SURVEY OF BIOCHEMISTRY Enzyme Kinetics and Inhibition

Rates of Chemical Reactions Enzyme kinetics is the study of rates of reactions catalyzed by enyzmes. v = A P k The rxn rate (velocity, v) can be described in several ways: [1] disappearance of reactant, A [2] appearance of product, P These eqn’s relate velocity to concentration of reactants and products.

Rate Laws Enzyme kinetics is the study of rates of reactions catalyzed by enyzmes. v = A P k A rate law is an equation describing the velocity of a chemical reaction. Differential Rate Laws Integrated Rate Laws

Differential Rate Laws Differential rate laws correspond to order of the reaction. Order of Reaction Rate Law 0 v = k 1 v = k [A] 2 v = k [A]2 or k[B]2 or v = k [A] x [B]

Integrated Rate Laws: First Order Integrated rate laws express the rxn velocity in terms of time. A products Rate of Disappearance of A - d[A] dt = k [A] first order rxn Rearranging… d[A] [A] = - k dt

Integrated Rate Laws: First Order Rearranging… d[A] [A] = - k dt [A]t Integrate on both sides of eqn: dA = - k dt [A]0 (ln [A]t + constant) - (ln [A]0 + constant) = - kt ln [A]t - ln [A]0 = - kt

Integrated Rate Laws: First Order ln [A]t - ln [A]0 = - kt ln [A] = ln [A]0 - kt

Integrated Rate Law: Other Versions of First Order ln [A]t - ln [A]0 = - kt ln [A]t [A]0 = - kt first order rxn Rearranging: Take exponent of both sides: [A]t [A]0 = e -kt [A]t = [A]0 e -kt first order rxn

Integrated Rate Law: Second Order How does the integrated rate law change if the order of the reaction is second order? 2A products Rate of Disappearance of A - d[A] dt = k [A]2 second order rxn Show result on board Rearranging… d[A] [A]2 = - k dt

Michaelis-Menten Equation Many enzymes obey Michaelis-Menten kinetics behavior: E + S ES E + P k1 k-1 k2 Rate limiting step Problem: [ES] is difficult to measure! What can we do?

Michaelis-Menten Equation E + S ES E + P k1 k-1 k2 Recall Assume equilibrium is maintained in 1st step Assume “steady state” k1 [E] [S] - k-1 [ES] - k2 [ES] = 0 Formation of ES Depletion of ES See notes on board…

Michaelis-Menten Kinetics

Lineweaver-Burk Plot

bind to different site in E than S Enzyme Inhibition What is an inhibitor? Modes of Inhibition Competitive binds to same site in E as S Uncompetitive Noncompetitive Mixed bind to different site in E than S Note: Text does not distinguish “non” and “mixed”

Competitive Inhibition Competitive inhibitors bind to the same site on E as S

Competitive Inhibition

Competitive Inhibition

Uncompetitive Inhibition Uncompetitive inhibitors bind directly to the ES complex but not to the free enzyme

Uncompetitive Inhibition

Mixed Inhibition Mixed inhibitors can bind to E or ES complex S cannot bind if I is already bound!

Mixed Inhibition

Noncompetitive Inhibition Noncompetitive inhibitors can bind to E or ES complex S can bind even if I is already bound! + I See board for plot

Exam #2 in two weeks (June 26) Updates and Reminders Exam #2 in two weeks (June 26) Chapter 7: Protein Function Chapter 11: Enzyme Catalysis Chapter 12: Kinetics & Inhibition Chapter 8: Carbohydrates Chapter 14: Introduction to Metabolism Suggested HW problems online this weekend Resources: What You Should Know more coming soon