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**Andy Howard Introductory Biochemistry 10 November 2014**

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

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**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

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**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

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**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

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**Graphical interpretation**

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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

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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

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**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

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**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

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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

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**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

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**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

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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

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**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

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**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

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**Figure 13.19, without the incorrect equation**

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**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

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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

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**Ping-pong equation & plot**

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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

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**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

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**Hexokinase conformational changes**

G&G Fig 11/10/2014 Enzyme Kinetics

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**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

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**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

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**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

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**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

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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

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**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

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**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

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**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

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**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

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**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

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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

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**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

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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

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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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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