4.Enzymes

4.Enzymes - Reaction rates Recall the velocity(v at which a...

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Reaction rates Recall, the velocity ( v ) at which a reaction proceeds is expressed in terms of a rate constant ( k ), typically with units: sec –1 M –1 sec –1 another convenient way to express rates is in terms of the half-life: t 1/2 = ln2 / k expressed in units of time (sec) Enzymes are macromolecular catalysts that function to accelerate the rates of biological reactions.
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Intrinsic Reaction Rates Without enzymes, life would be impossibly slow.
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Enzyme Catalyzed Reaction Rates Catalyzed rates vary, but are typically faster than 1 sec –1 KSI – keto steriod isomerase PEP – carboxypeptidase MAN – mandelate racemase GLU – β -amylase STN – staph nuclease R. Wolfenden
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Enzymes Enzymes are subject to the same forces of nature as all other substance; however, they do differ from typical chemical catalysts: higher reaction rates mild reaction conditions (for example, 37 °C, pH 7.4) much greater reaction specificity can be highly regulated geometric and physical complementarity in an enzyme- substrate (ES) complex
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The Enzyme-Substrate ( ES ) Complex Can readily differentiate two pro -chiral substituents ethanol – CH 3 C H 2 OH
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Enzyme Kinetics Cannot integrate this equation. velocity (rate) = v = d [P] / dt = k 2 [ES] d [ES] / dt = k 1 [E][S] k -1 [ES] k 2 [ES] ES k 1 k -1 E + S k 2 E + P
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Michaelis-Menten Assumption (1913) First Step in Pre-Equilibrium k -1 >> k 2 It is much more likely that S will dissociate from E than for S to be converted to P. K s = k -1 / k 1 = [E][S] / [ES] This assumption is NOT ALWAYS CORRECT in real enzymatic reactions, but it does make it possible to integrate the equation on the previous slide. If not correct, reaction is said “not to obey Michaelis-Menten kinetics.” ES K S E + S k 2 E + P
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(much more general) Steady State Assumption (1925) then d [ES] / dt = 0 Except for first few milliseconds of a reaction, [ES] remains constant. if [S] >> [E] T This usually is true.
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General Equation for Enzyme Kinetics So far, we have obtained equations as a function of [ES] and [E], but it is not generally possible to measure these quantities. But, we know that: [E] T = [E] + [ES] (conservation equation) Substituting, d [ES]/ dt = 0 (steady state assumption) into: d [ES] / dt = k 1 [E][S] k -1 [ES] k 2 [ES] yields: k 1 ([E] T [ES])[S] = ( k -1 + k 2 )[ES] divide by k 1 and solve for [ES]: where K M is the Michaelis constant: [ΕΣ] = [Ε] Τ [Σ] Κ Μ + [Σ] Μ = κ -1 + 2 1
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General Equation for Enzyme Kinetics Almost done! Now, the initial reaction velocity is: v 0 = d [P] / dt = k 2 [ES] The maximal velocity , V max , occurs at high [S] when the enzyme is saturated : V max = k 2 [E] T Therefore , ω 0 = κ 2 [ES ] = k 2 [E] T [S] K M + [S] 0 = ς μαξ [Σ] Κ Μ + [Σ] Michaelis-Menten equation, the basic equation of enzyme kinetics
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v o v o = initial reaction velocity Point at which steady state is first achieved, usually a few milliseconds after t=0 Makes it possible to avoid problems with reversibility, product inhibition, and inactivation of the enzyme.
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4.Enzymes - Reaction rates Recall the velocity(v at which a...

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