Effects of topological constraints on linked ring polymers in solvents of varying quality.

We investigate the effects of topological constraints in catenanes composed of interlinked ring polymers on their size in a good solvent as well as on the location of their θ-point when the solvent quality is worsened. We mainly focus on poly[n]catenanes consisting of n ring polymers each of length m interlocked in a linear fashion. Using molecular dynamics simulations, we study the scaling of the poly[n]catenane's radius of gyration in a good solvent, assuming in general that Rg ∼ mμnν and we find that μ = 0.65 ± 0.02 and ν = 0.60 ± 0.01 for the range of n and m considered. These findings are further rationalized with the help of a mean-field Flory-like theory yielding the values of μ = 16/25 and ν = 3/5, consistent with the numerical results. We show that individual rings within catenanes feature a surplus swelling due to the presence of NL topological links. Furthermore, we consider poly[n]catenanes in solvents of varying quality and we demonstrate that the presence of topological links leads to an increase of its θ-temperature in comparison to isolated linear and ring chains with the following ordering: Tθcatenane > Tθlinear > Tθring. Finally, we show that the presence of links similarly raises the θ-temperature of a single linked ring in comparison to an unlinked one, bringing its θ-temperature close to the one of a poly[n]catenane.

[1]  K. Kremer,et al.  Threading of Unconcatenated Ring Polymers at High Concentrations: Double-Folded vs Time-Equilibrated Structures , 2019, ACS macro letters.

[2]  A. Grosberg,et al.  Minimal Surfaces on Unconcatenated Polymer Rings in Melt. , 2016, ACS macro letters.

[3]  C. Micheletti,et al.  Mechanical Pulling of Linked Ring Polymers: Elastic Response and Link Localisation , 2017, Polymers.

[4]  J. M. Deutsch.  Equilibrium size of large ring molecules , 1999 .

[5]  Davide Michieletto,et al.  A topologically driven glass in ring polymers , 2015, Proceedings of the National Academy of Sciences.

[6]  B. Eslami-Mossallam,et al.  Stiffer double-stranded DNA in two-dimensional confinement due to bending anisotropy. , 2016, Physical review. E.

[7]  J. Fischer,et al.  The formation and structure of Olympic gels. , 2015, The Journal of chemical physics.

[8]  M. Werner,et al.  Swelling of Olympic gels. , 2014, Physical review letters.

[9]  Alexander Vologodskii,et al.  Simulation of DNA catenanes. , 2009, Physical chemistry chemical physics : PCCP.

[10]  Sundus Erbas-Cakmak,et al.  Artificial Molecular Machines , 2015, Chemical reviews.

[11]  Yuen A. Lau,et al.  Mechanised nanoparticles for drug delivery. , 2009, Nanoscale.

[12]  A. V. Lukashin,et al.  Statistical mechanics and topology of polymer chains , 1975, Nature.

[13]  William H. Press,et al.  Numerical Recipes 3rd Edition: The Art of Scientific Computing , 2007 .

[14]  W. Köhler,et al.  Poly[2]catenanes and cyclic oligo[2] catenanes containing alternating topological and covalent bonds: Synthesis and characterization , 1999 .

[15]  Christos N. Likos,et al.  Topology-Sensitive Microfluidic Filter for Polymers of Varying Stiffness. , 2017, ACS macro letters.

[16]  C. N. Likos,et al.  Effects of Knots on Ring Polymers in Solvents of Varying Quality , 2013, Macromolecules.

[17]  C. Micheletti,et al.  Numerical Study of Linear and Circular Model DNA Chains Confined in a Slit: Metric and Topological Properties , 2012, 1204.1983.

[18]  E. Wasserman,et al.  THE PREPARATION OF INTERLOCKING RINGS: A CATENANE1 , 1960 .

[19]  Enzo Orlandini,et al.  Linking of Ring Polymers in Slit-Like Confinement , 2017 .

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

[21]  B. Eslami-Mossallam,et al.  Extreme bendability of DNA double helix due to bending asymmetry. , 2015, The Journal of chemical physics.

[22]  David A Leigh,et al.  Catenanes: Fifty Years of Molecular Links , 2015, Angewandte Chemie.

[23]  C. Han,et al.  Computer simulation of linkage of two ring chains. , 2012, The Journal of chemical physics.

[24]  C. N. Likos,et al.  Influence of topology on effective potentials: coarse-graining ring polymers , 2010 .

[25]  Anne-Sophie Duwez,et al.  Probing the mobility of catenane rings in single molecules , 2014 .

[26]  Michael Famulok,et al.  Interlocked DNA nanostructures controlled by a reversible logic circuit , 2014, Nature Communications.

[27]  Stuart J. Rowan,et al.  Poly[n]catenanes: Synthesis of molecular interlocked chains , 2017, Science.

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

[29]  N. Cozzarelli,et al.  Biochemical topology: applications to DNA recombination and replication. , 1986, Science.

[30]  Stuart J. Rowan,et al.  Topological Effects in Isolated Poly[n]catenanes: Molecular Dynamics Simulations and Rouse Mode Analysis. , 2018, ACS macro letters.

[31]  W. Goddard,et al.  Effect of cyclic chain architecture on properties of dilute solutions of polyethylene from molecular dynamics simulations , 2003 .

[32]  Kurt Kremer,et al.  Active topological glass , 2020, Nature Communications.

[33]  Itamar Willner,et al.  A polycatenated DNA scaffold for the one-step assembly of hierarchical nanostructures , 2008, Proceedings of the National Academy of Sciences.

[34]  C. N. Likos,et al.  Architecture-Induced Size Asymmetry and Effective Interactions of Ring Polymers: Simulation and Theory , 2013, Macromolecules.

[35]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[36]  Hao Zhang,et al.  Topoisomerase-Based Preparation and AFM Imaging of Multi-Interlocked Circular DNA. , 2016, Bioconjugate chemistry.

[37]  C. Micheletti,et al.  Hydrodynamics and Filtering of Knotted Ring Polymers in Nanochannels , 2019, Macromolecules.

[38]  Itamar Willner,et al.  Recent Advances in the Synthesis and Functions of Reconfigurable Interlocked DNA Nanostructures. , 2016, Journal of the American Chemical Society.

[39]  Sharon C. Glotzer,et al.  Efficient neighbor list calculation for molecular simulation of colloidal systems using graphics processing units , 2016, Comput. Phys. Commun..

[40]  B. Eslami-Mossallam,et al.  Stretching an anisotropic DNA. , 2008, The Journal of chemical physics.

[41]  Grosberg.  Critical exponents for random knots , 1999, Physical review letters.

[42]  D Richter,et al.  Unexpected power-law stress relaxation of entangled ring polymers. , 2008, Nature materials.

[43]  C. N. Likos,et al.  Effective interactions of knotted ring polymers. , 2013, Biochemical Society transactions.

[44]  Nahum Shiffeldrim,et al.  Cyclization of short DNA fragments and bending fluctuations of the double helix. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[45]  Kurt Kremer,et al.  From a melt of rings to chromosome territories: the role of topological constraints in genome folding , 2013, Reports on progress in physics. Physical Society.

[46]  Glassiness and Heterogeneous Dynamics in Dense Solutions of Ring Polymers. , 2017, Physical review letters.

[47]  T. Pakula,et al.  Simulation of Single Complex Macromolecules. 1. Structure and Dynamics of Catenanes , 1999 .

[48]  I. Willner,et al.  Switchable Reconfiguration of a Seven-Ring Interlocked DNA Catenane Nanostructure. , 2015, Nano letters.

[49]  Iurii Chubak,et al.  Ring polymers are much stronger depleting agents than linear ones , 2018, Molecular Physics.

[50]  C. Micheletti,et al.  Self-assembly of knots and links , 2017 .

[51]  Jean-Pierre Sauvage,et al.  Templated synthesis of interlocked macrocyclic ligands, the catenands. Preparation and characterization of the prototypical bis-30 membered ring system , 1990 .

[52]  Thomas E. Gartner,et al.  Scaling Exponent and Effective Interactions in Linear and Cyclic Polymer Solutions: Theory, Simulations, and Experiments , 2019, Macromolecules.

[53]  H. Schiessel,et al.  Molecular Dynamics Simulation of Supercoiled DNA Rings , 2015 .

[54]  C. Dorman.  DNA supercoiling and transcription in bacteria: a two-way street , 2019, BMC Molecular and Cell Biology.

[55]  Pak Lui,et al.  Strong scaling of general-purpose molecular dynamics simulations on GPUs , 2014, Comput. Phys. Commun..

[56]  Dieter W Heermann,et al.  Topological interactions between ring polymers: Implications for chromatin loops. , 2010, The Journal of chemical physics.

[57]  J. Vinograd,et al.  Catenated Circular DNA Molecules in HeLa Cell Mitochondria , 1967, Nature.

[58]  Nicholas R Cozzarelli,et al.  The topology of the kinetoplast DNA network , 1995, Cell.

[59]  R. Blaak,et al.  Star Polymers in Solvents of Varying Quality , 2009 .

[60]  Zhen‐Gang Wang,et al.  The scaling behavior of the second virial coefficient of linear and ring polymer , 2016, Science China Chemistry.

[61]  J. Arsuaga,et al.  The effect of volume exclusion on the formation of DNA minicircle networks: implications to kinetoplast DNA , 2015 .

[62]  Christos N. Likos,et al.  Trefoil Knot Hydrodynamic Delocalization on Sheared Ring Polymers. , 2018, ACS macro letters.

[63]  J. D. Cloizeaux.  Ring polymers in solution : topological effects , 1981 .

[64]  K. Robeyns,et al.  Catenane-based mechanically-linked block copolymers. , 2016, Chemical communications.

[65]  T. C. B. McLeish,et al.  Polymer Physics , 2009, Encyclopedia of Complexity and Systems Science.