1. Enzyme Kinetics and Enzyme Regulation Robert F. Waters, PhD. Level one with some calculus.

2. Michaelis-Menten Equation Describes enzymatic activity of enzymes that are NOT allosterically controlled – Allosterically controlled enzymes have sigmoidal curve

3. Enzymes Cannot Alter Equilibria Exergonic versus Endergonic

4. Activation Energy and Delta G Enzymes lower activation energy – Enzymes accelerate Reactions by lowering  G G (Gibbs Free Energy of activation) -  G=exergonic +  G=endergonic

5. Transition Configurations of [ES] May be multiple transition states in a reaction

6. Maximal Velocity V m At a constant [E], the reaction rate increases with increasing [S] concentration until Vmax is reached. – When [s] concentration is sufficiently high, then the highest probability of [ES] formed and reaches Vmax Saturation of enzyme active sites This is indirect proof of ES complexes Note: – 1 st order kinetics – Mixed order kinetics – Zero order kinetics

7. Analysis of Enzymatic Reactions NMR (Nuclear Magnetic Resonance) ESR (Electron Spin Resonance) Fluorescent Spectroscopy

8. Example: Fluorescent Spectroscopy (Bacteria) Spectroscopic changes during different ES configurations – Bacterial tryptophan synthetase with pyridoxal phosphate prosthetic group forms L-tryptophan from L-Serine and indole – Note fluorescence differences

9. Enzyme Active Sites Active sites are relatively small areas of enzyme structure Active sites are 3-dimensional Substrates are bound to active sites by multiple weak interactions Active sites are crevices or protrusions Specificity depends upon atomic arrangement at the active site

10. Derivation of Michaelis-Menten The dissociation constant k 4 is dropped because of the small amount of E + P forming ES.

11. M-M Variables E=uncombined enzyme ES=enzyme combined with substrate S=substrate P=product k 1,k 2,k 3,k 4 – Association and dissociation constants

12. Assumptions [ ] = molar concentration Total enzyme concentration (All Forms) Total substrate concentration

13. M-M Assumptions Cont: We can assume – [ES] and [P] are very small compared to [S] because: [S]>>[ES] since [S] concentrations are always much greater than [E] or [S]>>>[E] – Velocity and rate measurements are usually conducted as soon as possible after enzyme and substrate are mixed. THEREFORE, at very little P exists.

14. Velocity and M-M Equation Velocity is related to the rate of formation of the product. Product (P) is formed from ES. The velocity of the reaction is proportional to [ES]

15. M-M Equation Continued Express ES in terms of rate of formation and breakdown. – Rate of formation of ES from E + S – Rate of formation of ES from E + P Small amount so neglected – Rate of conversion of ES to E + P – Rate of dissociation of ES to E + S

16. Total Concentration Change of ES with Time (rate of formation of ES)-(rate of breakdown or conversion of ES)

17. Michaelis-Menten Derivation Since, Therefore, Substituting for [E] in

18. Michaelis-Menten Derivation, Cont: Therefore, Briggs and Haldane suggested a steady-state condition where rate of formation = rate of dissociation.

19. Michaelis-Menten Derivation, Cont: By substitution from: Where, Segregating [E t ] and [ES in above equation]

20. Solving for [ES] Yields From

21. Dividing Numerator and Denominator by k 1 We get,

22. Michaelis-Menten Derivation, Cont: We can define the M-M constant: Substituting into With We get,

23. Michaelis-Menten Derivation, Cont: Velocity (v) is defined as rate of formation of product Substituting for [ES] Or rearranging..

24. Michaelis-Menten Derivation, Cont: At very high saturating substrate concentrations, the enzyme is found essentially all in the [ES] form so that.. Under these conditions..

25. Michaelis-Menten Derivation, Cont: By substitution.. Then.. This equation is a hyperbola..

26. Michaelis-Menten Derivation, Cont: We generally say in M-M derivation that is the [S] where the velocity his half-maximal or… Dividing both sides by We get.. Where = [S] when velocity is half-maximal.

27. Michaelis-Menten Derivation, Cont: Therefore, is the equilibrium constant for the dissociation of the ES complex Then, the M-M equation is…

28. Example Problem Let’s use the form

29. Determine Vmax and Km Initial [S] in M(Moles)V 0 (  moles/L) 1 x 10 -2 75.0 1 x 10 -3 74.9 1 x 10 -4 60.0 7.5 x 10 -5 56.25 6.25 x 10 -6 15.0

30. Assumptions and Computations

31. Pick Another Initial Velocity and Compute K m What will the maximum velocity be?

32. Comparison of Enzymes Same substrate with two separate enzymes. Higher the K m the lower the affinity. Differences in first order and mixed order kinetics.

33. Linear Representation:Lineweaver- Burk Plot

34. Lineweaver-Burk Representation

35. Competitive Inhibition Inhibitor binds to same site as substrate. Reversible Vmax is the same. Km increases with inhibitor.

36. Example of Competitive Inhibitor Malonate with Succinate – Malonate 3 carbon dicarboxylate

37. Non-Competitive Inhibitor Km is unchanged. Vmax decreases with inhibitor.

38. Uncompetitive Inhibitor Km increases Vmax decreases. Inhibitors bind to the ES complex not to the dissociated enzyme alone.

39. Example: Inhibitor in Medicine

40. IRREVERSIBLE Competitive Inhibitors Affinity Labels – Blocks active site of enzyme by covalently binding to side group(s) on amino acids Mechanism-Based or Suicide Inhibitors – Product of ES complex will inhibit the active site of the enzyme itself. Transition-state analogs – Are NOT covalently bound, however, resemble substrates so closely they bind very tightly to enzyme active site and enzymatic activity is lost

41. Examples of Irreversible Inhibitors InhibitorTarget EnzymeEffect AspirinCyclooxygenaseAnti-inflammatory AllopuranolXanthine oxidaseGout treatment 5-fluorouracilThymidylate synthetase Anti-cancer drug ParagylineMonoamine oxidase Anti-hypertensive drug PenicillinTranspeptidaseAnti-bacterial SarinCholinesteraseChemical warfare

42. Regulation of Enzymes pH ( Optimum pH based on pseudo-bell curve) Temperature ( Optimum temperature) Product Inhibition (Affects enzyme itself) – Feedback control (Modulator) Covalent Modification – Phosphorylation – Proteolytic cleavage (Zymogen System) Blood clotting Allosteric Control (Allosteric means “other site”) (Genetic) – Effectors (Modifiers, Modulators) Activators Inhibitors – Feedback inhibition (e.g., hemin and ALA-  -aminolevulinate synthase (  -delta)

43. Some Diagnostic Enzymes Acid Phosphatase (Prostate Cancer) Alanine Aminotransferase (Viral Hepatitis, Liver Damage) Alkaline Phosphatase (Liver disease, Bone Disorders) Amylase (Acute Pancreatitis) Creatine Kinase (Muscle Disorders, Heart Attack) Lactate Dehydrogenase (Heart Attack)