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Unformatted text preview: Lectures 7 & 8
Chapter 8: Stryer
Overview: structure/classiﬁcation enzyme thermodynamics transition state stabilization enzyme kinetics Michaelis-Menton kinetic parameters enzyme inhibition Homework: 8.2, 8.4, 8.7, 8.11, 8.15 Enzymes Enzymes are proteins (mostly) that are capable of catalyzing covalent bond cleavage and formation. Enzymes are agents of metabolic function. Key attributes: Components: enzyme (active site) substrate product (cofactor) (coenzyme) -alter the rate of product formation -speciﬁcity -reactivity conditions e.g., carbonic anhydrase in red blood cells; 107 rate acceleration Substrate binding to the enzyme active site Enzymes are organized into six classes based on the type of chemical reaction that they catalyze chymotrypsin (a protease) active site - residues that bind substrate and are involved with the catalytic mechanism enzyme = protease proteolysis: hydrolysis of a peptide bond substrate = peptide/protein Enzymes unnatural substrate: ester Enzyme speciﬁcity Cofactors: metal ions Coenzymes: organic Assist enzymes in their functions trypsin cleaves on the carboxyl side of arginine and lysine residues Know deﬁnitions: -prosthetic group -holoenzyme -apoenzyme -apoprotein thrombin cleaves ArgGly bonds in particular sequences only k = rate constant Free energy and enzyme kinetics k Rate (v) = – d[A]/dt = d[B]/dt A –> B v = – d[A]/dt = k[A] 1st order reaction units time-1 Free energy and enzyme kinetics A+B C+D (1) "G = "G° + RTln [C][D] [A][B]
standard state is pH 7, units are kJ or kcal k A + B –> C – d[A]/dt = k[A][B] Rate (v) = – d[A]/dt = – d[B]/dt = d[C]/dt 2nd order reaction units conc/time-1 at equilibrium "G = 0 0 = "G°! + RTln [C][D] (2) [A][B] K!eq = [C][D] [A][B] (4) (6) "G°! = – RTln [C][D] [A][B] "G°! = – RTlnK!eq
K!eq = 10–"G°!/2.303RT (3) (5) (7) k mA + nB –> C d[C]/dt = k[A]m[B]n m+n order reaction Most enzyme reactions are ﬁrst order reactions. "G°! = – 2.303RTlog10K!eq Free energy and enzyme kinetics Enzymes alter rates of reactions, not the reaction equilibrium S 10-4 s-1 10-6 s-1 P K!eq = 10–"G°!/2.303RT (7) K!eq R = 8.315 ! 10-3 kJ/mol•deg T = 298 K (25 °C) K!eq = 10–"G°!/5.69 kJ/mol (8) Keq = [P]/[S]= kF/kR 10-4 s-1 10-6 s-1 = = 100 relates equilibrium constants to free energy K is not dependent on the enzyme. The same equilibrium point is reached, but much more quickly in the presence of the enzyme. Enzyme reactions and energy changes compare S P E+S S X‡ ES P EP E+P Evidence for ES complex: saturation effects E+S S X‡ ES P EP E+P activation energy First step: formation of enzymesubstrate complex (ES) (at active site) If [E] is held constant, the reaction velocity will increase with increasing [S], until a maximal velocity is reached (uncatalyzed reactions do not display this saturation effect). At saturation, all catalytic sites are ﬁlled and rate cannot increase. "G‡ = GX‡ – GS
Note that the "G value for the reaction is the same for the catalyzed and uncatalyzed reactions. "G‡, on the other hand, is different. Enzymes accelerate reactions by decreasing "G‡. k = k0e–"G‡ /RT Evidence for ES complex: X-ray crystal structures Evidence for ES complex: spectroscopic changes Tryptophan synthetase (a bacterial enzyme) contains a pyridoxal phosphate (PLP) prosthetic group. E L-Ser + indole -> L-Trp Addition of L-Ser to E leads to a large increase in PLP ﬂuorescence. Addition of indole leads to a large decrease in ﬂuorescence. Enzyme P450 bound to substrate camphor: note presence of heme cofactor The enzyme active site The active site contains the catalytic groups. These amino acids participate in binding substrate. Speciﬁc interactions between E and S promote formation of the transition state (and lower !G‡ ). Some residues are involved directly in the reaction. Models for enzyme-substrate binding lock-and-key model induced-ﬁt model lysozyme substrates are bound to enzymes through multiple weak interactions residues in the active site can be far apart in sequence The binding energy between E and S is important for catalysis. Enzyme kinetics • quantitative study of enzyme catalysis • measure rate at which an enzyme can catalyze a reaction • rate can be established by measuring the following over time: • disappearance of substrate(s) (starting materials) • appearance of product(s) • what kinetic studies are good for: • measure binding of substrate and inhibitor to active site • contribute to understanding of enzyme mechanism • understanding metabolic pathways • basis for common clinical assays • drug design - inhibit speciﬁc enzymes Determining initial velocity E+S ES E+P Terms: rate (v, velocity); rate constant (k); rate law How fast does enzyme convert S to P? v = d[P]/dt = -d[S]/dt = change molarity/ change time = µM/sec v =k[A][B], for A + B -> C Enzyme kinetics E+S ES E+P v = d[P]/dt = -d[S]/dt = change molarity/ change time = µM/sec v =k[A][B], for A + B -> C Km = [S] when enzyme is half of its Vmax lower Km, better substrate Initial velocity (V0) vs. substrate concentration [S] V0 = Vmax[S]/(Km + [S]) Can you derive this equation? What is the steady state assumption? at low [S], V0 = Vmax[S]/Km at high [S], V0 = Vmax The Lineweaver-Burke equation or double-reciprocal plot Understanding Km Vmax[S] Km + [S] the 'Michaelis constant' Km is a constant for a particular substrate and enzyme under speciﬁed solution conditions Km is an approximation of the dissociation constant (Kd) of E for S (estimate of afﬁnity) small Km implies tight binding; high Km implies weak binding A substrate with a high Km for a given enzyme requires a higher [S] to achieve a given reaction rate than a substrate with a low Km v= at low [S], 1 = Km +1 V0 Vmax[S] Vmax y = mx + b 1/Vmax = b Km /Vmax = m Understanding Vmax Vmax is a constant v= Vmax[S] Km + [S] Vmax is the theoretical maximal rate of the reaction - but never achieved in reality To reach Vmax would require that all enzyme molecules are tightly bound to substrate Vmax is asymptotically approached as substrate is increased Understanding kcat kcat, turnover number, is the number of substrate molecules converted to product per enzyme molecule per unit of time, when E is saturated with substrate if Michaelis-Menton applies, k2 = kcat = Vmax/Et kcat values range from less than 1/s to many millions per s Enzymes with kcat/Km close to diffusion-controlled limit (108 to 109 M-1s -1) Upper limit on kcat/Km imposed by how fast E and S can diffuse together in solution The importance of understanding sequential reactions The importance of understanding sequential reactions Double-displacement (Ping-Pong) reactions Kinetics of an allosteric enzyme What is the basis for the sigmoidal shape of this curve? Remember Hb and O2 binding (Ch.7)? Enzyme inhibition reversible inhibitors; these are kinetically distinguishable Kinetics of a competitive inhibitor Enzyme binds substrate (ES) or inhibitor (EI), but not both (ESI). Competitor may resemble substrate and bind to the active site. Kinetics of an uncompetitive inhibitor Inhibitor only binds to ES, not E. Kinetics of a noncompetitive inhibitor I and S bind simultaneously to E at different sites. Irreversible enzyme inhibition Irreversible enzyme inhibition These reactions can be used to map the enzyme active site. Irreversible enzyme inhibition Mechanism-based (suicide) inhibitors Transition-state analogs as enzyme inhibitors Penicillin: irreversibly inactivates bacterial cellwall synthesis penicillin antibiotic bacterial cell wall target Glycopeptide transpeptidase: catalyzes peptidebond formation between glycine and D-Ala Transpeptidation involves an acyl-enzyme intermediate Penicillin inhibition: the Trojan horse strategem ...
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