Lecture 13: Kinetics II Michaelis-Menten Kinetics Margaret A. Daugherty Fall 2003 Enzyme Reactions E + S ES ES* EP E + P E = enzyme ES = enzyme-substrate complex ES* = enzyme/transition state complex EP = enzyme product complex P = product Physically interact with their substrates to effect catalysis; Substrates bind to the enzyme s active site Return to a simple case: single-order kinetics A B A B v = [A] rate of disappearance of A: v = -d[a]/dt = k[a]
Enzyme kinetics: substrate saturation! (substrate saturation curves) Enzyme kinetics: what do we want to know? How well does an enzyme bind a substrate? K m How fast does an enzyme do its chemistry? V max What is it s maximal catalytic activity? How efficient is the enzyme? /K m Michaelis-Menton Kinetics: I ONE SUBSTRATE ---------> ONE PRODUCT REVERSIBLE IRREVERSIBLE (minimally reversible) Michaelis-Menton Kinetics: I ES E + P Inclusive in the step: ES --> ES Enzyme creates strain on substrate so that chemistry can occur ES --> EP Enzyme performs chemistry on substrate EP --> E + P Product dissociates from enzyme; enzyme free to go another round
Michaelis-Menton Kinetics: II 1) Equilibrium is fast. E + S ES K S = / = [E][S] [ES] Initial velocity (v o ) measurements Determine v o by analyzing early time points Measure absorbance fluorescence vs. time v o = rate of product formation = d[p]/dt 2). Steady-state: When [S] >>> [E] d[es] = 0 dt 3). Initial velocity measurements: No E + P --> EP Michaelis-Menton Kinetics: III RATE OF FORMATION OF P V = [ES] * Need to measure both and [ES] Michaelis-Menton Kinetics: IV TOTAL CONCENTRATION OF ENZYME [E] t = [E] + [ES] Express the rate in terms of [S] and [E] t
Progress Curves for an Enzyme Catalyzed Reaction [E] f as [ES] ; [S] as [P] ; Michaelis-Menton Kinetics: V STEADY STATE ASSUMPTION Formation ES = Breakdown ES [E][S] = [ES] + [ES] Pre-steady state: ES forming Steady state: [ES] almost constant Formation from E + S Breakdown into E + S Breakdown into E + P Michaelis-Menton Kinetics: VI Michaelis-Menton Kinetics: VII Formation ES = Breakdown ES rearrange equation: [ES] = [E][S] + K M = + Michaelis constant
Michaelis-Menton Kinetics: VIII Now, we have a definition for K M & [E] t Rewriting the previous equation: K M [ES] = [E] t [S] - [ES][S] Solve for [ES] [ES] = [E] t[s] K M + [S] Michaelis-Menton Kinetics: IX Returning to: Michaelis-Menton Kinetics: III RATE OF FORMATION OF P V = [ES] Replaced the need to measure both and [ES] [E] t [S] V = K M + [S] MICHAELIS-MENTON PLOT V max = [E] t ; V max α [E] t V = V max [S] K M + [S] K M : Substrate concentration when V = V max /2
V max, K M and V max : reached when enzyme molecules are saturated; every enzyme carrying out a catalytic reaction K M :Substrate concentration when V = V max /2; the higher the K M, the higher the concentration of S to reach a given velocity. : direct measure of the catalytic ability of an enzyme Significance of K M Where [S] = K M, v = V max 2 Thus, K M is the substrate concentration at which the reaction velocity is half-maximal. K M range: 10-1 to 10-8 M Note: K M is unique for EACH enzyme-substrate pair! How does Km relate to physiological concentrations of substrate? Area in pink highlights a theoretical concentration range of an enzyme; Typical Km values usually just above this concentration range. Glucose metabolism and you; small changes in blood glucose activate different metabolic pathways. fed fasting less starved **
Turnover Number K cat = turnover number of the enzyme : number of reaction processes (turnovers) that each active site catalyses per unit time. Catalytic Efficiency Catalytic efficiency = /K M varies for each substrate with an enzyme! V max, K M and /K M : ratio measures enzyme efficiency catalytic perfection 10 9 M -1 sec -1 /K M = large Arises from large or a small K M Experimental Design I want to measure the reactivity of my enzyme how? Measure production of [P] Measure the decrease of [S] Note: The velocity of an enzyme-catalyzed reaction is dependent upon the substrate concentration [S] Expt must have... const [E] const T const ph
Extrapolate Lineweaver-Burke Plot 1 V V = V max [S] K M + [S] K M V max =. 1 1 + [S] y = mx + b V max REVIEW Free energy provides information on whether a reaction is favorable, not its rate. Enzymes are biological catalysts (usually proteins) that result in higher reaction rates; they do not affect the thermodynamics of a reaction. Enzymes lower the activation energy of the transition state for a reaction. Michaelis-Menten kinetics describe the simple catalyzed reaction of one substrate - one product. Also called the double reciprocal plot; Actual values for K M and V max can be determined. The Lineweaver-Burke plot (double-reciprocal plot) permits Vmax and Km to be accurately determined. What is the significance of V max, K M, and catalytic efficiency /K M?