Tethered DNA shear dynamics in the flow gradient plane: application to double tethering

  • Published : 2007.11.30

Abstract

We examine the wall contact of a $3\;{\mu}m$ tethered DNA chain's free end under shear with a focus on developing schemes for double-tethering in the application of making scaffolds for molecular wires. At this scale our results are found to be highly dependent on small length scale rigidity. Chain-end-wall contact frequency, mean fractional extension deficit upon contact, and standard deviation in extension upon contact are examined for scaling with dimensionless flow strength, Wi. Predictions made using a one dimensional approximation to the Smoluchowski equation for a dumbbell and three dimensional dumbbell simulations produce extension deficit, standard deviation, and frequency scaling exponents of -1/3, -1/3, and 2/3, respectively whereas more fine-grained Kratky-Porod (KP) simulations produce scaling exponents of -0.48, -0.42, and 0.76. The contact frequency scaling of 2/3 is derived from the known results regarding cyclic dynamics Analytical scaling predictions are in agreement with those previously proposed for ${\lambda}-DNA$. [Ladoux and Doyle, 2000, Doyle et al., 2000]. Our results suggest that the differences between the dumbbell and the KP model are associated with the addition of chain discretization and the correct bending potential in the latter. These scaling results will aide future exploration in double tethering of DNA to a surface.

Keywords

References

  1. Beck, V. A. and E. S. G. Shaqfeh, 2006, Ergodicity breaking and conformational hysteresis in the dynamics of a polymer tethered at a surface stagnation point, J. Chem. Phys. 124, 094902
  2. Bird, R. B., Curtiss, C. F., Armstrong, R. C., and O. Hassager, 1987, Dynamics of Polymeric Liquids, volume 2. Wiley, New York
  3. Braun, E., Y. Eichen, U. Sivan, and G. Ben-Yoseph, 1998, DNAtemplated assembly and electrode attachment of conducting silver wire. Nature 391, 775-778 https://doi.org/10.1038/35826
  4. Bustamante, C., J. F. Marko, E. D. Siggia, and S. Smith, 1994, Entropic elasticity of $\gamma$-phage DNA, Science 265, 1599-1600 https://doi.org/10.1126/science.8079175
  5. Ottinger, H. C., 1996, Stochastic Processes in Polymer Fluids, Springer
  6. Doyle, P. S., B. Ladoux, and J. L. Viovy, 2000, Dynamics of a tethered polymer in shear flow, Physical Review Letters 84, 4769-4772 https://doi.org/10.1103/PhysRevLett.84.4769
  7. Ermak, D. L. and J. A. McCammon, 1978, Brownian dynamics with hydrodynamic interactions. J. Chem. Phys. 69, 1352-1360 https://doi.org/10.1063/1.436761
  8. Evans, A. R. 1995, An experimental and theoretical investigation of polymer conformation during flow through a dilute fiber bed, PhD thesis, Stanford University
  9. Hsieh, C. C., L. Li, and R. G. Larson, 2003, Modeling hydrodynamic interaction in brownian dynamics: simulations of extensional flows of dilute solutions of DNA and polystyrene, J. Non-Newtonian Fluid Mech. 113, 147-191 https://doi.org/10.1016/S0377-0257(03)00107-1
  10. Jendrejack, R. M., D. C. Schwartz, J. J. de Pablo, and M. D. Graham, 2004, Shear-induced migration in flowing polymer solutions: simulation of long-chain DNA in microchannels, J. Chem. Phys. 120, 2513
  11. Kramers, H. A. 1956, Collected Scientific Papers, North-Holland Publishing Co
  12. Kratky, O. and G. Porod, 1949, Röntgenuntersuchung gelöster fadenmoleküle. Rec. Trav. Chim. 68, 1106 https://doi.org/10.1002/recl.19490681203
  13. Ladoux, B. and P. S. Doyle, 2000, Stretching tethered DNA chains in shear flow, Europhysics Letters 52, 511-517 https://doi.org/10.1209/epl/i2000-00467-y
  14. Liu, T. W., 1989, Flexible polymer chain dynamics and rheological properties in steady flows, J. Chem. Phys. 90, 5826-5842 https://doi.org/10.1063/1.456389
  15. Marko, J. F. and E. D. Siggia, 1995, Stretching DNA, Macromolecules 28, 8759-8770 https://doi.org/10.1021/ma00130a008
  16. Schroeder, C. M., R. E. Teixei, E. S. G. Shaqfeh, and S. Chu, 2005, Characteristic periodic motion of polymers in shear flow, Physical Review Letters 95, 018301
  17. Somasi, M., B. Khomami, N. J. Woo, J. S. Hur, and E. S. G. Shaqfeh 2002, Brownian dynamics simulations of bead-rod and bead-spring chains: numerical algorithms and coarsegraining issues, J. Non-Newtonian Fluid Mech. 108, 227-255 https://doi.org/10.1016/S0377-0257(02)00132-5
  18. Yamakawa, H., 1971, Modern Theory of Polymer Solutions, Harper & Row