Abstract
Using 3-dimensional Langevin dynamics simulations, we investigated the dynamics of loop formation of chains with excluded volume interactions, and the stability of the formed loop. The mean looping time τ l scales with chain length N and corresponding scaling exponent α increases linearly with the capture radius scaled by the Kuhn length a/l due to the effect of finite chain length. We also showed that the probability density function of the looping time is well fitted by a single exponential. Finally, we found that the mean unlooping time τ u hardly depends on chain length N for a given a/l and that the stability of a formed loop is enhanced with increasing a/l.
Similar content being viewed by others
References
Wilemski G, Fixman M. Diffusion-controlled intrachain reactions of polymers. 1. Theory. J Chem Phys, 1974, 60: 866–877
Wilemski G, Fixman M. Diffusion-controlled intrachain reactions of polymers. 2. J Chem Phys, 1974, 60: 878–890
Doi M. Diffusion-controlled reaction of polymers. Chem Phys, 1975, 9: 455–466
Szabo A, Schulten K, Schulten Z. First passage time approach to diffusion controlled reactions. J Chem Phys, 1980, 72: 4350–4357
Fernández JLG, Rey A, Freire J, de Piérola IF. Cyclization dynamics of flexible polymers. Numerical results from Brownian trajectories. Macromolecules, 1990, 23: 2057–2061
Rey A, Freire J. Numerical simulation of the cyclization dynamics for flexible chains with excluded volume. Macromolecules, 1991, 24: 4673–4678
Friedman B, O’Shaughnessy B. Theory of polymer cyclization. Phys Rev A, 1989, 40: 5950–5959
Friedman B, O’Shaughnessy B. Intermolecular reactions in dilute polymer solutions: nonexistence of diffusion-controlled limit. Europhys Lett, 1993, 23: 667–672
Friedman B, O’Shaughnessy B. Theory of intramolecular reactions in polymeric liquids. Macromolecules, 1993, 26: 4888–4898
Friedman B, O’Shaughnessy B. Kinetics of intermolecular reactions in dilute polymer solutions and unentangled melts. Macromolecules, 1993, 26: 5726–5739
Stampe J, Sokolov IM. Cyclization of a polymer with charged reactive end groups. J Chem Phys, 2001, 114: 5043–5048
Jun S, Bechhoefer J, Ha B. Diffusion-limited loop formation of semiflexible polymers: Kramers theory and the intertwined time scales of chain relaxation and closing. Europhys Lett, 2003, 64: 420–426
Dua A, Cherayil BJ. The dynamics of chain closure in semiflexible polymers. J Chem Phys, 2002, 116: 399–409
Afra R, Todd BA. Kinetics of loop formation in worm-like chain polymers. J Chem Phys, 2013, 138: 174908
Toan NM, Marenduzzo D, Cook PR, Micheletti C. Depletion effects and loop formation in self-avoiding polymers. Phys Rev Lett, 2006, 97: 178302
Bhattacharyya P, Sharma R, Cherayil BJ. Confinement and viscoelastic effects on chain closure dynamics. J Chem Phys, 2012, 136: 234903
Chan SH, Dill KA. Intrachain loops in polymers: effects of excluded volume. J Chem Phys, 1989, 90: 492–509
Podtelezhnikov A, Vologodskii A. Simulations of polymer cyclization by Brownian dynamics. Macromolecules, 1997, 30: 6668–6673
Ortiz-Repiso M, Freire JJ, Rey A. Intramolecular reaction rates of flexible polymers. 1. Simulation results and the classical theory. Macromolecules, 1998, 31: 8356–8262
Kim J, Lee S. The optimized Rouse-Zimm theory of excluded volume effects on chain dynamics. J Chem Phys, 2004, 121: 12640
Kim J, Lee W, Sung J, Lee S. Excluded volume effects on intrachain reaction kinetics. J Phys Chem B, 2008, 112: 6250–6258
Debnath P, Cherayil BJ. Dynamics of chain closure: approximate treatment of nonlocal interactions. J Chem Phys, 2004, 120: 2482–2489
Toan NM, Morrison G, Hyeon C, Thirumalai D. Kinetics of loop formation in polymer chains. J Phys Chem B, 2008, 112: 6094–6106
Chen JZY, Tsao H, Sheng Y. Diffusion-controlled first contact of the ends of a polymer: crossover between two sacling regimes. Phys Rev E, 2005, 72: 031804
Sokolov IM. Cyclization of a polymer: first-passage problem for a non-Markovian process. Phys Rev Lett, 2003, 90: 080601
Guérin T, Bénichou O, Voituriez R. Non-Markovian polymer reaction kinetics. Nature Chem, 2012, 4: 568–573
Doucet D, Roitberg A, Hagen SJ. Kinetics of interal-loop formation in polymer chains: a simulation study. Biophys J, 2007, 92: 2281–2121
Yeh I, Hummer G. Peptide loop-closure kinetics from microsecond molecular dynamics simulations in explicit solvent. J Am Chem Soc, 2002, 124: 6563–6568
Uzawa T, Isoshima T, Ito Y, Ishimori K, Makarov, DE, Plaxco KW. Sequence and temperature dependence of the end-to-end collision dynamics of single-stranded DNA. Biophys J, 2013, 104: 2485–2492
Everaers R, Rosa A. Multi-scale modeling of diffusion-controlled reactions in polymers: renormalisation of reactivity parameters. J Chem Phys, 2012, 136: 014902
Amitai A, Kupka I, Holcman D. Computation of the mean first-encounter time between the ends of a polymer chain. Phys Rev Lett, 2012, 109: 108302
Amitai A, Holcman D. Diffusing polymers in confined microdomains and estimation of chromosomal territory sizes from chromosome capture data. Phys Rev Lett, 2013, 110: 248105
Lapidus LJ, Eaton WA, Hofrichter J. Measuring the rate of intramolecular contact formation in polypeptides. Proc Natl Acad Sci USA, 2000, 97: 7220–7225
Lapidus LJ, Steinbach PJ, Eaton WA, Szabo A, Hofrichter J. Effects of chain stiffness on the dynamics of loop formation in polypeptides. Appendix: testing a 1-dimensional diffusion model for peptide dynamics. J Phys Chem B, 2002, 106: 11628–11640
Buscaglia M, Lapidus LJ, Eaton WA, Hofrichter J. Effects of denaturants on the dynamics of loop formation in polypeptides. Biophys J, 2006, 91: 276–288
Neuweiler H, Schulz A, Böhmer M, Enderlein J, Sauer M. Measurement of submicrosecond intramolecular contact formation in peptides at the single-molecule level. J Am Chem Soc, 2003, 125: 5324–5330
Neuweiler H, Löllmann M, Doose S, Sauer M. Dynamics of unfolded polypeptide chains in crowded environment studied by fluorescence correlation spectroscopy. J Mol Biol, 2007, 365: 856–869
Allemand J, Cocco S, Douarche N, Lia G. Loops in DNA: an overview of experimental and theoretical approaches. Eur Phys J E Soft Matter, 2006, 19: 293–302
Chandler D. Introduction to Modern Statistical Mechanism. Oxford: Oxford University Press, 1987
Ermak DL, Buckholz H. Numerical integration of the Langevin equation: Monte Carlo simulation. J Comput Phys, 1980, 35: 169–182
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yu, W., Luo, K. Loop formation and stability of self-avoiding polymer chains. Sci. China Chem. 58, 689–693 (2015). https://doi.org/10.1007/s11426-014-5203-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11426-014-5203-y