The size of knots in polymers

Physical Biology

Volumn 6, Issue 2, 2009, Pages

  Orlandini, Enzo ^a   Stella, Attilio L ^a   Vanderzande, Carlo ^b,c  

^a UNIVERSITY OF PADOVA   (Italy)

^b HASSELT UNIVERSITY   (Belgium)

^c UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

DNA TOPOISOMERASE (ATP HYDROLYSING); POLYMER; SOLVENT; BACTERIAL DNA; BIOPOLYMER; CIRCULAR DNA; VIRUS DNA;

ADSORPTION; ARTICLE; COMPOSITE MATERIAL; ENTROPY; EQUILIBRIUM CONSTANT; MOLECULAR DOCKING; MOLECULAR DYNAMICS; MOLECULAR IMAGING; MOLECULAR INTERACTION; MOLECULAR SIZE; NONHUMAN; PRIORITY JOURNAL; RING CLOSING METATHESIS; BACTERIUM; CHEMICAL STRUCTURE; CHEMISTRY; COMPUTER SIMULATION; CONFORMATION; GENETICS; VIRUS;

ADSORPTION; BACTERIA; BIOPOLYMERS; COMPUTER SIMULATION; DNA, BACTERIAL; DNA, CIRCULAR; DNA, VIRAL; MODELS, MOLECULAR; MOLECULAR CONFORMATION; NUCLEIC ACID CONFORMATION; SOLVENTS; VIRUSES;

EID: 68349125248     PISSN: 14783967     EISSN: 14783975     Source Type: Journal    
DOI: 10.1088/1478-3975/6/2/025012     Document Type: Article

References (60)

1. Liu L F, Depew R E and Wang J C 1976 Knotted single-stranded DNA rings: a novel topological isomer of circular single-stranded DNA formed by treatment with Escherichia coli omega protein J. Mol. Biol. 106 439-52
2. Liu L F, Perkocha L, Calendar R and Wang J C 1981 Knotted DNA from bacteriophage capsids Proc. Natl. Acad. Sci. 78 5498-502
3. Arsuaga J, Vazquez J, Trigueros S, Sumners D W and Roca J 2002 Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids Proc. Natl. Acad. Sci. 99 5373-7
4. Shaw S Y and Wang J C 1993 Knotting of a DNA chain during ring closure Science 260 533-6
5. Rybenkov V V, Cozzarelli N R and Vologodskii A V 1993 Probability of DNA knotting and the effective diameter of the DNA double helix Proc. Natl. Acad. Sci. 90 5307-11
6. Delbruck M 1962 Knotting problems in biology Proc. Symp. Appl. Math. 14 55-63
7. Sumners D W and Whittington S G 1988 Knots in self-avoiding walks J. Phys. A: Math. Gen. 21 1689-94
8. Pippenger N 1989 Knots in random walks Disc. Appl. Math. 25 273-8
9. Tesi M C, Janse van Rensburg E J, Orlandini E, Sumners D W and Whittington S G 1994 Knotting and supercoiling in circular DNA: a model incorporating the effect of added salt Phys. Rev. E 49 868-72
10. Bates A D and Maxwell A 2005 DNA Topology (Oxford: Oxford University Press)
11. Koster D A, Croquette V, Dekker C, Shuman S and Dekker N H 2005 Friction and torque govern the relaxation of DNA supercoils by eukaryotic topoisomerase IB Nature 434 671-4
12. Rybenkov V V, Ullsperger C, Vologodskii A V and Cozzarelli N R 1997 Simplification of DNA topology below equilibrium values by type II topoisomerases Science 277 690-3
13. Bates A D and Maxwell A 2007 Energy coupling in type II topoisomerases: Why do they hydrolyse ATP? Biochemistry 46 7929-41
14. Orlandini E and Whittington S G 2007 Statistical topology of closed curves: some applications in polymer physics Rev. Mod. Phys. 79 611-42
15. Vologodskii A V, Zhang W, Rybenkov V V, Podtelezhnikov A A, Subramanian D, Griffith J D and Cozzarelli N R 2001 Mechanism of topology simplification by type II DNA topoisomerases Proc. Natl. Acad. Sci. 98 3045-9
16. Buck G R and Zechiedrich E L 2004 DNA disentangling by type-2 topoisomerases J. Mol. Biol. 340 933-9
17. Liu Z, Mann J K, Zechiedrich E L and Chan H S 2006 Topological information embodied in local juxtaposition geometry provides a statistical mechanical basis for unknotting by type-2 DNA topoisomerases J. Mol. Biol. 361 268-85
18. Vologodskii A V, Crisona N J, Laurie B, Pieranski P, Katrich V, Dubochet J and Stasiak A 1998 Sedimentation and electrophoretic migration of DNA knots and catenanes J. Mol. Biol. 278 1-3
19. Vanderzande C 1998 Lattice Models of Polymers (Cambridge: Cambridge University Press)
20. Adams C C 2004 The Knot Book (Providence, RI: American Mathematical Society)
21. Guida R and Zinn-Justin J 1998 Critical exponents of the N-vector model J. Phys. A: Math. Gen. 31 8103-21 (Pubitemid 128381689)
22. Li B, Madras N and Sokal A D 1995 Critical exponents, hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks J. Stat. Phys. 80 661-754
23. Rolfsen D 1976 Knots and Links (Wimington: Publish or Perish Press)
24. Orlandini E, Tesi M C, Janse van Rensburg E J and Whittington S G 1996 Entropic exponents of lattice polygons with specified knot type J. Phys. A: Math. Gen. 29 L299-303
25. Orlandini E, Tesi M C, Janse van Rensburg E J and Whittington S G 1998 Asymptotics of knotted lattice polygons J. Phys. A: Math. Gen. 31 5953-67 (Pubitemid 128380285)
26. Katrich V, Olson W K, Vologodskii A, Dubochet J and Stasiak A 2000 Tightness of random knotting Phys. Rev. E 61 5545-9
27. Guitter E and Orlandini E 1999 Monte Carlo results for projected self-avoiding polygons: a two-dimensional model for knotted polymers J. Phys. A: Math. Gen. 32 1359-85
28. Metzler R, Hanke A, Dommersnes P G, Kantor Y and Kardar M 2002 Equilibrium shapes of flat knots Phys. Rev. Lett. 88 188101
29. Maier B and Rädler J O 1999 Conformation and self-diffusion of single DNA molecules confined to two dimensions Phys. Rev. Lett. 82 1911-4
30. Duplantier B 1986 Polymer network of fixed topology: renormalization, exact critical exponent γ in two dimensions, and d = 4 - ε Phys. Rev. Lett. 57 941-4
31. Duplantier B 1989 Statistical mechanics of polymer networks of any topology J. Stat. Phys. 54 581-680
32. Marcone B, Orlandini E, Stella A L and Zonta F 2005 What is the length of a knot in a polymer? J. Phys. A: Math. Gen. 38 L15-21
33. Marcone B, Orlandini E, Stella A L and Zonta F 2007 Size of knots in ring polymers Phys. Rev. E 75 041105-11
34. Orlandini E, Stella A L and Vanderzande C 2003 Polymer -point as a knot delocalization transition Phys. Rev. E 68 031804-8
35. Hanke A, Metzler R, Dommersnes P G, Kantor Y and Kardar M 2003 Tight and loose shapes in flat entangled dense polymers Eur. Phys. J. E 12 347-54
36. Orlandini E, Stella A L and Vanderzande C 2004 Loose, flat knots in collapsed polymers J. Stat. Phys. 115 681-700
37. Duplantier B and Saleur H 1987 Exact tricritical exponents for polymers at the -point in two dimensions Phys. Rev. Lett. 59 539-42
38. Virnau P, Kantor Y and Kardar M 2005 Knots in globule and coil phases of a model polyethylene J. Am. Chem. Soc. 127 15102-6
39. De'Bell K and Lookman T 1993 Surface phase transitions in polymer systems Rev. Mod. Phys. 65 87-113
40. Marcone B, Orlandini E and Stella A L 2007 Knot localization in adsorbing polymer rings Phys. Rev. E 76 051804
41. Hegger R and Grassberger P 1994 Chain polymers near an adsorbing surface J Phys A: Math. Gen. 27 4069-81
42. Ercolini E, Valle F, Adamcik J, Witz G, Metzler R, De Los Rios P, Roca J and Dietler G 2007 Fractal dimension and localization of DNA knots Phys. Rev. Lett. 98 058102
43. Lai P Y 2002 Dynamics of polymer knots at equilibrium Phys. Rev. E 66 021805
44. Trigueros S and Roca J 2007 Production of highly knotted DNA by means of cosmid circularization inside phage capsids BMC Biotechnol. 7 94
45. Orlandini E, Stella A L, Vanderzande C and Zonta F 2008 Slow topological time scale of knotted polymers J. Phys. A: Math. Theor. 41 122002
46. Rouse P E 1953 A theory of the linear viscoelastic properties of dilute solutions of coiling polymers J. Chem. Phys. 21 1272-80
47. de Gennes P-G 1979 Scaling Concepts in Polymer Physics (Ithaca, NY: Cornell University Press)
48. Shusterman R, Alon R S, Gavrinyov T and Krichevsky O 2004 Monomer dynamics in double- and single-stranded DNA polymers Phys. Rev. Lett. 92 048303
49. Downey J P, Crabb C C and Kovac J 1986 Dynamics of a face-centered cubic lattice model for polymer chains Macromolecules 19 2202-6
50. Metzler R, Reisner W, Riehn R, Austin R, Tegenfeldt J and Sokolov I M 2006 Diffusion mechanisms of localised knots along a polymer Europhys. Lett. 76 696-702
51. Stasiak A, Katrich V, Bednar J, Michoud D and Dubochet J 1996 Electrophoretic mobility of DNA knots Nature 384 122
52. Rawdon E J, Dobay A, Kern J, Millett K, Piatek M, Plunkett P and Stasiak A 2008 Scaling behavior and equilibrium lengths of knotted polymers Macromolecules 41 4444-51
53. Obukhov S P, Rubinstein M and Duke T 1994 Dynamics of a ring polymer in a gel Phys. Rev. Lett. 73 1263-6
54. Orlandini E, Stella A L and Vanderzande C (in preparation)
55. Marko J 1999 Coupling of intramolecular and intermolecular linkage complexity of two DNAs Phys. Rev. E 59 900-12
56. Burnier Y, Dorier J and Stasiak A 2008 DNA supercoiling inhibits DNA knotting Nucl. Acid. Res. 36 4956-63
57. Bao X R, Lee H J and Quake S R 2003 Behavior of complex knots in single DNA molecules Phys. Rev. Lett. 91 265506
58. Huang L and Makarov D E 2007 Langevin dynamics simulations of the diffusion of molecular knots in tensioned polymer chains J. Phys. Chem. A 111 10338-44
59. Vologodskii A 2006 Brownian dynamics simulation of knot diffusion along a stretched DNA molecule Biophys. J. 90 1594-97
60. Grosberg A Y and Rabin Y 2007 Metastable tight knots in a wormlike polymer Phys. Rev. Lett. 99 217801