Abstract
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].
Keywords
- Chain Representation
- Finite Fourier Series
- Monte Carlo Simulated Annealing
- Virtual Rotation
- Superhelical Turn
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bates, A. D. & Maxwell, A., DNA Topology, IRL Press, Oxford, Chapter 6 (1993).
Travers, A., DNA-Protein Interactions, Chapman & Hall, London, Chapter 7 (1993).
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).
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).
White, J. H., Self-linking and the Gauss integral in higher dimensions, Amer. J. Math. 91, 693–728 (1969).
Fuller, F. B., The writhing number of a space curve, Proc. Natl. Acad. Sci., USA 68, 815–819(1971).
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).
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).
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).
Mortenson, M. E., Geometric Modeling, John Wiley & Sons, New York, Chapter 2 (1985).
Dill, E. H., Kirchhoff’s theory of rods, Archive for History of Exact Science 44, 1–23 (1992).
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).
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).
Gorin, A. A., Zhurkin, V. B. & Olson, W. K. DNA twisting correlates with base pair morphology, J. Mol. Biol. 247, 34–48 (1995).
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).
Marky, N. L. & Olson, W. K., Loop formation in polynucleotide chains. I. Theory of hairpin loop closure, Biopolymers 21, 2329–2344 (1982).
Hagerman, P. J., Analysis of ring-closure probabilities of isotropic wormlike chains: Application to duplex DNA, Biopolymers 24, 1881–1897 (1985).
Levene, S. D. & Crothers, D. M., Ring closure probabilities for DNA fragments by Monte Carlo simulation, J. Mol. Biol. 189, 61–72 (1986).
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).
Frank-Kamenetskii, M. D., Lukashin, A. V. & Vologodskii, A. V., Statistical mechanics and topology of polymer chains, Nature (London) 258, 398–402 (1975).
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).
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).
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).
Tan, R. K.-Z. & Harvey, S. C., Molecular mechanics models of supercoiled DNA, J. Mol. Biol. 205, 573–591 (1989).
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).
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).
Yang, Y., Tobias, I. & Olson, W. K., Finite element analysis of DNA supercoiling, J. Chem. Phys. 98, 1673–1686 (1993).
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).
Hao, M.-H. & Olson, W. K., Modeling DNA supercoils and knots with B-spline functions, Biopolymers 28, 873–900 (1989).
Hao, M.-H. & Olson, W. K., Searching the global equilibrium configurations of supercoiledDNA by simulated annealing, Macromolecules 22, 3292–3303 (1989).
Schlick, T. & Olson, W. K., Supercoiled DNA energetics and dynamics by computer simulation, J. Mol. Biol. 223, 1089–1119 (1992).
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).
Olson, W. K. & Zhang, P., Computer simulation of DNA supercoiling, Methods in Enzymology 203, 403–432 (1991).
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).
Schlick, T., Olson, W. K., Westcott, T. & Greenberg, J. P., On higher buckling transitions in supercoiled DNA, Biopolymers 34, 565–597 (1994).
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).
Liu, G., Olson, W. K. & Schlick, T., Application of Fourier analysis to computer simulation of supercoiled DNA, Comp. Polymer Sci. 5, 7–27 (1995).
Schlick, T. & Overton, M., A powerful truncated method for potential energy minimization, J. Comp. Chem. 8, 1025–1039 (1987).
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).
Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T., Numerical Recipes, Cambridge University Press, Cambridge, Chapter 9 (1986).
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).
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).
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).
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).
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).
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).
Klug, A., Finch, J. T. & Richmond, T. J., Crystallographic structure of the octamer histone core of the nucleosome, Science 229, 1109–1110 (1985).
Bates, A. D. & Maxwell, A. DNA gyrase can supercoil DNA circles as small as 174 base pairs, EMBO J. 8, 1861–1866 (1989).
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).
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).
Fenley, M. O., Olson, W. K., Tobias, I. & Manning, G. S., Electrostatic effects in short superhelicai DNA, Biophys. Chem. 50, 255–271 (1994).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Olson, W.K., Westcott, T.P., Martino, J.A., Liu, GH. (1996). Computational Studies of Spatially Constrained DNA. In: Mesirov, J.P., Schulten, K., Sumners, D.W. (eds) Mathematical Approaches to Biomolecular Structure and Dynamics. The IMA Volumes in Mathematics and its Applications, vol 82. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4066-2_12
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4066-2_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94838-6
Online ISBN: 978-1-4612-4066-2
eBook Packages: Springer Book Archive