How molecular knots can pass through each other

Proceedings of the National Academy of Sciences of the United States of America

Volumn 111, Issue 22, 2014, Pages 7948-7951

  Trefz, Benjamin ^a   Siebert, Jonathan ^a   Virnau, Peter ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

Diffusion; Molecular dynamics

Indexed keywords

DNA; MONOMER; POLYMER;

ARTICLE; DIFFUSION; DNA STRAND; MATHEMATICAL MODEL; MOLECULAR BIOLOGY; MOLECULAR DYNAMICS; MOLECULAR KNOTS; PRIORITY JOURNAL;

DIFFUSION; MOLECULAR DYNAMICS;

COMPUTERS; DIFFUSION; DNA; MODELS, MOLECULAR; NANOSTRUCTURES; NUCLEIC ACID CONFORMATION; POLYMERS; THERMODYNAMICS;

EID: 84901820972     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1319376111     Document Type: Article

References (33)

1. Thompson W (1867) On vortex atoms. Philos Mag 34:15-24.
2. Mansfield ML (1994) Are there knots in proteins? Nat Struct Biol 1(4):213-214.
3. Taylor WR (2000) A deeply knotted protein structure and how it might fold. Nature 406(6798):916-919.
4. Lua RC, Grosberg AY (2006) Statistics of knots, geometry of conformations, and evolution of proteins. PLOS Comput Biol 2(5):e45.
5. Virnau P, Mallam A, Jackson S (2011) Structures and folding pathways of topologically knotted proteins. J Phys Condens Matter 23(3):033101.
6. Potestio R, Micheletti C, Orland H (2010) Knotted vs. unknotted proteins: Evidence of knot-promoting loops. PLOS Comput Biol 6(7):e1000864.
7. Bölinger D, et al. (2010) A Stevedore's protein knot. PLOS Comput Biol 6(4):e1000731.
8. Nureki O, et al. (2004) Deep knot structure for construction of active site and cofactor binding site of tRNA modification enzyme. Structure 12(4):593-602. (Pubitemid 38447162)
9. King NP, Jacobitz AW, Sawaya MR, Goldschmidt L, Yeates TO (2010) Structure and folding of a designed knotted protein. Proc Natl Acad Sci USA 107(48):20732-20737.
10. Liu LF, Liu CC, Alberts BM (1980) Type II DNA topoisomerases: Enzymes that can unknot a topologically knotted DNA molecule via a reversible double-strand break. Cell 19(3):697-707. (Pubitemid 10134849)
11. Dean FB, Stasiak A, Koller T, Cozzarelli NR (1985) Duplex DNA knots produced by Escherichia coli topoisomerase I. Structure and requirements for formation. J Biol Chem 260(8):4975-4983. (Pubitemid 15038693)
12. Arsuaga J, Vázquez M, Trigueros S, Sumners DW, Roca J (2002) Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids. Proc Natl Acad Sci USA 99(8):5373-5377. (Pubitemid 34411555)
13. Marenduzzo D, Micheletti C, Orlandini E (2010) Biopolymer organization upon confinement. J Phys Condens Matter 22(28):283102.
14. Arsuaga J, et al. (2005) DNA knots reveal a chiral organization of DNA in phage capsids. Proc Natl Acad Sci USA 102(26):9165-9169. (Pubitemid 40923535)
15. Marenduzzo D, Micheletti C (2003) Thermodynamics of DNA packaging inside a viral capsid: The role of DNA intrinsic thickness. J Mol Biol 330(3):485-492. (Pubitemid 36808682)
16. Reith D, Cifra P, Stasiak A, Virnau P (2012) Effective stiffening of DNA due to nematic ordering causes DNA molecules packed in phage capsids to preferentially form torus knots. Nucleic Acids Res 40(11):5129-5137.
17. Bao XR, Lee HJ, Quake SR (2003) Behavior of complex knots in single DNA molecules. Phys Rev Lett 91(26 Pt 1):265506.
18. Vologodskii A (2006) Brownian dynamics simulation of knot diffusion along a stretched DNA molecule. Biophys J 90(5):1594-1597.
19. Saitta AM, Soper PD, Wasserman E, Klein ML (1999) Influence of a knot on the strength of a polymer strand. Nature 399(6731):46-48.
20. Saitta MA, Klein ML (1999) Polyethylene under tensil load: Strain energy storage and breaking of linear and knotted alkanes probed by first-principles molecular dynamics calculations. J Chem Phys 111(20):9434-9440.
21. Millett KC, Rawdon EJ, Stasiak A, Sułkowska JI (2013) Identifying knots in proteins. Biochem Soc Trans 41(2):533-537.
22. Matthews R, Louis AA, Yeomans JM (2009) Knot-controlled ejection of a polymer from a virus capsid. Phys Rev Lett 102(8):088101.
23. Sułkowska JI, Sułkowski P, Onuchic J (2009) Dodging the crisis of folding proteins with knots. Proc Natl Acad Sci USA 106(9):3119-3124.
24. Branton D, et al. (2008) The potential and challenges of nanopore sequencing. Nat Biotechnol 26(10):1146-1153.
25. Rybenkov VV, Cozzarelli NR, Vologodskii AV (1993) Probability of DNA knotting and the effective diameter of the DNA double helix. Proc Natl Acad Sci USA 90(11): 5307-5311. (Pubitemid 23183027)
26. Shaw SY, Wang JC (1993) Knotting of a DNA chain during ring closure. Science 260(5107):533-536. (Pubitemid 23161616)
27. Rosa A, Di Ventra M, Micheletti C (2012) Topological jamming of spontaneously knotted polyelectrolyte chains driven through a nanopore. Phys Rev Lett 109(11): 118301.
28. Halverson JD, Lee WB, Grest GS, Grosberg AY, Kremer K (2011) Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics. J Chem Phys 134(20):204904.
29. Anderson JA, Lorenz CD, Travesset A (2008) General purpose molecular dynamics simulations fully implemented on graphics processing units. J Comput Phys 227(10): 5342-5359.
30. Virnau P (2010) Detection and visualization of physical knots in macromolecules. Physics Procedia 6:117-125.
31. Virnau P, Kantor Y, Kardar M (2005) Knots in globule and coil phases of a model polyethylene. J Am Chem Soc 127(43):15102-15106. (Pubitemid 41547376)
32. Vologodskii AV, Anshelevich VV, Lukashin AV, Frank-Kamenetskii MD (1979) Statistical mechanics of supercoils and the torsional stiffness of the DNA double helix. Nature 280(5720):294-298. (Pubitemid 10199170)
33. Gross P, et al. (2011) Quantifying how DNA stretches, melts and changes twist under tension. Nat Phys 7(9):731-736.