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Enzyme Properties and Kinetics

Enzyme Properties and Kinetics. Andy Howard Introductory Biochemistry, Fall 2008 14 October 2008. Enzymes catalyze reactions. We need to classify them and get an idea of how they affect the rates of reactions. Classes of enzymes Enzyme kinetics Michaelis-Menten kinetics: overview

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Enzyme Properties and Kinetics

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  1. Enzyme Properties and Kinetics Andy HowardIntroductory Biochemistry, Fall 200814 October 2008 Biochemistry: Enzyme Properties

  2. Enzymes catalyze reactions • We need to classify them and get an idea of how they affect the rates of reactions. Biochemistry: Enzyme Properties

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

  4. 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 Biochemistry: Enzyme Properties

  5. 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 Biochemistry: Enzyme Properties

  6. IUBMB Major Enzyme Classes Biochemistry: Enzyme Properties

  7. EC System Porcine pancreatic elastasePDB 3EST 1.65 Å 26kDa monomer • 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 Biochemistry: Enzyme Properties

  8. Category 1:Oxidoreductases • General reaction:Aox + Bred Ared + Box • 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+ Biochemistry: Enzyme Properties

  9. Category 2:Transferases • These catalyze transfers ofgroups like phosphate or amines. • Example: L-alanine + a-ketoglutarate pyruvate + L-glutamate • Kinases are transferases:they transfer a phosphate from ATP to something else Biochemistry: Enzyme Properties

  10. O O- Category 3:hydrolases HO-P-O-P-OH O O- • Water is acceptor of transferred group • Ultrasimple: pyrophosphatase:Pyrophosphate + H2O ->2 Phosphate • Proteases,many other sub-categories Biochemistry: Enzyme Properties

  11. C=C Category 4:Lyases • Non-hydrolytic, nonoxidative elimination (or addition) reactions • Addition across a double bond or reverse • Example: pyruvate carboxylase:pyruvate + H+ acetaldehyde + CO2 • More typical lyases add across C=C Biochemistry: Enzyme Properties

  12. 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) Biochemistry: Enzyme Properties

  13. Category 6: Ligases • Catalyze joining of 2 substrates,e.g.L-glutamate + ATP + NH4+L-glutamine + ADP + Pi • 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 Biochemistry: Enzyme Properties

  14. 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. Biochemistry: Enzyme Properties

  15. iClicker quiz, question 2 • Triosephosphate isomerase, whose structure we discussed earlier, interconverts glyceraldehyde-3-phosphate and dhydroxyacetone phosphate. What would you expect the approximate DG 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. Biochemistry: Enzyme Properties

  16. 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] = A0, [B] = 0: • then the rate or velocity of the reaction is expressed as d[B]/dt. Biochemistry: Enzyme Properties

  17. [B] Kinetics, continued t • In most situations more product will be produced per unit time if A0 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. Biochemistry: Enzyme Properties

  18. 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. Biochemistry: Enzyme Properties

  19. Bimolecular reaction • If in the reactionA + D  Bthe 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 Biochemistry: Enzyme Properties

  20. 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 k1, the backward rate typically designated as k-1. Biochemistry: Enzyme Properties

  21. 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  Cwe can write rate constantsk1, k-1, k2, and k-2as the rate constants associated with converting A to B, converting B to A, converting B to C, and converting C to B. Biochemistry: Enzyme Properties

  22. [ES] Michaelis-Menten kinetics t • 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. Biochemistry: Enzyme Properties

  23. 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 =vf = k1([E]tot - [ES])[S]because the enzyme that is already substrate-bound is unavailable! Biochemistry: Enzyme Properties

  24. Equating the rates • Rate of disappearance of ES on right and left isvd = k-1[ES] + k2[ES] = (k-1+ k2)[ES] • This rate of disappearance should be equal to the rate of appearance • Under these conditions vf = vd. Biochemistry: Enzyme Properties

  25. Derivation, continued • Thus since vf = vd. k1([E]tot - [ES])[S] = (k-1+ k2)[ES] • Km (k-1+ k2)/k1 = ([E]tot - [ES])[S] / [ES] • [ES] = [E]tot [S] / (Km + [S]) • But the rate-limiting reaction is the formation of product: v0 = k2[ES] • Thus v0 = k2[E]tot [S] / (Km + [S]) Biochemistry: Enzyme Properties

  26. 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 getVmax = v0 = k2[ES] = k2[E]tot Biochemistry: Enzyme Properties

  27. Using Vmax inM-M kinetics • Thus sinceVmax = k2[E]tot, • v0 = Vmax [S] / (Km+[S]) • That’s the famous Michaelis-Mentenequation Biochemistry: Enzyme Properties

  28. Graphical interpretation Biochemistry: Enzyme Properties

  29. Physical meaning of Km • As we can see from the plot, the velocity is half-maximal when [S] = Km • Trivially derivable: if [S] = Km, thenv0 = Vmax[S] / ([S]+[S]) = Vmax /2 • We can turn that around and say that the Km is defined as the concentration resulting in half-maximal velocity • Km is a property associated with binding of S to E, not a property of turnover Biochemistry: Enzyme Properties

  30. kcat • A quantity we often want is the maximum velocity independent of how much enzyme we originally dumped in • That would be kcat =Vmax / [E]tot • Oh wait: that’s just the rate of our rate-limiting step, i.e. kcat = k2 Biochemistry: Enzyme Properties

  31. Physical meaning of kcat • Describes turnover of substrate to product:Number of product molecules produced per sec per molecule of enzyme • More complex reactions may not have kcat = k2, but we can often approximate them that way anyway • Some enzymes very efficient:kcat > 106 s-1 Biochemistry: Enzyme Properties

  32. Specificity constant, kcat/Km • kcat/Km 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) Biochemistry: Enzyme Properties

  33. 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. Biochemistry: Enzyme Properties

  34. 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! Biochemistry: Enzyme Properties

  35. Sequential, ordered reactions W.W.Cleland • Substrates, products must bind in specific order for reaction to complete A B P Q_____________________________E EA (EAB) (EPQ) EQ E Biochemistry: Enzyme Properties

  36. 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 Biochemistry: Enzyme Properties

  37. 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 QE EA FA F FB FQ E Biochemistry: Enzyme Properties

  38. Induced fit Daniel Koshland • 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. Cartoon from textbookofbacteriology.net Biochemistry: Enzyme Properties

  39. Kinase reactions • unwanted reactionATP + H-O-H ⇒ ADP + Pi • will compete with the desired reactionATP + 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 Biochemistry: Enzyme Properties

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