Abstract.
The conformations of topologically constrained double-folded ring polymers can be described as wrappings of randomly branched primitive trees. We extend previous work on the tree statistics under different (solvent) conditions to explore the conformational statistics of double-folded rings in the limit of tight wrapping. In particular, we relate the exponents characterizing the ring statistics to those describing the primitive trees and discuss the distribution functions \(p(\overrightarrow{r}\vert\ell)\) and \(p(L\vert\ell)\) for the spatial distance, \(\overrightarrow{r}\), and tree contour distance, L, between monomers as a function of their ring contour distance, \(\ell\).
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References
A.R. Khokhlov, S.K. Nechaev, Phys. Lett. A 112, 156 (1985)
M. Rubinstein, Phys. Rev. Lett. 57, 3023 (1986)
S.P. Obukhov, M. Rubinstein, T. Duke, Phys. Rev. Lett. 73, 1263 (1994)
A.Y. Grosberg, Soft Matter 10, 560 (2014)
A. Rosa, R. Everaers, Phys. Rev. Lett. 112, 118302 (2014)
J. Smrek, A.Y. Grosberg, J. Phys.: Condens. Matter 27, 064117 (2015)
D. Michieletto, Soft Matter 12, 9485 (2016)
B. Alberts, Molecular Biology of the Cell, 5th edition (Garland Science, New York, 2007)
M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, New York, 1986).
A.Y. Grosberg, A.R. Khokhlov, Statistical Physics of Macromolecules (AIP Press, New York, 1994)
M. Rubinstein, R.H. Colby, Polymer Physics (Oxford University Press, New York, 2003)
J. Isaacson, T.C. Lubensky, J. Phys. (Paris) Lett. 41, L469 (1980)
M. Daoud, J.F. Joanny, J. Phys. (Paris) 42, 1359 (1981)
A.M. Gutin, A.Y. Grosberg, E.I. Shakhnovich, Macromolecules 26, 1293 (1993)
R. Everaers, A.Y. Grosberg, M. Rubinstein, A. Rosa, Soft Matter 13, 1223 (2017)
B.H. Zimm, W.H. Stockmayer, J. Chem. Phys. 17, 1301 (1949)
P.-G. De Gennes, Biopolymers 6, 715 (1968)
G. Parisi, N. Sourlas, Phys. Rev. Lett. 46, 871 (1981)
A. Rosa, R. Everaers, Phys. Rev. E 95, 012117 (2017)
A. Rosa, R. Everaers, J. Phys. A: Math. Theor. 49, 345001 (2016)
A. Rosa, R. Everaers, J. Chem. Phys. 145, 164906 (2016)
M. Kapnistos et al., Nat. Mater. 7, 997 (2008)
D. Michieletto, D. Marenduzzo, E. Orlandini, M.S. Turner, Polymers 9, 349 (2017)
M.E. Cates, J.M. Deutsch, J. Phys. (Paris) 47, 2121 (1986)
T. Ge, S. Panyukov, M. Rubinstein, Macromolecules 49, 708 (2016)
A. Grosberg, Y. Rabin, S. Havlin, A. Neer, Europhys. Lett. 23, 373 (1993)
A. Rosa, R. Everaers, Plos Comput. Biol. 4, e1000153 (2008)
T. Vettorel, A.Y. Grosberg, K. Kremer, Phys. Biol. 6, 025013 (2009)
L.A. Mirny, Chromosome Res. 19, 37 (2011)
M. Lang, Macromolecules 46, 1158 (2013)
J. Smrek, A.Y. Grosberg, ACS Macro Lett. 5, 750 (2016)
E.J. Janse van Rensburg, N. Madras, J. Phys. A: Math. Gen. 25, 303 (1992)
S. Redner, J. Phys. A: Math. Gen. 13, 3525 (1980)
J. des Cloizeaux, G. Jannink, Polymers in Solution (Oxford University Press, Oxford, 1989)
M.E. Fisher, J. Chem. Phys. 44, 616 (1966)
P. Pincus, Macromolecules 9, 386 (1976)
O. Kratky, G. Porod, Recl. Trav. Chim. Pays-Bas 68, 1106 (1949)
J.P. Wittmer, H. Meyer, J. Baschnagel, A. Johner, S. Obukhov, L. Mattioni, M. Müller, A.N. Semenov, Phys. Rev. Lett. 93, 147801 (2004)
W.A. Seitz, D.J. Klein, J. Chem. Phys. 75, 5190 (1981)
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.F. Flannery, Numerical Recipes in Fortran, 2nd edition (Cambridge University Press, Cambridge, 1992)
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Rosa, A., Everaers, R. Conformational statistics of randomly branching double-folded ring polymers. Eur. Phys. J. E 42, 7 (2019). https://doi.org/10.1140/epje/i2019-11765-3
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DOI: https://doi.org/10.1140/epje/i2019-11765-3