Principles of Protein Structure - G. Schultz 1982

Structural Basis of Protein Mechanism, Action, and Function
Enzymatic Catalysis
Transition State Theory

At each stage of a chemical reaction, the reacting species pass from one relatively stable state to another via a higher-energy state (Fig. 11.2). The Transition State is a state of higher Free energy through which reactants must pass to proceed from one stable state to another [738–740]. Reaching the transition state requires additional free energy, $\Delta$G^≠, known as the Free energy of activation. According to the Arrhenius equation, $k = s \cdot \exp(-\Delta G^{\neq}/RT) = s \cdot \exp(-\Delta H^{\neq}/RT + T\Delta S/RT)$, The rate of a chemical reaction depends on the activation energy [697].

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Fig. 11.2. Transition state theory and Enzymatic Catalysis [740]. Free energy profiles are shown for the uncatalyzed reaction (dashed line) and the corresponding enzyme-catalyzed reaction (solid line). Only a single compound (substrate) is considered; the reaction in question may be, specifically, an isomerization. Both the catalyzed and uncatalyzed reactions are assumed to follow the same mechanism. The following notations are used:

E — enzyme, S — substrate, P — product, — substrate transition state. Free Energy Changes refer to the following reactions: $\Delta G_S$ — formation of ES from E and S; $\Delta G_{\text{t}}$ — formation of ES^≠ from E and ; — formation of S^≠ from S; $\Delta G^{\neq}_{E}$ — formation of ES^≠ from ES. Parameters assumed for the calculation of free energy changes: $K_S$ — association constant for ES, 10⁴ M^-1; $K_P$ — association constant for EP, 10⁴ M^-1; $k_d$ — first-order rate constant for the dissociation of ES into E and S and of EP into E and P, 10⁴ s^-1; $k_E$ — first-order reaction rate constant for The conversion of ES into EP, 10² s^-1; $k_N$ — first-order rate constant of the corresponding uncatalyzed reaction, 10^-5 ∙ s^-1; concentrations of S and P are assumed to be 1 M; the Equilibrium Constant for The formation of P from S is 1.0.

The activation energy has an entropic component reflecting the additional ordering the system must acquire to reach the transition state, for instance, when atoms must approach closely enough to interact. Another, enthalpic part of the activation energy represents the work required to bring atoms close enough for a covalent bond to form between them. Enzymes can lower the enthalpy of activation (compared to Reactions in Solution) through specific binding of substrates, thereby selecting a favorable reaction pathway from the several pathways available in solution.