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

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 • 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 order 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

3 1. DNA replication speed masked by pauses We measure distance between beads Force s.d. p.e. • during s.d. (unwinding + replication) Laser trap distance increases Pol Distance X (  m) • during p.e. (only replication) + dNTPs distance decreases Pipette  x1 Distance between beads  Force  x2 polymerase trajectory (after using the force extension curves for single wild-type sdd mutant and for double stranded DNA) 1.5 1,5 s.d. p.e. s.d. p.e. 1,4 1.4 Distance (  m)  x2 • Mutant Phi29 DNA polymerase 1,3 1.3 showed slower s.d. replication  x1 1,2 1.2 speed than wild type. 1.1 1,1 Trajectories suggest difference is due to 1.0 1,0 the appearance of long pauses. 0 5 10 15 20 25 30 35 We have to substract pauses to compare Time (seconds)

4 Wild type Phi29 polymerase V pe 140 • Primer extension: Tension Mean velocity (nt/s) 120 100 V sd independent replication 80 velocity. Replication rate k 0 60 40 ~ 128 nt/s. 20 0 • Strand displacement: 2 4 6 8 10 12 14 Tension (pN) Replication velocity is 18 smaller and depends on 3GC 6GC 9GC 12GC residence time(seconds/10nt) 0.3 tension. Tension helps Tension (pN) 16 DNA unwinding. 0.2 14 0.1 • During sd more time in GC 0 100 200 300 400 500 600 positions (stronger binding Template Position than AT)

5 Mutant Phi29 polymerase • Primer extension: same 140 V pe Mean velocity (nt/s) 120 replication velocity as 100 wild type. Replication 80 V sd 60 No pauses rate k 0 ~ 128 nt/s. 40 V sd 20 with pauses • Strand displacement: 0 2 4 6 8 10 12 Tension (pN) smaller replication velocity 500 Template position 12GC Velocity (nt/s) 400 -50 0 50 100 150 9GC 300 • Strand displacement Probability 6GC 0.08 200 deficiency is due to the 0.04 3GC 100 appearance of long 0 0 20 40 60 80 100 120 140 Time (seconds) pauses in the dynamics

6 Wild type pauses 500 Template Position 12GC 400 • Wild type also has Velocity (nt/s) 9GC 0 50 100 150 300 pauses, but only shorter 6GC Probability 0.06 200 ones (with small 0.04 3GC 100 0.02 influence in replication 0 0 2 4 6 8 10 12 velocity). Time (seconds) 0 1x10 -2 ) Pause Freq Distrib (s -1 1x10 • Short pauses only -2 1x10 appear at GC locations, and pause frequency -3 1x10 0 1 2 3 Time (seconds) decreases with tension. k 1a Active Short state Pause 1 k a1 (f)

7 Mutant pauses • Mutant polymerase shows 500 Template position 12GC long pauses during strand Velocity (nt/s) 400 -50 0 50 100 150 9GC displacement. 300 Probability 6GC 0.08 200 0.04 3GC 100 • Pause length frequency 0 distribution during s.d. shows 0 20 40 60 80 100 120 140 Time (seconds) two characteristic times 0 1x10 indicating that there are at -2 ) p.e. Pause Freq Distrib (s least two type of pauses -1 1x10 (short and long). s.d. -2 1x10 -3 1x10 • Short pauses are also Short Long present in p.e. and have a -4 1x10 0 5 10 15 20 25 30 35 similar characteristic time as Time (seconds) in wild type polymerase. k 1a k a2 (f) Short Active Long Pause 1 Pause 2 state k a1 (f) k 2a (f)

8 Replication speed without pauses Wild type • After pause subtraction 140 (empty circles), Mean velocity (nt/s) 120 replication speeds are 100 80 the same 60 • Analysis of trajectories 40 20 showed that the 0 2 4 6 8 10 12 14 mutation induced Tension (pN) additional long pauses Mutant • In addition we have 140 Mean velocity (nt/s) 120 been able to give an 100 hypothesis for the origin 80 of the pauses using its 60 40 force dependence. 20 0 2 4 6 8 10 12 Tension (pN)

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

10 Different options for the stepping procces A dNTP PPi Condensation Chemistry binding release DNAP DNAP- DNAP- DNAP- DNAP • We aim to determine n dNTP dNTP* PP i n+1 which is the stepping k cat B Model 1: dNTP binding drives translocation process (= the process k on (F)[dNTP] k cat k ppi … where displacement k off (F) k -cat PPi occurs) within the n n- n+1-PP i n+1  dNTP Pre Pre Post polymerization cycle C Model 2: PPi release drives translocation k on [dNTP] k ppi (F) k cat … k off k -cat PPi n n-dNTP n+1- n+1  Post PP i Post Pre D Model 3: Translocation after PPi release and before dNTP binding k on [dNTP] k ppi k T (F) k cat … k off k -cat k -T (F) n n-dNTP n+1-PP i PPi n+1 n+1  Post Pre Post

11 Force and concentration dependence of speed gives the answer • Increased nucleotide concentrations [dNTP] makes faster the nucleotide binding step • Pushing force favors Replication velocity as a function of nucleotide concentration in the the stepping process, solution, for forces of 20, 5, -5, - pulling force disfavors 10, -15 and -20 pN (from top to bottom curve, positive forces are it. aiding forces).

12 The stepping process A dNTP PPi Condensation Chemistry binding release DNAP DNAP- DNAP- DNAP- DNAP • Data favors the n dNTP dNTP* PP i n+1 k cat stepping process B Model 1: dNTP binding drives translocation to be located after k on (F)[dNTP] k cat k ppi … PPi release and k off (F) k -cat PPi n n- n+1-PP i n+1  dNTP Pre before nucleotide Pre Post C Model 2: PPi release drives translocation binding. k on [dNTP] k ppi (F) k cat … k off k -cat PPi n n-dNTP n+1- n+1  Post PP i Post Pre D Model 3: Translocation after PPi release and before dNTP binding k on [dNTP] k ppi k T (F) k cat … k off k -cat k -T (F) n n-dNTP n+1-PP i PPi n+1 n+1  Post Pre Post

13 Brownian ratchet mechanism • Stepping occurs in a process that in the absence of force is -Fd T energetically disfavored • However the Free Energy -F  energetically favored  G trans and fast nucleotide  incorporation, which d T d -T follows, fix the slow events of going to the Pre- Post- post-translocation state. Translocation of DNAP

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 of 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.

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 one of the DNA strands during replication