Catalysis transition state theory

Enzyme catalysis requires that Kj- < Kg. According to transition-state theory (see references at end of chapter), the rate constants for the enzyme-catalyzed k ) and uncatalyzed k reactions can be related to Kg and K by ... 

Transition state theory, 46,208 Transmission factor, 42,44-46,45 Triosephosphate isomerase, 210 Trypsin, 170. See also Trypsin enzyme family active site of, 181 activity of, steric effects on, 210 potential surfaces for, 180 Ser 195-His 57 proton transfer in, 146, 147 specificity of, 171 transition state of, 226 Trypsin enzyme family, catalysis of amide hydrolysis, 170-171. See also Chymotrypsin Elastase Thrombin Trypsin Plasmin Tryptophan, structure of, 110... 

In the classical world (and biochemistry textbooks), transition state theory has been used extensively to model enzyme catalysis. The basic premise of transition state theory is that the reaction converting reactants (e.g. A-H + B) to products (e.g. A + B-H) is treated as a two-step reaction over a static potential energy barrier (Figure 2.1). In Figure 2.1, [A - H B] is the transition state, which can interconvert reversibly with the reactants (A-H-l-B). However, formation of the products (A + B-H) from the transition state is an irreversible step. 

The transition state theory is likely an oversimplification when applied to enzyme catalysis - it was originally developed to account for gas phase... 

Finally, we will apply transition state theory and collision theory to some elementary surface reactions that are important in catalysis. 

We have just discussed several common strategies that enzymes can use to stabilize the transition state of chemical reactions. These strategies are most often used in concert with one another to lead to optimal stabilization of the binary enzyme-transition state complex. What is most critical to our discussion is the fact that the structures of enzyme active sites have evolved to best stabilize the reaction transition state over other structural forms of the reactant and product molecules. That is, the active-site structure (in terms of shape and electronics) is most complementary to the structure of the substrate in its transition state, as opposed to its ground state structure. One would thus expect that enzyme active sites would bind substrate transition state species with much greater affinity than the ground state substrate molecule. This expectation is consistent with transition state theory as applied to enzymatic catalysis. 

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. 

The field of chemical kinetics is far reaching and well developed. If the full energy surface for the atoms participating in a chemical reaction is known (or can be calculated), sophisticated rate theories are available to provide accurate rate information in regimes where simple transition state theory is not accurate. A classic text for this field is K. J. Laidler, Chemical Kinetics, 3rd ed., Prentice Hall, New York, 1987. A more recent book related to this topic is I. Chorkendorff and J. W. Niemantsverdriet, Concepts of Modern Catalysis and Kinetics, 2nd ed., Wiley-VCH, Weinheim, 2007. Many other books in this area are also available. 

In this chapter, we discuss the fundamental principles of chemical reactivity and catalysis to understand the organic chemistry of catalysis and how to analyze it. We begin with transition state theory because it provides a simple framework for understanding much about reactivity and kinetics. We progress to structure-activity relationships and also discuss some fundamental concepts in analyzing mechanisms. 

The high effective concentration of intramolecular groups is one of the most important reasons for the efficiency of enzyme catalysis. This can be explained theoretically by using transition state theory and examining the entropy term in the rate equation (2.7). It will be seen that effective concentrations may be calculated by substituting certain entropy contributions into the exp (AS /R) term of equation 2.7. 

Important milestones in the rationalization of enzyme catalysis were the lock-and-key concept (Fischer, 1894), Pauling s postulate (1944) and induced fit (Koshland, 1958). Pauling s postulate claims that enzymes derive their catalytic power from transition-state stabilization the postulate can be derived from transition state theory and the idea of a thermodynamic cycle. The Kurz equation, kaJkunat Ks/Kt, is regarded as the mathematical form of Pauling s postulate and states that transition states in the case of successful catalysis must bind much more tightly to the enzyme than ground states. Consequences of the Kurz equation include the concepts of effective concentration for intramolecular reactions, coopera-tivity of numerous interactions between enzyme side chains and substrate molecules, and diffusional control as the upper bound for an enzymatic rate. 

For the above applied oxidation of methane to carbon dioxide on some metal oxide catalysts, also a first-order reaction was assumed [10, pp. 182 and 193], However, in combinatorial catalysis it may be sufficient to have a first rough idea about the underlying kinetics. Without having prior information about the kinetics, the performance of a reactor is provided with a huge uncertainty. This is obvious if one considers the wide variation of reaction rates. Pre-exponential factors of reaction rate constants derived by the transition-state theory vary widely from approximately 10 to 1016 s-1 [10]. This first information might then be used to develop a pilot plant for the up-scaling and for further detailed kinetic examinations. 

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