Statistical mechanics of supercoiled DNA.

The conformation of long supercoiled DNA loops under near physiological conditions has been the subject of a long series of laboratory and Monte Carlo experiments, and impressive agreement between theory and experiment has been achieved [1–2]. A closed unnicked DNA loop has fixed linking number: this constraint leads to a competition between twisting and bending (writhing) elastic energy which drives plectonemic supercoiling. However, entropy, as manifest through a fluctuation induced repulsive force, overwhelms this elastic effect for fractional linking number perturbations ∣σ∣ 0.02, plectonemic supercoils are stable, but thermal fluctuations continue to play an important role, competing with bending and twisting elastic energy to set the superhelical radius. We have constructed an analytic theory for this effect that agrees well with experiment [3], using methods from polymer statistical mechanics.

[1]  N R Cozzarelli,et al.  Probability of DNA knotting and the effective diameter of the DNA double helix. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[2]  D. Crothers,et al.  Topological distributions and the torsional rigidity of DNA. A Monte Carlo study of DNA circles. , 1986, Journal of molecular biology.

[3]  V. Anshelevich,et al.  Statistical mechanics of supercoils and the torsional stiffness of the DNA double helix , 1979, Nature.

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

[5]  J Langowski,et al.  Modulation of intramolecular interactions in superhelical DNA by curved sequences: a Monte Carlo simulation study. , 1995, Biophysical journal.

[6]  A. Worcel,et al.  On the structure of the folded chromosome of Escherichia coli. , 1972, Journal of molecular biology.

[7]  T. Odijk.  On the ionic-strength dependence of the intrinsic viscosity of DNA. , 1979, Biopolymers.

[8]  D. Jackson,et al.  The size of chromatin loops in HeLa cells. , 1990, The EMBO journal.

[9]  M. L. Bret.  Catastrophic variation of twist and writhing of circular DNAs with constraint , 1979 .

[10]  W. Storzer,et al.  Cyclische Oxyphosphorane mit dem Spinlabel 4-Oxy-1-oxyl-2.2.6.6-tetramethylpiperidin / Spin-Labeled Cyclic Oxyphosphoranes 4-Oxy-1-oxyl-2,2,6,6-tetramethylpiperidine , 1978 .

[11]  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.

[12]  D M Crothers,et al.  Intrinsically bent DNA. , 1990, The Journal of biological chemistry.

[13]  J. Dubochet,et al.  Direct visualization of supercoiled DNA molecules in solution. , 1990, The EMBO journal.

[14]  W. Bauer,et al.  Calculation of the twist and the writhe for representative models of DNA. , 1986, Journal of molecular biology.

[15]  N. Cozzarelli,et al.  The stereostructure of knots and catenanes produced by phage λ integrative recombination: implications for mechanism and DNA structure , 1985, Cell.

[16]  K. Klenin,et al.  Computer simulation of DNA supercoiling. , 1991, Journal of molecular biology.

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

[18]  Eric D. Siggia,et al.  Bending and Twisting Elasticity of DNA , 1994 .

[19]  T Schlick,et al.  Supercoiled DNA energetics and dynamics by computer simulation. , 1992, Journal of molecular biology.

[20]  S. Leibler,et al.  On Supercoiling Instability in Closed DNA , 1992 .

[21]  J. Wang,et al.  Conformational fluctuations of DNA helix. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[22]  M. Le Bret,et al.  Twist and writhing in short circular DNAs according to first‐order elasticity , 1984, Biopolymers.

[23]  H. Vosberg,et al.  Action of nicking-closing enzyme on supercoiled and nonsupercoiled closed circular DNA: formation of a Boltzmann distribution of topological isomers. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[24]  R. Podgornik,et al.  Molecular fluctuations in the packing of polymeric liquid crystals , 1990 .

[25]  O. Berg.  Diffusion‐controlled protein–DNA association: Influence of segemental diffusion of the DNA , 1984, Biopolymers.

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

[27]  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.

[28]  M. Bedzyk,et al.  Lattice location of trace elements within minerals and at their surfaces with X-ray standing waves. , 1994, Science.

[29]  J. Wang,et al.  DNA topoisomerases: why so many? , 1991, The Journal of biological chemistry.

[30]  Fumihiko Tanaka,et al.  Elastic theory of supercoiled DNA , 1985 .

[31]  Christian N. Parker,et al.  Dynamics of long-range interactions on DNA: The speed of synapsis during site-specific recombination by resolvase , 1991, Cell.

[32]  J. Kovac,et al.  Polymer conformational statistics. III. Modified Gaussian models of stiff chains , 1973 .

[33]  J. Dubochet,et al.  The twist, writhe and overall shape of supercoiled DNA change during counterion-induced transition from a loosely to a tightly interwound superhelix. Possible implications for DNA structure in vivo. , 1994, Journal of molecular biology.

[34]  M. Daoud,et al.  Conformation of branched polymers , 1981 .

[35]  Benham.  Onset of writhing in circular elastic polymers. , 1989, Physical review. A, General physics.

[36]  D. Stigter,et al.  Interactions of highly charged colloidal cylinders with applications to double‐stranded DNA , 1977 .

[37]  E. Siggia,et al.  Fluctuations and supercoiling of DNA. , 1994, Science.

[38]  M Frank-Kamenetskii,et al.  Conformational and thermodynamic properties of supercoiled DNA. , 1992, Journal of molecular biology.

[39]  C. Post.  Excluded volume of an intermediate‐molecular‐weight DNA. A Monte Carlo analysis , 1983, Biopolymers.

[40]  C. Benham.  Geometry and mechanics of DNA superhelicity , 1983, Biopolymers.

[41]  J. Wang,et al.  Supercoiling of the DNA template during transcription. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[42]  P. Dröge.  Protein tracking‐induced supercoiling of DNA: A tool to regulate DNA transactions in vivo? , 1994, BioEssays : news and reviews in molecular, cellular and developmental biology.

[43]  N R Cozzarelli,et al.  Structure of plectonemically supercoiled DNA. , 1990, Journal of molecular biology.

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

[45]  J. Schellman,et al.  Electrical double layer, zeta potential, and electrophoretic charge of double‐stranded DNA , 1977, Biopolymers.

[46]  L. Onsager.  THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES , 1949 .

[47]  N. Cozzarelli,et al.  The role of topoisomerase IV in partitioning bacterial replicons and the structure of catenated intermediates in DNA replication , 1992, Cell.

[48]  P. Hagerman.  Flexibility of DNA. , 1988, Annual review of biophysics and biophysical chemistry.

[49]  Rau,et al.  Measured entropy and enthalpy of hydration as a function of distance between DNA double helices. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[50]  J. Wang,et al.  Knotting of a DNA chain during ring closure. , 1993, Science.

[51]  D. Crothers,et al.  Detection of localized DNA flexibility , 1994, Nature.

[52]  Bruno H. Zimm,et al.  The Dimensions of Chain Molecules Containing Branches and Rings , 1949 .

[53]  R. Watson,et al.  The twisted circular form of polyoma viral DNA. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

[54]  V A Parsegian,et al.  Direct measurement of the intermolecular forces between counterion-condensed DNA double helices. Evidence for long range attractive hydration forces. , 1992, Biophysical journal.

[55]  N R Cozzarelli,et al.  Conformational and thermodynamic properties of supercoiled DNA. , 1994, Annual review of biophysics and biomolecular structure.

[56]  J. Shimada,et al.  Moments for DNA topoisomers: The helical wormlike chain , 1988, Biopolymers.

[57]  W. Bauer,et al.  Structure and reactions of closed duplex DNA. , 1978, Annual review of biophysics and bioengineering.

[58]  T. Odijk.  Similarity applied to the statistics of confined stiff polymers , 1984 .

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

[60]  G. S. Manning.  A procedure for extracting persistence lengths from light-scattering data on intermediate molecular weight DNA , 1981 .

[61]  J. Sawitzke,et al.  Multiple bacterial topoisomerases: Specialization or redundancy? , 1993, BioEssays : news and reviews in molecular, cellular and developmental biology.

[62]  V. Anshelevich,et al.  Torsional and bending rigidity of the double helix from data on small DNA rings. , 1985, Journal of biomolecular structure & dynamics.

[63]  John E. Hearst,et al.  Elastic model of DNA supercoiling in the infinite-length limit , 1991 .

[64]  N. Cozzarelli,et al.  Supercoiling, knotting, looping and other large-scale conformational properties of DNA , 1994 .

[65]  M. Schmid.  Structure and function of the bacterial chromosome. , 1988, Trends in biochemical sciences.

[66]  V V Anshelevich,et al.  Variance of writhe for wormlike DNA rings with excluded volume. , 1989, Journal of biomolecular structure & dynamics.

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

[68]  A. Worcel,et al.  Isolation, characterization, and structure of the folded interphase genome of Drosophila melanogaster , 1976, Cell.

[69]  V. Parsegian,et al.  Direct measurement of temperature-dependent solvation forces between DNA double helices. , 1992, Biophysical journal.