to succinyl-CoA. The cofactor adenosylcobalamin (AdoCbl) serves as a radical reservoir that generates the S -deoxyadenosine radical (dAdo ) via homolysis of the Co—C5 bond [67], The mechanisms by which the enzyme stabilizes the homolysis products and achieve an observed 1012-fold rate acceleration are yet not fully understood. Co—C bond homolysis is directly kineti-cally coupled to the proceeding hydrogen atom transfer step and the products of the bond homolysis step have therefore not been experimentally characterized. 

A key question in the action of enzymes is the understanding of the mechanisms by which they attain their catalytic rate enhancement relative to the uncatalyzed reactions. Some enzymes have been shown to produce rate accelerations as large as 1019 [1], The theoretical determination of the reaction mechanisms by which enzymes carry out the chemical reactions has been an area of great interests and intense development in recent years [2-11], A common approach for the modeling of enzyme systems is the QM/MM method proposed by Warshel and Levitt [12], In this method the enzyme is divided into two parts. One part includes the atoms or molecules that participate in the chemical process, which are treated by quantum mechanical calculations. The other contains the rest of the enzyme and the solvent, generally thousands of atoms, which is treated by molecular mechanics methods. 

We are applying the principles of enzyme mechanism to organometallic catalysis of the reactions of nonpolar and polar molecules for our early work using heterocyclic phosphines, please see ref. 1.(1) Here we report that whereas uncatalyzed alkyne hydration by water has a half-life measured in thousands of years, we have created improved catalysts which reduce the half-life to minutes, even at neutral pH. These data correspond to enzyme-like rate accelerations of >3.4 x 109, which is 12.8 times faster than our previously reported catalyst and 1170 times faster than the best catalyst known in the literature without a heterocyclic phosphine. In some cases, practical hydration can now be conducted at room temperature. Moreover, our improved catalysts favor anti-Markovnikov hydration over traditional Markovnikov hydration in ratios of over 1000 to 1, with aldehyde yields above 99% in many cases. In addition, we find that very active hydration catalysts can be created in situ by adding heterocyclic phosphines to otherwise inactive catalysts. The scope, limitations, and development of these reactions will be described in detail. 

Another alternative is for the enzyme to actually form a covalent bond between the enzyme and the substrate. This direct, covalent participation of the enzyme in the chemical reaction is termed covalent catalysis. The enzyme uses one of its functional groups to react with the substrate. This enzyme-substrate bond must form fast, and the intermediates must be reasonably reactive if this kind of catalysis is going to give a rate acceleration. 

The most well-studied enzyme catalyzes the reaction S P. The kinetic question is how time influences the amount of S and P. In the absence of enzyme, the conversion of S to P is slow and uncontrolled. In the presence of a specific enzyme (S-to-Pase1), S is converted swiftly and specifically to product. S-to-Pase is specific it will not convert A to B or X to Y. Enzymes also provide a rate acceleration. If you compare the rate of a chemical reaction in solution with the rate of the same reaction with the reactants bound to the enzyme, the enzyme reaction will occur up to 1014 times faster. 

A most significant advance in the alkyne hydration area during the past decade has been the development of Ru(n) catalyst systems that have enabled the anti-Markovnikov hydration of terminal alkynes (entries 6 and 7). These reactions involve the addition of water to the a-carbon of a ruthenium vinylidene complex, followed by reductive elimination of the resulting hydridoruthenium acyl intermediate (path C).392-395 While the use of GpRuGl(dppm) in aqueous dioxane (entry 6)393-396 and an indenylruthenium catalyst in an aqueous medium including surfactants has proved to be effective (entry 7),397 an Ru(n)/P,N-ligand system (entry 8) has recently been reported that displays enzyme-like rate acceleration (>2.4 x 1011) (dppm = bis(diphenylphosphino)methane).398... 

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