Conformational analysis of stiff chiral polymers with end-constraints

Molecular Simulation

Volumn 32, Issue 14, 2006, Pages 1139-1154

  Kim, J S ^a   Chirikjian, G S ^a  

^a Johns Hopkins University   (United States)

Author keywords

Elastica; Lie group theoretic method; Normal mode analysis; Stiff polymer; Variational calculus

Indexed keywords

CHIRALITY; CONFORMATIONS; DNA; DYNAMIC ANALYSIS; KINEMATICS; PARAMETER ESTIMATION; STIFFNESS;

ELASTIC RODS; LIE-GROUP-THEORETIC METHOD; NORMAL MODE ANALYSIS; STIFF POLYMERS;

INORGANIC POLYMERS;

EID: 34548387408     PISSN: 08927022     EISSN: 10290435     Source Type: Journal    
DOI: 10.1080/08927020601024137     Document Type: Article

References (74)

1. B.D. Coleman, I. Tobias, D. Swigon. Theory of the influence of end conditions on self-contact in DNA loops. J. Chem. Phys., 103, 9101 (1995).
2. D. Swigon, B.D. Coleman, I. Tobias. The elastic rod model for DNA and its application to the tertiary structure of DNA minicircles in Mononucleosomes. Biophys. J., 74, 2515 (1998).
3. I. Tobias, D. Swigon, B.D. Coleman. Elastic stability of DNA configurations. I: general, theory. Phys. Rev. E, 61, 747 (2000).
4. B.D. Coleman, D. Swigon, I. Tobias. Elastic stability of DNA configurations. II: supercoiled Plasmides with self-contact. Phys. Rev. E, 61, 759 (2000).
5. F.B. Fuller. Decomposition of the linking number of a closed ribbon: a problem from molecular biology. Proc Natl Acad. Sci. USA, 75, 3557 (1978).
6. F.B. Fuller. The writhing number of a space curve. Proc. Natl. Acad. Sci. USA, 68, 815 (1971).
7. D.S. Horowitz, J.C. Wang. Torsional rigidity of DNA and length dependence of the free-energy of DNA supercoiling. J. Mol. Biol., 173, 75 (1984).
8. J.D. Moroz, P. Nelson. Torsional directed walks, entropie elasticity, and DNA twist stiffness. Proc. Natl. Acad. Sci. USA, 94, 14418 (1997).
9. W.F. Pohl. The self-linking number of a cloased space curve. J. Math. Mech., 17, 975 (1968).
10. A.A. Podtelezhnikov, N.R. Cozzarelli, A.V. Vologodskii. Equilibrium distributions of topological states in circular DNA: interplay of supercoling and knotting. Proc. Natl. Acad. Sci. USA, 96, 12974 (1999).
11. A. Vologodskii. Topology and Physics of Circular DNA, CRC Press, Boca Raton (1992).
12. J.H. White, W.R. Bauer. Calculation of the twist and the writhe for representative models of DNA. J. Mol. Biol, 189, 329 (1986).
13. R. Zandi, J. Rudnick. Constraints, histones, and 30-n.m spiral. Phys. Rev. E, 64 (2001) Art. No. 051918.
14. B. Fain, J. Rudnick. Conformations of closed DNA. Phys. Rev. E, 60, 7239 (1999).
15. B. Fain, J. Rudnick, S. Ostlund. Conformations of linear DNA. Phys. Rev. E, 55, 7364 (1997).
16. H. Schiessel, J. Rudnick, R. Bruinsma, W.M. Gelbart. Organized condensation of worm-like chains. Europhys. Lett., 51, 237 (2000).
17. A. Balaeff, L. Mahadevan, K. Schulten. Modeling DNA loops using the theory of elasticity, E-print archieve arXiv.org (http://arxiv.org/abs/ physics/0301006, 2003).
18. A. Balaeff, L. Mahadevan, K. Schulten. Structural basis for cooperative DNA binding by CAP and Lac repressor. Structure, 12, 123 (2004).
19. B.D. Coleman, W.K. Olson, D. Swigon. Theory of sequence-dependent DNA elasticity. J. Chem. Phys., 118, 7127 (2003).
20. A.E.H. Love. A Treatise on the Mathematical Theory of Elasticity, Dover, New York (1944).
21. S.S. Antman. Nonlinear Problems of Elasticity, Springer-Verlag, New York (1995).
22. J.C. Simo, L. Vu-Quoc. A three dimensional, finite-strain rod model. Part II: computational aspects. Comput. Meth. Appl. Mech. Eng., 58, 79 (1986).
23. D.J. Donald, Y. Li, J.H. Maddocks. Hamiltonian formulations and symmetries in rod mechanics. Mathematical Approaches to Biomolecular Structure and Dynamics, p. 71, Springer-Verlag, New York (1995).
24. B.D. Coleman, E.H. Dill, M. Lembo, Z. Lu, I. Tobias. On the dynamics of rods in the theory of Kirchhoff and Clebsch. Arch. Rational Mech. Anal., 121, 339 (1993).
25. D.J. Steigmann, M.G. Faulkner. Variational theory for spatial, rods. Arch. Rational Mech. Anal, 133, 1 (1993).
26. O. Gonzalez, J.H. Maddocks. Extracting parameters for base-pair level models of DNA from molecular dynamics simulations. Theor. Chem. Acc., 106, 76 (2001).
27. S. Goyal, N.C. Perkins, C.L. Lee. Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables. J. Comp. Phys., 209, 371 (2005).
28. G.S. Chirikjian, Y. Wang. Conformational statistics of stiff macromolecules as solutions to partial differential equations on the rotation and motion group. Phys. Rev. E, 62, 880 (2000).
29. O. Kratky, G. Porod. Rontgenuntersuchung geloster fadenmolekule. Rec. Trav. Chim., 68, 1106 (1949).
30. R.P. Mondescu, M. Muthukumar. Brownian motion and polymer statistics on certain curved manifolds. Phys. Rev. E, 57, 4411 (1998).
31. A.V. Vologodskii, V.V. Anshelevich, A.V. Lukashin, M.D. Frank-Kamenetskii. Statistical mechanics of supercoils and the torsional stiffness of the DNA double helix. Nature, 280, 294 (1979).
32. H. Yamakawa. Helical Wormlike Chains in Polymer Solutions, Springer, New York (1997).
33. R.C Maroun, W.K. Olson. Base sequence effects in double-helical DNA. 2. Configurational statistics of rodlike chains. Biopolymers, 27, 561 (1988).
34. T. Odijk. Stiff chains and filaments under tension. Macromolecules, 28, 7016 (1995).
35. W.K. Olson, N.L. Marky, R.L. Jernigan, V.B. Zhurkin. Influence of fluctuation on DNA curvature. A comparison of flexible and static wedge models of intrinsically bent DNA. J. Mol Biol, 232, 530 (1993).
36. T.R. Strick, J.F. Allemand, D. Bensimon, A. Bensimon, V. Croquette. The elasticity of a single supercoiled DNA molecule. Science, 271, 1835 (1996).
37. D. Shore, R.L. Baldwin. Energetics of DNA twisting. J. Mol. Biol., 170, 957 (1983).
38. H. Zhou, Z. Ou-Yang. Bending and twisting elasticity: a revised Marko-Siggia model on DNA chirality. Phys. Rev. E, 58, 4816 (1998).
39. C.G. Baumann, S.B. Smith, V.A. Bloomfield, C. Bustamante. Ionic effects on the elasticity of single DNA molecules. Proc Natl. Acad. Sci. USA, 94, 6185 (1997).
40. J.F. Marko, E.D. Siggia. Bending and twisting elasticity of DNA. Macromolecules, 27, 981. (1994).
41. P. Nelson. Sequence-disorder effects on DNA entropic elasticity. Phys. Rev. Lett., 80, 5810 (1998).
42. P. Nelson. New measurements of DNA twist elasticity. Biophys. J., 74, 2501 (1998).
43. P.A. Wiggins, R. Phillips, P.C. Nelson. Exact theory of kinkable elastic polymers, E-print archieve arXiv.org (arXiv:cond-mat/0409003 v1.31. Aug. 2004).
44. P. Cluzel, A. Lebrun, C. Heller, R. Lavery, J. Viory, D. Chatenay, F. Caron. DNA: an extensible molecule. Science, 271, 792 (1996).
45. J.F. Marko. Stretching must twist DNA. Europhys. Lett., 38, 183 (1997).
46. C.S. O'Hern, R.D. Kamien, T.C. Lubensky, P. Nelson. Twiststretch elasticity of DNA, E-print archieve arXiuorg (arX.iv:cond-mat/961.2085 v1.9Dec. 1996)
47. R.D. Kamien, T.C. Lubensky, P. Nelson. Direct determination of DNA twist-stretch coupling, E-print archieve arXiuorg (arXiv:cond-mat/9611224 v1.27 Nov. 1996).
48. C. Storm, P.C. Nelson. Theory of high-force DNA stretching and overstretching. Phys. Rev. E, 67, 051906 (2003).
49. Y. Shi, S. He, J.E. Hearst. Statistical mechanics of the extensible and shearable elastic rod and of DNA. J. Chem. Phys., 105, 714 (1996).
50. J. Ma. Usefulness and limitations of normal mode analysis in modeling dynamics of biomolecular complexes. Structure, 13(373) (2005).
51. V. Alexandrov, U. Lehnen, N. Echols, D. Milburn, D. Engelman, M. Gerstein. Normal modes for predicting protein motions: a comprehensive database assessment and associated Web tool. Protein Sci., 14, 633 (2005).
52. I. Tobias. A theory of thermal fluctuations in DNA miniplasmids. Biophys. J., 74, 2545 (1998).
53. A. Matsumoto, W.K. Olson. Sequence-dependent motions of DNA: a normal model analysis at the base-pair level. Biophys. J., 83, 22 (2002).
54. A. Matsumoto, I. Tobias, W.K. Olson. Normal-mode analysis of circular DNA at the base-pair level. 1. Comparison of computed motions with the predicted behavior of an ideal elastic rod. J. Chem. Theor. Comput., 1, 117 (2005).
55. A. Matsumoto, I. Tobias, W.K. Olson. Normal-mode analysis of circular DNA at the base-pair level. 2. Large-scale configurational transformation of a naturally curved molecule. J. Chem. Theor. Comput., 1, 130 (2005).
56. T.H. Duong, K. Zakrzewska. Influence of drug binding on DNA flexibility: a normal, mode analysis. J. Biomol. Struct., 14, 691 (1997).
57. V.I. Arnol'd. Mathematical Methods of Classical Mechanics, Springer-Verlag, New York (1978).
58. R. Abraham, J.E. Marsden. Foundations of Mechanics, Benjamin/Cummings, San Mateo, CA (1978).
59. R.W. Brockett. Robotic manipulators and the product of exponentials formula. In Mathematical Theory of Networks and Systems, A. Fuhrman (Ed.), p. 120, Springer-Verlag, New York (1984).
60. A. Karger, j. Novák. Space Kinematics and Lie Groups, Gordon and Breach Science Publishers, New York (1985).
61. J.M. McCarthy. An Introduction to Theoretical Kinematics, MIT Press, Cambridge (1990).
62. R.M. Murray, Z. Li, S.S. Sastry. A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton (1994).
63. J.M. Selig. Geometrical Methods in Robotics, Springer, New York (1996).
64. G.S. Chirikjian, A.B. Kyatkin. Engineering Applications of Noncommutative Harmonic Analysis, CRC Press, Boca Raton (2001).
65. Y. Han, F.C. Park. Least square tracking on the Euclidean group. IEEE Trans. Autom. Control, 46, 1127 (2001).
66. F.C. Park. Distance metrics on the rigid-body motions with applications to mechanism design. J. Mech. Des., 117, 48 (1995).
67. L. Meirovitch. Analytical Methods in Vibrations, Macmillan, New York (1967).
68. A, Wolffe. Chromatin: Structure and Function, Academic Press, San diego (1998).
69. Y. Zivanovic, I. Goulet, B. Revet, M.L. Bret, A. Prunell. Chromatin reconstitution on small DNA rings. II. DNA supercoiling on the nucleosome. J. Mol. Biol., 200, 267 (1988).
70. F.D. Lucia, M. Alilat, A. Sivolob, A. Prunell. Nucleosome dynamics III. Histone tail-dependent fluctuation of nucleosomes between open and closed DNA conformations. Implications for chromatin dynamics and the linking number paradox. A relaxation study of mononucleosomes on DNA minicircles. J. Mol Biol., 285, 1101 (1999).
71. G.S. Chirikjian, J.W. Burdick. Kinematically optimal, hyper-redundant manipulator configurations. IEEE Trans. Robot. Autom., 11, 794 (1995).
72. H. Poincaré. Sur une forme nouvelle des equations de la mechanique. Cr. Hebd. Acad. Sci., 132, 369 (1901).
73. A. Bloch, P.S. Krishnaprasad, J.E. Marsden, T.S. Ratiu. The Euler-Poincaré equations and double bracket dissipation. Commun. Math. Phys., 175, 1 (1996).
74. D.D. Holm, J.E. Marsden, T.S. Ratiu. The Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. Math., 137, 1 (1998).