Biochemistry I - Lecture 14 - Enzyme Kinetics PDF

BIOL or CHEM 3361 Biochemistry I Enzyme Kinetics Reading: Chapter 13 Context ΔG tells us how favorable a reaction is… it tells us about thermodynamic potentiality Kinetics tells us how fast a favorable reaction will occur Enzymes are important to kinetics as they a...

BIOL or CHEM 3361 Biochemistry I Enzyme Kinetics Reading: Chapter 13 Context ΔG tells us how favorable a reaction is… it tells us about thermodynamic potentiality Kinetics tells us how fast a favorable reaction will occur Enzymes are important to kinetics as they accelerate reaction rates Enzymes are mostly (but not always) proteins that bind substrate through weak interactions at their active site In the active site, the protonation of key amino acids influences enzyme mechanism Characteristics of Enzymes 1. Enzymes catalyze thermodynamically favorable reactions causing them to proceed at extraordinarily rapid rates Accelerate as much as 1021 times over uncatalyzed rates Rates expressed per unit time (normally sec-1) Normally 109-1020 2. Enzymes bind specific substrates and catalyze specific reactions with high (>95%) yields Specificity comes from structural determinants at the active site E. g. a single molecule, bond, stereochemistry etc. 3. Enzymes are regulated and are the agents of metabolism E.g. Urease Urea Ammonia Uncatalyzed rate: 3x10 -10/sec Catalyzed rate (I.e. with Urease): 3x104/sec Catalytic power (or the ratio of the catalyzed rate to the uncatalyzed rate) is 1x1014 Classification of Enzymes Many (but not all) enzymes have a prefix related to their substrate and the suffix ‘ase’ - urease, phosphatase, protease, kinase… International Commission on Enzymes official classification - E.C. Number - Class (6) (Know these!) - Sub-class - Sub sub-class - Protein Enzyme Classification EC A- + B ↔ A + B- A-B + C ↔ A + B-C A-B + H2O ↔ A-H + B-OH XY | | A-B ↔ A=B + X-Y XY YX | | | | A-B ↔ A-B A + B ↔ AB Terminology Apoenzyme: protein part of an enzyme Holoenzyme: protein part of an enzyme plus cofactors Cofactor: non-protein part that is essential for catalytic function (e.g. metal ions) Coenzyme: non-protein organic molecule (e.g. B vitamin) Substrate: the compound(s) whose reaction an enzyme catalyzes Active site: the specific portion of the enzyme to which a substrate binds during a reaction Coenzymes and Cofactors Not all Enzymes are Proteins Ribozymes: segments of RNA that display enzyme activity in the absence of protein E.g. peptidyl transferase Figure 13.26 (a) The 50S subunit from H. marismortui. (b) The aminoacyl- tRNA (yellow) and the peptidyl-tRNA (orange) in the peptidyl transferase active site. Not all Enzymes are Proteins Figure 13.27 The peptidyl transferase reaction. Kinetics Introduction – No Enzyme AP Assume irreversible; P to A is slow or [P] is small Velocity (v) is P formed or A consumed per time v = d[P] or -d[A] dt dt Rate law writes this as v = k[A] k is the rate constant (time)-1 Standard chemical reaction: At equilibrium k1[R]eq= k-1[P]eq k1/k-1 = [P]eq/[R]eq At any point during the reaction v =k1[R] - k-1[P] v0 = k1[R] Simplify to initial velocity (really short time points) Kinetics Introduction – Enzyme A+BP E + S  ES Rate law writes this as v = k[A][B] or k[E][S] k is the rate constant (concentration)-1(time)-1 e.g. M-1sec-1 Two exponents in rate law means second-order reaction Plot v versus [S] (Hyperbolic Substrate Saturation Curve) At high [S] the rate is independent of S like a zero-order reaction (approaching Vmax) E is completely bound by S At low [S] the rate is proportional to S like a first-order reaction (vo) [Tangent] 1913 – Michaelis-Menten Equation You can read an interesting synopsis of Menten’s career at http://chemheritage.org/women_chemistry/body/menten.html Michaelis-Menten Equation is v([S]) For an enzyme-catalyzed reaction: k1 k2 S + E  ES  E + P k-1 Rapid equilibrium assumption is that k1 and k-1 >> k2 This means the breakdown of ES to form products is slower than: - the formation of the ES complex Second arrow isn’t reversible as there is little product Michaelis-Menten Equation is v([S]) For an enzyme-catalyzed reaction: Assumptions: k1 k2 So >> E S + E  ES  E + P Po = 0 k-1 k2 is rate limiting 1. v = k2[ES] Want v([So]) 2. [E]total = [E] + [ES] (No EP) 3. Keq = [E][S] = k-1 = KS = 1 (Dissociation constant) [ES] k1 KA (Describes relative amounts of E, S and ES) Michaelis-Menten Equation is v([S]) 1. v = k2[ES] 2. [E]total = [E] + [ES] 3. Keq = [E][S] = k-1 = KS [ES] k1 Sub. 2. as [E] into 3. and rearrange [ES] = [E]total[S] Ks + [S] Sub this into 1. v = k2[E]total[S] Plot v versus [S] Ks + [S] When S > Ks v is Vmax Michaelis versus Allosteric Enzymes Allosteric enzymes are an exception to the Michaelis-Menten model. Because they have more than two subunits and active sites, they do not obey the Michaelis- Menten kinetics but instead have sigmoidal kinetics. 1925 – Briggs and Haldane For an enzyme-catalyzed reaction: k1 k2 S + E  ES  E + P k-1 Generalized v([S]) by assuming that ES quickly reaches a constant value (Steady-state assumption) d[ES] = 0 dt I.e. rate of ES formation = rate of ES breakdown Steady State Zoomed in… 1925 – Briggs and Haldane For an enzyme-catalyzed reaction: k1 k2 S + E  ES  E + P k-1 I.e. rate of ES formation = rate of ES breakdown [S][E]k1 = [ES](k2 + k-1) 3. [S][E] = (k2 + k-1) = Km the Michaelis Constant (units of M) [ES] k1 1925 – Briggs and Haldane 1. v = k2[ES] 2. [E]total = [E] + [ES] 3. [S][E] = (k2 + k-1) = Km [ES] k1 From 3. Km is Ks when k-1>>k2 !!! [ES] = [E][S] / Km Use 2. [ES] = ([E]total- [ES])[S] / Km Rearrange to get [ES] = [E]total[S] / (Km + [S]) Sub into 1. v = k2 [E]total[S] / (Km + [S]) Vmax v = k2 [E]total[S] / (Km + [S]) Define special circumstances… If [S] is at saturation then v is maximal At saturation [ES] = [E]total and v = Vmax = k2[E]total Thus, The Equations where and Remember… Steady State Assumption  If k2