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Coil to globule transition of homo- and block-copolymer with different topological constraint and chain stiffness

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Abstract

In this paper, we present the coil-to-globule (CG) transitions of homopolymers and multiblock copolymers with different topology and stiffness by using molecular dynamics with integrated tempering sampling method. The sampling method was a novel enhanced method that efficiently sampled the energy space with low computational costs. The method proved to be efficient and precise to study the structural transitions of polymer chains with complex topological constraint, which may not be easily done by using conventional Monte Carlo method. The topological constraint affects the globule shape of the polymer chain, thus further influencing the CG transition. We found that increasing the topological constraint generally decreased CG transition temperature for homopolymers. For semiflexible chains, an additional first-order like symmetry-broken transition emerged. For block copolymers, the topological constraint did not obviously change the transition temperature, but greatly reduced the energy signal of the CG transition.

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References

  1. Dulbecco R, Vogt M. Evidence for a ring structure of polyoma virus DNA. Proc Natl Acad Sci USA, 1963, 50: 236–243

    Article  CAS  Google Scholar 

  2. Vinogard J, Lebowitz J. Physical and topological properties of circular DNA. J Gen Physiol, 1966, 49: 103–125

    Article  Google Scholar 

  3. Craik DJ, Daly NL, Bond T, Waine C. Plant cyclotides: a unique family of cyclic and knotted proteins that defines the cyclic cystine knot structural motif. J Mol Biol, 1999, 294: 1327–1336

    Article  CAS  Google Scholar 

  4. Craik DJ, Conibear AC. The chemistry of cyclotides. J Org Chem, 2011, 76: 4805–4817

    Article  CAS  Google Scholar 

  5. Mallam AL, Jackson SE. Folding studies on a knotted protein. J Mol Biol, 2005, 346: 1409–1421

    Article  CAS  Google Scholar 

  6. Hsieh T. Knotting of the circular duplex DNA by type II DNA topoisomerase from Drosophila melanogaster. J Biol Chem, 1983, 258: 8413–8420

    CAS  Google Scholar 

  7. Trigueros S, Roca J. Production of highly knotted DNA by means of cosmid circularization inside phage capsids. BMC Biotechnol, 2007, 7: 94

    Article  Google Scholar 

  8. Oike H. Supramolecular approach for synthesis and functionalization of cyclic macromolecules. React Funct Polym, 2007, 67: 1157–1167

    Article  CAS  Google Scholar 

  9. Jia Z, Monteiro MJ. Cyclic polymers: methods and strategies. J Polym Sci A: Polym Chem, 2012, 50: 2085–2097

    Article  CAS  Google Scholar 

  10. Xiong XQ, Yi C. Application of click chemistry in the synthesis of cyclic polymers. Sci China Chem, 2013, 43: 783–800

    CAS  Google Scholar 

  11. Ohta Y, Kushida Y, Matsushita Y, Takano A. SEC-MALS characterization of cyclization reaction products: formation of knotted ring polymer. Polymer, 2009, 50: 1297–1299

    Article  CAS  Google Scholar 

  12. Ohta Y, Nakamura M, Matsushita Y, Takano A. Synthesis, separation and characterization of knotted ring polymers. Polymer, 2012, 53: 466–470

    Article  CAS  Google Scholar 

  13. Cates ME, Deutsch JM. Conjectures on the statistics of ring polymers. J Phys France, 1986, 47: 2121–2128

    Article  CAS  Google Scholar 

  14. Baiesi M, Orlandini E. Universal properties of knotted polymer rings. Phys Rev E, 2012, 86: 031805

    Article  CAS  Google Scholar 

  15. Rosa A, Orlandini E, Tubiana L, Micheletti C. Structure and dynamics of ring polymers: entanglement effects because of solution density and ring topology. Macromolecules, 2011, 44: 8668–8680

    Article  CAS  Google Scholar 

  16. Rawdon EJ, Kern JC, Piatek M, Plunkett P, Stasiak A, Millett KC. Effect of knotting on the shape of polymers. Macromolecules, 2008, 41: 8281–8287

    Article  CAS  Google Scholar 

  17. Millett KC, Plunkett P, Piatek M, Rawdon EJ, Stasiak A. Effect of knotting on polymer shapes and their enveloping ellipsoids. J Chem Phys, 2009, 130: 165104

    Article  Google Scholar 

  18. Rawdon E, Dobay A, Kern JC, Millett KC, Piatek M, Plunkett P, Stasiak A. Scaling behavior and equilibrium lengths of knotted polymers. Macromolecules, 2008, 41: 4444–4451

    Article  CAS  Google Scholar 

  19. Kanaeda N, Deguchi T. Universality in the diffusion of knots. Phy Rev E, 2009, 79: 021806

    Article  Google Scholar 

  20. Orlandini E, Stella AL, Vanderzande C, Zonta F. Slow topological time scale of knotted polymers. J Phys A Math Theor, 2008, 41: 122002

    Article  Google Scholar 

  21. Narros A, Moreno AJ, Likos CN. Effects of knots on ring polymers in solvents of varying quality. Macromolecules, 2013, 46: 3654–3668

    Article  CAS  Google Scholar 

  22. Chen WD, Chen JZ, Liu LJ, Xu XL, An LJ. Simulation study on conformational and dynamical properties of individual ring polymers in good solution. Sci China Chem, 2014, 44: 320–326

    Article  CAS  Google Scholar 

  23. Ivanov VA, Paul W, Binder K. Finite chain length effects on the coil-globule transition of stiff-chain macromolecules: a Monte Carlo simulation. J Chem Phys, 1998, 109: 5659

    Article  CAS  Google Scholar 

  24. Ivanov VA, Stukan MR, Vasilevskaya VV, Paul W, Binder K. Structures of stiff macromolecules of finite chain length near the coil-globule transition: a Monte Carlo simulation. Macromol Theor Simul, 2000, 9: 488–499

    Article  CAS  Google Scholar 

  25. Bachmann M, Janke W. Thermodynamics of lattice heteropolymers. J Chem Phys, 2004, 120: 6779–6791

    Article  CAS  Google Scholar 

  26. Bachmann M, Arkın H, Janke W. Multicanonical study of coarse-grained off-lattice models for folding heteropolymers. Phys Rev E, 2005, 71: 031906

    Article  Google Scholar 

  27. Wang L, Chen T, Lin X, Liu Y, Liang H. Canonical and microcanonical analysis of nongrafted homopolymer adsorption by an attractive substrate. J Chem Phys, 2009, 131: 244902

    Article  Google Scholar 

  28. Chen T, Wang L, Lin X, Liu Y, Liang H. Microcanonical analysis of adsorption of homopolymer chain on a surface. J Chem Phys, 2009, 130: 244905

    Article  Google Scholar 

  29. Wang Z, He X. Phase transition of a single star polymer: a Wang-Landau sampling study. J Chem Phys, 2011, 135: 094902

    Article  Google Scholar 

  30. Guo J, Liang H, Wang ZG. Coil-to-globule transition by dissipative particle dynamics simulation. J Chem Phys, 2011, 134: 244904

    Article  Google Scholar 

  31. Seaton DT, Schnabel S, Landau DP, Bachmann M. From flexible to stiff: systematic analysis of structural phases for single semiflexible polymers. Phys Rev Lett, 2013, 110: 028103

    Article  Google Scholar 

  32. Arkin H, Janke W. Gyration tensor based analysis of the shapes of polymer chains in an attractive spherical cage. J Chem Phys, 2013, 138: 054904

    Article  Google Scholar 

  33. Wang Z, Wang L, He X. Phase transition of a single protein-like copolymer chain. Soft Matter, 2013, 9: 3106

    Article  CAS  Google Scholar 

  34. Chi P, Wang Z, Yin Y, Li BH, Shi AC. Finite-length effects on the coil-globule transition of a strongly charged polyelectrolyte chain in a salt-free solvent. Phy Rev E, 2013, 87: 042608

    Article  Google Scholar 

  35. Wang W, Zhao P, Yang X, Lu ZY. Coil-to-globule transitions of homopolymers and multiblock copolymers. J Chem Phys, 2014, 141: 244907

    Article  Google Scholar 

  36. Swetnam A, Brett C, Allen MP. Phase diagrams of knotted and unknotted ring polymers. Phys Rev E, 2012, 85: 031804

    Article  Google Scholar 

  37. Zhao Y, Ferrari F. A numerical technique for studying topological effects on the thermal properties of knotted polymer rings. J Stat Mech-Theory E, 2012: P11022

  38. Zhao Y, Ferrari F. A study of polymer knots using a simple knot invariant consisting of multiple contour integrals. J Stat Mech-Theory E, 2013: P10010

  39. Yang L, Gao YQ. A selective integrated tempering method. J Chem Phys, 2009, 131: 214109

    Article  Google Scholar 

  40. Yang L, Shao Q, Gao YQ. Comparison between integrated and parallel tempering methods in enhanced sampling simulations. J Chem Phys, 2009, 130: 124111

    Article  Google Scholar 

  41. Zhao P, Yang LJ, Gao YQ, Lu ZY. Facile implementation of integrated tempering sampling method to enhance the sampling over a broad range of temperatures. Chem Phys, 2013, 415: 98–105

    Article  CAS  Google Scholar 

  42. Zhu YL, Liu H, Li ZW, Qian HJ, Milano G, Lu ZY. GALAMOST: GPU-accelerated large-scale molecular simulation toolkit. J Comput Chem, 2013, 34: 2197–2211

    Article  CAS  Google Scholar 

  43. Roovers J, Toporowski PM. Synthesis of high molecular weight ring polystyrenes. Macromolecules, 1983, 16: 843–849

    Article  CAS  Google Scholar 

  44. Roovers J. Dilute-solution properties of ring polystyrenes. J Polym Sci Polym Phys Ed, 1985, 23: 1117–1126

    Article  CAS  Google Scholar 

  45. Takano A, Kushida Y, Ohta Y, Masuoka K, Matsushita Y. The second virial coefficients of highly-purified ring polystyrenes in cyclohexane. Polymer, 2009, 50: 1300–1303

    Article  CAS  Google Scholar 

  46. des Cloizeaux J. Ring polymers in solution: topological effects. J Phys Lett, 1981, 42: L–433

    Google Scholar 

  47. Tanaka F. Osmotic pressure of ring-polymer solutions. J Chem Phys, 1987, 87: 4201

    Article  CAS  Google Scholar 

  48. Iwata K. temperature of ring polymers: another evidence of topological interaction. Macromolecules, 1989, 22: 3702–3706

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Supramolecular Structure and Materials; Institute of Theoretical Chemistry, Jilin University, Changchun, 130023, China

    Wei Wang, Yanchun Li & Zhongyuan Lu

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  1. Wei Wang
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  2. Yanchun Li
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  3. Zhongyuan Lu
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Correspondence to Zhongyuan Lu.

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Wang, W., Li, Y. & Lu, Z. Coil to globule transition of homo- and block-copolymer with different topological constraint and chain stiffness. Sci. China Chem. 58, 1471–1477 (2015). https://doi.org/10.1007/s11426-015-5430-x

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  • DOI: https://doi.org/10.1007/s11426-015-5430-x

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