Computational Studies of Spatially Constrained DNA

  • Wilma K. Olson
  • Timothy P. Westcott
  • Jennifer A. Martino
  • Guo-Hua Liu
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 82)


Closed loops of double stranded DNA are ubiquitous in nature, occurring in systems ranging from plasmids, bacterial chromosomes, and many viral genomes, which form single closed loops, to eu-karyotic chromosomes and other linear DNAs, which appear to be organized into topologically constrained domains by DNA-binding proteins [1,2]. The topological constraints in the latter systems are determined by the spacing of the bound proteins along the contour of the double helix along with the imposed turns and twists of DNA in the intermolecular complexes [3,4]. As long as the duplex remains unbroken, the linking number Lk, or number of times the two strands of the DNA wrap around one another, is conserved [5–8]. If one of the strands is nicked and later re-sealed, the change in overall folding that accompanies DNA-protein interactions leads to a change in Lk. The supercoiling brought about by such protein action, in turn, determines a number of key biological events, including replication, transcription, and recombination [9].


Chain Representation Finite Fourier Series Monte Carlo Simulated Annealing Virtual Rotation Superhelical Turn 
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  1. [1]
    Bates, A. D. & Maxwell, A., DNA Topology, IRL Press, Oxford, Chapter 6 (1993).Google Scholar
  2. [2]
    Travers, A., DNA-Protein Interactions, Chapman & Hall, London, Chapter 7 (1993).CrossRefGoogle Scholar
  3. [3]
    Zhang, P., Tobias, I. & Olson, W. K., Computer simulation of protein-induced structural changes in closed circular DNA, J. Mol. Biol. 242, 271–290 (1994).CrossRefGoogle Scholar
  4. [4]
    Tobias, I., Coleman, B. & Olson, W. K., Dependence of DNA tertiary structure on end conditions: Theory and implications for topological transitions, J. Chem. Phys. 101, 10990–10996 (1994).CrossRefGoogle Scholar
  5. [5]
    White, J. H., Self-linking and the Gauss integral in higher dimensions, Amer. J. Math. 91, 693–728 (1969).CrossRefGoogle Scholar
  6. [6]
    Fuller, F. B., The writhing number of a space curve, Proc. Natl. Acad. Sci., USA 68, 815–819(1971).CrossRefGoogle Scholar
  7. [7]
    Fuller, F. B., Decomposition of the linking number of a closed ribbon: A problem from molecular biology, Proc. Natl. Acad. Sci., USA 75, 3557–3561 (1978).CrossRefGoogle Scholar
  8. [8]
    White, J. H., An introduction to the geometry and topology of DNA structure, in Mathematical Methods for DNA Sequences, Waterman, M. S., Ed., CRC Press, Boca Raton, FL, pp. 225–253 (1989).Google Scholar
  9. [9]
    Benjamin, H. W. & Cozzarelli, N. R., DNA-directed synapsis in recombination: Slithering and random collision of sites, Proc. R. A. Welch Found. Conf. Chem. Res. 29, 107–126 (1986).Google Scholar
  10. [10]
    Mortenson, M. E., Geometric Modeling, John Wiley & Sons, New York, Chapter 2 (1985).Google Scholar
  11. [11]
    Dill, E. H., Kirchhoff’s theory of rods, Archive for History of Exact Science 44, 1–23 (1992).CrossRefGoogle Scholar
  12. [12]
    Berman, H. M., Olson, W. K., Beveridge, D. L., Westbrook, J., Gelbin, A., Demeny, T., Hsieh, S.-H., Srinivasan, A. R. & Schneider, B., The nucleic acid database: A comprehensive relational database of three-dimensional structures of nucleic acids, Biophys. J. 63, 751–759 (1992).CrossRefGoogle Scholar
  13. [13]
    Olson, W. K., Babcock, M. S., Gorin, A., Liu, G.-H., Marky, N. L., Martino, J. A., Pedersen, S. C., Srinivasan, A. R., Tobias, I., Westcott, T. P. & Zhang, P., Flexing and folding double helical DNA, Biophys. Chem. 55, 7–29 (1995).CrossRefGoogle Scholar
  14. [14]
    Gorin, A. A., Zhurkin, V. B. & Olson, W. K. DNA twisting correlates with base pair morphology, J. Mol. Biol. 247, 34–48 (1995).CrossRefGoogle Scholar
  15. [15]
    Yoon, D. Y. & Flory, P. J., Moments and distribution functions for polymer chains of finite length. II. Poly methylene chains, J. Chem. Phys. 61, 5366–5380 (1974).CrossRefGoogle Scholar
  16. [16]
    Marky, N. L. & Olson, W. K., Loop formation in polynucleotide chains. I. Theory of hairpin loop closure, Biopolymers 21, 2329–2344 (1982).CrossRefGoogle Scholar
  17. [17]
    Hagerman, P. J., Analysis of ring-closure probabilities of isotropic wormlike chains: Application to duplex DNA, Biopolymers 24, 1881–1897 (1985).CrossRefGoogle Scholar
  18. [18]
    Levene, S. D. & Crothers, D. M., Ring closure probabilities for DNA fragments by Monte Carlo simulation, J. Mol. Biol. 189, 61–72 (1986).CrossRefGoogle Scholar
  19. [19]
    Vologodskii, A. V., Levene, S. D., Frank-Kamenetskii, M. D. & Cozzarelli, N. R., Conformational and thermodynamic properties of supercoiled DNA, J. Mol. Biol. 227, 1224–1243(1992).CrossRefGoogle Scholar
  20. [20]
    Frank-Kamenetskii, M. D., Lukashin, A. V. & Vologodskii, A. V., Statistical mechanics and topology of polymer chains, Nature (London) 258, 398–402 (1975).CrossRefGoogle Scholar
  21. [21]
    Vologodskii, A. V., Anshelevich, V. V., Lukashin, A. V. & Frank-Kamenetskii, M. D., Statistical mechanics of supercoils and the torsional stiffness of the DNA double helix, Nature (London) 280, 294–298 (1979).CrossRefGoogle Scholar
  22. [22]
    Frank-Kamenetskii, M. D. & Vologodskii, A. V., Topological aspects of the physics of polymers: The theory and its biophysical applications, Sov. Phys. Usp. (Eng. ed.) 24, 679–696 (1981).CrossRefGoogle Scholar
  23. [23]
    Klenin, K. V., Vologodskii, A. V., Anshelevich, V. V., Dykhne, A. M. & Frank-Kamenetskii, M. D., Computer simulation of DNA supercoiling, J. Mol. Biol. 217, 413–419(1991).CrossRefGoogle Scholar
  24. [24]
    Tan, R. K.-Z. & Harvey, S. C., Molecular mechanics models of supercoiled DNA, J. Mol. Biol. 205, 573–591 (1989).CrossRefGoogle Scholar
  25. [25]
    Tan, R. K.-Z. & Harvey, S. C., Succinct macromolecularmodels: Application to supercoiled DNA in Theoretical Biochemistry and Molecular Biophysics Volume 1: DNA, Beveridge, D. L. & Lavery, R., Eds., Adenine Press, Schenectady, NY, pp. 125–137 (1990).Google Scholar
  26. [26]
    Malhotra, A., Tan, R. K.-Z. & Harvey, S. C., Modeling large RNAs and ribonucleoprotein particles using molecular mechanics techniques, Biophys. J. 66, 1777–1795 (1994).CrossRefGoogle Scholar
  27. [27]
    Yang, Y., Tobias, I. & Olson, W. K., Finite element analysis of DNA supercoiling, J. Chem. Phys. 98, 1673–1686 (1993).CrossRefGoogle Scholar
  28. [28]
    Bauer, W. R., Lund, R. A. & White, J. H., Twist and writhe of a DNA loop containing intrinsic bends, Proc. Natl. Acad. Sci., USA 90, 833–837 (1993).CrossRefGoogle Scholar
  29. [29]
    Hao, M.-H. & Olson, W. K., Modeling DNA supercoils and knots with B-spline functions, Biopolymers 28, 873–900 (1989).CrossRefGoogle Scholar
  30. [30]
    Hao, M.-H. & Olson, W. K., Searching the global equilibrium configurations of supercoiledDNA by simulated annealing, Macromolecules 22, 3292–3303 (1989).CrossRefGoogle Scholar
  31. [31]
    Schlick, T. & Olson, W. K., Supercoiled DNA energetics and dynamics by computer simulation, J. Mol. Biol. 223, 1089–1119 (1992).CrossRefGoogle Scholar
  32. [32]
    Zhang, P., Olson, W. K. & Tobias, I., (1991) Accelerated record keeping Fourier series Monte Carlo simulations of an isotropic elastic rod model of DNA, Comp. Polymer Sci. 1, 3–17 (1991).Google Scholar
  33. [33]
    Olson, W. K. & Zhang, P., Computer simulation of DNA supercoiling, Methods in Enzymology 203, 403–432 (1991).CrossRefGoogle Scholar
  34. [34]
    Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. & Teller, E., Equation of state calculations by fast computing machines, J. Chem. Phys. 21, 1087–1092 (1953).CrossRefGoogle Scholar
  35. [35]
    Schlick, T., Olson, W. K., Westcott, T. & Greenberg, J. P., On higher buckling transitions in supercoiled DNA, Biopolymers 34, 565–597 (1994).CrossRefGoogle Scholar
  36. [36]
    Schlick, T., Li, B. & Olson, W. K., The influence of salt on the structure and energetics of supercoiled DNA, Biophys. J. 67, 2146–2166 (1994).CrossRefGoogle Scholar
  37. [37]
    Liu, G., Olson, W. K. & Schlick, T., Application of Fourier analysis to computer simulation of supercoiled DNA, Comp. Polymer Sci. 5, 7–27 (1995).Google Scholar
  38. [38]
    Schlick, T. & Overton, M., A powerful truncated method for potential energy minimization, J. Comp. Chem. 8, 1025–1039 (1987).CrossRefGoogle Scholar
  39. [39]
    Schlick, T. & Fogelson, A., TNPACK — A truncated Newton minimization package for large-scale problems: I. Algorithm and usage, and II. Implementation example, ACM Trans. Math. Soft. 18, 46–70 and 71–111 (1992).CrossRefGoogle Scholar
  40. [40]
    Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T., Numerical Recipes, Cambridge University Press, Cambridge, Chapter 9 (1986).Google Scholar
  41. [41]
    Olson, W. K., Marky, N. L., Jernigan, R. L. & Zhurkin, V. B., Influence of fluctuations on DNA curvature. A comparison of flexible and static wedge models of intrinsically bent DNA, J. Mol. Biol. 232, 530–554 (1993).CrossRefGoogle Scholar
  42. [42]
    Rybenkov, V. V., Cozzarelli, N. R. & Vologodskii, A. V., Probability of DNA knotting and the effective diameter of the DNA double helix, Proc. Natl. Acad. Sci., USA 90, 5307–5311 (1993).CrossRefGoogle Scholar
  43. [43]
    Germond, J. E., Hirt, B., Oudet, P., Gross-Bellard, M. & Chambon, P., Folding of the DNA double helix in chromatin-likestructures from simian virus 40, Proc. Natl. Acad. Sci., USA 72, 1843–1847 (1975).CrossRefGoogle Scholar
  44. [44]
    Zivanovic, Y., Goulet, I., Revet, B., Le Bret, M. & Prunell, A., Chromatin reconstitution on small DNA rings II. DNA supercoiling on the nucleosome, J. Mol. Biol. 200, 267–290 (1988).CrossRefGoogle Scholar
  45. [45]
    Moore, C. L., Klevan, L., Wang, J. C. & Griffith, J. D., GyraseDNA complexes visualized as looped structures by electron microscopy, J. Biol. Chem. 258, 4612–4617(1983).Google Scholar
  46. [46]
    Richmond, T. J., Finch, J. T., Rushton, B., Rhodes, D. & Klug, A., Structure of the nucleosome core particle at 7 Å resolution, Nature (London) 311, 532–537 (1984).CrossRefGoogle Scholar
  47. [47]
    Klug, A., Finch, J. T. & Richmond, T. J., Crystallographic structure of the octamer histone core of the nucleosome, Science 229, 1109–1110 (1985).CrossRefGoogle Scholar
  48. [48]
    Bates, A. D. & Maxwell, A. DNA gyrase can supercoil DNA circles as small as 174 base pairs, EMBO J. 8, 1861–1866 (1989).Google Scholar
  49. [49]
    Champoux, J. J., Mechanistic aspects of type-I topoisomerases, in DNA Topology and Its Biological Effects, Cozzarelli, N. R. & Wang, J. C., Eds., Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, pp. 217–242 (1990).Google Scholar
  50. [50]
    Hsieh, T.-S., Mechanistic aspects of type-II DNA topoisomerases in DNA Topology and Its Biological Effects, Cozzarelli, N. R. & Wang, J. C., Eds., Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, pp. 243–263 (1990).Google Scholar
  51. [51]
    Fenley, M. O., Olson, W. K., Tobias, I. & Manning, G. S., Electrostatic effects in short superhelicai DNA, Biophys. Chem. 50, 255–271 (1994).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Wilma K. Olson
    • 1
  • Timothy P. Westcott
    • 1
  • Jennifer A. Martino
    • 1
  • Guo-Hua Liu
    • 1
  1. 1.Department of Chemistry, Rutgersthe State University of New JerseyNew BrunswickUSA

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