BMB Lecture 9

Transcription

1 BMB Lecture 9 Class 11, November 7, 2018 Steady-state kinetics (I)

2 Case 3. Viscosity Variation If k cat /K m decreases with increasing viscosity, then the reaction is diffusion-limited (S binding is RD). Controls: (1) k cat values are not affected by viscosity (2) With slow substrates for which chemistry is RDS, k cat /K m is insensitive to viscosity variations.

3 Brouwer & Kirsch, Biochemistry 21: 1302 (1982)

4 Rate constants of biological reactions Protein conformational changes: µs s Bi-molecular associations: small molecules M -1 s -1 Protein-ligand M -1 s -1 (theoretical limit 10 9 M -1 s -1 ) Protein-protein M -1 s -1 translation: amino acids / sec transcription: >40 min

5 Steady State Kinetics 1. Rate equations 2. Kinetic shortcuts 3. Positional isotope exchange 4. Inhibition

6 Definition of steady state: d[es]/dt = 0 k 2 [P]/[E] 0 [ES]/[E] 0 Hence, [S] >> [E] (multiple turnover) Measure within linear range (<10 15% S reacted) Beware of product inhibition

7 Saturation curves in enzyme kinetics (k cat /K m ) E + S > products E S > products (k cat ) K m 1. Complex formation [S] K m = K d 2. Change in rate-limiting step K m >> K d

8 A simple steady-state rate expression Steady-state assumption: Mass conservation: Assumption:

9 Michaelis-Menten Treatment Assumption: E-S binding is rapid and reversible (k 2 << k -1 )

10 Michaelis-Menten Treatment k 2 << k -1 DG sub-saturating [S] saturating [S]

11 Briggs-Haldane Situation k -1 << k 2 When [S] > 0, k obsd = k 1 [S t ] k cat /K m = k 1

12 Briggs-Haldane Situation k 2 >> k -1 DG sub-saturating [S] saturating [S]

13 k 2 << k -1 k -1 << k 2

14 Steady-state kinetics: Algebra time! 1. Identify all the enzyme species: E, ES, EI, etc. 2. Write down equations that relates different enzyme species - Apply steady-state assumption to the last irreversible step - Mass conservation - Equilibria # equations = # species 3. Solve for the last enzyme species. v obsd = k j [E j ]

15 Intermediates during reaction

16 DG Intermediates during reaction k 2 >> k 3

17 Representation of Kinetic Data

18 Representation of Kinetic Data

19 Kinetic shortcuts: Use of transit times instead of rate constants Convert into net rate constants Cleland, Biochemistry 1975

20 Convert into net rate constants (conductance) Cleland, Biochemistry 1975

21 Bi-molecular reactions K 5, k 3 and k 1 are Calculate V max : [A] fi, 1st step drops out Cleland, Biochemistry 1975

22 Biomolecular reactions Calculate V max /K m : limv when [A] fi 0 Cleland, Biochemistry 1975

23 In understanding a reaction mechanism, the task of the kineticist is to define the number and sequence of complexes, intermediates, and conformational states, define their approximate nature, and measure the rate constants of their conversion.

24 Multi-Substrate Reactions No coupling between A & B binding coupled substrate binding

25 Multi-Substrate Reactions Order of substrate binding: Sequential 1. Random (with S coupling) 2. Ordered Both substrates bind before reaction; Reactions will obey Michaelis Menten kinetics with intercepting lines on 1/v -1/[S] plots

26 Multi-Substrate Reactions Order of substrate binding: double displacement 3. Ping-pong Highly suggestive of a covalent intermediate

27 DG Ping-Pong Reactions

28 Examples of Ping-pong kinetics Phosphate-transfer (phosphoglycerate mutase) Acyl transfer (acetyl-coa acyltransferase)

29 Product Partitioning If different substrates share a covalent intermediate, E-B formed by different substrates partition to different products at a constant ratio

30 Positional Isotope Exchange Glutamine Synthase: Is a glutamyl-p intermediate on the pathway?

31 Test the presence of a covalent intermediate by positional isotope exchange 18 O at b,g-bridging position will be found in non-bridging positions Midelfort & Rose, 1976

32 Functional Groups for PIX

33 Competitive Inhibition: I binds to E but not ES [E] t = [E] + [ES] + [EI]

34 Competitive Inhibition: I binds to E but not ES

35 Substrate inhibition to characterize two-step substrate binding in Tetrahymena ribozyme I = AGGAGG I = GGGAGG Narlikar et al, Biochemistry 36: 2465 (1997)

36 Competitive Inhibition: I binds to E but not ES Increased K m No change in V max

37 Noncompetitive inhibition: both S and I bind to E Decrease in k cat No change in K m

38 Uncompetitive inhibition: I binds to ES Both K m and V max change No change in k cat /K m Effects similar to nonproductive binding

39 Inhibition: A case study of acetylcholine esterase Two substrate binding sites in active site Reaction involves a covalent intermediate

40 N-CH 3 -amino propylethyl ester is a slow substrate Tertiary amine acts as a competitive inhibitor

41 Good substrate: tertiary amines exhibit noncompetitive inhibition

42 Reason for different inhibition patterns Good substrate: Deacylation is rate-limiting R 3 NH + can bind to Acyl-Enz Poor substrate: Acylation is rate-limiting R 3 NH + cannot bind to ES

43 SRP and TF direct nascent proteins to distinct fates Competing Hypotheses SRP SR Trigger Factor SRP and TF compete with one another SRP and TF can bind the same RNC SRP binds short nascent chains, TF prefers longer nascent chains

44 How Are Nascent Chains Sorted A. Competitive Binding between SRP and TF? B. Anti-Cooperative Co-Binding Ariosa et al, PNAS 2015; Bornemann et al, Nature Comm. 2014

45 TF binds to SRP-loaded RNCs and changes SRP conformation [TF] Ariosa et al, PNAS 2015; Bornemann et al, Nature Comm. 2014

46 Reversible inhibitors as mechanistic tools to determine substrate binding order Random: Inhibitor for A: competitive with A noncompetitive with B Inhibitor for B: noncompetitive with A competitive with B

47 Reversible inhibitors as mechanistic tools to determine substrate binding order Ordered: Inhibitor for A: competitive with A noncompetitive with B Inhibitor for B: uncompetitive with A competitive with B

48 Recommended Readings