Interaction and multiscale mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

On the continuum formulation for modeling DNA loop formation

  • Teng, Hailong (Civil & Environmental Engineering Department, University of California, Los Angeles (UCLA)) ;
  • Lee, Chung-Hao (Civil & Environmental Engineering Department, University of California, Los Angeles (UCLA)) ;
  • Chen, Jiun-Shyan (Civil & Environmental Engineering Department, University of California, Los Angeles (UCLA))
  • Received : 2011.04.28
  • Accepted : 2011.06.06
  • Published : 2011.09.25
⟨ Previous Next ⟩

Abstract

Recent advances in scientific computing enable the full atomistic simulation of DNA molecules. However, there exists length and time scale limitations in molecular dynamics (MD) simulation for large DNA molecules. In this work, a two-level homogenization of DNA molecules is proposed. A wavelet projection method is first introduced to form a coarse-grained DNA molecule represented with superatoms. The coarsened MD model offers a simplified molecular structure for the continuum description of DNA molecules. The coarsened DNA molecular structure is then homogenized into a three-dimensional beam with embedded molecular properties. The methods to determine the elasticity constants in the continuum model are also presented. The proposed continuum model is adopted for the study of mechanical behavior of DNA loop.

Keywords

References

  1. Adhya, S. (1989), "Multipartite genetic control elements: communication by DNA loop", Ann. Rev. Genetics, 23(1), 227-250. https://doi.org/10.1146/annurev.ge.23.120189.001303
  2. Allemand, J.F., Cocco, S., Douarche, N. and Lia, G. (2006), "Loops in DNA: an overview of experimental and theoretical approaches", Eur. Phys. J. E, 19, 293-302. https://doi.org/10.1140/epje/i2005-10073-y
  3. Arroyo, M. and Belytschko, T. (2004), "Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes", Int. J. Numer. Meth. Eng., 59, 419-456. https://doi.org/10.1002/nme.944
  4. Balaeff, A., Koudella, C.R., Mahadevan, L. and Schulten, K. (2004), "Modelling DNA loops using continuum and statistical mechanics", Philos. T. R. Soc. A, 362, 1355-1371. https://doi.org/10.1098/rsta.2004.1384
  5. Balaeff, A., Mahadevan, L. and Schulten, K. (1999), "Elastic rod model of a DNA loop in the lac operon", Phys Rev. Lett., 83, 4900-4903. https://doi.org/10.1103/PhysRevLett.83.4900
  6. Balaeff, A., Mahadevan, L. and Schulten, K. (2006), "Modeling DNA loops using the theory of elasticity", Phys Rev. E, 73, 031919. https://doi.org/10.1103/PhysRevE.73.031919
  7. Baumann, C.G., Smith, S.B., Bloomfield, V.A. and Bustamante, C. (1997), "Ionic effects on the elasticity of single DNA molecules", Proc. Natl. Acad. Sci. USA, 94, 6185-6190. https://doi.org/10.1073/pnas.94.12.6185
  8. Born, M. and Huang, K. (1954), Dynamical theory of crystal lattices, Oxford University Press, New York.
  9. Chamekh, M., Mani-Aouadi, S. and Moakher, M. (2009), "Modeling and numerical treatment of elastic rods with frictionless self-contact", Comput. Method. Appl. M., 198, 3751-3764. https://doi.org/10.1016/j.cma.2009.08.005
  10. Chen, J.S., Lee, C.H., Teng, H. and Wang, H. (2011), Atomistic to continuum modeling of DNA molecules, Advances in Soft Matter Materials, Springer.
  11. Chen, J.S., Teng, H. and Nakano, A. (2007), "Wavelet-based multi-scale coarse graining approach for DNA molecules", Finite Elem. Anal. Des., 43, 346-360. https://doi.org/10.1016/j.finel.2006.12.004
  12. Chui, C.K. (1992), An introduction to wavelets, Academic Press, New York.
  13. Clausen-Schaumann, H., Rief, M., Tolksdorf, C. and Gaub, H.E. (2000), "Mechanical stability of single DNA molecules", Biophys. J., 78, 1997-2007. https://doi.org/10.1016/S0006-3495(00)76747-6
  14. Cluzel, P., Lebrun, A., Heller, C., Lavery, R., Viovy, J.L., Chatenay, D. and Caron, F. (1996), "DNA: an extensible molecule", Science, 271, 792-794. https://doi.org/10.1126/science.271.5250.792
  15. Coleman, B.D. and Swigon, D. (2004), "Theory of self-contact in Kirchhoff rods with applications to supercoiling of knotted and unknotted DNA plasmids", Philos. T. R. Soc. A, 362, 1281-1299. https://doi.org/10.1098/rsta.2004.1393
  16. Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz, K.M., Ferguson, D.M., Spellmeyer, D.C., Fox, T., Caldwell, J.M. and Kollman P.A. (1996), "A second generation force field for the simulation of proteins, nucleic acids, and organic molecules", J. Am. Chem. Soc., 117, 2309-2309.
  17. Crossley, M. and Orkin, S.H. (1993), "Regulation of the -globin locus", Curr. Opin. Genet. Dev., 3, 232-237. https://doi.org/10.1016/0959-437X(93)90028-N
  18. Daubechies, I. (1992), "Ten lectures on wavelets", CBMS-NSF Series in Applied Mathematics, 61, SIAM, Philadelphia, PA.
  19. de Borst, R., Réthoré J., Abellan, M.A. (2008), "Two-scale approaches for fracture in fluid-saturated porous media", Interact. Multiscale Mech., 1(1), 83-101. https://doi.org/10.12989/imm.2008.1.1.083
  20. Dunn, T.M., Hahn, S., Ogden, S., and Schleif, R. F. (1984), "An operator at - 280 base pairs that is required for repression of araBAD operon promoter: addition of DNA helical turns between the operator and promoter cyclically hinders repression", Proc. Natl. Acad. Sci. USA, 81, 5017-5020. https://doi.org/10.1073/pnas.81.16.5017
  21. Edelman, L.M., Cheong, R. and Kahn, J.D. (2003), "Fluorescence resonance energy transfer over - 130 basepairs in hyperstable lac repressor-DNA loops", Biophys. J., 84, 1131-1145. https://doi.org/10.1016/S0006-3495(03)74929-7
  22. Ericksen, J. (1984), The Cauchy-Born hypothesis for crystals, in Phase transformation and material instabilities in solid [Ed. Gurtin, M.], 61-77, Academic Press, New York.
  23. Garrivier, D. and Fourcade, B. (2000), "Twisting DNA with variable intrinsic curvature", Europhys. Lett., 49, 390-395. https://doi.org/10.1209/epl/i2000-00161-8
  24. Gent, A.N. (1996), "A new constitutive relation for rubber", Rubber Chem. Technol., 69, 59-61. https://doi.org/10.5254/1.3538357
  25. Gevorkian, S.G. and Khudaverdian, E.E. (1990), "Mechanical properties of DNA films", Biopolymers, 30, 279-285. https://doi.org/10.1002/bip.360300306
  26. Hughes, T.J.R. and Liu, W.K. (1981a), "Nonlinear finite element analysis of shells: Part I Three-dimensional shells", Comput. Method. Appl. M., 26, 331-362. https://doi.org/10.1016/0045-7825(81)90121-3
  27. Hughes, T.J.R. and Liu, W.K. (1981b), "Nonlinear finite element analysis of shells: Part II Two-dimensional shells", Comput. Method. Appl. M., 27, 167-181. https://doi.org/10.1016/0045-7825(81)90148-1
  28. Kramer, H., Niemöller, M., Amouyal, M., Revet, R., von Wilcken-Bergmann, B. and Müller-Hill, B. (1987), "lac repressor forms loops with linear DNA carrying two suitably spaced lac operators", EMBO J., 6, 1481-1491.
  29. Lewis, M., Chang, G., Horton, N.C., Kercher, M.A., Pace, H.C., Schumacher, M.A., Brennan, R.G. and Lu, P.Z. (1996), "Crystal structure of the lactose operon repressor and its complexes with DNA and inducer", Science, 271, 1247-1254. https://doi.org/10.1126/science.271.5253.1247
  30. Manning, G.S. (1985), "Packaged DNA-an elastic model", Cell Biophy., 7, 57-89. https://doi.org/10.1007/BF02788639
  31. Marko, J.F. and Siggia, E.D. (1994), "Fluctuations and supercoiling of DNA", Science, 265, 506-508. https://doi.org/10.1126/science.8036491
  32. Mehraeen, S. and Chen, J.S. (2004), "Wavelet-based multi-scale projection method in homogenization of heterogeneous media", Finite Elem. Anal. Des., 40, 1665-1679. https://doi.org/10.1016/j.finel.2004.01.006
  33. Muller, J., Oehler, S. and Müller-Hill, B. (1996), "Repression of lac promoter as a function of distance, phase and quality of an auxially lac operator", J. Mol. Biol., 257, 21-29. https://doi.org/10.1006/jmbi.1996.0143
  34. Ogden, R.W., Saccomandi, G., and Sgura, I. (2008), "Phenomenological modeling of DNA overstretching", Quant Biol, Biomol, arXiv:0802.3323v1.
  35. Purohit, P.K. and Nelson, P.C. (2006), "Effect of supercoiling on formation of protein-mediated DNA loops", Phys. Rev. E, 74, 061907. https://doi.org/10.1103/PhysRevE.74.061907
  36. Reissner, E. (1973), "On one-dimensional, large-displacement, finite-strain beam-theory", Stud. Appl. Math., 52, 87-95. https://doi.org/10.1002/sapm197352287
  37. Rojek, J., Onate, E. (2008), "Multiscale analysis using a coupled discrete/finite element model", Interact. Multiscale Mech., 1(1), 1-31. https://doi.org/10.12989/imm.2008.1.1.001
  38. Saiz, L., Rubi, M. and Vilar, J.M.G. (2005) "Inferring the in vivo looping properties of DNA", Proc. Natl. Acad. Sci., 102, 17642-17645. https://doi.org/10.1073/pnas.0505693102
  39. Schleif, R. (1992), "DNA looping", Ann. Rev. Biochem., 61, 199-223. https://doi.org/10.1146/annurev.bi.61.070192.001215
  40. Serfling, E., Jasin, M. and Schaffner, W. (1985), "Enhancers and eukaryotic gene transcription", Trends Genet., 1, 224-230. https://doi.org/10.1016/0168-9525(85)90088-5
  41. Smith, S.B., Cui, Y. and Bustamante, C. (1996), "Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules", Science, 271, 795-799. https://doi.org/10.1126/science.271.5250.795
  42. Smith, S.B., Finzi, L. and Bustamante, C. (1992), "Direct mechanical measurement of the elasticity of single DNA molecules by using magnetic beads", Science, 258, 1122-1126. https://doi.org/10.1126/science.1439819
  43. Villa, E., Balaeff, A., Mahadevan, L. and Schulten, K. (2004), "Multiscale method for simulating protein-DNA complexes", Multiscale. Model. Simul., 2, 527-553. https://doi.org/10.1137/040604789
  44. Wadati, M. and Tsuru, H. (1986), "Elastic model of looped DNA", Physica, 21D, 213-226.
  45. Whirley, R.G. and Engelmann, B.E. (1993), DYNA3D: A nonlinear, explicit, three-dimensional finite element code for solid and structural mechanics, user manual and theoretical manual.
  46. White, J.H., Lund, R.A. and Bauer, W.R. (1999), "Effect of salt-dependent stiffness on the conformation of a stressed DNA loop containing initially coplanar bends", Biopolymers, 49, 605-619. https://doi.org/10.1002/(SICI)1097-0282(199906)49:7<605::AID-BIP6>3.0.CO;2-H

Cited by

  1. Energy and force transition between atoms and continuum in quasicontinuum method vol.7, pp.1, 2014, https://doi.org/10.12989/imm.2014.7.1.543
  2. RBF-POD reduced-order modeling of DNA molecules under stretching and bending vol.6, pp.4, 2013, https://doi.org/10.12989/imm.2013.6.4.395