Enzymes Kinetics Inhibition Andy Howard Introductory Biochemistry 29
Enzymes: Kinetics & Inhibition Andy Howard Introductory Biochemistry 29 October 2013 Enzyme Kinetics & Inhibition 10/29/2013
What we’ll discuss n Enzymes Induced fit n Bisubstrate reactions n Calculations n n n Inhibition (concluded) Types of reversible n Kinetics n Pharmaceuticals n Inhibition Concept n Irreversible & reversible n 10/29/2013 Enzyme Kinetics & Inhibition P. 2 of 58
Induced fit Daniel Koshland n 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 10/29/2013 Enzyme Kinetics & Inhibition P. 3 of 58
Kinase reactions n n 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 10/29/2013 Enzyme Kinetics & Inhibition P. 4 of 58
i. Clicker quiz, question 1 n The Michaelis constant Km has dimensions of n n n (a) concentration per unit time (b) inverse concentration per unit time (c) concentration (d) inverse concentration (e) none of the above 10/29/2013 Enzyme Kinetics & Inhibition P. 5 of 58
i. Clicker quiz question 2 n kcat is a measure of n n (a) substrate binding (b) turnover (c) inhibition potential (d) none of the above 10/29/2013 Enzyme Kinetics & Inhibition P. 6 of 58
Hexokinase conformational changes G&G Fig. 13. 28 10/29/2013 Enzyme Kinetics & Inhibition P. 7 of 58
Measurements and calculations n The standard Michaelis-Menten formulation is v 0=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. 10/29/2013 Enzyme Kinetics & Inhibition P. 8 of 58
Lineweaver-Burk n n Dean Burk Simple linearization of Michaelis-Menten: v 0 = Vmax[S]/(Km+[S]). Take reciprocals: 1/v 0 = (Km +[S])/(Vmax[S]) = Km /(Vmax[S]) + [S]/(Vmax[S]) 1/v 0 = (Km/Vmax)*1/[S] + 1/Vmax Thus a plot of 1/[S] as the independent Hans variable vs. 1/v 0 as the dependent Lineweaver variable will be linear with Y-intercept = 1/Vmax and slope Km/Vmax 10/29/2013 Enzyme Kinetics & Inhibition P. 9 of 58
How to use this n n n Y-intercept is useful directly: compute. Vmax = 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! 10/29/2013 Enzyme Kinetics & Inhibition P. 10 of 58
Demonstration that the X -intercept is at -1/Km n n n 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. 10/29/2013 Enzyme Kinetics & Inhibition P. 11 of 58
Graphical form of L-B 1/v 0, s L mol-1 1/Vmax, s L mol-1 Slope=Km/Vmax 1/[S], M-1 -1/Km, L mol-1 10/29/2013 Enzyme Kinetics & Inhibition P. 12 of 58
Are those values to the left of 1/[S] = 0 physical? n n 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. 10/29/2013 Enzyme Kinetics & Inhibition P. 13 of 58
Advantages and disadvantages of L-B plots n n Easy conceptual reading of Km and Vmax (but remember to take the reciprocals!) Suboptimal error analysis n n [S] and v 0 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 10/29/2013 Enzyme Kinetics & Inhibition P. 14 of 58
Don’t fall into the trap! n n n 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 -4 M Remember that the X intercept is negative, but Km is positive! 10/29/2013 Enzyme Kinetics & Inhibition P. 15 of 58
Sanity checks n Sanity check #1: typically 10 -7 M < Km < 10 -2 M (table 13. 3) n Typically kcat ~ 0. 5 to 107 s-1 (table 13. 4), so for typical [E]tot =10 -7 M, Vmax = [E]totkcat = 10 -6 Ms-1 to 1 Ms-1 n If you get Vmax or Km values outside of these ranges, you’ve probably done something wrong 10/29/2013 Enzyme Kinetics & Inhibition P. 16 of 58
i. Clicker quiz: question 3 n The hexokinase reaction just described probably operates according to a n n (a) sequential, random mechanism (b) sequential, ordered mechanism (c) ping-pong mechanism (d) none of the above. 10/29/2013 Enzyme Kinetics & Inhibition P. 17 of 58
i. Clicker quiz #4 n 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 a Moves toward origin Unchanged b Moves away from origin Unchanged c Unchanged Moves away from origin d Unchanged Moves toward origin 10/29/2013 Y-intercept Enzyme Kinetics & Inhibition P. 18 of 58
i. Clicker question 5 n Enzyme E has a tenfold stronger affinity for substrate A than for substrate B. Which of the following is true? n n n (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. 10/29/2013 Enzyme Kinetics & Inhibition P. 19 of 58
Another physical significance of Km n n n 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 m. M for the primary substrate of an enzyme, then we expect that the steady-state concentration of that substrate is between 4 µM and 10 m. M. 10/29/2013 Enzyme Kinetics & Inhibition P. 20 of 58
Example: hexokinase isozymes n n Mutant human type I hexokinase PDB 1 DGK, 2. 8Å 110 k. Da monomer 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. 1 m. M so they work efficiently in blood, where [glucose] ~ 4 m. M Liver glucokinase has Km = 10 m. M, which is around the liver [glucose] and can respond to fluctuations in liver [glucose] 10/29/2013 Enzyme Kinetics & Inhibition P. 21 of 58
Using kinetics to determine mechanisms n n n 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/v 0 vs 1/[A] How those curves appear on a single plot tells us which kind of mechanism we have. 10/29/2013 Enzyme Kinetics & Inhibition P. 22 of 58
L-B plots for ordered sequential reactions n n Plot 1/v 0 vs. 1/[A] for various [B] values; flatter slopes correspond to larger [B] Lines intersect @ a point in between X intercept and Y intercept 10/29/2013 Enzyme Kinetics & Inhibition P. 23 of 58
L-B plots for pingpong reactions n n Again we plot 1/v vs 1/[A] for various [B] Parallel lines (same kcat/Km); lower lines correspond to larger [B] 10/29/2013 Enzyme Kinetics & Inhibition P. 24 of 58
Using exchange reactions to discern mechanisms n n n 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 32 P tracers with G-1 -P: G-1 -P + 32 Pi Pi + G-1 -32 Pi … so what happens with these two enzymes? 10/29/2013 Enzyme Kinetics & Inhibition P. 25 of 58
Sucrose & maltose phosphorylase n n Sucrose phosphorylase does catalyze the exchange; not maltose phosphorylase Sucrose This suggests that Suc. Pase uses phosphorylase double-displacement reaction; Bifidobacterium Mal. Pase uses a single-displacement 113 k. Da dimer Sucrose + E E-glucose + fructose PDB 1 R 7 A, 1. 77Å E-glucose + Pi E + glucose-1 -P EC 2. 4. 1. 7 Maltose + E + Pi Maltose: E: Pi glucose-1 P + glucose 10/29/2013 Enzyme Kinetics & Inhibition P. 26 of 58
Why study inhibition? • Let’s look at how enzymes get inhibited. • At least two reasons to do this: • We can use inhibition as a probe for understanding the kinetics and properties of enzymes in their uninhibited state; • 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. 10/29/2013 Enzyme Kinetics & Inhibition P. 27 of 58
The concept of inhibition n n 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. The ability of an enzyme (particularly a proteinaceous enzyme) to catalyze a reaction can be altered by binding small molecules to it 10/29/2013 Enzyme Kinetics & Inhibition P. 28 of 58
Inhibitors and accelerators n 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. 10/29/2013 Enzyme Kinetics & Inhibition P. 29 of 58
Why more inhibitors than accelerators? n n 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. 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. 10/29/2013 Enzyme Kinetics & Inhibition P. 30 of 58
Distinctions we can make n Inhibitors can be reversible or irreversible n Where do they bind? n n At the enzyme’s active site n At a site distant from the active site. To what do they bind? n To the unliganded enzyme E n To the enzyme-intermediate complex or the enzyme-substrate complex (ES) n To both (E or ES) 10/29/2013 Enzyme Kinetics & Inhibition P. 31 of 58
n Types of inhibitors (G&G § 13. 4) Irreversible n n Inhibitor binds without possibility of release Usually covalent Each inhibition event effectively removes a molecule of enzyme from availability Reversible n n n Usually noncovalent (ionic or van der Waals) Several kinds Classifications somewhat superseded by detailed structure-based knowledge of mechanisms, but not entirely 10/29/2013 Enzyme Kinetics & Inhibition P. 32 of 58
Types of reversible inhibition n Competitive n n n Noncompetitive n n n Inhibitor binds distant from active site (E or ES) Interferes with turnover Uncompetitive (rare? ) n n n Inhibitor binds at active site of unliganded enzyme Prevents binding of substrate Inhibitor binds only to ES complex Removes ES, interferes with turnover Mixed n n Usually Competitive + Noncompetitive Characterized by KI KI’ 10/29/2013 Enzyme Kinetics & Inhibition P. 33 of 58
How to tell them apart n Reversible vs irreversible n n n dialyze an enzyme-inhibitor complex against a buffer free of inhibitor if turnover or binding still suffers, it’s irreversible Competitive vs. other reversible: n n Structural studies if feasible Kinetics 10/29/2013 Enzyme Kinetics & Inhibition P. 34 of 58
Competitive inhibition n n 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 10/29/2013 Enzyme Kinetics & Inhibition P. 35 of 58
Competitive inhibitors don’t affect turnover n If the substrates manages to bind even though there is inhibitor present, then it can be turned over just as quickly as if the inhibitor is absent; so the inhibitor influences binding but not turnover. 10/29/2013 Enzyme Kinetics & Inhibition P. 36 of 58
Kinetics of competition n Competitive inhibitor hinders binding of substrate but not reaction velocity: Affects the Km of the enzyme, not Vmax. Which way does it affect it? n n n 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 10/29/2013 Enzyme Kinetics & Inhibition P. 37 of 58
L-B: pure competitive inhibitor (G&G Fig. 13) n n Km goes up so -1/ Km moves toward origin Vmax unchanged so Y intercept unchanged 10/29/2013 Enzyme Kinetics & Inhibition P. 38 of 58
Competitive inhibitor: Quantitation of Ki n n Define inhibition constant Ki to be the concentration of inhibitor that increases Km by a factor of two. Km, obs = Km{1+([Ic]/Ki)} So [Ic] that moves Km halfway to the origin is Ki. If Ki = 100 n. M and [Ic] = 1 µM, then we’ll increase Km, obs elevenfold! 10/29/2013 Enzyme Kinetics & Inhibition P. 39 of 58
Think about that equation! n n n Remember that it says Km, obs = Km{1 + ([Ic]/Ki)} It does NOT say Km, obs = Km{(1+[Ic])/Ki} … which would be nonsensical because [Ic] has dimensions and 1 doesn’t In fact, Ic and Ki have the same dimensions, so they cancel like they should! But every year several students get that wrong. Don’t be among them! 10/29/2013 Enzyme Kinetics & Inhibition P. 40 of 58
Don’t get lazy! n n n A competitive inhibitor doesn’t automatically double Km The amount by which the inhibitor increases Km is dependent on [I]c If it happens that [Ic] = KI, then Km will double, as the equation shows 10/29/2013 Enzyme Kinetics & Inhibition P. 41 of 58
Noncompetitive I inhibition n S Inhibitor binds distant from active site, so it binds to the enzyme whether the substrate is present or absent. Noncompetitive inhibitor has no influence on how available the binding site for substrate is, so it does not 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. 10/29/2013 Enzyme Kinetics & Inhibition P. 42 of 58
n n L-B for pure noncompetitive inhibitors Decrease in Vmax 1/Vmax is larger X-intercept unaffected Cf. G&G Fig. 13. 15 10/29/2013 Enzyme Kinetics & Inhibition P. 43 of 58
Ki for noncompetitives n n 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 10/29/2013 Enzyme Kinetics & Inhibition P. 44 of 58
Same warning as before. . . n n n Correct: Vmax, obs = Vmax/{1 + ([In]/Ki)} Incorrect: Vmax, obs = Vmax/{(1 + [In])/Ki} As in the previous instance, the incorrect formula makes no sense because [In] has dimensions and 1 doesn’t. 10/29/2013 Enzyme Kinetics & Inhibition P. 45 of 58
Uncompetitive inhibition n n Inhibitor binds only if ES has already formed It creates a ternary ESI complex This removes ES, so by Le. Chatelier’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. 10/29/2013 Enzyme Kinetics & Inhibition P. 46 of 58
L-B for uncompetitives n n n -1/Km moves away from origin 1/Vmax moves away from the origin Slope ( Km/Vmax) is unchanged Cf. G&G fig. 13. 17 10/29/2013 Enzyme Kinetics & Inhibition P. 47 of 58
Ki for uncompetitives Defined as inhibitor concentration that cuts Vmax or Km in half n Easiest to read from Vmax value n Vmax, obs = Vmax/{1+([I]u/KI)} n Iu labeled “high” is Ki in this plot n 10/29/2013 Enzyme Kinetics & Inhibition P. 48 of 58
i. Clicker quiz, question 6 6. Treatment of enzyme E with compound Y doubles Km and leaves Vmax unchanged. Compound Y is: n (a) an accelerator of the reaction n (b) a competitive inhibitor n (c) a non-competitive inhibitor n (d) an uncompetitive inhibitor 10/29/2013 Enzyme Kinetics & Inhibition P. 49 of 58
i. Clicker quiz, question 7 7. Treatment of enzyme E with compound X doubles Vmax and leaves Km unchanged. Compound X is: n (a) an accelerator of the reaction n (b) a competitive inhibitor n (c) a non-competitive inhibitor n (d) an uncompetitive inhibitor 10/29/2013 Enzyme Kinetics & Inhibition P. 50 of 58
Mixed inhibition n n 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’ 10/29/2013 Enzyme Kinetics & Inhibition Cf. G&G fig. 13. 16 P. 51 of 58
Summary: reversible inhibitors Type Binds to Km kcat equation Competitive E only Up Flat Kmeff= Km{1+([I]C/KI)} Noncom- E or ES Flat petitive Uncompetitive Mixed Down kcateff= kcat/{1+[I]n/Ki)} ES only Down kcateff= kcat/{1+[I]u/Ki)} E or ES Up ~ 10/29/2013 Down kcateff= kcat/{1+[I]m/Ki)} Enzyme Kinetics & Inhibition P. 52 of 58
Most pharmaceuticals are enzyme inhibitors n n n Some are inhibitors of enzymes that are necessary for functioning of pathogens Others are inhibitors of some protein whose inappropriate expression in a human causes a disease. Others are targeted at enzymes that are produced more energetically by tumors than they are by normal tissues. 10/29/2013 Enzyme Kinetics & Inhibition P. 53 of 58
Characteristics of Pharmaceutical Inhibitors n n Usually competitive, i. e. they raise Km without affecting Vmax Some are mixed, i. e. Km up, Vmax down Iterative design work will decrease Ki from millimolar down to nanomolar Sometimes design work is purely blind HTS; other times, it’s structure-based 10/29/2013 Enzyme Kinetics & Inhibition P. 54 of 58
Amprenavir n n Competitive inhibitor of HIV protease, Ki = 0. 6 n. M for HIV-1 No longer sold: mutual interference with rifabutin, which is an antibiotic used against a common HIV secondary bacterial infection, Mycobacterium avium 10/29/2013 Enzyme Kinetics & Inhibition P. 55 of 58
When is a good inhibitor a good drug? n n n It needs to be bioavailable and nontoxic Beautiful 20 n. M 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 10/29/2013 Enzyme Kinetics & Inhibition P. 56 of 58
How do we lessen toxicity and improve bioavailability? n n n 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 10/29/2013 Enzyme Kinetics & Inhibition P. 57 of 58
Drug-design timeline Research 0 2 10/29/2013 Cost/yr, 106 $ Stage II clin ical trials 100 Sta ge I clinical trials Preliminary toxicity testing -8 Toxicity and bioavailability log Ki -3 2 years of research, 8 years of trials Improv ing affinity n 10 Clinical Trials Time, Yrs Enzyme Kinetics & Inhibition 10 P. 58 of 58
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