Enzyme Kinetics

1. Enzyme Kinetics

2. Enzymes • What are enzymes? • How do enzymes work (kinetics) • How are enzymes used in reactors

3. Enzymes • Enzymes: • Proteins with rare exceptions • Catalysts for a variety of reactions • Most common - hydrolysis – breakdown of chemical bond with addition of water • Carboxylases “cut” C – 0 – C bond in sugar polymers • Proteases (aka Proteinases, Peptidases) cut N- C=O (amide) bond • Isomerases rearrange bonds in various molecules • xylose isomerase = glucose isomerase converts glucose to fructose • Various other types, kinases, decarboxylases etc.

4. Industrially Important Corn milling (starch to sugar)

5. Enzyme Visualization Penicillin Acylase 1FXV

6. Enzyme with substrate Penicillin Acylase 1FXV

7. ES complex S Reaction/hydrolysis Binding Product release Enzyme regeneration EP complex E General Enzymatic Catalysis

8. Enzyme Assays • Enzymes are detected by their “activity” – the ability to catalyze a particular reaction • Often “artificial” or natural substrates which change color (absorbance) after the reaction are used to measure enzyme activity • The rate of an enzymatic reaction is proportional to the amount of enzyme present.

9. Enzyme Activity 2 x enzyme Absorbance 1 x enzyme time

10. Activity Relative rate of absorbance change Enzyme conc

11. Specific Activity • The specific activity is the rate of change in absorbance per g of enzyme.

12. Specific activity • 10 units/mg of protein • 1 unit hydrolyzes 1 umole of penicillin per minute at the conditions specified. • The specific activity is 10 umole of penicillin per minute per mg.

13. Turnover # • 1 mg of protein is about 1.5 x 10-2 umole of protein (MW = 75000 daltons) • Turnover is 10 umole/min/1.5 x 10-2 umole = 6 x 102 per minute = 10/second. • For each molecule of enzyme 10 molecules of penicillin are reacted per second. • (typical turnovers range from 1 to 1000/sec)

14. Michaelis-Menten Kinetics s-1 k1 (second order) k3 = kcat (first order) mM-1s-1 E + S ES EP E + P1 + P2 The reverse reactions are usually considered slow. k2 (first order) s-1 Rate of reaction = rate of appearance of product(s) = rate of disappearance of substrate units moles/min-L. Total (all forms) enzyme concentration mM Substrate conc mM mM

15. M-M analysis • Assumptions: • Collision of S and E is fast compared to other processes • Enzyme molarity is small compared to substrate molarity • k4, k6 small (Thermo toward EP vs ES complex;P does not bind well to enzyme • k5 large (P does not bind well to enzyme) • Definitions: • Eo = total enzyme concentration • E = Free enzyme (open binding site) • ES= “bound enzyme” or “ES complex” (EP small)

16. M-M Math • E + ES ~ Eo (assume EP is small) • Since S>>E and k1 fast: • Algebra gives:

17. Math • Substitution for E gives: • Solving for ES gives:

18. Math • The rate of substrate lost = -rate of product formation = • Sometimes k3Eo is called Vmax

19. M-M kinetics • Consequences: • The rate of reaction of substrate is proportional to the concentration of enzyme used, regardless of the substrate concentration. • Plots of P or S vs Eot should collapse to a single curve for different enzyme levels • If not, enzyme might be deactivating • Or non-enzymatic reaction occurring along with enzymatic reaction DP/Dt data (rate data) vs Eo should give a straight line (low conversion)

20. kcatEo = Vmax Rate of reaction (mM/s) Km Substrate available (mM) Rate vs S

21. M-M kinetics • Features • At high substrate concentration the rate of reaction becomes zero order. kapp = kcatEo (mM/s) • At low substrate concentration the rate of reaction becomes 1st order. kapp = kcatEo/Km (1/s) • Rate is proportional to the amount of enzyme used (Eo) • Values for kcat range widely, from 0 to 1000 s-1. • Km values from 10-3 mM to 10 mM.

22. Substrate vs Time in Batch Reactor Starts out zero order Substrate Ends up first order time

23. Reversible Reactions(Isomerizations) E + S ES EP E + P Equilibrium favors P in the case shown P curve S or P S curve Time (s)

24. Inhibitors E + S ES E + P + I EI An inhibitor binds to the enzyme and reduces the amount of enzyme available ES complex S E EP complex EI complex

25. Enzyme Deactivation • Proteins can deactivate with use • Unfold, oxidize, hydrolyze. • The reaction rate will slow because: Eo = Eoo exp (-kd t) Deactivation rate constant. Active enzyme at time t. Original active enzyme

26. Case Study • Potato starch saccharification by A. niger glucoamylase • Milan Polakovic, Jolanta Bryjak • Biochemical Engineering Journal (2003) in press

27. What is Starch • Branched chains of poly 1->4 glucose

28. Branched structure 1,6 bond 1,4 bonds

29. Issues • Glucoamylase works from 4 (non-reducing) end, one glucose at a time. (end group concentration stays fairly constant for a long time) • Glucoamylase may have 1,6 activity but if so it is slower – “pullanase” has better 1,6 activity.

30. Issues • Science: • Mode of action • Determination of kcat, k1, k2 etc. • Engineering • Progress curves • Effect of enzyme concentration** • Effect of substrate concentration • Inhibitor effect • Effect of conditions (pH) • Effect of temperature

31. Designing a Reactor • For modeling a “rate expression” is needed • Describes the rate of substrate “disappearance” as a function of enzyme conc etc. • Control volume Reactor “side” Input –output – rate side

32. Reactor balance • Solve for P(t) • Decide the reactor volume needed

33. Example • Glucose production using glucoamylase The manufacturer of glucoamylase says that 1 unit of enzyme produces 1 milligram of glucose per minute at the conditions specified (pH 5.0, temp = 20 C). Their solution contains 100 units per mL.

34. Some Data

35. Example You want to design a reactor system to produce 100 kg/hr of glucose from a 10% (100 g/L) solution of starch.

36. Example • Stoichiometry • 100 grams of starch will produce 110 grams of glucose. • To produce 100 kg of glucose will require 91 kg of starch or 910 L of 10% starch solution • Design 1: 1000 L reactor containing 910 L of 10% starch solution (100 kg of glucose).

37. Example • Add enough enzyme to produce this in 1 hour • 100,000,000 milligrams requires 100,000,000/60 units • 1500000 units added to a 1000 L reactor (1500 units/L) • 1500000 units = 15000 cc = 15 L • Preliminary Design • Add 15 L of enzyme solution to a 1000 L reactor containing 910 L of a 10% solution.

38. Continuous Reactors Plug Flow vs CSTR zero order regime (high substrate conc) low conversion –only one rate Rate puv is the same as in PFR. Rate puv is the same along reactor length. Volume of PFR is same as CSTR

39. Continuous Reactors Plug Flow vs CSTR First order regime (low substrate conc) High conversion – rate depends on S conc Rate puv is rate for final (exit) concentra- tion. Rate puv starts out high gradually drops along reactor length. Volume of PFR is smaller than CSTR

40. Approximating a PFR Multiple CSTR’s in series approximate a PFR (Easier to build); 3 – 5 usually close enough with similar total volume as PFR Concentration reduced gradually

41. Immobilized Enzymes • Enzymes coupled to a solid surface or entrapped in a solid • Stay separate from the fluid being processed • Can be reused • Work well in a packed bed reactor

42. Immobilized Enzyme Reactor Enzyme is physically tethered or physically entrapped in the solid matrix. The matrix may be (cross linked) agarose, polyacrylamide, dextran, cellulose (biocompatible)

43. Problems/Limitations when Enzymes are Immobilized • Diffusion hinders substrate access to • enzyme (Theile modulus) 3. Not feasible with insoluble substrates. 2. pH may be different inside vs on the surface of the particle

44. Summary • Enzymes are proteins that act as catalysts • The rate expression most often follows Michaelis-Menten kinetics (saturation kinetics) • Enzymes can be used as soluble catalysts in batch, CSTR and plug flow reactors. • Enzymes can be used in immobilized form – often in packed bed reactors.