Entropic Elasticity of Twist-Storing Polymers

We investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modeled as a fluctuating rod with bend stiffness AkBT and twist stiffness CkBT. In such a model, thermal bend fluctuations couple geometrically to an applied torque through the relation Lk = Tw + Wr. We explore this coupling and find agreement between the predictions of our model and recent experimental results on single λ-DNA molecules. This analysis affords an experimental determination of the microscopic twist stiffness (averaged over a helix repeat). Quantitative agreement between theory and experiment is obtained using C = 109 nm (i.e., twist rigidity CkBT = 4.5 × 10-19 erg cm). The theory further predicts a thermal reduction of the effective twist rigidity induced by bend fluctuations. Finally, we find a small reflection of molecular chirality in the experimental data and interpret it in terms of a twist−stretch coupling of the DNA duplex.

[1]  J. Michael Schurr,et al.  Effect of bending strain on the torsion elastic constant of DNA. , 1996, Journal of molecular biology.

[2]  S. Harvey,et al.  Static contributions to the persistence length of DNA and dynamic contributions to DNA curvature. , 1995, Biophysical chemistry.

[3]  E. Sezgin,et al.  Aspects of κ symmetry , 1993 .

[4]  R. L. Baldwin,et al.  Energetics of DNA twisting. I. Relation between twist and cyclization probability. , 1983, Journal of molecular biology.

[5]  A. Vologodskii.  DNA Extension under the Action of an External Force , 1994 .

[6]  R. L. Baldwin,et al.  Energetics of DNA twisting. II. Topoisomer analysis. , 1983, Journal of molecular biology.

[7]  F. John,et al.  Stretching DNA , 2022 .

[8]  SELF-AVOIDING WALKS WITH WRITHE , 1997, cond-mat/9705066.

[9]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[10]  G. Fredrickson.  The theory of polymer dynamics , 1996 .

[11]  A. Messiah.  Quantum Mechanics , 1961 .

[12]  D. Crothers,et al.  DNA bending, flexibility, and helical repeat by cyclization kinetics. , 1992, Methods in enzymology.

[13]  Michelle D. Wang,et al.  Stretching DNA with optical tweezers. , 1997, Biophysical journal.

[14]  J. Schellman,et al.  Flexibility of DNA , 1974, Biopolymers.

[15]  CONFORMATIONS OF LINEAR DNA , 1996, cond-mat/9610126.

[16]  R. Yasuda,et al.  Direct measurement of the torsional rigidity of single actin filaments. , 1996, Journal of molecular biology.

[17]  William H. Press,et al.  Numerical recipes , 1990 .

[18]  Elasticity theory of a twisted stack of plates , 1997, cond-mat/9707040.

[19]  John F. Marko,et al.  DNA UNDER HIGH TENSION : OVERSTRETCHING, UNDERTWISTING, AND RELAXATION DYNAMICS , 1998 .

[20]  S. Shaner,et al.  Double helical DNA: conformations, physical properties, and interactions with ligands. , 1981, Annual review of biochemistry.

[21]  P. Nelson,et al.  Torsional directed walks, entropic elasticity, and DNA twist stiffness. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[22]  R. Kamien.  Local writhing dynamics , 1997, cond-mat/9703137.

[23]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[24]  J. Marko.  STRETCHING MUST TWIST DNA , 1997 .

[25]  A. Bensimon,et al.  The Elasticity of a Single Supercoiled DNA Molecule , 1996, Science.

[26]  Stretching a heteropolymer , 1998 .

[27]  F. Young.  Biochemistry , 1955, The Indian Medical Gazette.

[28]  J. Wang,et al.  Torsional rigidity of DNA and length dependence of the free energy of DNA supercoiling. , 1984, Journal of molecular biology.

[29]  F. B. Fuller.  The writhing number of a space curve. , 1971, Proceedings of the National Academy of Sciences of the United States of America.

[30]  R. Lavery,et al.  DNA: An Extensible Molecule , 1996, Science.

[31]  P. Nelson,et al.  New measurements of DNA twist elasticity. , 1997, Biophysical journal.

[32]  Sequence-Disorder Effects on DNA Entropic Elasticity , 1997, cond-mat/9711285.

[33]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[34]  J. Marko,et al.  Extension of torsionally stressed DNA by external force. , 1997, Biophysical journal.

[35]  E. Siggia,et al.  Entropic elasticity of lambda-phage DNA. , 1994, Science.

[36]  R. Lathe.  Phd by thesis , 1988, Nature.

[37]  J. Linnett,et al.  Quantum mechanics , 1975, Nature.

[38]  R. Larson,et al.  Stretching of a single tethered polymer in a uniform flow. , 1995, Science.

[39]  Marko,et al.  Statistical mechanics of supercoiled DNA. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[40]  T. Strick,et al.  Behavior of supercoiled DNA. , 1998, Biophysical journal.

[41]  P. Hagerman,et al.  Application of the method of phage T4 DNA ligase-catalyzed ring-closure to the study of DNA structure. II. NaCl-dependence of DNA flexibility and helical repeat. , 1990, Journal of molecular biology.

[42]  J. Michael Schurr,et al.  Theory for the extension of a linear polyelectrolyte attached at one end in an electric field , 1990 .

[43]  C. O’Hern,et al.  Direct determination of DNA twist-stretch coupling , 1996, cond-mat/9611224.

[44]  S. Smith,et al.  Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads. , 1992, Science.

[45]  J. Michael Schurr,et al.  Dependence of the torsional rigidity of DNA on base composition , 1990, Nature.

[46]  James S. Langer,et al.  Theory of the condensation point , 1967 .

[47]  G. M.,et al.  A Treatise on the Mathematical Theory of Elasticity , 1906, Nature.

[48]  R. Feynman,et al.  Quantum Mechanics and Path Integrals , 1965 .

[49]  Wu-Ki Tung,et al.  Group Theory in Physics , 1985 .

[50]  James H. White.  Self-Linking and the Gauss Integral in Higher Dimensions , 1969 .

[51]  M. Mézard,et al.  Elasticity model of a supercoiled DNA molecule , 1997, cond-mat/9706050.

[52]  C. Bustamante,et al.  Overstretching B-DNA: The Elastic Response of Individual Double-Stranded and Single-Stranded DNA Molecules , 1996, Science.

[53]  Raymond E. Goldstein,et al.  VISCOUS NONLINEAR DYNAMICS OF TWIST AND WRITHE , 1998 .

[54]  Jiro Shimada,et al.  Ring-closure probabilities for twisted wormlike chains: application to DNA , 1984 .

[55]  F. B. Fuller.  Decomposition of the linking number of a closed ribbon: A problem from molecular biology. , 1978, Proceedings of the National Academy of Sciences of the United States of America.

[56]  C. Tanford.  Macromolecules , 1994, Nature.