Enzyme catalysis 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 ... 

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. 

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... 

Cisneros GA, Wang M, Silinski P, Fitzgerald MC, Yang WT (2004) The protein backbone makes important contributions to 4-oxalocrotonate tautomerase enzyme catalysis understanding from theory and experiment. Biochemistry 43 6885-6892... 

Enzymes are often considered to function by general acid-base catalysis or by covalent catalysis, but these considerations alone cannot account for the high efficiency of enzymes. Proximity and orientation effects may be partially responsible for the discrepancy, but even the inclusion of these effects does not resolve the disparity between observed and theoretically predicted rates. These and other aspects of the theories of enzyme catalysis are treated in the monographs by Jencks (33) and Bender (34). 

Tapia, O. and Andres, J. On a quantum theory of chemical reactions and the role of in vacuum transition stmetures. Primary and secondary sources of enzyme catalysis, J.Mol.Str (THEOCHEM), 335 (1995), 267-286... 

BIFUNCTIONAL CATALYSIS BIFUNCTIONAL ENZYME BIFURCATION THEORY BILIVERDIN REDUCTASE BIMOLECULAR... 

The mechanism of enzyme catalysis drawn, using (a)random ternary complex theory, (b)ordered ternary complex mechanism and (c) ping-pong bi-bi mechanism ... 

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. 

The mechanism and theory of bioelectrocatalysis is still under development. Electron transfer and variation of potential in the electrodeenzyme-electrolyte system has therefore to be investigated. Whether the enzyme is soluble and the electron transfer process occurs through a mediator, or whether there is direct enzyme immobilization on the electrode surface, the homogeneous process in the enzyme active centre has to be described by the laws of enzyme catalysis, and the heterogeneous processes on the electrode surface by the laws of electrochemical kinetics. Besides this there are other aspects outside electrochemistry or... 

O. Tapia, Beyond standard quantum chemical semi-classic approaches Towards a quantum theory of enzyme catalysis, in P. Paneth, A. Dybala-Defratyka (Eds.), Kinetics and Dynamics, From nano- to bio-scale, Challenges and advances in computational chemistry and physics 12, Springer Science, Dordrecht, 2010, p. 267-298. 

Application of Marcus rate theory to proton transfer in enzyme-catalyzed reactions was discussed by Kresge and Silverman, 1999. Relationships of log KIE and kinetics of the enzyme catalysis (kcat) and parameters of the reaction driving force were found to be in agreement with the Marcus model. 

Quantum dynamics effects for hydride transfer in enzyme catalysis have been analyzed by Alhambra et. al., 2000. This process is simulated using canonically variational transition-states for overbarrier dynamics and optimized multidimensional paths for tunneling. A system is divided into a primary zone (substrate-enzyme-coenzyme), which is embedded in a secondary zone (substrate-enzyme-coenzyme-solvent). The potential energy surface of the first zone is treated by quantum mechanical electronic structure methods, and protein, coenzyme, and solvent atoms by molecular mechanical force fields. The theory allows the calculation of Schaad-Swain exponents for primary (aprim) and secondary (asec) KIE... 

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