MODEL AND PARAMETER DETERMINATION FOR MOLECULAR MOTORS FROM SINGLE - - PowerPoint PPT Presentation

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MODEL AND PARAMETER DETERMINATION FOR MOLECULAR MOTORS FROM SINGLE - - PowerPoint PPT Presentation

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MODEL AND PARAMETER DETERMINATION FOR MOLECULAR MOTORS FROM SINGLE MOLECULE EXPERIMENTS Francisco J. Cao Universidad Complutense de Madrid (Spain) Dedicated to the memory of my PhD. Advisor Hector J. de Vega (CNRS, France) 2 Introduction

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SLIDE 1

MODEL AND PARAMETER DETERMINATION FOR MOLECULAR MOTORS FROM SINGLE MOLECULE EXPERIMENTS

Francisco J. Cao Universidad Complutense de Madrid (Spain)

Dedicated to the memory of my PhD. Advisor Hector J. de Vega (CNRS, France)

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SLIDE 2

Introduction

  • Molecular motors = proteins able to do work

perform different task in the cell (replication of DNA, transport of compounds, or of the whole cell, …)

  • Their binding and conformational changes energies are of the
  • rder of or one order of magnitude greater

⇒ thermal fluctuations are very present

  • Single molecule experiments allow only to monitor one or a few

distances of system.

  • Thermal noise partially mask the signal of the system
  • From this limited and noisy information one has to infer which

is the system dynamics: determining the correct model and the values of its parameters. We will show examples from our recent works

2

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SLIDE 3
  • 1. DNA replication speed masked by

pauses

We measure distance between beads

  • during s.d. (unwinding + replication)

distance increases

  • during p.e. (only replication)

distance decreases Distance between beads  polymerase trajectory

(after using the force extension curves for single and for double stranded DNA)

  • Mutant Phi29 DNA polymerase

showed slower s.d. replication speed than wild type.

Trajectories suggest difference is due to the appearance of long pauses. We have to substract pauses to compare

Force Force x1 x2

s.d. p.e.

Distance X (m) Laser trap Pipette Pol + dNTPs

5 10 15 20 25 30 35 1,0 1,1 1,2 1,3 1,4 1,5

Distance (m) Time (seconds)

x1 x2

s.d. p.e. wild-type s.d. p.e. sdd mutant

1.5 1.4 1.3 1.2 1.1 1.0

3

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SLIDE 4

Wild type Phi29 polymerase

  • Primer extension: Tension

independent replication

  • velocity. Replication rate k0

~ 128 nt/s.

  • Strand displacement:

Replication velocity is smaller and depends on

  • tension. Tension helps

DNA unwinding.

  • During sd more time in GC

positions (stronger binding than AT)

14 16 18

Tension (pN)

100 200 300 400 500 600 0.1 0.2 0.3

residence time(seconds/10nt) Template Position

3GC 6GC 9GC 12GC

2 4 6 8 10 12 14 20 40 60 80 100 120 140

Mean velocity (nt/s) Tension (pN) Vpe Vsd

4

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SLIDE 5

2 4 6 8 10 12 20 40 60 80 100 120 140

Mean velocity (nt/s) Tension (pN)

Mutant Phi29 polymerase

  • Primer extension: same

replication velocity as wild type. Replication rate k0 ~ 128 nt/s.

  • Strand displacement:

smaller replication velocity

  • Strand displacement

deficiency is due to the appearance of long pauses in the dynamics

Vsd No pauses Vsd with pauses Vpe

20 40 60 80 100 120 140 100 200 300 400 500

Template position Time (seconds)

  • 50

50 100 150 0.04 0.08

Probability

Velocity (nt/s)

3GC 6GC 9GC 12GC

5

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SLIDE 6

2 4 6 8 10 12 100 200 300 400 500

Template Position Time (seconds)

50 100 150 0.02 0.04 0.06

Velocity (nt/s)

Probability

Wild type pauses

  • Wild type also has

pauses, but only shorter

  • nes (with small

influence in replication velocity).

  • Short pauses only

appear at GC locations, and pause frequency decreases with tension.

3GC 6GC 9GC 12GC

Short Pause 1 Active state

k1a ka1(f)

1 2 3 1x10

  • 3

1x10

  • 2

1x10

  • 1

1x10

Pause Freq Distrib (s

  • 2)

Time (seconds)

6

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SLIDE 7

Mutant pauses

  • Mutant polymerase shows

long pauses during strand displacement.

  • Pause length frequency

distribution during s.d. shows two characteristic times indicating that there are at least two type of pauses (short and long).

  • Short pauses are also

present in p.e. and have a similar characteristic time as in wild type polymerase.

5 10 15 20 25 30 35 1x10

  • 4

1x10

  • 3

1x10

  • 2

1x10

  • 1

1x10

Pause Freq Distrib (s

  • 2)

Time (seconds) Short Long

Short Pause 1 Active state

ka1(f) k1a k2a(f) ka2(f)

Long Pause 2

20 40 60 80 100 120 140 100 200 300 400 500

Template position Time (seconds)

  • 50

50 100 150 0.04 0.08

Probability

Velocity (nt/s)

3GC 6GC 9GC 12GC

p.e. s.d.

7

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SLIDE 8

Replication speed without pauses

  • After pause subtraction

(empty circles), replication speeds are the same

  • Analysis of trajectories

showed that the mutation induced additional long pauses

  • In addition we have

been able to give an hypothesis for the origin

  • f the pauses using its

force dependence.

2 4 6 8 10 12 14 20 40 60 80 100 120 140

Mean velocity (nt/s) Tension (pN)

2 4 6 8 10 12 20 40 60 80 100 120 140

Mean velocity (nt/s) Tension (pN)

Wild type Mutant

8

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SLIDE 9
  • 2. Stepping process in the DNA replication

cycle

  • Different force

configuration

  • Force pushes or pulls

polymerase

⇒force will increase or decrease the rate of the stepping process

9

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SLIDE 10

Different options for the stepping procces

  • We aim to determine

which is the stepping process (= the process where displacement

  • ccurs) within the

polymerization cycle

B

Model 1: dNTP binding drives translocation

C

Model 2: PPi release drives translocation

D

Model 3: Translocation after PPi release and before dNTP binding

n Post n-dNTP n+1- PPi Pre

kppi (F) kcat kon[dNTP] koff k-cat

PPi

…

n+1 Post

…

koff(F) n Pre n- dNTP Post

n+1-PPi n+1 Pre kcat kppi kon (F)[dNTP] k-cat

PPi

DNAP n DNAP- dNTP DNAP- PPi DNAP n+1 DNAP- dNTP* Condensation Chemistry dNTP binding PPi release

A

kcat n Post n-dNTP n+1 Pre kcat n+1-PPi kppi kon[dNTP] koff k-cat

PPi

kT (F)

k-T (F)

…

n+1 Post

10

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SLIDE 11

Force and concentration dependence of speed gives the answer

  • Increased nucleotide

concentrations [dNTP] makes faster the nucleotide binding step

  • Pushing force favors

the stepping process, pulling force disfavors it.

Replication velocity as a function

  • f nucleotide concentration in the

solution, for forces of 20, 5, -5, - 10, -15 and -20 pN (from top to bottom curve, positive forces are aiding forces).

11

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SLIDE 12

The stepping process

  • Data favors the

stepping process to be located after PPi release and before nucleotide binding.

B

Model 1: dNTP binding drives translocation

C

Model 2: PPi release drives translocation

D

Model 3: Translocation after PPi release and before dNTP binding

n Post n-dNTP n+1- PPi Pre

kppi (F) kcat kon[dNTP] koff k-cat

PPi

…

n+1 Post

…

koff(F) n Pre n- dNTP Post

n+1-PPi n+1 Pre kcat kppi kon (F)[dNTP] k-cat

PPi

DNAP n DNAP- dNTP DNAP- PPi DNAP n+1 DNAP- dNTP* Condensation Chemistry dNTP binding PPi release

A

kcat n Post n-dNTP n+1 Pre kcat n+1-PPi kppi kon[dNTP] koff k-cat

PPi

kT (F)

k-T (F)

…

n+1 Post

12

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SLIDE 13

Brownian ratchet mechanism

  • Stepping occurs in a

process that in the absence of force is energetically disfavored

  • However the

energetically favored and fast nucleotide incorporation, which follows, fix the slow events of going to the post-translocation state.

d-T dT

Pre- Post- 

Free Energy Translocation of DNAP

Gtrans

  • FdT
  • F

13

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SLIDE 14
  • 3. Open problems
  • Determination of the step size when it is below the experimental
  • resolution. We have a proposal to solve this problem which is

expected to work for certain polymerases.

  • Determination of possible transitions between fast and slow pause

states, for the ssd mutant studied or for other molecular motors with two pause states.

  • Detailed determination of whether stepping distributed among several
  • f the processes in the chemical cycle can be excluded and in which

cases, for the DNA polymerase studied or for other molecular motors. Two last points imply the introduction of additional parameters, giving rise to degeneracies (i.e., several sets of values or even a region of the parameter space lead to good fits to the experimental data). Statistical inference can help to extract further information from the physical trajectories, and to combine the information of different experiments in a rigorous way.

14

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SLIDE 15
  • 4. Conclusions
  • The rich stochastic dynamics of molecular motors challenge statistical physicist and

stochastic dynamics mathematicians

  • Single molecule experiments provide very detailed information of one or several of the

distances involved in the system dynamics.

Biochemists provide their ability to completely inhibit certain processes or to block them with a certain probability, providing experimental data with more information in particular aspects of the involved dynamics.

  • Close collaboration with biochemists and biologists is recommended to be able to do relevant

contributions.

  • References:
  • J. A. Morin, F. J. Cao, J. M. Lázaro, J. R. Arias-Gonzalez, J. M. Valpuesta, J. L. Carrascosa, M. Salas, B.

Ibarra, Active DNA unwinding dynamics during processive DNA replication, Proc. Natl. Acad. Sci. U. S.

  • A. 109, 8115 (2012) .
  • J. A. Morin, F. J. Cao, J. M. Valpuesta, J. L. Carrascosa, M. Salas, and B. Ibarra, Manipulation of single

polymerase-DNA complexes: A mechanical view of DNA unwinding during replication, Cell Cycle 11, 2967 (2012).

  • J. A. Morin, F. J. Cao, J. M. Lázaro, J. R. Arias-Gonzalez, J. M. Valpuesta, J. L. Carrascosa, M. Salas, B.

Ibarra, Mechano-chemical kinetics of DNA replication: identification of the translocation step of a replicative DNA polymerase, Nucleic Acids Res. 47, 3643–3652 (2015).

  • Future work: DNA replication in human mitochondria, effects of the SSB protein that protects
  • ne of the DNA strands during replication

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