1. 10/14/2008 Biochemistry: Enzyme Properties Enzyme Properties and Kinetics Andy Howard Introductory Biochemistry, Fall 2008 14 October 2008

2. 10/14/2008 Biochemistry: Enzyme Properties p. 2 of 39 Enzymes catalyze reactions We need to classify them and get an idea of how they affect the rates of reactions.

3. 10/14/2008 Biochemistry: Enzyme Properties p. 3 of 39 Plans for Today Classes of enzymes Enzyme kinetics Michaelis-Menten kinetics: overview Kinetic Constants Kinetic Mechanisms Induced Fit Bisubstrate reactions

4. 10/14/2008 Biochemistry: Enzyme Properties p. 4 of 39 Enzymes Okay. Having reminded you that not all proteins are enzymes, we can now zero in on enzymes Understanding a bit about enzymes makes it possible for us to characterize the kinetics of biochemical reactions and how they’re controlled

5. 10/14/2008 Biochemistry: Enzyme Properties p. 5 of 39 Enzymes have 3 features Catalytic power (they lower  G ‡ ) Specificity They prefer one substrate over others Side reactions are minimized Regulation Can be sped up or slowed down by inhibitors and accelerators Other control mechanisms exist

6. 10/14/2008 Biochemistry: Enzyme Properties p. 6 of 39 IUBMB Major Enzyme Classes EC #ClassReactionsSampleComments 1oxidoreductasesOxidation- reduction LDHNAD,FMN 2 transferasesTransfer big group AATIncludes kinases 3 hydrolasesTransfer of H 2 O Pyrophos hydrolase Includes proteases 4 LyasesAddition across = Pyr decar- boxylase synthases 5 IsomerasesUnimolec- ular rxns Alanine racemase Includes mutases 6 LigasesJoining 2 substrates Gln synthetase Often need ATP

7. 10/14/2008 Biochemistry: Enzyme Properties p. 7 of 39 EC System 4-component naming system, sort of like an internet address Pancreatic elastase: Category 3: hydrolases Subcategory 3.4: hydrolases acting on peptide bonds (peptidases) Sub-subcategory 3.4.21: Serine endopeptidases Sub-sub-subcategory 3.4.21.36: Pancreatic elastase Porcine pancreatic elastase PDB 3EST 1.65 Å 26kDa monomer

8. 10/14/2008 Biochemistry: Enzyme Properties p. 8 of 39 Category 1: Oxidoreductases General reaction: A ox + B red  A red + B ox One reactant often a cofactor (see ch.7) Cofactors may be organic (NAD or FAD) or metal ions complexed to proteins Typical reaction: H-X-OH + NAD +  X=O + NADH + H +

9. 10/14/2008 Biochemistry: Enzyme Properties p. 9 of 39 Category 2: Transferases These catalyze transfers of groups like phosphate or amines. Example: L-alanine +  -ketoglutarate  pyruvate + L-glutamate Kinases are transferases: they transfer a phosphate from ATP to something else

10. 10/14/2008 Biochemistry: Enzyme Properties p. 10 of 39 Category 3: hydrolases Water is acceptor of transferred group Ultrasimple: pyrophosphatase: Pyrophosphate + H 2 O -> 2 Phosphate Proteases, many other sub-categories HO-P-O-P-OH O O O-O- O-O-

11. 10/14/2008 Biochemistry: Enzyme Properties p. 11 of 39 Category 4: Lyases Non-hydrolytic, nonoxidative elimination (or addition) reactions Addition across a double bond or reverse Example: pyruvate carboxylase: pyruvate + H +  acetaldehyde + CO 2 More typical lyases add across C=C C=C

12. 10/14/2008 Biochemistry: Enzyme Properties p. 12 of 39 Category 5: Isomerases Unimolecular interconversions (glucose-6-P  fructose-6-P) Reactions usually almost exactly isoergic Subcategories: Racemases: alter stereospecificity such that the product is the enantiomer of the substrate Mutases: shift a single functional group from one carbon to another (phosphoglucomutase)

13. 10/14/2008 Biochemistry: Enzyme Properties p. 13 of 39 Category 6: Ligases Catalyze joining of 2 substrates,e.g. L-glutamate + ATP + NH4 +  L-glutamine + ADP + P i Require input of energy from XTP (X=A,G) Usually called synthetases (not synthases, which are lyases, category 4) Typically the hydrolyzed phosphate is not incorporated into the product

14. 10/14/2008 Biochemistry: Enzyme Properties p. 14 of 39 iClicker quiz, question 1 Collagenase catalyzes the cleavage of the  -glycosidic bonds holding collagen together. Which IUBMB enzyme category would collagenase fall into? (a) ligases (6) (b) oxidoreductases (1) (c ) hydrolases (3) (d) isomerases (5) (e) none of the above.

15. 10/14/2008 Biochemistry: Enzyme Properties p. 15 of 39 iClicker quiz, question 2 Triosephosphate isomerase, whose structure we discussed earlier, interconverts glyceraldehyde-3- phosphate and dhydroxyacetone phosphate. What would you expect the approximate  G value for this reaction to be? (a) -30 kJ mol -1 (d) 0 kJ mol -1 (b) 30 kJ mol -1 (e) no way to tell. (c ) -14 kJ mol -1.

16. 10/14/2008 Biochemistry: Enzyme Properties p. 16 of 39 Enzyme Kinetics Kinetics: study of reaction rates and the ways that they depend on concentrations of substrates, products, inhibitors, catalysts, and other effectors. Simple situation A  B under influence of a catalyst C, at time t=0, [A] = A 0, [B] = 0: then the rate or velocity of the reaction is expressed as d[B]/dt.

17. 10/14/2008 Biochemistry: Enzyme Properties p. 17 of 39 Kinetics, continued In most situations more product will be produced per unit time if A 0 is large than if it is small, and in fact the rate will be linear with the concentration at any given time: d[B]/dt = v = k[A] where v is the velocity of the reaction and k is a constant known as the forward rate constant. Here, since [A] has units of concentration and d[B]/dt has units of concentration / time, the units of k will be those of inverse time, e.g. sec -1. [B] t

18. 10/14/2008 Biochemistry: Enzyme Properties p. 18 of 39 More complex cases More complicated than this if >1 reactant involved or if a catalyst whose concentration influences the production of species B is present. If >1 reactant required for making B, then usually the reaction will be linear in the concentration of the scarcest reactant and nearly independent of the concentration of the more plentiful reactants.

19. 10/14/2008 Biochemistry: Enzyme Properties p. 19 of 39 Bimolecular reaction If in the reaction A + D  B the initial concentrations of [A] and [D] are comparable, then the reaction rate will be linear in both [A] and [D]: d[B]/dt = v = k[A][D] = k[A] 1 [D] 1 i.e. the reaction is first-order in both A and D, and it’s second-order overall

20. 10/14/2008 Biochemistry: Enzyme Properties p. 20 of 39 Forward and backward Rate of reverse reaction may not be the same as the rate at which the forward reaction occurs. If the forward reaction rate of reaction 1 is designated as k 1, the backward rate typically designated as k -1.

21. 10/14/2008 Biochemistry: Enzyme Properties p. 21 of 39 Multi-step reactions In complex reactions, we may need to keep track of rates in the forward and reverse directions of multiple reactions. Thus in the conversion A  B  C we can write rate constants k 1, k -1, k 2, and k -2 as the rate constants associated with converting A to B, converting B to A, converting B to C, and converting C to B.

22. 10/14/2008 Biochemistry: Enzyme Properties p. 22 of 39 Michaelis-Menten kinetics A very common situation is one in which for some portion of the time in which a reaction is being monitored, the concentration of the enzyme-substrate complex is nearly constant. Thus in the general reaction E + S  ES  E + P where E is the enzyme, S is the substrate, ES is the enzyme-substrate complex (or "enzyme- intermediate complex"), and P is the product We find that [ES] is nearly constant for a considerable stretch of time. [ES] t

23. 10/14/2008 Biochemistry: Enzyme Properties p. 23 of 39 Michaelis-Menten rates Rate at which new ES molecules are being produced in the first forward reaction is equal to the rate at which ES molecules are being converted to (E and P) and (E and S). Rate of formation of ES from left = v f = k 1 ([E] tot - [ES])[S] because the enzyme that is already substrate-bound is unavailable!

24. 10/14/2008 Biochemistry: Enzyme Properties p. 24 of 39 Equating the rates Rate of disappearance of ES on right and left is v d = k -1 [ES] + k 2 [ES] = (k -1 + k 2 )[ES] This rate of disappearance should be equal to the rate of appearance Under these conditions v f = v d.

25. 10/14/2008 Biochemistry: Enzyme Properties p. 25 of 39 Derivation, continued Thus since v f = v d. k 1 ([E] tot - [ES])[S] = (k -1 + k 2 )[ES] K m  (k -1 + k 2 )/k 1 = ([E] tot - [ES])[S] / [ES] [ES] = [E] tot [S] / (K m + [S]) But the rate-limiting reaction is the formation of product: v 0 = k 2 [ES] Thus v 0 = k 2 [E] tot [S] / (K m + [S])

26. 10/14/2008 Biochemistry: Enzyme Properties p. 26 of 39 Maximum velocity What conditions would produce the maximum velocity? Answer: very high substrate concentration ([S] >> [E] tot ), for which all the enzyme would be bound up with substrate. Thus under those conditions we get V max = v 0 = k 2 [ES] = k 2 [E] tot

27. 10/14/2008 Biochemistry: Enzyme Properties p. 27 of 39 Using V max in M-M kinetics Thus since V max = k 2 [E] tot, v 0 = V max [S] / (K m +[S]) That’s the famous Michaelis-Menten equation

28. 10/14/2008 Biochemistry: Enzyme Properties p. 28 of 39 Graphical interpretation

29. 10/14/2008 Biochemistry: Enzyme Properties p. 29 of 39 Physical meaning of K m As we can see from the plot, the velocity is half-maximal when [S] = K m Trivially derivable: if [S] = Km, then v 0 = V max [S] / ([S]+[S]) = V max /2 We can turn that around and say that the K m is defined as the concentration resulting in half-maximal velocity K m is a property associated with binding of S to E, not a property of turnover

30. 10/14/2008 Biochemistry: Enzyme Properties p. 30 of 39 k cat A quantity we often want is the maximum velocity independent of how much enzyme we originally dumped in That would be k cat = V max / [E] tot Oh wait: that’s just the rate of our rate-limiting step, i.e. k cat = k 2

31. 10/14/2008 Biochemistry: Enzyme Properties p. 31 of 39 Physical meaning of k cat Describes turnover of substrate to product: Number of product molecules produced per sec per molecule of enzyme More complex reactions may not have k cat = k 2, but we can often approximate them that way anyway Some enzymes very efficient: k cat > 10 6 s -1

32. 10/14/2008 Biochemistry: Enzyme Properties p. 32 of 39 Specificity constant, k cat /K m k cat /K m measures affinity of enzyme for a specific substrate: we call it the specificity constant or the molecular activity for the enzyme for that particular substrate Useful in comparing primary substrate to other substrates (e.g. ethanol vs. propanol in alcohol dehydrogenase)

33. 10/14/2008 Biochemistry: Enzyme Properties p. 33 of 39 Kinetic Mechanisms If a reaction involves >1 reactant or >1 product, there may be variations in kinetics that occur as a result of the order in which substrates are bound or products are released. Examine eqns. 13.48, 13.49, 13.50, and the unnumbered eqn. on p. 430 in G&G, which depict bisubstrate reactions of various sorts. As you can see, the possibilities enumerated include sequential, random, and ping-pong mechanisms.

34. 10/14/2008 Biochemistry: Enzyme Properties p. 34 of 39 Historical thought Biochemists, 1935 - 1970 examined effect on reaction rates of changing [reactants] and [enzymes], and deducing the mechanistic realities from kinetic data. In recent years other tools have become available for deriving the same information, including static and dynamic structural studies that provide us with slide-shows or even movies of reaction sequences. But diagrams like these still help!

35. 10/14/2008 Biochemistry: Enzyme Properties p. 35 of 39 Sequential, ordered reactions Substrates, products must bind in specific order for reaction to complete A B P Q _____________________________ E EA (EAB) (EPQ) EQ E W.W.Cleland

36. 10/14/2008 Biochemistry: Enzyme Properties p. 36 of 39 Sequential, random reactions Substrates can come in in either order, and products can be released in either order A B P Q EA EQ __ E (EAB)(EPQ) E EB EP B A Q P

37. 10/14/2008 Biochemistry: Enzyme Properties p. 37 of 39 Ping-pong mechanism First substrate enters, is altered, is released, with change in enzyme Then second substrate reacts with altered enzyme, is altered, is released Enzyme restored to original state A P B Q E EA FA F FB FQ E

38. 10/14/2008 Biochemistry: Enzyme Properties p. 38 of 39 Induced fit Conformations of enzymes don't change enormously when they bind substrates, but they do change to some extent. An instance where the changes are fairly substantial is the binding of substrates to kinases. Daniel Koshland Cartoon from textbookofbacteriology.net

39. 10/14/2008 Biochemistry: Enzyme Properties p. 39 of 39 Kinase reactions unwanted reaction ATP + H-O-H ⇒ ADP + P i will compete with the desired reaction ATP + R-O-H ⇒ ADP + R-O- P Kinases minimize the likelihood of this unproductive activity by changing conformation upon binding substrate so that hydrolysis of ATP cannot occur until the binding happens. Illustrates the importance of the order in which things happen in enzyme function