Transition state, enzyme-catalyzed reactions

In a special circumstance the rate equation for parallel reactions may be misleading.If two parallel reactions are catalyzed by a common catalyst, and if a significant fraction of the catalyst is tied up in the form of intermediates, then the two reactions are not independent, and the rate equation will not give the transition state composition. King has analyzed this case in terms of enzyme-catalyzed reactions. 

Reactions proceed via transition states in which AGp is the activation energy. Temperature, hydrogen ion concentration, enzyme concentration, substrate concentration, and inhibitors all affect the rates of enzyme-catalyzed reactions. 

Figure 1.3. Schematic representation of an enzyme-catalyzed reaction. Enzymes often match the shape of the substrates they bind to, or the transition state of the reaction they catalyze. Enzymes are highly efficient catalysts and represent a great source of inspiration for designing technical catalysts.

Figure 2.1 Free energy diagram for the reaction pathway of a chemical reaction, and the same reaction catalyzed by an enzyme. Note the significant reduction in activation energy (the vertical distance between the reactant state and the transition state) achieved by the enzyme-catalyzed reaction.

In this chapter we have seen that enzymatic catalysis is initiated by the reversible interactions of a substrate molecule with the active site of the enzyme to form a non-covalent binary complex. The chemical transformation of the substrate to the product molecule occurs within the context of the enzyme active site subsequent to initial complex formation. We saw that the enormous rate enhancements for enzyme-catalyzed reactions are the result of specific mechanisms that enzymes use to achieve large reductions in the energy of activation associated with attainment of the reaction transition state structure. Stabilization of the reaction transition state in the context of the enzymatic reaction is the key contributor to both enzymatic rate enhancement and substrate specificity. We described several chemical strategies by which enzymes achieve this transition state stabilization. We also saw in this chapter that enzyme reactions are most commonly studied by following the kinetics of these reactions under steady state conditions. We defined three kinetic constants—kai KM, and kcJKM—that can be used to define the efficiency of enzymatic catalysis, and each reports on different portions of the enzymatic reaction pathway. Perturbations... 

The AG for binding the substrate and the transition state is shown as a difference between the energies of the ES complex and E + S. The AG for binding the transition state is shown as a difference between the energies of the E TS complex and E + TS. If the transition state binds tighter (bigger AG) than the substrate, the enzyme-catalyzed reaction must have a lower activation energy. 

The relationship between the geometry of the saddle point of index one (SPi-1) and the accessibility to the quantum transition states cannot be proved, but it can be postulated [43,172], To some extent, invariance of the geometry associated with the SPi-1 would entail an invariance of the quantum states responsible for the interconversion. Thus, if a chemical process follows the same mechanism in different solvents, the invariance of the geometry of the SPi-1 to solvent effects would ensure the mechanistic invariance. This idea has been proposed by us based on computational evidence during the study of some enzyme catalyzed reactions [94, 96, 97, 100-102, 173, 174, 181-184],... 

Scheme 1 is a gross over-simplification for almost any enzyme-catalyzed reaction of a specific substrate, based as it is on a one-step reaction with a single, rate-determining transition state but it is appropriate for many, if not most reactions catalyzed by simple enzyme mimics. Most important for present purposes, it emphasises the most important properties of enzyme reactions which the design of mimics, or artificial enzymes, must address, namely ... 

Secondary isotope effects measure transition-state structure 37 Quantum tunneling in enzyme-catalyzed reactions breakthroughs 42 Experimental phenomenology of quantum tunneling in enzyme-catalyzed... 

Kinetic complexity definition, 43 Klinman s approach, 46 Kinetic isotope effects, 28 for 2,4,6-collidine, 31 a-secondary, 35 and coupled motion, 35, 40 in enzyme-catalyzed reactions, 35 as indicators of quantum tunneling, 70 in multistep enzymatic reactions, 44-45 normal temperature dependence, 37 Northrop notation, 45 Northrop s method of calculation, 55 rule of geometric mean, 36 secondary effects and transition state, 37 semiclassical treatment for hydrogen transfer,... 

Although conformational changes are essential features of proteins, the conformational basis of protein activity is not yet understood at the molecular and atomic levels. It is generally assumed that the mechanism of enzyme-catalyzed reactions would he defined if all the intermediates and transition states between the initial and final stages, as well as the rate constants, could be characterized. But in spite of constant progress in such characterization, most enzymatic mechanisms are not understood in terms of physical organic chemistry and enzyme activity is still regarded as a miracle as compared to classical catalysis. 

Finally, yet another issue enters into the interpretation of nonlinear Arrhenius plots of enzyme-catalyzed reactions. As is seen in the examples above, one typically plots In y ax (or. In kcat) versus the reciprocal absolute temperature. This protocol is certainly valid for rapid equilibrium enzymes whose rate-determining step does not change throughout the temperature range studied (and, in addition, remains rapid equilibrium throughout this range). However, for steady-state enzymes, other factors can influence the interpretation of the nonlinear data. For example, for an ordered two-substrate, two-product reaction, kcat is equal to kskjl ks + k ) in which ks and k are the off-rate constants for the two products. If these two rate constants have a different temperature dependency (e.g., ks > ky at one temperature but not at another temperature), then a nonlinear Arrhenius plot may result. See Arrhenius Equation Owl Transition-State Theory van t Hoff Relationship... 

Many of the 60 known reactions catalyzed by monoclonal antibodies involve kinetically favored reactions e.g., ester hydrolysis), but abzymes can also speed up kinetically disfavored reactions. Stewart and Benkovic apphed transition-state theory to analyze the scope and limitations of antibody catalysis quantitatively. They found the observed rate accelerations can be predicted from the ratio of equilibrium binding constants of the reaction substrate and the transition-state analogue used to raise the antibody. This approach permitted them to rationalize product selectivity displayed in antibody catalysis of disfavored reactions, to predict the degree of rate acceleration that catalytic antibodies may ultimately afford, and to highlight some differences between the way that they and enzymes catalyze reactions. 

Mandelate racemase, another pertinent example, catalyzes the kinetically and thermodynamically unfavorable a-carbon proton abstraction. Bearne and Wolfenden measured deuterium incorporation rates into the a-posi-tion of mandelate and the rate of (i )-mandelate racemi-zation upon incubation at elevated temperatures. From an Arrhenius plot, they obtained a for racemization and deuterium exchange rate was estimated to be around 35 kcal/mol at 25°C under neutral conditions. The magnitude of the latter indicated mandelate racemase achieves the remarkable rate enhancement of 1.7 X 10, and a level of transition state affinity (K x = 2 X 10 M). These investigators also estimated the effective concentrations of the catalytic side chains in the native protein for Lys-166, the effective concentration was 622 M for His-297, they obtained a value 3 X 10 M and for Glu-317, the value was 3 X 10 M. The authors state that their observations are consistent with the idea that general acid-general base catalysis is efficient mode of catalysis when enzyme s structure is optimally complementary with their substrates in the transition-state. See Reference Reaction Catalytic Enhancement... 

An approach to studying transition states in enzyme-catalyzed reactions using solvent isotope effects. In this treatment, very useful in isotope effect experiments, the relative rates of contributing steps in a multistep reaction are grouped into a fraction referred to as the commitment factor ... 

A potential factor affecting the catalytic power of enzyme-catalyzed reactions in which the enzyme forces the attacking moiety into the valence shell of the entity under attack. Compression is thought to be manifested in the transition state complex. The results of kinetic isotope effect measurements have suggested that compression events factor in the catechol methyltransferase re-actionh... 

A number of methods can assist in identifying and characterizing enol intermediates (as well as eneamine and carbanion intermediates) in enzyme-catalyzed reactions. These include (1) proton isotope exchange (2) oxidation of the intermediate (3) coupled elimination (4) spectrophotometric methods (5) use of transition-state inhibitors (6) use of suicide inhibitors (7) isolation of the enol and (8) destructive analysis. 

An approach and construct used to understand isotope effects. The isotope effect observed in an enzyme-catalyzed reaction is a weighted average of several steps in the reaction. The transition state that one constructs from these studies is also a weighted average of several transition states thus, the virtual transition state. 

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