Non-enzymatic rates

1. RatesTransition state theory Free energy of reaction versus free energy of activation Temperature dependence of rates: Arrhenius and Eyring equations

2. Non-enzymatic rates • How do the rates of enzyme-catalyzed reactions compare to uncatalyzed reactions? • Some enzyme-catalyzed reactions are so slow in the absence of an enzyme catalyst that their half-lives begin to approach the age of the earth itself!

3. Rate Enhancements (kcat/knon) Peptide hydrolysis Uncatalyzed: 10-10 s-1 Catalyzed: 103 s-1 Rate acceleration: = catalyzed/uncatalyzed = 1013 What is the basis for rate acceleration?

4. Rate acceleration • Enzymes use the following mechanisms to accelerate reaction rates: • General acid-base catalysis • Proximity

5. Basis for increased reaction rate Preferential Transition State Binding “I think that enzymes are molecules that are complementary in structure to the activated complexes of the reactions that they catalyzed, that is, the molecular configuration (of the activated complexes) is intermediate between the reacting substances and the products of the reaction” Linus Pauling, 1948

7. Enzyme binds the transition state of the reaction it catalyzes with far greater affinity than it binds either the substrates or the products. Michaelis Complex Tetrahedral Intermediate

8. DG‡ G …. ... DGrxn A B C What is transition state or an activated complex? A + B-C A-B + C The transition state represents the point of highest free energy for a reaction step.

9. DG‡ G DGrxn Free energy of activation DG‡ is the free energy of activation. It is the difference in energy between the transition state and the reactants or the minimum amount of energy required to reach the transition state. Indicator for how fast a reaction will occur. Lower the DG‡, faster the reaction.

10. DG‡ G DGrxn Free energy of reaction DGrxnis the free energy of the reaction. DGrxn = Gproducts - Greactants if < 0, exothermic (spontaneous) if > 0, endothermic DGrxnsays nothing about the rate of the reaction. DGrxn : Indicator of whether reaction is thermodynamically favorable.

11. Free energy • The free energy (G) is the net work done on a system in a reversible process at constant temperature and pressure. • DG = DH - TDS is the change in free energy of a system at constant pressure (P) and temperature (T) • DH is the change in enthalpy (heat content) of the system • DS is the change in entropyof the system. • The properties of the surroundings do not enter into this equation. • Standard free energy: DGois defined as the free energy at standard state, i.e., 1M concentration

12. Free energy of a reaction Can be determined from measurement of enthalpy and entropy Or from the equilibrium constant (Keq) of the reaction. A + B C +D Keq Keq provides the standard free energy or vice versa

13. Keq A + B C +D Relationship of G° to Keq

14. Free energy of a reaction A + B C +D • A reaction is spontaneous only if DG < 0 • A reaction is at equilibrium if DG = 0 • a reaction cannot occurspontaneously if DG > 0 • DG is only dependent on the difference in free energy between the final and initial states and is independent of the path of the reaction.

15. DG‡ • Activation energy: difference in free energy between reactants and transition state • Greater the value of DG‡ slower the reaction • Enzymes decrease the free energy of activation

16. Distinguish between DGrxn and DG‡ DGrxn Reaction free energy says nothing about the rate of the reaction. Enzymes do not alter free energy of reaction or Keq of reaction DG‡ Activation free energy Provides information about rate Enzymes decrease activation free energy

17. Temperature dependence of reaction rates Average thermal energy of the activated molecules that determine the rate

19. Temperature dependence of reaction rates The plot of ln k against 1/T gives a straight line. This behaviour is explained by the Arrhenius equation: ln A ln k Ea is the activation energy R is the gas constant T is temperature in degree Kelvin 1/T

20. Arrhenius Factors: A and Ea Ea, the Activation Energy the energy of activation for the reaction Arrhenius A factor or Collision Frequency Only some molecules with energy greater than or equal to Ea react because of steric effects. Not all collisions lead to reaction because the geometry of the molecules may not be 'favorable'.

21. S‡ G S P Rxn coordinate [S‡] K‡ = [S] K‡ S S‡ – DG‡ RT Derivation of the Eyring equation S is converted to P through the transition state, S‡. Assume that S is in equilibrium with S‡, defined by the equilibrium constant, K‡. DG = –RT ln K (R is the gas constant and T is the absolute temperature) DG ‡ = –RT ln K‡ DG ‡ = –RT ln( [S]‡ / [S] )  [S]‡ = [S] exp (eq. 1)

22. K‡ k‡ S S‡ P -d[S] dt S and S‡ are in rapid equilibrium, and therefore the rate of the reaction is controlled by the decomposition of S‡ into P. = k‡ [S‡] The transition state is an extremely fleeting species. It’s lifetime is equivalent to the vibrational frequency of the bond that is breaking. Thus, the rate constant, k‡, is equal to the vibrational frequency,u, of a bond. k‡ = u = kBT (eq. 2) (kB is the Boltzmann constant and h is the Planck constant) (u = 6.212  1012 at 25ºC) h

23. -d[S] -d[S] dt dt – DG‡ – DG‡ – DG‡ RT RT RT substitute eq. 1 & eq. 2 into the rate equation: kBT = k‡ [S‡] = [S] exp h kBT Let the rate constant, k = exp According to transition state theory, then: h if DG‡ k if DG‡ k kBT = k [S], where k = exp h Thus, the rate constant, k, is inversely proportional to DG‡

24. – DG‡ RT Comparison between Eyring’s equation and Arrhenius equation Eyring’s equation from transition state theory Arrhenius equation kBT k = exp h

25. Enzymes accelerate the rate by lowering the activation energy ...by binding tightly to the activated complex or the transition state

26. How tightly does the enzyme bind to the transition state structure? Rate acceleration Peptide hydrolysis Uncatalyzed rate: 10-10 s-1 Catalyzed rate: 103 s-1 Rate acceleration = catalyzed/uncatalyzed = 1013 Enzyme binds the transition state structure about 1013 fold tighter than it does the substrate. ~ 3 kcal/mol ‡  G E+S  G E+P progress of reaction Basis for drug design

27. transition states D ‡ G EP ES E+S D G E+P progress of reaction Transition state theory predicts that enzymes have a high affinity for the transition state structures Any molecule resembling the substrate in its transition state should bind more strongly than the substrate itself.

28. Transition State Analogue Inhibitors • If an enzyme is so extremely preferential to the transition state, then it can be expected that the enzyme will be especially sensitive to inhibitors that mimic the transition state. • Transition state analogues are stable molecules that resemble geometric and/or electronic features of the highly unstable transition state.

29. Transition State Analogs are Enzyme Inhibitors OH H HN O= N R 10,000x tighter Cytidine deaminase OH O= H2N H2N HN HN HN Km = 10-5 M Km = 10-17 M Km = 10-4 M O= O= O= N R N R N R uridine

30. Transition State Analogue Inhibitors • Adenosine 5’-monophosphate (AMP) deaminase: • Involved in the purine nucleotide cycle • Since adenosine is a known cardioprotective agent and AMP deaminase shunts adenine nucleotides away from adenosine, AMP deaminase inhibitors could have therapeutic value in speeding recovery from heart attacks. AMP IMP

31. Transition State Analogue Inhibitors AMP Deaminase (KTx = 1.3  10–17 M)

32. Transition State Analogue Inhibitors Nucleoside Hydrolase Km (nucleosides) = 0.2 - 10 mM

33. Transition State Analogue Inhibitors A few examples of therapeutic targets for transition state analogue inhibitors: Alzheimer’s disease g-secretases < 1 mM HIV HIV-1 protease 10 – 100 pM human cyclophilin 15 mM Cancer 5’-methylthioadenosine 200 pM human glyoxylase I 1 nM Lymphoma nucleoside phosphorylase 20 pM Sexual arousal disorders arginase 52 mM Parasitic infections nucleoside hydrolase 2 nM Disease Target enzyme Potency