How molecular knots can pass through each other

Significance We suggest and explain a mechanism in which two molecular knots on a DNA strand can pass through each other and swap positions along the strand: One of the two knots expands in size and the other diffuses along the contour of the former. This peculiar mechanism, which only requires a few kBT, is not only interesting from an aesthetic point of view but may also play a role in future technological applications such as nanopore sequencing once strand sizes exceed 100,000 base pairs. We propose a mechanism in which two molecular knots pass through each other and swap positions along a polymer strand. Associated free energy barriers in our simulations only amount to a few kBT, which may enable the interchange of knots on a single DNA strand.

[1]  A. Marco Saitta,et al.  Influence of a knot on the strength of a polymer strand , 1999, Nature.

[2]  Peter Virnau,et al.  Detection and visualization of physical knots in macromolecules , 2010 .

[3]  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.

[4]  Joshua A. Anderson,et al.  General purpose molecular dynamics simulations fully implemented on graphics processing units , 2008, J. Comput. Phys..

[5]  D. Branton,et al.  The potential and challenges of nanopore sequencing , 2008, Nature Biotechnology.

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

[7]  T Koller,et al.  Duplex DNA knots produced by Escherichia coli topoisomerase I. Structure and requirements for formation. , 1985, The Journal of biological chemistry.

[8]  Rhonald C. Lua,et al.  Statistics of Knots, Geometry of Conformations, and Evolution of Proteins , 2006, PLoS Comput. Biol..

[9]  S. TOLVER PRESTON,et al.  Vortex Atoms , 1880, Nature.

[10]  C Micheletti,et al.  Topological jamming of spontaneously knotted polyelectrolyte chains driven through a nanopore. , 2012, Physical review letters.

[11]  Marc L. Mansfield,et al.  Are there knots in proteins? , 1994, Nature Structural Biology.

[12]  Sir William Thomson F.R.S..  II. On vortex atoms , 1867 .

[13]  Hiroyuki Hori,et al.  Deep knot structure for construction of active site and cofactor binding site of tRNA modification enzyme. , 2004, Structure.

[14]  Peter Virnau,et al.  Structures and folding pathways of topologically knotted proteins , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[15]  Chung-Cheng Liu,et al.  Type II DNA topoisomerases: Enzymes that can unknot a topologically knotted DNA molecule via a reversible double-strand break , 1980, Cell.

[16]  E. Peterman,et al.  Quantifying how DNA stretches, melts and changes twist under tension , 2011 .

[17]  Javier Arsuaga,et al.  DNA knots reveal a chiral organization of DNA in phage capsids. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Lukasz Goldschmidt,et al.  Structure and folding of a designed knotted protein , 2010, Proceedings of the National Academy of Sciences.

[19]  Kurt Kremer,et al.  Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. II. Dynamics. , 2011, The Journal of chemical physics.

[20]  A. Marco Saitta,et al.  Polyethylene under tensil load: Strain energy storage and breaking of linear and knotted alkanes probed by first-principles molecular dynamics calculations , 1999 .

[21]  Daniel Reith,et al.  Effective stiffening of DNA due to nematic ordering causes DNA molecules packed in phage capsids to preferentially form torus knots , 2012, Nucleic acids research.

[22]  Richard Matthews,et al.  Knot-controlled ejection of a polymer from a virus capsid. , 2009, Physical review letters.

[23]  C Micheletti,et al.  Biopolymer organization upon confinement , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[24]  Joanna I. Sulkowska,et al.  A Stevedore's Protein Knot , 2010, PLoS Comput. Biol..

[25]  Raffaello Potestio,et al.  Knotted vs. Unknotted Proteins: Evidence of Knot-Promoting Loops , 2010, PLoS Comput. Biol..

[26]  Stephen R Quake,et al.  Behavior of complex knots in single DNA molecules. , 2003, Physical review letters.

[27]  Peter Virnau,et al.  Knots in globule and coil phases of a model polyethylene. , 2005, Journal of the American Chemical Society.

[28]  Alexander Vologodskii,et al.  Brownian dynamics simulation of knot diffusion along a stretched DNA molecule. , 2006, Biophysical journal.

[29]  William R. Taylor,et al.  A deeply knotted protein structure and how it might fold , 2000, Nature.

[30]  Piotr Sułkowski,et al.  Dodging the crisis of folding proteins with knots , 2009, Proceedings of the National Academy of Sciences.

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

[32]  Kurt Kremer,et al.  Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics. , 2011, The Journal of chemical physics.

[33]  Davide Marenduzzo,et al.  Thermodynamics of DNA packaging inside a viral capsid: the role of DNA intrinsic thickness. , 2003, Journal of molecular biology.

[34]  M. Vázquez,et al.  Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids , 2002, Proceedings of the National Academy of Sciences of the United States of America.