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K.L. Sebastian IPC Department, Indian Institute of Science Bangalore

Rate processes involving long chain molecules. K.L. Sebastian IPC Department, Indian Institute of Science Bangalore. They seem to do it very efficiently. Problems How do long chain molecules go through pores? DNA entry into nucleus?. DNA packaging into a viral capsid.

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K.L. Sebastian IPC Department, Indian Institute of Science Bangalore

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  1. Rate processes involving long chain molecules K.L. Sebastian IPC Department, Indian Institute of Science Bangalore

  2. They seem to do it very efficiently • Problems • How do long chain molecules go through pores? • DNA entry into nucleus? • DNA packaging into a viral capsid. • Loop formation and Opening. • Mechanical Unzipping of DNA.

  3. How do long chain molecules go over barriers? • Outline • The barrier crossing problem • Generalization to polymers • Why worry? • Previous work • Our approach • Experiments • Biological translocation • Other problems

  4. Drunken walker What is the rate of escape? The Barrier Crossing (Kramers problem) Arrhenius form

  5. Polymer dynamics = Dynamics of a chain of DRUNKEN walkers! The Kramers problem for a long chain molecule

  6. 2.6nm Why worry? • Long chain molecules go through pores - How do they Cross Free Energy barriers? Kasianowicz et. al. PNAS 93, 13770 (1996) DNA forced through a nano-pore

  7. 90 nm 1m Electric field Free energy profile DNAforced through micro-fabricated channel Han et. al. PRL 83, 1688 (1999)

  8. Park and Sung Rather inefficient! Muthukumar and Baumgartner Nelson and Lubensky

  9. w Polymer will be on both the sides simultaneously! Our Analysis Our Analysis: Length >> w >> l (w - width of the barrier)

  10. Which is the transition state? Siphoning Kink

  11. Resembles Action Integral! The Free Energy

  12. Free energy of the chain stretched across the barrier Extremising action leads to Newton’s equation! extremise Activation EnergyEa Ea = Motion in the upside down potential!

  13. Temperature dependence

  14. The simplest possible Dynamics - Rouse Model! The Dynamics

  15. What is the use? Has kink solution Deterministic part

  16. is unique - Polymer moves forward with a steady velocity! Crossing time

  17. Conclusion not changed! Fluctuations

  18. Simulations

  19. Kasianowicz et. al. PNAS 93, 13770 (1996) 2.6nm

  20. Analogous to field emission The channel experiments Experiment shows: Ea independent of N, inversely proportional to the electric field E Electric field

  21. All this is in one dimension! What about 3D? In 3D too, kink solution exists! Conclusions, same 3-Dimensions

  22. BIOLOGICAL TRANSLOCATION Hydrophobic Hydrophilic Hydrophobic Pore: at first a well and then barrier!

  23. B. Alberts et. al - Essential Cell Biology The TS

  24. Barrier Crossing In agreement with expts Relevant to biological translocation Conclusions

  25. Acknowledgements Dr. Alok Paul K.P. Santo Ananya Debnath Dr. Rosabella Puthur Keshav Kumar Kiran Kumar Supported by the Indian Academy

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