Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables

Journal of Computational Physics

Volumn 209, Issue 1, 2005, Pages 371-389

  Goyal, S ^a   Perkins, N C ^a   Lee, C L ^b  

^a University of Michigan   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Cable mechanics; DNA mechanics; Dynamics; Kirchhoff rod; Looping; Supercoiling

Indexed keywords

BIOCHEMISTRY; CABLES; DNA; MARINE APPLICATIONS; TORSIONAL STRESS;

CABLE MECHANICS; DNA LOOPS; DNA MECHANICS; KIRCHHOFF ROD; LOADING RATE; LOOP FORMATION; LOOPING; NUMERICAL SOLUTION; QUASI STATIC RESPONSE; SUPERCOILING;

DYNAMICS;

EID: 20344370700     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.03.027     Document Type: Article

References (47)

1. F. Rosenthal The application of Greenhill's formula to cable hockling J. Appl. Mech. T. ASME 43 1976 681
2. C.L. Lu N.C. Perkins Nonlinear spatial equilibria and stability of cables under uniaxial torque J. Appl. Mech. T. ASME 61 1994 879
3. J. Coyne Analysis of the formation and elimination of loops in twisted cable IEEE J. Oceanic Eng. 15 1990 72
4. E.E. Zajac Stability of two planar loop elasticas J. Appl. Mech. 29 1962 136
5. I. Klapper Biological applications of the dynamics of twisted elastic rods J. Comput. Phys. 125 1996 325
6. T. Schlick Modeling superhelical DNA: Recent analytical and dynamic approaches Curr. Opin. Struct. Biol. 5 1995 245
7. W.K. Olson Simulating DNA at low resolution Curr. Opin. Struct. Biol. 6 1996 242
8. S. Goyal, N.C. Perkins, C.L. Lee, Torsional buckling and writhing dynamics of elastic cables and DNA, in: Proceedings of ASME 2003 Design Engineering and Technical Conference, Chicago, USA, September 2-6, 2003, paper no. DETC2003/MECH-48322
9. H. Yin M.D. Wang K. Svoboda R. Landick, S.M. Block J. Gelles Transcription against an applied force Science 270 1995 1653
10. L. Finzi J. Gelles Measurement of lactose repressor-mediated loop formation and breakdown in single DNA molecules Science 267 1995 378
11. R.A. Mehta J.D. Kahn Designed hyperstable lac repressor DNA loop topologies suggest alternative loop geometries J. Mol. Biol. 294 1999 67
12. S.B. Smith Y.J. Cui C. Bustamante Overstretching B-DNA: The elastic response of individual double-stranded and single-stranded DNA molecules Science 271 1996 795
13. J. Howard Mechanics of motor proteins and the cytoskeleton 2001 Sinauer Associates Sunderland
14. G. Kirchhoff Vorlesungen Ub̈er Mathematische Physik, Mechanik Vorl. 28 1876 Tuebner Leipzig
15. S.S. Antman Nonlinear problems of elasticity 2004 Springer Berlin
16. A.E.H. Love A treatise on the mathematical theory of elasticity 1927 Dover Publications New York
17. S.P. Timoshenko J.M. Gere Theory of elastic stability 1961 McGraw-Hill New York
18. C.L. Lu N.C. Perkins Complex spatial equilibria of U-joint supported cables under torque, thrust and self-weight Int. J. Non-Linear Mech. 30 1995 271
19. I. Tobias D. Swigon B.D. Coleman Elastic stability of DNA configurations. I. General theory Phys. Rev. E 61 2000 747
20. B.D. Coleman D. Swigon I. Tobias Elastic stability of DNA configurations. II. Supercoiled plasmids with self-contact Phys. Rev. E 61 2000 759
21. G.H.M. Van der Heijden S. Neukirch V.G.A. Goss J.M.T. Thompson Instability and self-contact phenomena in the writhing of clamped rods Int. J. Mech. Sci. 45 2003 161
22. C. Gatti-Bono N.C. Perkins Dynamic analysis of loop formation in cables under compression Int. J. Offshore Polar Eng. 12 2002 217
23. C. Gatti-Bono N.C. Perkins Physical and numerical modelling of the dynamic behavior of a fly line J. Sound Vibr. 225 2002 555
24. S. Goyal, N.C. Perkins, C.L. Lee, Writhing dynamics of cables with self-contact, in: Proceedings of the 5th International Symposium on Cable Dynamics, Santa Margherita Ligure, Italy, September 15-18, 2003, pp. 27-36
25. A. Balaeff L. Mahadevan K. Schulten Structural basis for cooperative DNA binding by CAP and Lac repressor Structure 12 2004 123
26. S. Kehrbaum, J.H. Maddocks, Effective properties of elastic rods with high intrinsic twist, in: 16th IMACS World Congress, 2000
27. J. Chung G.M. Hulbert A time integration algorithm for structural dynamics with improved numerical dissipation - The generalized-alpha method J. Appl. Mech. T. ASME 60 1993 371
28. J.I. Gobat M.A. Grosenbaugh M.S. Triantafyllou Generalized-alpha time integration solutions for hanging chain dynamics J. Eng. Mech. ASCE 128 2002 677
29. J.I. Gobat M.A. Grosenbaugh Application of the generalized-alpha method to the time integration of the cable dynamics equations Comput. Meth. Appl. Mech. Eng. 190 2001 4817
30. C.L. Bottasso M. Borri Integrating finite rotations Comput. Methods Appl. Mech. Eng. 164 1998 307
31. P.E. Nikravesh Computer-aided analysis of mechanical systems 1988 Prentice-Hall Englewood Cliffs, NJ
32. D.W. Zachmann Non-linear analysis of a twisted axially loaded elastic rod Q. Appl. Math. 37 1979 67
33. G. Domokos Global description of elastic bars Z. Angew. Math. Mech. 74 1994 T289
34. C.J. Benham Onset of writhing in circular elastic polymers Phys. Rev. A 39 1989 2582
35. M. Le Bret Catastrophic variation of twist and writhing of circular DNAs in constraint Biopolymers 18 1979 1709
36. T.J. Healey Material symmetry and chirality in nonlinearly elastic rods Math. Mech. Solids 7 2002 405
37. G.A. Costello Theory of wire rope 1997 Springer New York
38. J.F. Marko Stretching must twist DNA Europhys. Lett. 38 1997 183
39. C. Branden J. Tooze Introduction to protein structure 1999 Garland Publishing New York
40. C.R. Calladine H.R. Drew B.F. Luisi A.A. Travers Understanding DNA, the molecule and how it works 2004 Academic Press London
41. A.L. Lehninger D.L. Nelson M.M. Cox Lehninger principles of biochemistry 2005 Worth Publishers
42. M. Lewis G. Chang N.C. Horton M.A. Kercher H.C. Pace M.A. Schumacher R.G. Brennan P.Z. Lu Crystal structure of the lactose operon repressor and its complexes with DNA and inducer Science 271 1996 1247
43. J.R. Morison M.P. O'Brien J.W. Johnson S.A. Schaaf The force exerted by surface waves on piles T. Am. I. Min. Mat. Eng. 189 1950 149
44. M.M. Tirado J. Garciadelatorre Translational friction coefficients of rigid symmetric top macromolecules - Application to circular-cylinders J. Chem. Phys. 71 1979 2581
45. M.M. Tirado J. Garciadelatorre Rotational-dynamics of rigid symmetric top macromolecules - Application to circular-cylinders J. Chem. Phys. 73 1980 1986
46. H. Lamb Hydrodynamics 1945 Dover Publications New York
47. C. Moler C. Van-Loan 19 Dubious ways to compute exponential of a matrix SIAM Rev. 20 1978 801