Lecture 11: Enzyme Kinetics, Part I

Transcription

1 Biological Chemistry Laboratory Biology 3515/Chemistry 3515 Spring 2018 Lecture 11: Enzyme Kinetics, Part I 13 February 2018 c David P. Goldenberg University of Utah goldenberg@biology.utah.edu

2 Back to Enzyme Kinetics E + S E + P E: Enzyme, S: Substrate (reactant), P: Product The basic experiment: Measure reaction rate ( velocity ) as a function of both enzyme concentration ([E]) and substrate concentration ([S]). [P] (M) [P] (M) [E] [S] Time (min) Time (min) Rate = d[p] dt (slope of [P] vs. time)

3 Clicker Question #1 How does velocity change with enzyme concentration? Reaction Velocity Enzyme Concentration All answers count (for now).

4 Clicker Question #2 How does velocity change with substrate concentration? Reaction Velocity Substrate Concentration All answers count (for now).

5 Why Doesn t Velocity Increase Linearly with Substrate Concentration? A plumbing analogy:

6 Our Heroes Leonor Michaelis ( ) Maude Leonora Menten ( ) Michaelis, L. & Menten, M. L. (1913). Die kinetik der invertinwirkung. Biochem. Z., 49, Johnson, K. A. & Goody, R. S. (2011). The original Michaelis constant: Translation of the 1913 Michaelis-Menten paper. Biochemistry, 50,

7 A Simple Mechanism Accounts for Hyperbolic Kinetics E + S k 1 k 1 ES k cat E + P V = [S]V max K m + [S]

8 The Individual Steps and Rate Constants E + S k 1 ES A second-order reaction In the absence of other reactions: d[es] = k dt 1 [E][S] The second-order rate constant, k 1, has units of M 1 s 1 or M 1 min 1 d[es] dt Units: M min 1 k 1 [E][S] Units: min 1 M 1 M M = M min 1

9 The Individual Steps and Rate Constants E + S k 1 ES A first-order reaction In the absence of other reactions: d[es] = k dt 1 [ES] The first-order rate constant, k 1, has units of s 1 or min 1 d[es] dt Units: M min 1 k 1 [ES] Units: min 1 M = M min 1

10 The Individual Steps and Rate Constants ES k cat E + P A first-order reaction In the absence of other reactions: d[es] = k dt cat [ES] The first-order rate constant, k cat has units of s 1 or min 1 d[es] dt Units: M min 1 k cat [E][S] Units: min 1 M 1 M M = M min 1

11 An Important Point The rate constants, k 1, k 2 and k cat are konstant! They do not change with concentration. The fine print: This is an assumption that may break down at extreme concentrations. The values of the rate constants generally depend on other factors, such as temperature or other solution conditions.

12 Approaching Steady State after Mixing Substrate and Enzyme Concentration (M) S P E. S E + S k 1 k 1 ES k cat E + P d[es] = k dt 1 [E][S] k 1 [ES] k cat [ES] Time (min) At steady state: d[es] dt = k 1 [E][S] k 1 [ES] k cat [ES] = 0 Solving this equation gives the Michaelis-Menten equation.

13 The Michaelis-Menten Mechanism and Equation E + S k 1 k 1 ES k cat E + P where: V = [S]V max K m + [S] V max = k cat ([E] + [E S]) = k cat [E] T Units : M min 1 = M/min and: K m = k 1 + k cat k 1 Units : The fraction, min 1 + min 1 min 1 M 1 = M V V max, represents the fraction of enzyme with substrate bound.

14 When [S] K m : [S] K m V = [S]V max K m + [S] V [S]V max [S] = V max Velocity (M/min) [S] (M) When V /V max approaches 1, nearly all of the enzyme molecules have substrate bound.

15 When [S] K m : [S] K m V = [S]V max K m + [S] V [S]V max K m Velocity (M/min) [S] (M) In this regime, the fraction of enzyme with substrate bound is: V V max [S] K m

16 When [S] equals K m : [S] = K m V = [S]V max K m + [S] V = [S]V max 2 [S] = V max 2 Velocity (M/min) [S] (M) When V /V max = 1/2, one half of the enzyme molecules have substrate bound.

17 K m is not equal to 1/2 V max! The equation: V = [S]V max K m + [S] The units: K m has units of concentration, like [S]. V max has units of reaction velocity, e.g., M/min, like V. K m equals the substrate concentration at which V = V max /2. Writing K m = V max /2 in a lab report or quiz will cost lots of points!

18 A Chromogenic Substrate for Studying Trypsin Benzoyl-Phe-Val-Arg-p-nitroanilide Arg Val Phe Chromogenic: generates color. Nitroanilide (substrate) is colorless. Nitroaniline (product) absorbs violet light. Solutions look yellowish.

19 Experiment 3, Part A: Velocity as a Function of Enzyme Concentration The Michaelis-Menten equation predicts that V is proportional to [E] T : V = V max [S] K m + [S] = k cat[e] T [S] K m + [S] A [E] Velocity (µm/min) Time (min) µg Enzyme What might cause deviations from linearity in these plots?

20 Experiment 3, Part B: Measurement of Trypsin Concentration To determine k cat, we need to know both V max and the total enzyme concentration: V max = [E] T k cat k cat = V max /[E] T (k cat is more interesting than V max!) Why not just measure enzyme concentration by UV absorbance or Bradford assay? Both measure protein concentration. Not all of the protein may be active enzyme. This is a particular problem with proteases, which tend to lose activity due to proteolysis.

21 Experiment 3, Part B: Measurement of Trypsin Concentration Using BPTI + BPTI (I) Trypsin (E) Complex (E. I) Strength of binding is commonly expressed as a dissociation equilibrium constant: K d = [E][I] [E I] Related to, but not identical to, K m. Has units of concentration, and a low value indicates tight binding. For BPTI and bovine β-trypsin, K d M. One of the tightest biological complexes known.

22 Experiment 3, Part B: Titration of Trypsin with Bovine Pancreatic Trypsin Inhibitor (BPTI) Determine [BPTI] from A Mix fixed [trypsin] with increasing [BPTI] Measure residual trypsin activity Calculate trypsin concentration from equivalence point. % Trypsin Activity 50 [BPTI] = [Trypsin] nmoles BPTI