Perfect enzymes

But k must always be greater than or equal to k h / (A i + kf). That is, the reaction can go no faster than the rate at which E and S come together. Thus, k sets the upper limit for A ,. In other words, the catalytic effieiency of an enzyme cannot exceed the diffusion-eontroUed rate of combination of E and S to form ES. In HgO, the rate constant for such diffusion is approximately (P/M - sec. Those enzymes that are most efficient in their catalysis have A , ratios approaching this value. Their catalytic velocity is limited only by the rate at which they encounter S enzymes this efficient have achieved so-called catalytic perfection. All E and S encounters lead to reaction because such catalytically perfect enzymes can channel S to the active site, regardless of where S hits E. Table 14.5 lists the kinetic parameters of several enzymes in this category. Note that and A , both show a substantial range of variation in this table, even though their ratio falls around 10 /M sec. 

Simoponlos, T. T, and Jencks, W. P., 1994. Alkaline phosphatase is an almost perfect enzyme. Biochemistry 33 10375-10380. 

The demand for monitoring common metabolites of diagnostic utility such as glucose, urea and creatinine continue to provide the impetus for a staggering research effort towards more perfect enzyme electrodes. The inherent specificity of an enzyme for a given substrate, coupled with the ability to electrochemically detect many of the products of enzymatic reactions initiated the search for molecule-selective electrodes. 

There have been more sophisticated attempts to derive optimal values for rate constants for the perfectly evolved enzyme. Without any structural constraints, the perfect enzyme is bound to be one that has all the rate constants in the favorable direction equal to the maximum possible (6 X 1012 s"1 at 25°C, equation 2.2) and all the association rate constants at the diffusion-controlled limit. 

Another way of evaluating enzymatic activity is by comparing k2 values. This first-order rate constant reflects the capacity of the enzyme-substrate complex ES to form the product P. Confusingly, k2 is also known as the catalytic constant and is sometimes written as kcal. It is in fact the equivalent of the enzyme s TOF, since it defines the number of catalytic cycles the enzyme can undergo in one time unit. The k2 (or kcat) value is obtained from the initial reaction rate, and thus pertains to the rate at high substrate concentrations. Some enzymes are so fast and so selective that their k2/Km ratio approaches molecular diffusion rates (108—109 m s-1). This means that every substrate/enzyme collision is fruitful, and the reaction rate is limited only by how fast the substrate molecules diffuse to the enzyme. Such enzymes are called kinetically perfect enzymes [26],... 

Today we know that proteins are flexible molecules. This led Daniel E. Koshland, Jr., to propose a more sophisticated model of the way enzymes and substrates interact. This model, proposed in 1958, is called the induced fit model (Figure 20.3b). In this model the active site of the enzyme is not a rigid pocket into which the substrate fits precisely rather, it is a flexible pocket that approximates the shape of the substrate. When the substrate enters the pocket, the active site "molds" itself around the substrate. This produces the perfect enzyme-substrate "fit."... 

The fecat/J M ratios of the enzymes superoxide dismutase, acetylcholinesterase, and triosephosphate isomerase are between 10 and lO" s Enzymes such as these that have fecat/ M ratios at the upper limits have attained kinetic perfection. Their catalytic velocity is restricted only by the rate at which they encounter substrate in the solution (Table 8.8). Any further gain in catalytic rate can come only by decreasing the time for diffusion. Remember that the active site is only a small part of the total enzyme structure. Yet, for catalytically perfect enzymes, every encounter between enzyme and substrate is productive. In these cases, there may be attractive electrostatic forces on the enzyme that entice the substrate to the active site. These forces are sometimes referred to poetically as Circe effects. 

Figure 8.58 Schematic illustration of reaction coordinate diagram of Triose Phosphate Isomerase (TIM) enzyme illustrating near perfect energy landscape pathway allowing for near perfect 1 1 1 stoichiometric equilibrium between all enzyme-bound species optimal for flux through from one enzyme-bound species to another. Enzyme turnover rate kobs is at the diffusion limit, the rate determining step is the association of dihydroxy acetone phosphate (DHAP) with the TIM catalytic site, see Fig. 8.1, hence chemistry is not rate limiting. Therefore, TIM is considered a perfect enzyme For TIM enzyme assay see Fig. 8.17 for TIM enzyme mechanism see Fig. 8.49 (illustration adapted from Knowles, 1991, Fig. 2).

In the above situation, a perfect enzyme should function by organizing all kinetically important species, including the substrate and the possible intermediates, in a stereoelectronically favorable conformation. This scenario would require a conformationally flexible enzyme active site with the multiplicity of conformational states, each suited for a different intermediate/tiansition state combination. 

Chin, ]. "Perfect Enzymes Is the Equilibrium Constant Between the Enzyme s Bound Species Unity " /. Am. Chem. Soc., 105,6502-6503 (1983). 

The first stage in enzymatic catalysis is the diffusion of a substrate into its binding site in the enzyme. For enzymes that are diffusion controlled, this is the rate-limiting step. No improvement in the rates of the chemical steps of the reaction win increase the overall rate of these enzymes, which have consequently been described as perfect enzymes . Such enzymes typically have high, viscosity-dependent, bimolecu-lar rate constants ( lO to 10 s ). Brownian dynamics... 

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