Thermal fluctuations of small rings of intrinsically helical DNA treated like an elastic rod

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 362, Issue 1820, 2004, Pages 1387-1402

  Tobias, Irwin ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

DNA elasticity; Intrinsically helical DNA; Normal mode analysis; Rings of DNA; Thermal fluctuations; Writhe distribution

Indexed keywords

EID: 3042572328     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2004.1389     Document Type: Article

References (26)

1. Anderson, P. & Bauer, W. 1978 Supercoiling in closed circular DNA: dependence upon ion type and concentration. Biochemistry 17, 594-600.
2. Bauer, W. & Vinograd, J. 1968 The interaction of closed circular DNA with intercalative dyes. I. The superhelix density of SV40 DNA in the presence and absence of dye. J. Mol. Biol. 33, 141-171.
3. Bauer, W. & Vinograd, J. 1970 Interaction of closed circular DNA with intercalative dyes. II. The free energy of superhelix formation in SV40 DNA. J. Mol. Biol. 47, 419-435.
4. Calagareanu, G. 1961 Sur les classes d'isotopie des noeuds tridimensionnels et leur invariants. Czech. Math. J. 11, 588-625.
5. Clebsch, A. 1862 Theorie der Elastizität fester Körper. Leipzig: Teubner.
6. Coleman, B. D., Dill, E. H., Lembo, M., Lu, Z. & Tobias, I. 1993 On the dynamics of rods in the theory of Kirchhoff and Clebsch. Arch. Ration. Mech. Analysis 121, 339-359.
7. Coleman, B. D., Lembo, M. & Tobias, I. 1996 A new class of flexure-free torsional vibrations of annular rods. Meccanica 31, 565-575.
8. Depew, R. E. & Wang, J. C. 1975 Conformational fluctuations of DNA helix. Proc. Natl. Acad. Sci. USA 72, 4275-4279.
9. Dill, E. H. 1992 Kirchhoff's theory of rods. Arch. Hist. Exact Sci. 44, 1-23.
10. Fuller, F. B. 1971 The writhing number of a space curve. Proc. Natl Acad. Sci. USA 68, 815-819.
11. Goriely, A. & Tabor, M. 1997 Nonlinear dynamics of filaments I. Dynamical instabilities. Physica D105, 20-14.
12. Hagerman, P. J. 1988 Flexibility of DNA. A. Rev. Biophys. Biophys. Chem. 17, 265-286.
13. Horowitz, D. S. & Wang, J. C. 1984 Torsional rigidity of DNA and length dependence of the free energy of DNA supercoiling. J. Mol. Biol. 173, 75-91.
14. Hsieh, T.-S. & Wang, J. C. 1975 Thermodynamic properties of superhelical DNAs. Biochemistry 14, 527-535.
15. Kirchhoff, G. 1859 Über das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes. J. Reine Angew. Math. 56, 285-313.
16. Manning, R. S. & Hoffman, K. A. 2001 Stability of n-covered circles for elastic rods with constant planar intrinsic curvature. J. Elasticity 62, 1-23.
17. Pulleyblank, D. E., Shure, M., Tang, D., Vinograd, J. & Vosberg, H.-P. 1975 Action of nicking-closing enzyme on supercoiled and nonsupercoiled closed circular DNA: formation of a Boltzmann distribution of topological isomere. Proc. Natl Acad. Sci. USA 72, 4280-4284.
18. Shore, D. & Baldwin, R. L. 1983 Energetics of DNA twisting. II. Topoisomer analysis. J. Mol. Biol. 170, 983-1007.
19. Tobias, I. 1998 A theory of thermal fluctuations in DNA miniplasmids. Biophys. J. 74, 2545-2553.
20. Tobias, I. 2000 The writhe distribution in DNA plasmids as derived from the free energy of supercoiling. J. Chem. Phys. 113, 6950-6956.
21. Tobias, I. & Olson, W. K. 1993 The effect of intrinsic curvature on supercoiling: predictions of elasticity theory. Biopolymers 33, 639-646.
22. Tobias, I., Coleman, B. D. & Lembo, M. 1996 A class of exact dynamical solutions in the elastic rod model of DNA with implications for the theory of fluctuations in the torsional motion of plasmids. J. Chem. Phys. 105, 2517-2526.
23. White, J. H. 1969 Self-linking and the Gauss-integral in higher dimensions. Am. J. Math. 91, 693-728.
24. White, J. H. 1989 An introduction to the geometry and topology of DNA structure. In Mathematical methods for DNA sequences (ed. M. S. Waterman), pp. 225-253. Boca Raton, FL: Chemical Rubber Company.
25. Zajac, E. E. 1962 Stability of two planar loop elasticas. Trans. ASME J. Appl. Mech. 29, 136-142.
26. Zelen, M. & Severo, M. C. 1965 Probability functions. In Handbook of mathematical functions (ed. M. Abramowitz & I. A. Stegun), ch. 26. New York: Dover.