Semiflexible polymer rings whose bonds obey both angular and dihedral restrictions [M. Dolgushev and A. Blumen, J. Chem. Phys. 138, 204902 (2013)], are treated under exact closure constraints. This allows us to obtain semianalytic results for their dynamics, based on sets of Langevin equations. The dihedral restrictions clearly manifest themselves in the behavior of the mean-square monomer displacement. The determination of the equilibrium ring conformations shows that the dihedral constraints influence the ring curvature, leading to compact folded structures. The method for imposing such constraints in Gaussian systems is very general and it allows to account for heterogeneous (site-dependent) restrictions. We show it by considering rings in which one site differs from the others.
REFERENCES
1.
M.
Bixon
and R.
Zwanzig
, J. Chem. Phys.
68
, 1896
(1978
).2.
A.
Perico
and M.
Guenza
, J. Chem. Phys.
84
, 510
(1986
).3.
M.
Guenza
and A.
Perico
, Macromolecules
25
, 5942
(1992
).4.
R. G.
Winkler
, P.
Reineker
, and L.
Harnau
, J. Chem. Phys.
101
, 8119
(1994
).5.
B.-Y.
Ha
and D.
Thirumalai
, J. Chem. Phys.
103
, 9408
(1995
).6.
L.
Harnau
, R. G.
Winkler
, and P.
Reineker
, J. Chem. Phys.
106
, 2469
(1997
).7.
J. J.
Portman
, S.
Takada
, and P. G.
Wolynes
, J. Chem. Phys.
114
, 5069
(2001
).8.
M. G.
Guenza
, J. Phys.: Condens. Matter
20
, 033101
(2008
).9.
M.
Dolgushev
and A.
Blumen
, J. Chem. Phys.
131
, 044905
(2009
).10.
R. G.
Winkler
, J. Chem. Phys.
133
, 164905
(2010
).11.
G. T.
Barkema
and J. M. J.
van Leeuwen
, J. Stat. Mech.
2012
, P12019
.12.
A.
Kumar
, G. J.
Rai
, and P.
Biswas
, J. Chem. Phys.
138
, 104902
(2013
).13.
R. D.
Groot
, J. Chem. Phys.
138
, 224903
(2013
).14.
D. T.
Seaton
, S.
Schnabel
, D. P.
Landau
, and M.
Bachmann
, Phys. Rev. Lett.
110
, 028103
(2013
).15.
Y.
Jiang
and J. Z. Y.
Chen
, Phys. Rev. Lett.
110
, 138305
(2013
).16.
C.
Bustamante
, J. F.
Marco
, E. D.
Siggia
, and S.
Smith
, Science
265
, 1599
(1994
).17.
J.
Käs
, H.
Strey
, J. X.
Tang
, D.
Finger
, R.
Ezzel
, E.
Sackmann
, and P. A.
Janmey
, Biophys. J.
70
, 609
(1996
).18.
R.
Götter
, K.
Kroy
, E.
Frey
, M.
Bärmann
, and E.
Sackmann
, Macromolecules
29
, 30
(1996
).19.
M.
Dolgushev
and A.
Blumen
, J. Chem. Phys.
132
, 124905
(2010
).20.
M.
Dolgushev
, G.
Berezovska
, and A.
Blumen
, J. Chem. Phys.
133
, 154905
(2010
).21.
M.
Dolgushev
, G.
Berezovska
, and A.
Blumen
, Macromol. Theory Simul.
20
, 621
(2011
).22.
F.
Fürstenberg
, M.
Dolgushev
, and A.
Blumen
, J. Chem. Phys.
136
, 154904
(2012
).23.
F.
Fürstenberg
, M.
Dolgushev
, and A.
Blumen
, J. Chem. Phys.
138
, 034904
(2013
).24.
A. A.
Gurtovenko
and A.
Blumen
, Adv. Polym. Sci.
182
, 171
(2005
).25.
P. J.
Flory
, Statistical Mechanics of Chain Molecules
(Oxford University Press
, New York
, 1988
).26.
A.
Korkut
and W. A.
Hendrickson
, Proc. Natl. Acad. Sci. U.S.A.
106
, 15667
(2009
).27.
A.
Altis
, M.
Otten
, P. H.
Nguyen
, R.
Hegger
, and G.
Stock
, J. Chem. Phys.
128
, 245102
(2008
).28.
M.
Dolgushev
and A.
Blumen
, J. Chem. Phys.
138
, 204902
(2013
).29.
M.
Trabi
and D. J.
Craik
, Trends Biochem. Sci.
27
, 132
(2002
).30.
K.
Alim
and E.
Frey
, Phys. Rev. Lett.
99
, 198102
(2007
).31.
Z.
Benková
and P.
Cifra
, Macromolecules
45
, 2597
(2012
).32.
W.
Chen
, J.
Chen
, L.
Liu
, X.
Xu
, and L.
An
, Macromolecules
46
, 7542
(2013
).33.
M.
Dolgushev
, G.
Berezovska
, and A.
Blumen
, J. Chem. Phys.
135
, 094901
(2011
).34.
A. Y.
Grosberg
, Macromolecules
41
, 4524
(2008
).35.
36.
M. L.
Eaton
, Multivariate Statistics: A Vector Space Approach
(Institute of Mathematical Statistics
, Beachwood, OH
, 1983
), Vol. 53
.37.
T.
Guérin
, O.
Bénichou
, and R.
Voituriez
, Nat. Chem.
4
, 568
(2012
).38.
T.
Guérin
, O.
Bénichou
, and R.
Voituriez
, J. Chem. Phys.
138
, 094908
(2013
).39.
T.
Guérin
, O.
Bénichou
, and R.
Voituriez
, Phys. Rev. E
87
, 032601
(2013
).40.
41.
G.
Witz
, K.
Rechendorff
, J.
Adamcik
, and G.
Dietler
, Phys. Rev. Lett.
101
, 148103
(2008
).42.
D.
Kawaguchi
, Polym. J.
45
, 783
(2013
).43.
F.
Amblard
, A. C.
Maggs
, B.
Yurke
, A. N.
Pergellis
, and S.
Leibler
, Phys. Rev. Lett.
77
, 4470
(1996
).44.
E. T.
Jaynes
, Phys. Rev.
106
, 620
(1957
).45.
46.
J. M.
Ziman
, Principles of the Theory of Solids
(Cambridge University Press
, London
, 1972
).47.
See supplementary material at http://dx.doi.org/10.1063/1.4885445 for the detailed calculations.
48.
M.
Doi
and S. F.
Edwards
, The Theory of Polymer Dynamics
(Clarendon Press
, Oxford
, 1986
).49.
A. Y.
Grosberg
and A. R.
Khokhlov
, Statistical Physics of Macromolecules
(American Institute of Physics
, New York
, 1994
).50.
N.
Biggs
, Algebraic Graph Theory
, 2nd ed. (Cambridge University Press
, Cambridge
, 1993
).51.
V.
Bloomfield
and B. H.
Zimm
, J. Chem. Phys.
44
, 315
(1966
).52.
A. J.
Chompff
, J. Chem. Phys.
53
, 1566
(1970
).53.
C.
Satmarel
, A. A.
Gurtovenko
, and A.
Blumen
, Macromolecules
36
, 486
(2003
).54.
G.
Tsolou
, N.
Stratikis
, C.
Baig
, P. S.
Stephanou
, and V. G.
Mavrantzas
, Macromolecules
43
, 10692
(2010
).55.
H.
Schiessel
, Phys. Rev. E
57
, 5775
(1998
).56.
P.
Biswas
, R.
Kant
, and A.
Blumen
, Macromol. Theory Simul.
9
, 56
(2000
).57.
O. G.
Berg
, Biopolymers
18
, 2861
(1979
).58.
B. H.
Zimm
and W. H.
Stockmayer
, J. Chem. Phys.
17
, 1301
(1949
).59.
A.
Baumgärtner
, J. Chem. Phys.
76
, 4275
(1982
).60.
W. C.
Forsman
and R. E.
Hughes
, J. Chem. Phys.
38
, 2118
(1963
).61.
W. H.
Press
, S. A.
Teukolski
, W. T.
Vetterling
, and B. P.
Flannery
, Numerical Recipes in Fortran 77
, 2nd ed. (Cambridge University Press
, New York
, 2003
).62.
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