1. Modeling fluctuations in the force-extension single-molecule experiments Alexander Vologodskii New York University

2. Diagram of the force-extension experiment

3. The force-extension dependence for DNA is well studied

4. The force has entropic nature

5. From: J. W. Shaevitz1, E. A. Abbondanzieri, R. Landick & S. M. Block. Backtracking by single RNA polymerase molecules observed at near-base-pair resolution. Nature, 426, 684-687. The entropic force from extended DNA molecule is used in many single-molecule experiments

6. DNA model for Brownian dynamics simulations The intersegment interaction is specified by the Debye-Hückel potential Segments are stretchable Virtual beads of a certain diameter placed at chain vertices specify hydrodynamic interaction with solution and between the beads Discrete wormlike chain with some modifications:

7. Dynamics of the chain is described by the Langevin equations where is a configuration-dependent friction tensor is a force acting on bead represents the randomly fluctuating force resulting from the thermal motion of the surrounding fluid is the mass of bead

8. How accurate is Brownian dynamics simulation of DNA properties? Comparison of measured and simulated diffusion coefficients of knots along stretched DNA molecule shows that simulation is quite accurate

9. Tying knots by optical tweezers

10. Experimental measurement of knot diffusion X. R. Bao, H.J. Lee and S.R. Quake, Phys. Rev. Lett., 91, 265506 (2003)

11. Brownian dynamics simulation of knot diffusion Typical simulated conformations of knotted model chains

12. Comparison of the measured and computed diffusion coefficients of knots

13. Simulated values of the force fluctuate strongly

14. The force fluctuations do not depend on its average value Each point is the averaging over 1 ns

15. The force averaging does not occur over 0.1  s Each point is the averaging over 100 ns

16. The force averaging does not occur over 10  s

17. A good averaging of the force is achieved by averaging over 1 ms

18. Fluctuations of the force do not depend on DNA length

19. Presence of a protein-induced bend decreases DNA extension Can the extension measurement be used to determine the bend angle?

20. Simulated values of the extension reduction resulting from DNA bending by angle 

21. Large fluctuations of the extension and a finite time of the protein-bound state create a problem

22. The variations of the extensions are large

23. Extension of a single DNA molecule by force These are actual proportions for 1500 bp DNA

24. Fluctuations of DNA extension averaged over 0.4 ms

25. Fluctuations of DNA extension averaged over 40 ms

26. What averaging interval do we need?

27. The work was supported by NIH

29. Displacement of unknotted part of the model chain eliminates the chain length restriction