Enzyme Kinetics

1. EnzymeKinetics Andy HowardIntroductory Biochemistry 10 November 2014 Enzyme Kinetics

2. Michaelis-Menten Assumptions Constants Dimensions Graphical interp Kinetics Mechanisms Kinases Induced Fit Bisubstratereactions Calculations What we’ll discuss Enzyme Kinetics

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

4. Assumptions & results Our derivation depends on these assumptions: • [ES] is nearly constant over time • Rate of formation of [ES] is first-order in both [S] and available [E] • k-2 is insignificant • k2 is rate-limiting In practice some of these assumptions may not entirely hold, but Michaelis-Menten algebra will often still operate Enzyme Kinetics

5. Graphical interpretation Enzyme Kinetics

6. 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 Michaelis Constant:British Christian hiphop band Enzyme Kinetics

7. kcat • We’ve already discussed what Vmax is; but it will be larger for high [E]tot than otherwise. • 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 Enzyme Kinetics

8. 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 Enzyme Kinetics

9. 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) Enzyme Kinetics

10. Dimensions • Km must have dimensions of concentration (remember it corresponds to the concentration of substrate that produces half-maximal velocity) • Vmax must have dimensions of concentration over time (d[A]/dt) • kcat must have dimensions of inverse time • kcat / Km must have dimensions of inverse time divided by concentration, i.e.inverse time * inverse concentration Enzyme Kinetics

11. Typical units for kinetic parameters • Remember the distinction between dimensions and units! • Km typically measured in mM or µM • Vmax typically measured in mMs-1 or µMs-1 • kcat typically measured in s-1 • kcat / Km typically measured in s-1M-1 Enzyme Kinetics

12. Kinetic Mechanisms (G&G §13.4, §13.5) • 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 G&G eqns. 13.47 and 13.48 and the surrounding text and figures, which depict bisubstrate reactions of various sorts. As you can see, the possibilities enumerated include sequential, random, and ping-pong mechanisms. Enzyme Kinetics

13. 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! Enzyme Kinetics

14. 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 • Lineweaver-Burk for both is given on fig. 13.19, but it’s wrong; correct version on next slide. Enzyme Kinetics

15. Double-reciprocal form of rate equation: correction • The plot for fig. 13.19 in G&G is correct but the equation is wrong. It should be: • 1/v = (1/Vmax)(KmA+KsAKmB/[B])(1/[A]) + (1/Vmax)(1+KmB/[B]) That is, the second left parenthesis and its mate should be deleted from what you see in the textbook. Enzyme Kinetics

16. Figure 13.19, without the incorrect equation Enzyme Kinetics

17. 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 • Example: creatine kinase Enzyme Kinetics

18. 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 Enzyme Kinetics

19. Ping-pong equation & plot Enzyme Kinetics

20. 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 Enzyme Kinetics

21. 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 Enzyme Kinetics

22. Hexokinase conformational changes G&G Fig. 13.24 Enzyme Kinetics

23. iClicker quiz, question 1 1. The Michaelis constant Km has dimensions of • (a) concentration per unit time • (b) inverse concentration per unit time • (c) concentration • (d) inverse concentration • (e) none of the above Enzyme Kinetics

24. iClicker quiz question 2 2. kcat is a measure of • (a) substrate binding • (b) turnover • (c) inhibition potential • (d) none of the above Enzyme Kinetics

25. Measurements and calculations • The standard Michaelis-Menten formulation is v0=f([S]), but it’s not linear in [S]. We seek linearizations of the equation so that we can find Km and kcat, and so that we can understand how various changes affect the reaction. Enzyme Kinetics

26. Lineweaver-Burk Dean Burk • Simple linearization of Michaelis-Menten: • v0 = Vmax[S]/(Km+[S]). Take reciprocals: • 1/v0 = (Km +[S])/(Vmax[S])= Km /(Vmax[S]) + [S]/(Vmax[S])1/v0 =(Km/Vmax)*1/[S] + 1/Vmax • Thus a plot of 1/[S] as the independent variable vs. 1/v0 as the dependent variable will be linear with Y-intercept = 1/Vmax and slope Km/Vmax Hans Lineweaver Enzyme Kinetics

27. How to use this • Y-intercept is useful directly:computeVmax = 1/(Y-intercept) • We can get Km/Vmax from slope and then use our knowledge of Vmax to get Km; or • X intercept = -1/ Km… that gets it for us directly! Enzyme Kinetics

28. Demonstration that the X-intercept is at -1/Km • X-intercept means Y = 0 • In Lineweaver-Burk plot, • 0 = (Km/Vmax)*1/[S] + 1/Vmax • For nonzero 1/Vmax we divide through: • 0 = Km /[S] + 1, -1 = Km/[S], [S] = -Km. • But the axis is for 1/[S], so the intercept is at 1/[S] = -1/ Km. Enzyme Kinetics

29. Graphical form of L-B 1/v0, s L mol-1 1/Vmax,s L mol-1 Slope=Km/Vmax 1/[S], M-1 -1/Km, L mol-1 Enzyme Kinetics

30. Are those values to the left of 1/[S] = 0 physical? • No. It doesn’t make sense to talk about negative substrate concentrations or infinite substrate concentrations. • But if we can curve-fit, we can still use these extrapolations to derive the kinetic parameters. Enzyme Kinetics

31. Advantages and disadvantages of L-B plots • Easy conceptual reading of Km and Vmax(but remember to take the reciprocals!) • Suboptimal error analysis • [S] and v0 values have errors • Error propagation can lead to significant uncertainty in Km (and Vmax) • Other linearizations available(see homework) • Better ways of getting Km and Vmax available Enzyme Kinetics

32. Don’t fall into the trap! • When you’re calculating Km and Vmax from Lineweaver-Burk plots, remember that you need the reciprocal of the values at the intercepts • If the X-intercept is -5000 M-1, thenKm = -1/(X-intercept) =(-)(-1/5000 M-1) = 2*10-4M • Remember that the X intercept is negative, but Km is positive! Enzyme Kinetics

33. Sanity checks • Sanity check #1:typically 10-7M < Km < 10-2M (table 13.3) • Typically kcat ~ 0.5 to 107 s-1 (table 13.4),so for typical [E]tot =10-7M,Vmax = [E]totkcat = 10-6 Ms-1 to 1 Ms-1 • If you get Vmax or Km values outside of these ranges, you’ve probably done something wrong Enzyme Kinetics

34. iClicker quiz: question 3 The hexokinase reaction just described probably operates according to a • (a) sequential, random mechanism • (b) sequential, ordered mechanism • (c) ping-pong mechanism • (d) none of the above. Enzyme Kinetics

35. iClicker quiz #4 4. If we alter the kinetics of a reaction by increasing Km but leaving Vmax alone, how will the L-B plot change? Enzyme Kinetics

36. iClicker question 5 5. Enzyme E has a tenfold stronger affinity for substrate A than for substrate B. Which of the following is true? • (a) Km(A) = 10 * Km(B) • (b) Km(A) = 0.1 * Km(B) • (c) Vmax(A) = 10 * Vmax(B) • (d) Vmax(A) = 0.1 * Vmax(B) • (e) None of the above. Enzyme Kinetics

37. Another physical significance of Km • Years of experience have led biochemists to a general conclusion: • For its preferred substrate, the Km value of an enzyme is usually within a factor of 50 of the steady-state concentration of that substrate. • So if we find that Km = 0.2 mM for the primary substrate of an enzyme, then we expect that the steady-state concentration of that substrate is between 4 µM and 10 mM. Enzyme Kinetics

38. Example:hexokinase isozymes Mutant human type I hexokinase110 kDa monomer EC 2.7.1.1 PDB 1DGK, 2.8Å • Hexokinase catalyzeshexose + ATP  hexose-6-P + ADP • Most isozymes of hexokinase prefer glucose; some also work okay mannose and fructose • Muscle hexokinases have Km ~ 0.1mM so they work efficiently in blood, where [glucose] ~ 4 mM • Liver glucokinase has Km = 10 mM, which is around the liver [glucose] and can respond to fluctuations in liver [glucose] Enzyme Kinetics

39. Using kinetics to determine mechanisms • In a reaction involving substrates A and B, we hold [B] constant and vary [A]. • Then we move to a different [B] and again vary [A]. • Continue through several values of [B] • That gives us a family of Lineweaver-Burk plots of 1/v0 vs 1/[A] • How those curves appear on a single plot tells us which kind of mechanism we have. Enzyme Kinetics

40. L-B plots for ordered sequential reactions • Plot 1/v0 vs. 1/[A] for various [B] values;flatter slopes correspond to larger [B] • Lines intersect @ a pointin between X intercept and Y intercept Enzyme Kinetics

41. L-B plots for ping-pong reactions • Again we plot 1/v vs 1/[A] for various [B] • Parallel lines (same kcat/Km);lower lines correspond to larger [B] Enzyme Kinetics

42. Using exchange reactions to discern mechanisms • Example: sucrose phosphorylase and maltose phosphorylase both cleave disaccharides and add Pi to one product: • Sucrose + Pi glucose-1-P + fructose • Maltose + Pi glucose-1-P + glucose • Try 32P tracers with G-1-P:G-1-P + 32Pi Pi + G-1-32Pi • … so what happens with these two enzymes? Enzyme Kinetics

43. Sucrose & maltose phosphorylase • Sucrose phosphorylase doescatalyze the exchange;not maltose phosphorylase • This suggests that SucPase usesdouble-displacement reaction;MalPase uses a single-displacement • Sucrose + E  E-glucose + fructoseE-glucose + Pi E + glucose-1-P • Maltose + E + Pi Maltose:E:PiMaltose:E:Pi glucose-1P + glucose Sucrose phosphorylaseBifidobacterium113 kDa dimerPDB 1R7A, 1.77ÅEC 2.4.1.7 Enzyme Kinetics