Enzymes: Kinetics & Inhibition

Enzymes:Kinetics & Inhibition Andy HowardBiochemistry Lectures, Spring 2019Thursday 14 February 2019

Kinetics & Inhibition • After we finish describing Michaelis-Menten kinetics, we’ll introduce the notion of enzyme inhibition and its significance to pharmaceutical projects. Enzyme Kinetics & Inhibition

M-M kinetics kcat & meanings Characteristicvalues Bisubstrate reactions Calculations Inhibition Concept Irreversible Reversible … Kinetics Pharmaceuticals Topics for today Enzyme Kinetics & Inhibition

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 Enzyme Kinetics & Inhibition

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 Enzyme Kinetics & Inhibition

Enzymes with large kcat values Micrococcus catalase58 kDa monomerEC 1.11.1.6PDB 1GWE, 0.88Å Some enzymes very efficient:kcat > 106 s-1 (catalase: 4*107 s-1:2H2O2 -> 2H2O + O2) High values of kcat indicate rapid turnover; small values indicate slow turnover Enzyme Kinetics & Inhibition

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 & Inhibition

Meaning of kcat/Km Leishmania triosphosphate isomerase56 kDa dimer; monomer shownEC 5.3.1.1PDB 2VXN, 0.82Å High values of kcat/Km indicate strong affinity for the substrate;low values indicate weak affinity. High values mean near-diffusion-limited conditions TIM kcat=4300 s-1, Km=20 µM;kcat / Km = 2.4*108 s-1M-1 Enzyme Kinetics & Inhibition

Dimensions of Km and Vmax • Km must have dimensions of concentration (remember it corresponds to the concentration of substrate that produces half-maximal velocity) • Vmax must have dimensions ofconcentration over time (d[P]/dt) Enzyme Kinetics & Inhibition

Dimensions: kcat and kcat/Km 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 & Inhibition

Typical units for kinetic parameters • Remember the distinction between dimensions and units! • Km typically measured in mM or µM • Vmax typically measured in mM s-1 or µM s-1 • kcat typically measured in s-1 • kcat / Km typically measured in (mM )-1 s-1 Enzyme Kinetics & Inhibition

Characteristic values of Km and kcat • A good way to ensure that you’re doing kinetics problems correctly is to make sure that the values you get correspond to physical realities • Km for the biologically relevant substrate is typically between 1 µM and 10 mM • kcat is typically 0.5-107 s-1 Enzyme Kinetics & Inhibition

Sanity checks kcat/Km is therefore typically ~ 104 - 109 M-1s-1 Vmax = kcat*[E]tot is typically ~ 10-4 Ms-1 If you get answers outside that range, you’ve probably done something wrong! Enzyme Kinetics & Inhibition

Bisubstrate reactions • 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. • The possibilities enumerated include sequential, random, and ping-pong mechanisms. Enzyme Kinetics & Inhibition

Historical thought • Biochemists, 1935 - 1970 examined effect on reaction rates of changing [reactant] and [enzyme], and deducing the mechanistic realities from kinetic data. • Now other tools are 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 & Inhibition

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 Enzyme Kinetics & Inhibition

Sequential, random reactions • Substrates can come in in either order, and products can be released in either order • Example: creatine kinase Human B-type CK86kDa dimerEC 2.7.3.2PDB 3B6R, 2Å Enzyme Kinetics & Inhibition

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 FP F FB FQ F E Enzyme Kinetics & Inhibition

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 & Inhibition

Kinase reactions • unwanted reaction ATP + 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 & Inhibition

Hexokinase conformational changes G&G Fig. 13.28 Enzyme Kinetics & Inhibition

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 & Inhibition

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]))= (Km/Vmax)*1/[S] + 1/Vmax • Thus: plot of 1/[S] as independent variable vs. 1/v0 as dependent variable is linear:Y-intercept = 1/Vmaxand slope Km/Vmax Hans Lineweaver Enzyme Kinetics & Inhibition

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 & Inhibition

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 & Inhibition

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 & Inhibition

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 & Inhibition

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 Vmaxavailable Enzyme Kinetics & Inhibition

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 • Similarly, if the Y-intercept is 2000 sM-1,then Vmax = 5*10-4 Ms-1and if [E]tot=10-7M, then kcat = 5*103 s-1 Enzyme Kinetics & Inhibition

Sanity checks, revisited • Sanity check #1:typically 10-7M < Km < 10-2M (cf. table 5.2) • Typically kcat ~ 0.5 to 107 s-1 (table 5.1),so for typical [E]=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 • … and please don’t try to tell me that Km < 0! Enzyme Kinetics & Inhibition

iClicker quiz question #1 1. If we alter the kinetics of a reaction by increasing Km but leaving Vmax alone, how will the L-B plot change? Enzyme Kinetics & Inhibition

iClicker question 2 2. 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 & Inhibition

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. Enzyme Kinetics & Inhibition

What this means 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 & Inhibition

Example:hexokinase isozymes Mutant human type I hexokinase PDB 1DGK, 2.8Å110 kDa monomer • Hexokinase catalyzeshexose + ATP hexose-6-P + ADP • Most isozymes of hexokinase prefer glucose; some also work okay mannose and fructose Enzyme Kinetics & Inhibition

Muscle vs. liver isozymes 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 & Inhibition

1/v = (1/Vmax)(KmA+KsAKmB/[B])(1/[A]) + (1/Vmax)(1+KmB/[B]) 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 (= -1/KSA) Enzyme Kinetics & Inhibition

1/v = (KmA/Vmax)(1/[A]) +(1+KmB/[B])/(1/Vmax) L-B plots for ping-pong reactions • Again we plot 1/v vs 1/[A] for various [B] • Parallel lines (same kcat/Km);lower (rightmore) lines correspond to larger [B] Enzyme Kinetics & Inhibition

Why study inhibition? • Let’s look at how enzymes get inhibited. • At least two reasons to do this: • Use inhibition as a probe for understanding kinetics & properties of enzymes themselves • Many—perhaps most—drugs are inhibitors of specific enzymes. • We'll see these two reasons for understanding inhibition as we work our way through this topic. Enzyme Kinetics & Inhibition

The concept of inhibition • An enzyme is a biological catalyst, i.e. a substance that alters the rate of a reaction without itself becoming permanently altered by its participation in the reaction. Enzyme Kinetics & Inhibition

How to inhibit an enzyme • The ability of an enzyme (particularly a proteinaceous enzyme) to catalyze a reaction can be altered by binding small molecules to it: • sometimes at its active site • sometimes at a site distant from the active site. Enzyme Kinetics & Inhibition

Inhibitors and accelerators • Usually these alterations involve a reduction in the enzyme's ability to accelerate the reaction; less commonly, they give rise to an increase in the enzyme's ability to accelerate a reaction. Enzyme Kinetics & Inhibition

Why more inhibitors than accelerators? • Natural selection: if there were small molecules that can facilitate the enzyme's propensity to speed up a reaction, nature probably would have found a way to incorporate those facilitators into the enzyme over the billions of years that the enzyme has been available. Enzyme Kinetics & Inhibition

Additional reason Most enzymes are already fairly close to optimal in their properties; we can readily mess them up with effectors, but it's more of a challenge to find ways to make enzymes better at their jobs. Enzyme Kinetics & Inhibition

Irreversible inhibitors • Inhibitor binds without possibility of release • Usually covalent • Each inhibition event effectively removes a molecule of enzyme from availability • Example: diisopropylfluorophosphate for serine proteases Enzyme Kinetics & Inhibition

Reversible inhibitors Usually noncovalent(ionic or van der Waals) Several kinds Classifications somewhat superseded by detailed structure-based knowledge of mechanisms, but not entirely Enzyme Kinetics & Inhibition

Types of reversible inhibition: I • Competitive • Inhibitor binds at active site • Prevents binding of substrate • Noncompetitive • Inhibitor binds distant from active site • Interferes with turnover Enzyme Kinetics & Inhibition

Types of reversible inhibition: II • Uncompetitive (rare?) • Inhibitor binds to ES complex • Removes ES, interferes with turnover • Mixed(usually Competitive + Noncompetitive) Enzyme Kinetics & Inhibition

Putting that all together… Ligands that influence enzyme activity Accelerators Inhibitors (Usually allosteric) Irreversible Reversible (Usually covalent) Noncompetitive(often allosteric) Competitive Mixed Uncompetitive Enzyme Kinetics & Inhibition

How to tell them apart • Reversible vs irreversible • dialyze an enzyme-inhibitor complex against a buffer free of inhibitor • if turnover or binding still suffers, it’s irreversible • Competitive vs. other reversible: • Structural studies if feasible • Kinetics Enzyme Kinetics & Inhibition

Enzymes: Kinetics & Inhibition