Gaussian semiflexible rings under angular and dihedral restrictions.

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.

[1]  L. An,et al.  Effects of Chain Stiffness on Conformational and Dynamical Properties of Individual Ring Polymers in Shear Flow , 2013 .

[2]  D. Kawaguchi.  Direct observation and mutual diffusion of cyclic polymers , 2013 .

[3]  M. Dolgushev,et al.  Dynamics of discrete semiflexible chains under dihedral constraints: analytic results. , 2013, The Journal of chemical physics.

[4]  R. D. Groot.  Mesoscale simulation of semiflexible chains. I. Endpoint distribution and chain dynamics. , 2013, The Journal of chemical physics.

[5]  Ying Jiang,et al.  Influence of chain rigidity on the phase behavior of wormlike diblock copolymers. , 2013, Physical review letters.

[6]  Amit Kumar,et al.  Conformation and intramolecular relaxation dynamics of semiflexible randomly hyperbranched polymers. , 2013, The Journal of chemical physics.

[7]  Maxim Dolgushev,et al.  Dynamics of semiflexible regular hyperbranched polymers. , 2013, The Journal of chemical physics.

[8]  Daniel T. Seaton,et al.  From flexible to stiff: systematic analysis of structural phases for single semiflexible polymers. , 2013, Physical review letters.

[9]  O Bénichou,et al.  Reactive conformations and non-Markovian cyclization kinetics of a Rouse polymer. , 2012, The Journal of chemical physics.

[10]  R. Voituriez,et al.  Reactive conformations and non-Markovian reaction kinetics of a Rouse polymer searching for a target in confinement , 2012, 1210.5871.

[11]  G. Barkema,et al.  A model for the dynamics of extensible semiflexible polymers , 2012, 1212.0339.

[12]  O Bénichou,et al.  Non-Markovian polymer reaction kinetics. , 2012, Nature chemistry.

[13]  Maxim Dolgushev,et al.  Analytical model for the dynamics of semiflexible dendritic polymers. , 2012, The Journal of chemical physics.

[14]  P. Cifra,et al.  Simulation of Semiflexible Cyclic and Linear Chains Moderately and Strongly Confined in Nanochannels , 2012 .

[15]  Maxim Dolgushev,et al.  Branched Semiflexible Polymers: Theoretical and Simulation Aspects , 2011 .

[16]  M. Dolgushev,et al.  Maximum entropy principle applied to semiflexible ring polymers. , 2011, The Journal of chemical physics.

[17]  Pavlos S. Stephanou,et al.  Melt Structure and Dynamics of Unentangled Polyethylene Rings: Rouse Theory, Atomistic Molecular Dynamics Simulation, and Comparison with the Linear Analogues , 2010 .

[18]  R. Winkler.  Conformational and rheological properties of semiflexible polymers in shear flow. , 2010, The Journal of chemical physics.

[19]  M. Dolgushev,et al.  Cospectral polymers: Differentiation via semiflexibility. , 2010, The Journal of chemical physics.

[20]  Dynamics of chains and dendrimers with heterogeneous semiflexibility. , 2010, The Journal of chemical physics.

[21]  Wayne A Hendrickson,et al.  A force field for virtual atom molecular mechanics of proteins , 2009, Proceedings of the National Academy of Sciences.

[22]  G. Strobl.  The Physics of Polymers , 2009 .

[23]  Maxim Dolgushev,et al.  Dynamics of semiflexible treelike polymeric networks. , 2009, The Journal of chemical physics.

[24]  Gerhard Stock,et al.  Construction of the free energy landscape of biomolecules via dihedral angle principal component analysis. , 2008, The Journal of chemical physics.

[25]  K. Rechendorff,et al.  Conformation of circular DNA in two dimensions. , 2008, Physical review letters.

[26]  A. Grosberg.  Total Curvature and Total Torsion of a Freely Jointed Circular Polymer with n >> 1 Segments , 2008 .

[27]  Marina Guenza,et al.  Theoretical models for bridging timescales in polymer dynamics , 2008 .

[28]  Erwin Frey,et al.  Shapes of semiflexible polymer rings. , 2007, Physical review letters.

[29]  A. A. Gurtovenko,et al.  Generalized Gaussian Structures: Models for Polymer Systems with ComplexTopologies , 2005 .

[30]  A. Blumen,et al.  Viscoelastic relaxation of cross-linked, alternating copolymers in the free-draining limit , 2003 .

[31]  David J Craik,et al.  Circular proteins--no end in sight. , 2002, Trends in biochemical sciences.

[32]  Shoji Takada,et al.  Microscopic theory of protein folding rates. I. Fine structure of the free energy profile and folding routes from a variational approach , 2000, cond-mat/0008454.

[33]  Alexander Blumen,et al.  Polymer dynamics and topology: extension of stars and dendrimers in external fields , 2000 .

[34]  Helmut Schiessel,et al.  Unfold dynamics of generalized Gaussian structures , 1998 .

[35]  R. Winkler,et al.  Influence of stiffness on the dynamics of macromolecules in a melt , 1997 .

[36]  Maggs,et al.  Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks. , 1996, Physical review letters.

[37]  R Ezzell,et al.  F-actin, a model polymer for semiflexible chains in dilute, semidilute, and liquid crystalline solutions. , 1996, Biophysical journal.

[38]  E. Sackmann,et al.  Dynamic Light Scattering from Semidilute Actin Solutions: A Study of Hydrodynamic Screening, Filament Bending Stiffness, and the Effect of Tropomyosin/Troponin-Binding , 1996 .

[39]  D. Thirumalai,et al.  A MEAN-FIELD MODEL FOR SEMIFLEXIBLE CHAINS , 1995 .

[40]  Roland G. Winkler,et al.  MODELS AND EQUILIBRIUM PROPERTIES OF STIFF MOLECULAR CHAINS , 1994 .

[41]  E. Siggia,et al.  Entropic elasticity of lambda-phage DNA. , 1994, Science.

[42]  H. Stanley,et al.  Statistical physics of macromolecules , 1995 .

[43]  Angelo Perico,et al.  A reduced description of the local dynamics of star polymers , 1992 .

[44]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[45]  A. Perico,et al.  Viscoelastic relaxation of segment orientation in dilute polymer solutions. II. Stiffness dependence of fluorescence depolarization , 1986 .

[46]  A. Baumgärtner.  Statistics of self‐avoiding ring polymers , 1982 .

[47]  O. Berg.  Brownian motion of the wormlike chain and segmental diffusion of DNA , 1979 .

[48]  Robert Zwanzig,et al.  Optimized Rouse–Zimm theory for stiff polymers , 1978 .

[49]  T. J. Rivlin.  The Chebyshev polynomials , 1974 .

[50]  Normal Modes of Branched Polymers. I. Simple Ring and Star‐Shaped Molecules , 1970 .

[51]  M. Volkenstein,et al.  Statistical mechanics of chain molecules , 1970 .

[52]  B. Zimm,et al.  Viscosity, Sedimentation, et Cetera, of Ring- and Straight-Chain Polymers in Dilute Solution , 1966 .

[53]  J. Ziman.  Principles of the Theory of Solids , 1965 .

[54]  R. Hughes,et al.  Radii of Gyration for Random‐Flight Chains , 1963 .

[55]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[56]  Bruno H. Zimm,et al.  The Dimensions of Chain Molecules Containing Branches and Rings , 1949 .