Previous Lecture

• Enzyme functional properties • Enzyme specificity overview • Enzyme regulation importance

Objectives

• Transition state Theory • Hammond’s principle • Principles of Catalysis Transition state theory of reaction rates states that reactants pass through high-energy transition states before forming products. (Mechanism of interaction ignored)

Transition state

intermediate

G reactant

product

Reaction coordinate Activation Energy ∆G‡

• The transition state (T‡) is predicted to be the most unstable species in the T‡ reaction pathway between reactants and products ∆G‡ •The activation energy G R represents the difference in ∆Greaction ‡ energy between R and T . P • The higher the activation energy the slower the Reaction coord. reaction will proceed Activation Energy ∆G‡

• Activation energy can be thought of as an energy barrier T‡ • Rate of the reaction can be derived from ∆G‡ (free energy difference ∆G‡ between transition state and reactant) G R (related to the concentration of the ∆Greaction transition state) and the rate of P transition state decomposition. Reaction coord. • The rate equation and the rate constant, k, provides a macroscopic picture of the reaction Relationship between Rate and ∆G‡ S ←→ T‡ → P K k • We can approximate the relative concentrations of S and T‡ by an equilibrium distribution K‡ = [T‡]/ [S] • which can be rearranged to give [T‡]= K‡ [S] • The rate of formation of P can be given in terms of [T‡] • rate = k [T‡] substituting into the pre-equilibrium expression rate = k K‡ [S] • The relationship between free energy and the equilibrium constant is ∆G = -RT ln K • leads to the substitution of exp (- ∆G‡ / RT) for K‡

rate = k (e - ∆G‡ / RT)[S]

Eqn relates the rate of the reaction to the difference in free energy between the transition state and ground state Enzymes accelerate rates by reducing ∆G‡

rate = k (e - ∆G‡ / RT) [S]

Without Enzyme With Enzyme

T‡

T‡ ‡ ∆G ∆G‡ G G R R ∆Greaction ∆Greaction P P Reaction coord. Reaction coord. •Enzymes do not affect ∆G reaction (i.e. The enzyme has no effect on the equilibrium of the reaction) Enzymes accelerate rates by reducing ∆G‡ • If the transition state can be stabilized the free energy barrier of the reaction will be reduced • Binding energy can thus be used for rate enhancement • e.g. an enzyme often neutralizes charges that appear in the transition state • Advantageous for the enzyme’s active site to complement the structure of the transition state rather than the reactant (substrate). Hammond’s Postulate

"If two states, as for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have nearly the same energy content, their interconversion will involve only a small reorganization of the molecular structures." George S. Hammond, 1955 Hammond’s Postulate cont.

G

Reaction coord.

Hammond postulated that in highly exothermic reactions (left) the transition state (Ts) is structurally similar to the reactant (R), but that in highly endothermic reactions (right) the product (P) is a better model of the transition state. Hammond’s Postulate

• The Hammond postulate suggests that species that are sequential on the reaction coordinate and similar in energy are therefore similar in structure

• Therefore, an unstable intermediate on the reaction pathway (whose structure may be obtained by experimental means) is predicted to resemble the structure of the transition state

• Conversely, changes in structure that stabilize or destabilize reactive intermediates will stabilize or destabilize transition states leading to them. ….Why do we care about the structure of the transition state when it is unstable and transient? Applications of the transition state theory and Hammond’s Postulate

• Elucidating the structure of the transition state can lead to the design of transition state analogs whose ground state geometry is similar to the transition state. • These analogues can be used as enzyme inhibitors (Drug therapy) • These analogues can be used to elucidate the mechanism of the enzyme mediated reaction (Mechanistic details) Transition-state analogs are the best inhibitors of enzymes

Lysozyme example: Lysozyme hydrolyzes polysacchrides O Transition State predicted to be carbonium ion which is planar Transition state analog that would be O + a sugar with a planar carbon at the reactive centre (lactone) rather than chair shaped centre (glucose) should be a better inhibitor-which was proven to be the case. Transition-state analogs are the best inhibitors of enzymes chorismate mutase example:

Various catalytic antibodies were generated using different transition state analogs as the immunogen. The CATALYTIC ANTIBODIES demonstrated substantial rate accelerations (in replace of the mutase) demonstrating their value in obtaining mechanistic details on enzymatic processes. Active of site of the chorismate mutase showing solvent accessible surface with the transition state analog Active of site of the chorismate mutase antibody side-chain interactions with the transition state analog