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## Lecture Notes for Chapter 7 Enzyme Kinetics and Inhibition

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**Essential Biochemistry**Third Edition Charlotte W. Pratt | Kathleen Cornely Lecture Notes for Chapter 7 Enzyme Kinetics and Inhibition**KEY CONCEPTS: Section 7-1**• An enzyme’s activity, measured as the rate of product formation, varies with the substrate concentration.**Rates of Chemical Reactions**• Enzyme kinetics is the study of rates of reactions catalyzed by enzymes. k v= S P • The reaction rate (velocity, v) can be described in several ways. • Disappearance of substrate, S • Appearance of product, P • These equations relate velocity to concentration of reactants and products.**Consider the reaction catalyzed by triose phosphate**isomerase. • As [GAP] decreases, the [DHAP] increases. GAP DHAP**Reaction velocity can be thought of as concentration vs.**time.**Many enzymes react with substrates in a nonlinear fashion.**• The shape here is hyperbolic. • Shape indicates, in part, that E and S combine to form an ES complex E + S ES**KEY CONCEPTS: Section 7-2**• Simple chemical reactions are described in terms of rate constants. • The Michaelis-Menten equation describes enzyme-catalyzed reactions in terms of KM and Vmax.**Rate equations describe chemical processes.**• A unimolecular reaction has a velocity (rate) that is dependent on the concentration of only one substrate. • v = k [A], where k has units of sec-1 k v= A P**Rate equations describe chemical processes.**• A bimolecular (second order) reaction has a velocity (rate) that is dependent on two substrate concentrations. • v = k [A] [B] (or k [A]2 or k [B]2)where k has units of M-1 sec-1 k v= A + B P**k1**k2 E + S ES E + P k-1 Many enzymes obey Michaelis-Menten kinetics. Rate limiting step Problem: [ES] is difficult to measure!What can we do?**k1**k2 E + S ES E + P k-1 Try to re-express the rate. One point that helps: k1 [E] [S] - k-1 [ES] - k2 [ES] Formation of ES Depletion of ES**Assume steady state equilibrium.**• For most of the duration of the reaction, [ES] remains steady as substrate is converted to product.**k1**k2 E + S ES E + P k-1 Michaelis-Menten Equation = k1 [E] [S] - k-1 [ES] - k2 [ES]**Derivation of the Michaelis-Menten Equation**= k1 [E] [S] - k-1 [ES] - k2 [ES] Thus: k1 [E] [S] = [ES] (k-1 + k2 ) Since… [E]total = [ES] + [E] [E] = [E]total - [ES] Substitute here**Derivation of the Michaelis-Menten Equation**k1 ([E]total [S] - [ES] [S]) = [ES] (k-1 + k2 ) KM Divide both sides by k1 [E]total [S] - [ES] [S] = [ES] (k-1 + k2 ) k1 [E]total [S] - [ES] [S] = [ES] KM**Derivation of the Michaelis-Menten Equation**[E]total [S] - [ES] [S] = [ES] KM Rearrange: [E]total [S] = [ES] (KM + [S]) [ES] = [E]total [S] KM + [S]**Derivation of the Michaelis-Menten Equation**Vmax k2 [E]total [S] v = Vmax[S] KM + [S] The Michaelis-Menten Equation v = KM + [S]**The Michaelis-Menten equation is hyperbolic.**Vmax is where the reaction velocity reaches its plateau KM is the substrate concentration at ½ Vmax**KEY CONCEPTS: Section 7-2**• The kinetic parameters KM , kcat, and kcat/KM are experimentally determined. • KM and Vmax values can be derived for enzymes that do not follow the Michaelis-Menten model.**The catalytic rate constant determines how quickly an enzyme**can act. • kcat = catalytic rate constant, turnover • kcat = k2 • kcat = Vmax/[E]total**kcat/KM indicates catalytic efficiency.**• What limits the catalytic power of an enzyme? • Electronic rearrangements during formation of the transition state • Frequency of productive enzyme collision with substrate, with the maximum being the diffusion-controlled limit • Enzymes reach catalytic perfection when their rate is diffusion-controlled.**The Lineweaver-Burk plot linearizes Michaelis-Menten**kinetics data. Vmax[S] v = KM + [S] Take the reciprocal of both sides: KM 1 1 1 = + v [S] Vmax Vmax**The Lineweaver-Burk plot linearizes Michaelis-Menten**kinetics data. Notice how the data are weighted heavily here due to the linearization!**Not all enzymes fit the Michaelis-Menten model.**• Some enzymes have multiple substrates.**Not all enzymes fit the Michaelis-Menten model.**• Some enzyme-catalyzed reactions have many steps.**Not all enzymes fit the Michaelis-Menten model.**• With allosteric enzymes, binding of a substrate at one active site can affect the catalytic activity of other active sites.**Not all enzymes fit the Michaelis-Menten model.**• Allosteric enzymes exhibit cooperativity. • Velocity plot is sigmoidal!**KEY CONCEPTS: Section 7-3**• Substances that bind irreversibly to an enzyme can inhibit its activity. • A competitive inhibitor appears to increase KM without affecting Vmax. • Transition state analogs can act as competitive inhibitors. • Noncompetitive, mixed, and uncompetitive inhibitors decrease kcat. • Allosteric regulators can inhibit or activate enzymes.**Some inhibitors act irreversibly.**A “suicide inhibitor”**Competitive inhibitors bind to the same site as the**substrate.**Transition state analogs often make better inhibitors than**substrate analogs. Transition State Transition State Analog**Allosteric regulation can inhibit or enhance enzyme**activity. • Consider the example:**Phosphoenolpyruvate inhibits PFK by an allosteric feedback**mechanism.