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

Enzyme Kinetics & Inhibition After we finish describing Michaelis-Menten kinetics, we’ll introduce the notion of enzyme inhibition and its significance to pharmaceutical projects. 02/14/2019 Enzyme Kinetics & Inhibition

Enzyme Kinetics & Inhibition Topics for today M-M kinetics kcat & meanings Characteristic values Bisubstrate reactions Calculations Inhibition Concept Irreversible Reversible … Kinetics Pharmaceuticals 02/14/2019 Enzyme Kinetics & Inhibition

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 02/14/2019 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 02/14/2019 Enzyme Kinetics & Inhibition

Enzymes with large kcat values 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 Micrococcus catalase 58 kDa monomer EC 1.11.1.6 PDB 1GWE, 0.88Å 02/14/2019 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) 02/14/2019 Enzyme Kinetics & Inhibition

Enzyme Kinetics & Inhibition Meaning of kcat/Km 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 Leishmania triosphosphate isomerase 56 kDa dimer; monomer shown EC 5.3.1.1 PDB 2VXN, 0.82Å 02/14/2019 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 of concentration over time (d[P]/dt) 02/14/2019 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 02/14/2019 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 02/14/2019 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 02/14/2019 Enzyme Kinetics & Inhibition

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! 02/14/2019 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 02/14/2019

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 02/14/2019

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 02/14/2019

Sequential, random reactions Substrates can come in in either order, and products can be released in either order Example: creatine kinase Human B-type CK 86kDa dimer EC 2.7.3.2 PDB 3B6R, 2Å Enzyme Kinetics & Inhibition 02/14/2019

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 Q E EA FP F FB FQ F E Enzyme Kinetics & Inhibition 02/14/2019

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 02/14/2019

Enzyme Kinetics & Inhibition 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 Enzyme Kinetics & Inhibition 02/14/2019

Hexokinase conformational changes G&G Fig. 13.28 Enzyme Kinetics & Inhibition 02/14/2019

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 02/14/2019

Enzyme Kinetics & Inhibition Lineweaver-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/Vmax and slope Km/Vmax Dean Burk Hans Lineweaver Enzyme Kinetics & Inhibition 02/14/2019

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 02/14/2019

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 02/14/2019

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 02/14/2019

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 02/14/2019

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 & Inhibition 02/14/2019

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, then Km = -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-1 and if [E]tot=10-7M, then kcat = 5*103 s-1 Enzyme Kinetics & Inhibition 02/14/2019

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 02/14/2019

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? Answer X-intercept Y-intercept a Moves toward origin Unchanged b Moves away from origin c d 02/14/2019 Enzyme Kinetics & Inhibition

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. 02/14/2019 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. 02/14/2019 Enzyme Kinetics & Inhibition

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. 02/14/2019 Enzyme Kinetics & Inhibition

Example: hexokinase isozymes Mutant human type I hexokinase PDB 1DGK, 2.8Å 110 kDa monomer Hexokinase catalyzes hexose + ATP  hexose-6-P + ADP Most isozymes of hexokinase prefer glucose; some also work okay mannose and fructose 02/14/2019 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] 02/14/2019 Enzyme Kinetics & Inhibition

L-B plots for ordered sequential reactions 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 point in between X intercept and Y intercept (= -1/KSA) 02/14/2019 Enzyme Kinetics & Inhibition

L-B plots for ping-pong reactions 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] 02/14/2019 Enzyme Kinetics & Inhibition

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. 02/14/2019 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. 02/14/2019 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. 02/14/2019 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. 02/14/2019 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. 02/14/2019 Enzyme Kinetics & Inhibition

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. 02/14/2019 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 02/14/2019 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 02/14/2019 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 02/14/2019 Enzyme Kinetics & Inhibition

Types of reversible inhibition: II Uncompetitive (rare?) Inhibitor binds to ES complex Removes ES, interferes with turnover Mixed (usually Competitive + Noncompetitive) 02/14/2019 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 02/14/2019 Enzyme Kinetics & Inhibition

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 02/14/2019 Enzyme Kinetics & Inhibition

Competitive inhibition Put in a lot of substrate: ability of the inhibitor to get in the way of the binding is hindered: out-competed by sheer #s of substrate molecules. This kind of inhibition manifests itself as interference with binding, i.e. with an increase of Km 02/14/2019 Enzyme Kinetics & Inhibition

Competitive inhibitors don’t affect turnover Within the active site of any given molecule of the enzyme, one of three states are possible: The inhibitor is present The substrate is present Nothing is present Therefore rate of turnover isn’t affected by the inhibitor: just the availability of binding sites. 02/14/2019 Enzyme Kinetics & Inhibition

Kinetics of competition Competitive inhibitor hinders binding of substrate but not reaction velocity: Affects the Km of the enzyme, not Vmax. 02/14/2019 Enzyme Kinetics & Inhibition

Effect of competitive inhibitor Which way does it affect it? Km = amount of substrate that needs to be present to run the reaction velocity up to half its saturation velocity. Competitive inhibitor requires us to shove more substrate into the reaction in order to achieve that half-maximal velocity. So: competitive inhibitor increases Km 02/14/2019 Enzyme Kinetics & Inhibition

L-B: competitive inhibitor Km goes up so -1/ Km moves toward origin Vmax unchanged so Y intercept unchanged 02/14/2019 Enzyme Kinetics & Inhibition

Competitive inhibitor: Quantitation of KI Define inhibition constant KI to be the concentration of inhibitor that increases Km by a factor of two. Then Km,obs = Km{1+([Ic]/KI)} So [Ic] that moves Km halfway to the origin is KI. That corresponds to saying that KI is the value of [Ic] that doubles the Km. If Ki = 100 nM and [Ic] = 1 µM, then we’ll increase Km,obs elevenfold! 02/14/2019 Enzyme Kinetics & Inhibition

Enzyme Kinetics & Inhibition Sample problem Suppose a competitive inhibitor with KI = 5 µM is competing with a substrate for which Km = 100 µM, then the effective Km is Km, obs = Km {1 + ([Ic] / KI)} Thus if [Ic] = 20 µM, Km, obs = Km{1 + ([Ic] / KI)} = 100 µM {1 + (20 µM/5µM)} = 100 µM (1 + 4) = 100 µM (5) = 500 µM 02/14/2019 Enzyme Kinetics & Inhibition

Noncompetitive inhibition S Noncompetitive inhibitor has no influence on how available the binding site for substrate is, so it doesn’t affect Km at all However, it has a profound inhibitory influence on the speed of the reaction, i.e. turnover. So it reduces Vmax and has no influence on Km. 02/14/2019 Enzyme Kinetics & Inhibition

L-B for non-competitives Decrease in Vmax  1/Vmax is larger X-intercept unaffected 02/14/2019 Enzyme Kinetics & Inhibition

KI for noncompetitives KI defined as concentration of inhibitor that cuts Vmax in half Vmax,obs = Vmax/{1 + ([In]/KI)} In previous figure the “high” concentration of inhibitor is KI If KI = KI’, this is pure noncompetitive inhibition 02/14/2019 Enzyme Kinetics & Inhibition

Uncompetitive inhibition Inhibitor binds only if ES has already formed It creates a ternary ESI complex This removes ES, so by LeChatelier’s Principle it actually drives the original reaction (E + S  ES) to the right; so it decreases Km But it interferes with turnover so Vmax goes down If Km and Vmax decrease at the same rate, then it’s classical uncompetitive inhibition. 02/14/2019 Enzyme Kinetics & Inhibition

L-B for uncompetitives -1/Km moves away from the origin 1/Vmax moves away from the origin Slope ( Km/Vmax) is unchanged 02/14/2019 Enzyme Kinetics & Inhibition

Enzyme Kinetics & Inhibition Ki for uncompetitives Defined as inhibitor concentration that cuts Vmax or Km in half Easiest to read from Vmax value Same equation as for noncompetitves: Vmax,obs = Vmax / {1 + ([Iu]/KI)} Iu labeled “high” is equal to Ki in this plot 02/14/2019 Enzyme Kinetics & Inhibition

Enzyme Kinetics & Inhibition Mixed inhibition Usually involves interference with both binding and catalysis Km goes up, Vmax goes down Easy to imagine the mechanism: Binding of inhibitor alters the active-site configuration to interfere with binding, but it also alters turnover Same picture as with pure noncompetitive inhibition, but with Ki ≠ Ki’ 02/14/2019 Enzyme Kinetics & Inhibition

Warning: this terminology is becoming challenged Some biochemists say pure noncompetitive or pure uncompetitive inhibition are rare Pure noncompetitive inhibition implies that the binding of the inhibitor has no influence on binding of substrate; these people say that it’s more common for KI  KI’. I don’t agree, and in any case the approach we’ve taken helps you visualize realities. 02/14/2019 Enzyme Kinetics & Inhibition

Enzyme Kinetics & Inhibition iClicker question 3 3. If we compare the Lineweaver-Burk plot of an uninhibited enzyme to that of a noncompetitively inhibited enzyme, what will change? (a) The X-intercept (b) The Y-intercept (c) The slope (d) both (a) and (c) (e) both (b) and (c) 02/14/2019 Enzyme Kinetics & Inhibition

Most pharmaceuticals are enzyme inhibitors Some are inhibitors of enzymes that are necessary for functioning of pathogens Others are inhibitors of a protein whose inappropriate expression in a human causes disease. Others are targeted at enzymes that are produced more energetically by tumors than they are by normal tissues. 02/14/2019 Enzyme Kinetics & Inhibition

Characteristics of Pharmaceutical Inhibitors Usually competitive, i.e. they raise Km without affecting Vmax Some are mixed, i.e. Km up, Vmax down A few are allosteric and noncompetitive Iterative design work will decrease Ki from millimolar down to nanomolar Sometimes design work is purely blind HTS; other times, it’s structure-based 02/14/2019 Enzyme Kinetics & Inhibition

Enzyme Kinetics & Inhibition Amprenavir Competitive inhibitor of HIV protease, Ki = 0.6 nM for HIV-1 HIV-2 protease with amprenavir bound 23 kDa dimer EC 3.4.23.47 PDB 3S45, 1.5 Å 02/14/2019 Enzyme Kinetics & Inhibition

Collision with rifabutin No longer sold: mutual interference with rifabutin, which is an antibiotic used against a common HIV secondary bacterial infection, Mycobacterium avium 02/14/2019 Enzyme Kinetics & Inhibition

Pharmaceutical examples Trade Generic Enzyme Action Name Name Inhibited Viagra Sildenafil PDE5 cGMP remains active Aspirin COX 1&2 Prostaglandins slowed Lipitor Atorvastatin HMGCoAR Cholesterol slowed Crestor Rosuvastatin HMGCoAR Cholesterol slowed Nexium Esomeprazole ATPase Stomach acid slowed Januvia Sitagliptin DPP-4 Increases insulin Atripla Efavirenz HIV RT HIV can’t replicate Celebrex Celecoxib COX-2 Prostaglandins slowed 02/14/2019 Enzyme Kinetics & Inhibition

Biggest-selling drugs! adalimumab Biggest-selling drugs! Five of the top 12 sellers worldwide are monoclonal antibodies Another biologic (i.e. macromolecule) is a TNF inhibitor used for rheumatoid arthritis Two interfere with replication in hepatitis C virus by incorporation into the genome Some have complex or poorly understood mechanisms of action Net sales correlate poorly with social importance 02/14/2019 Enzyme Kinetics & Inhibition

When is a good inhibitor a good drug? It needs to be bioavailable and nontoxic Beautiful 20nM inhibitor is often neither Modest sacrifices of Ki in improving bioavailability and non-toxicity are okay if Ki is low enough when you start sacrificing 02/14/2019 Enzyme Kinetics & Inhibition

How do we lessen toxicity and improve bioavailability? Increase solubility… that often increases Ki because the van der Waals interactions diminish Solubility makes it easier to get the compound to travel through the bloodstream Toxicity is often associated with fat storage, which is more likely with insoluble compounds 02/14/2019 Enzyme Kinetics & Inhibition

Enzyme Kinetics & Inhibition 2 years of research, 8 years of trials Drug-design timeline 100 -3 Improving affinity Toxicity and bioavailability Stage I clinical trials Stage II clinical trials Cost/yr, 106 $ Preliminary toxicity testing log Ki -8 10 Research Clinical Trials 2 Time, Yrs 10 02/14/2019 Enzyme Kinetics & Inhibition