BMB Lecture 11 Class 13, November 14, Pre-steady state kinetics (II)

Transcription

1 BMB Lecture 11 Class 13, November 14, 2018 Pre-steady state kinetics (II)

2 Reversible reactions [A] = A e + (A 0 A e ) e k obsd t k obsd = k 1 + k -1 A obsd rx [A] forward rx only A e = k -1 /(k 1 +k -1 ) t (s)

3 Reversible 2nd Order Reaction Use E or S in large excess so that reaction becomes psuedo-first order k obsd This is how you measure binding rate constants

4 SRP binding to SRP receptor (SR or FtsY) SRP SR Fluorescence (a.u.) nm FtsY 100 nm FtsY 200 nm FtsY 400 nm FtsY Time (s)

5 SRP binding to SRP receptor (SR or FtsY) k obsd = k 1 [SR] + k k 1 = 4.6 x10 4 M -1 s -1 k obsd (s -1 ) k -1 = s FtsY (µm)

6 Pulse-chase: Measure dissociation rate constant k off = s -1 Controls: (1) Chase is effective; (2) Chase-binding is not rate-limiting; (3) Measured k off is independent of [chase]

7 Beware when k off does not stay constant

8 Beware when k off does not stay constant

9 Pulse-chase: Measure E S partitioning Induce reaction + chase k obsd = k c + k off

10 Tetrahymena Group I Ribozyme Pulse-chase to determine partition of E S* G vary

11 Tetrahymena Group I Ribozyme Pulse chase to measure S binding rate vary k on = 10 x 10 7 M -1 min -1 ~ (k cat /K m ) S

12 Time Courses with A Lag t (min) Two consecutive, irreversible steps

13 Two consecutive irreversible reactions [C] = A 0 - [A] - [B]

14 Lags in formation of C when k 1 ~ k 2 cannot distinguish between k 1 and k 2 based solely on C accumulation of B reports on relative values of k 1 vs k 2

15 BM exercise I. Two Irreversible Reactions [A] 0 = 100, [B] 0 = 0, [C] 0 = 0 Run basic simulation for 10 s. Plot A, B, C. Use parameters window to change parameters k 1f = 10 or k 2f = 10 How does this affect the kinetics and amount of each species? Batch runs: vary k 1f from 1 to 100. Parameters plot: plot B max vs. k 1f Use parameter sliders to vary k 1f and k 2f

16 Importing and fitting data 1. In Madonna, create the model. Run the simulation. 2. To import, save data as a.txt file. 3. In Madonna, choose File -> Import dataset 4. Choose Parameters -> Curve fit 5. Fit values will show up in the Parameters window.

17 Exercise: Bernstein data Series1 Series2 Series

18 Time Course with A Burst [P] or signal t (min) 1. Two populations of E or ES 2. Accumulation of an intermediate with partial signal 3. Burst kinetics: steps after chemistry rate-limiting

19 Two Populations of E or ES [P] = [ES] 0 - [ES 1 ] - [ES 2 ] or

20 Two Populations of E or ES (70%) (30%) 0.4 s s -1

21 Accumulation of an Intermediate SRP SR 1 + GMPPNP Fluorescence (a.u.) time (s)

22 1 + GMPPNP Fluorescence (a.u.) OR time (s)

23 Different kinetic behavior of 1st and 2nd phases 240 1st (burst phase) 2 2nd phase k obsd (s -1 ) 160 k obsd (s -1 ) [SR] (µm) [SR] (µm)

24 BM exercise 3. Accumulation of an Intermediate FRET = 0.6 FRET = 0.8 GMPPNP k 1,obsd = k 1 [SR] + k -1 k 2,obsd ~ k 2 Fluorescence (a.u.) GMPPNP GMPPNP time (s) k 1 = 5 x 10 6 M -1 s -1 k -1 = 62 s -1 k 2 = 1.2 s -1 [SRP] = 100 nm [SR] = 10 µm

25 Steps after chemistry is rate-limiting [E] = E 0 [EP] => d[p]/dt = k 2 [EP]

26 Steps after chemistry is rate-limiting when k 1 S 0 >> k -1 + k 2,

27 Steps after chemistry is rate-limiting slope = k 2 Burst: rate of 1st turnover

28 T7 DNA Polymerase Reaction + dttp T Steady-state measurement: k cat = 0.2 s -1 Patel et al., Biochemistry 1991

29 Burst of product formation in T7 DNA polymerase reaction linear phase: k = 0.2 s -1 = k cat burst: k obsd = 190 s -1 chemical step is much faster than k cat steady state turnover is rate-limited by a step after chemistry

30 Active site titration using burst phase amplitude K d DNA = 18 nm Patel et al., Biochemistry 1991

31 Rate of chemical step from burst analysis k chem ~ 250 s -1 K d dttp = 18 µm Patel et al., Biochemistry 1991

32 BM exercise 3. Steady state enzymatic reactions [E] 0 = 1 nm, [S] 0 = 100 nm 1. Run the simulation. Plot ES, S, P 2. Vary [S] 0 from nm in parameters plot. Plot [ES] max as a function of [S] 0. What is the K m value? Does it agree with the value of K d? 3. Change the rate of chemical step to 10 s -1. Repeat step (2). What is the K m value now? 4. Add an irreversible product dissociation step at 0.01 s -1. Set [S] 0 = 2000 nm, [E] 0 = 100 nm Run the simulation (Hint: total P = P + EP). Do you see a burst of product formation? What is the K m value in this case?

33 Case 1. DHFR NADPH + H 2 F NADP + H 4 F Steady state parameters: (k cat /K m ) H 2F = 2 x10 7 M -1 s -1 k cat ~ 12 s -1 no D/H isotope effect substrates binds randomly but with some coupling? product dissociation order? reaction is ph dependent with pk a ~ 8.2

34 Case 1. DHFR S/P binding measured by quenching of intrinsic enzyme fluorescence k on: E + H 4 F k off : E H 4 F Fierke et al, Biochemistry 26: 4085 (1987)

35 Case 1. DHFR k on H 2 F to E TNADPH ~ (k cat /K m ) H 2F k off H 4 F from E is slower than k cat k off H 4 F is accelerated in E NADPH and approaches k cat => burst of product formation H 2 F and NADP + synergistic binding

36 Summary of Kinetic Framework: DHFR substrate binding is random but with preferred pathway product dissociation through either pathway is slower than k cat and cannot exist during turnover ES is regenerated from the E H4F complex Fierke et al, Biochemistry 26: 4085 (1987)

37 Case 1. DHFR Pre-steady state burst of product formation Linear phase: k = 12 s -1 Burst phase: k H = 450 s -1 k D = 150 s -1 => k D /k H = 3 chemistry R.D. Fierke et al, Biochemistry 26: 4085 (1987)

38 Case 1. DHFR ph dependence of k c k EH + = 950 s -1 pk a = 6.5 k E = 12 s -1 Fierke et al, Biochemistry 26: 4085 (1987)

39 Case 1. DHFR Real vs Steady state pk a Burst phase measurement k cat Steady-state measurement Fierke et al, Biochemistry 26: 4085 (1987)

40 Summary of Kinetic Framework: DHFR k cat /K m is rate-limited by substrate binding Never regenerates free E regeneration of ES from the EP complex is RD for k cat Fierke et al, Biochemistry 26: 4085 (1987)

41 Recommended Readings