1. Andy Howard Introductory Biochemistry 10 November 2014
Enzyme Kinetics
Andy Howard Introductory Biochemistry
10 November 2014
Enzyme Kinetics
11/10/2014

2. What we’ll discuss Kinetics Michaelis-Menten Mechanisms Assumptions
Constants
Dimensions
Graphical interp
Kinetics
Mechanisms
Kinases
Induced Fit
Bisubstrate reactions
Calculations
11/10/2014
Enzyme Kinetics

3. Using Vmax in M-M kinetics
Thus since Vmax = k2[E]tot,
v0 = Vmax [S] / (Km+[S])
That’s the famous Michaelis-Menten equation
11/10/2014
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
11/10/2014
Enzyme Kinetics

5. Graphical interpretation
11/10/2014
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, then v0 = 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
11/10/2014
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
11/10/2014
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
11/10/2014
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)
11/10/2014
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
11/10/2014
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
11/10/2014
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 and 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.
11/10/2014
Enzyme Kinetics

13. Historical thought
Biochemists, 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!
11/10/2014
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 , but it’s wrong; correct version on next slide.
11/10/2014
Enzyme Kinetics

15. Double-reciprocal form of rate equation: correction
The plot for fig 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.
11/10/2014
Enzyme Kinetics

16. Figure 13.19, without the incorrect equation
11/10/2014
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
11/10/2014
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 Q E EA FA F FB FQ E
11/10/2014
Enzyme Kinetics

19. Ping-pong equation & plot
11/10/2014
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
11/10/2014
Enzyme Kinetics

21. Kinase reactions unwanted reaction ATP + H-O-H ⇒ ADP + Pi
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
11/10/2014
Enzyme Kinetics

22. Hexokinase conformational changes
G&G Fig
11/10/2014
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
11/10/2014
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
11/10/2014
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.
11/10/2014
Enzyme Kinetics

26. Lineweaver-Burk Simple linearization of Michaelis-Menten:
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
11/10/2014
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!
11/10/2014
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.
11/10/2014
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
11/10/2014
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.
11/10/2014
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
11/10/2014
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 M-1, then Km = -1/(X-intercept) =(-)(-1/5000 M-1) = 2*10-4M
Remember that the X intercept is negative, but Km is positive!
11/10/2014
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
11/10/2014
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.
11/10/2014
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?
Answer
X-intercept
Y-intercept a
Moves toward origin
Unchanged b
Moves away from origin c d
11/10/2014
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.
11/10/2014
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.
11/10/2014
Enzyme Kinetics

38. Example: hexokinase isozymes
Mutant human type I hexokinase 110 kDa monomer EC
PDB 1DGK, 2.8Å
Hexokinase catalyzes hexose + 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]
11/10/2014
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.
11/10/2014
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 a point in between X intercept and Y intercept
11/10/2014
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]
11/10/2014
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?
11/10/2014
Enzyme Kinetics

43. Sucrose & maltose phosphorylase
Sucrose phosphorylase does catalyze the exchange; not maltose phosphorylase
This suggests that SucPase uses double-displacement reaction; MalPase uses a single-displacement
Sucrose + E  E-glucose + fructose E-glucose + Pi  E + glucose-1-P
Maltose + E + Pi  Maltose:E:Pi Maltose:E:Pi  glucose-1P + glucose
Sucrose phosphorylase Bifidobacterium 113 kDa dimer PDB 1R7A, 1.77Å EC
11/10/2014
Enzyme Kinetics