受约束高分子链的拉伸

李凯; 叶天宇; 王记增

doi:10.21656/1000-0887.420279

受约束高分子链的拉伸

doi: 10.21656/1000-0887.420279

兰州大学土木工程与力学学院, 西部灾害与环境力学教育部重点实验室, 兰州 730000

基金项目:

国家杰出青年科学基金（11925204）

详细信息

作者简介:
李凯（1990—），男，博士（E-mail: lik17@lzu.edu.cn）；叶天宇（1996—），男，博士生（E-mail: yety21@lzu.edu.cn）；王记增(1974—)，男，长江学者特聘教授，博士（通讯作者. E-mail: jzwang@lzu.edu.cn）.

通讯作者:
王记增(1974—)，男，长江学者特聘教授，博士（通讯作者. E-mail: jzwang@lzu.edu.cn）.

中图分类号: O369
计量
- 文章访问数: 516
- HTML全文浏览量: 93
- PDF下载量: 94
- 被引次数: 0
出版历程
- 收稿日期: 2021-09-13
- 修回日期: 2021-09-27

Stretching a Polymer Chain in a Confined Space

Key Laboratory of Mechanics on Disaster and Environment in Western China, The Ministry of Education of China, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, P.R.China

摘要

摘要: 高分子生物材料微观力学性质的定量刻画，以及先进生物微纳米技术与器件的发展均需要定量分析生物大分子等高分子链在复杂微环境中的统计热力学性质与行为.在实现这一目标的过程中，连续介质力学与统计热力学的交叉研究扮演着很重要的角色.针对这一领域的力学问题，该综述先从DNA分子的受力拉伸出发，通过引入描述高分子链统计热力学性质的几类理论模型，指出了蠕虫链相较其他理想随机链模型在描述半柔性高分子链力与构型变化关系时具有较为显著的优势，从而使得人们对高分子在复杂微环境下,统计热力学性质与行为的定性与定量认识在很大程度上取决于基于蠕虫链模型的相关研究进展.根据这一事实，通过回顾与梳理空间几何约束对高分子链随机构象分布影响、高分子链在拉力与约束同时作用时的统计热力学建模、以及基于高性能计算机的高分子链统计物理性质仿真等各方面研究的现状，系统总结了蠕虫链在不同约束与受力微环境下,其统计热力学性质与行为研究的最新进展和依旧存在的挑战性难题.最后，通过总结分析,指出了蠕虫链在复杂微环境下的统计热力学研究是从分子与细胞尺度理解生命现象、发展先进微纳米技术以及构建软物质本构关系的重要基础，目前已成为极富挑战性的力学交叉科学前沿课题.
- 高分子链 /
- DNA /
- 蠕虫链模型 /
- 拉伸 /
- 约束 /
- 统计热力学
Abstract: The quantitative characterization of micromechanical properties of polymer biomaterials and the development of advanced biological micro-/nano- technology and devices need to quantitatively analyze the statistical thermodynamic properties and behaviors of polymer chains such as biological macromolecules in complex microenvironment. In the process of achieving this goal, the cross research of continuum mechanics and statistical thermodynamics plays a very important role. Aiming at the mechanics problems in this field, starting from the force stretching of DNA molecules, and by introducing several theoretical models describing the statistical thermodynamic properties of polymer chains, it is pointed out that the wormlike chain model has more significant advantages in describing the relationship between force and configuration change of semi-flexible polymer chains than other ideal random chain models, so that the qualitative and quantitative understanding of the statistical thermodynamic properties and behavior of polymers in complex microenvironment has become largely dependent on the relevant research progresses based on the wormlike chain model. Based on this fact, by reviewing the research on the influence of geometric constraints on the random conformation distribution of polymer chains, the research on the statistical thermodynamic model of polymer chains under the simultaneous action of tension and constraints, and the simulation research on the statistical physical properties of polymer chains based on high-performance computers, the latest progress and challenging problems in the research of statistical thermodynamic properties and behavior of worm chains under different constraints and stress microenvironments are summarized. Finally, through summary and analysis, it is pointed out that the study of statistical thermodynamics of worm chain in complex microenvironment is an important basis for understanding life phenomena from the molecular and cell scale, developing advanced micro- and nano- technology and constructing the constitutive relationship of soft matter. At present, it has become a very challenging frontier topic in the interdisciplinary of mechanics.
- polymer chain /
- DNA /
- wormlike chain model /
- stretching /
- confinement /
- statistical thermodynamics

HTML全文

参考文献(88)

RUBINSTEIN M, COLBY R H. Polymer Physics[M]. New York: Oxford University Press, 2003.

[2]ARRUDA E M, BOYCE M C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials[J]. Journal of the Mechanics and Physics of Solids,1993,41(2): 389-412.

[3]REISNER W, MORTON K J, RIEHN R, et al. Statics and dynamics of single DNA molecules confined in nanochannels[J]. Physical Review Letters,2005,94(19): 196101.

[4]REISNER W, PEDERSEN J N, AUSTIN R H. DNA confinement in nanochannels: physics and biological applications[J]. Reports on Progress in Physics,2012,75(10): 106601.

[5]BAO G. Mechanics of biomolecules[J]. Journal of the Mechanics and Physics of Solids,2002,50(11): 2237-2274.

[6]DAI L, RENNER C B, DOYLE P S. The polymer physics of single DNA confined in nanochannels[J]. Advances in Colloid and Interface Science,2016,232: 80-100.

[7]CHEN J Z. Theory of wormlike polymer chains in confinement[J]. Progress in Polymer Science,2016,54/55: 3-46.

[8]KSTER S, PFOHL T. An in vitro model system for cytoskeletal confinement[J]. Cell Motility and the Cytoskeleton,2009,66(10): 771-776.

[9]WOLFFE A. Chromatin: Structure and Function[M]. Academic Press, 1998.

[10]JUN S, MULDER B. Entropy-driven spatial organization of highly confined polymers: lessons for the bacterial chromosome[J]. Proceedings of the National Academy of Sciences,2006,103(33): 12388-12393.

[11]BELL S, TERENTJEV E M. Kinetics of tethered ligands binding to a surface receptor[J]. Macromolecules,2017,50(21): 8810-8815.

[12]CERRITELLI M E, CHENG N, ROSENBERG A H, et al. Encapsidated conformation of bacteriophage T7 DNA[J]. Cell,1997,91(2): 271-280.

[13]EARNSHAW W, HARRISON S. DNA arrangement in isometric phage heads[J]. Nature,1977,268(5621): 598-602.

[14]LAM E T, HASTIE A, LIN C, et al. Genome mapping on nanochannel arrays for structural variation analysis and sequence assembly[J]. Nature Biotechnology,2012,30(8): 771-776.

[15]DORFMAN K D. The fluid mechanics of genome mapping[J]. AICHE Journal,2013,59(2): 346-354.

[16]CHAN E Y, GONCALVES N M, HAEUSLER R A, et al. DNA mapping using microfluidic stretching and single-molecule detection of fluorescent site-specific tags[J]. Genome Research,2004,14(6): 1137-1146.

[17]HAN J, CRAIGHEAD H G. Separation of long DNA molecules in a microfabricated entropic trap array[J]. Science,2000,288(5468): 1026-1029.

[18]YAMAKAWA H. Modern Theory of Polymer Solutions[M]. New York: Harper & Row, 1971.

[19]AUSTIN R H, BRODY J P. Stretch genes[J]. Physics Today,1997,50(2): 32-38.

[20]BUSTAMANTE C, SMITH S B, LIPHARDT J, et al. Single-molecule studies of DNA mechanics[J]. Current Opinion in Structural Biology,2000,10(3): 279-285.

[21]KRATKY O, POROD G. Rntgenuntersuchung gelster fadenmoleküle[J]. Recueil des Travaux Chimiques des Pays-Bas,1949,68(12): 1106-1122.

[22]HERMANS J, ULLMAN R. The statistics of stiff chains, with applications to light scattering[J]. Physica,1952,18(11): 951-971.

[23]YAMAKAWA H. Helical Wormlike Chains in Polymer Solutions[M]. Springer, 1997.

[24]FREED K F. Functional integrals and polymer statistics[J]. Advaces in Chemical Physics,1972,22: 1. DOI: 10.1002/9780470143728.ch1.

[25]FEYNMAN R P, HIBBS A R, STYER D F. Quantum Mechanics and Path Integrals[M]. Courier Corporation, 2010.

[26]WANG M D, YIN H, LANDICK R, et al. Stretching DNA with optical tweezers[J]. Biophysical Journal,1997,72(3): 1335-1346.

[27]STRICK T, ALLEMAND J-F, CROQUETTE V, et al. Twisting and stretching single DNA molecules[J]. Progress in Biophysics and Molecular Biology,2000,74(1/2): 115-140.

[28]COCCO S, MARKO J F, MONASSON R. Theoretical models for single-molecule DNA and RNA experiments: from elasticity to unzipping[J]. Comptes Rendus Physique,2002,3(5): 569-584.

[29]SMITH S B, CUI Y, BUSTAMANTE C. Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules[J]. Science,1996,271(5250): 795-799.

[30]DE GENNES P G, GENNES P G. Scaling Concepts in Polymer Physics[M]. Cornell University Press, 1979.

[31]DOI M, EDWARDS S F, EDWARDS S F. The Theory of Polymer Dynamics[M]. Oxford University Press, 1988.

[32]MARKO J F, SIGGIA E D. Stretching DNA[J]. Macromolecules,1995,28(26): 8759-8770.

[33]KIERFELD J, NIAMPLOY O, SA-YAKANIT V, et al. Stretching of semiflexible polymers with elastic bonds[J]. The European Physical Journal E,2004,14(1): 17-34.

[34]FLORY P J. Principles of Polymer Chemistry[M]. Cornell University Press, 1953.

[35]DE GENNES P G. Dynamics of entangled polymer solutions, Ⅰ: the Rouse model[J]. Macromolecules,1976,9(4): 587-593.

[36]WANG J Z, LI L, GAO H J. Compressed wormlike chain moving out of confined space: a model of DNA ejection from bacteriophage[J]. Acta Mechanica Sinica,2012,28(4): 1219-1226.

[37]SCHIESSEL H. The physics of chromatin[J]. Journal of Physics: Condensed Matter,2003,15(19): R699.

[38]DAI L, VAN DER MAAREL J, DOYLE P S. Extended de Gennes regime of DNA confined in a nanochannel[J]. Macromolecules,2014,47(7): 2445-2450.

[39]ODIJK T. Physics of tightly curved semiflexible polymer chains[J]. Macromolecules,1993,26(25): 6897-6902.

[40]ODIJK T. The statistics and dynamics of confined or entangled stiff polymers[J]. Macromolecules,1983,16(8): 1340-1344.

[41]ODIJK T. Similarity applied to the statistics of confined stiff polymers[J]. Macromolecules,1984,17(3): 502-503.

[42]ODIJK T. DNA confined in nanochannels: hairpin tightening by entropic depletion[J]. The Journal of Chemical Physics,2006,125(20): 204904.

[43]DIJKSTRA M, FRENKEL D, LEKKERKERKER H N. Confinement free energy of semiflexible polymers[J]. Physica A,1993,193(3/4): 374-393.

[44]BICOUT D J, BURKHARDT T W. Simulation of a semiflexible polymer in a narrow cylindrical pore[J]. Journal of Physics A,2001,34(29): 5745.

[45]YANG Y, BURKHARDT T W, GOMPPER G. Free energy and extension of a semiflexible polymer in cylindrical confining geometries[J]. Physical Review E,2007,76(1): 011804.

[46]WANG J, GAO H. A generalized bead-rod model for Brownian dynamics simulations of wormlike chains under strong confinement[J]. The Journal of Chemical Physics,2005,123(8): 084906.

[47]CHEN J Z. Free energy and extension of a wormlike chain in tube confinement[J]. Macromolecules,2013,46(24): 9837-9844.

[48]BURKHARDT T W. Free energy of a semiflexible polymer in a tube and statistics of a randomly-accelerated particle[J]. Journal of Physics A: Mathematical and General,1997,30(7): L167-L172.

[49]GRASSBERGER P.Pruned-enriched Rosenbluth method: simulations of θ polymers of chain length up to 1 000 000[J]. Physical Review E,1997,56(3): 3682-3693.

[50]LI R, WANG J. Stretching a semiflexible polymer in a tube[J]. Polymers,2016,8(9): 328.

[51]WANG J, LI K. Statistical behaviors of semiflexible polymer chains stretched in rectangular tubes[J]. Polymers,2019,11(2): 260.

[52]TREE D R, WANG Y, DORFMAN K D. Extension of DNA in a nanochannel as a rod-to-coil transition[J]. Physical Review Letters,2013,110(20): 208103.

[53]CHEN J Z. Conformational properties of a back-folding wormlike chain confined in a cylindrical tube[J]. Physical Review Letters,2017,118(24): 247802.

[54]MURALIDHAR A, TREE D R, DORFMAN K D. Backfolding of wormlike chains confined in nanochannels[J]. Macromolecules,2014,47(23): 8446-8458.

[55]IARKO V, WERNER E, NYBERG L, et al. Extension of nanoconfined DNA: quantitative comparison between experiment and theory[J]. Physical Review E,2015,92(6): 062701.

[56]WERNER E, PERSSON F, WESTERLUND F, et al. Orientational correlations in confined DNA[J]. Physical Review E,2012,86(4): 041802.

[57]PUROHIT P K, KONDEV J, PHILLIPS R. Mechanics of DNA packaging in viruses[J]. Proceedings of the National Academy of Sciences,2003,100(6): 3173-3178.

[58]LI M, WANG J. Stretching wormlike chains in narrow tubes of arbitrary cross-sections[J]. Polymers,2019,11(12): 2050.

[59]DAI L, DOYLE P S. Comparisons of a polymer in confinement versus applied force[J]. Macromolecules,2013,46(15): 6336-6344.

[60]CHEN Y L, LIN P K, CHOU C F. Generalized force-extension relation for wormlike chains in slit confinement[J]. Macromolecules,2010,43(24): 10204-10207.

[61]TALONI A, YEH J W, CHOU C F. Scaling theory of stretched polymers in nanoslits[J]. Macromolecules,2013,46(19): 7989-8002.

[62]DE HAAN H W, SHENDRUK T N. Force-extension for DNA in a nanoslit: mapping between the 3D and 2D limits[J]. ACS Macro Letters,2015,4(6): 632-635.

[63]WANG J, GAO H. Stretching a stiff polymer in a tube[J]. Journal of Materials Science,2007,42(21): 8838-8843.

[64]BURKHARDT T W. Free energy of a semiflexible polymer confined along an axis[J]. Journal of Physics A: Mathematical and General,1995,28(24): L629.

[65]WANG J Z, LI R H. Stretching strongly confined semiflexible polymer chain[J]. Applied Mathematics and Mechanics(English Edition),2014,35(10): 1233-1238.

[66]THUROFF F, OBERMAYER B, FREY E. Longitudinal response of confined semiflexible polymers[J]. Physical Review E,2011,83(2): 021802.

[67]ERMAK D L, MCCAMMON J A. Brownian dynamics with hydrodynamic interactions[J]. The Journal of Chemical Physics,1978,69(4): 1352-1360.

[68]HUANG J, SCHLICK T. Macroscopic modeling and simulations of supercoiled DNA with bound proteins[J]. The Journal of Chemical Physics,2002,117(18): 8573-8586.

[69]LEWIS R J, ALLISON S A, EDEN D, et al. Brownian dynamics simulations of a three-subunit and a ten-subunit worm-like chain: comparison of results with trumbell theory and with experimental results from DNA[J]. The Journal of Chemical Physics,1988,89(4): 2490-2503.

[70]ALLISON S A. Brownian dynamics simulation of wormlike chains. Fluorescence depolarization and depolarized light scattering[J]. Macromolecules,1986,19(1): 118-124.

[71]JIAN H, VOLOGODSKII A V, SCHLICK T. A combined wormlike-chain and bead model for dynamic simulations of long linear DNA[J]. Journal of Computational Physics,1997,136(1): 168-179.

[72]NEELOV I M, ADOLF D B, LYULIN A V, et al. Brownian dynamics simulation of linear polymers under elongational flow: bead-rod model with hydrodynamic interactions[J]. The Journal of Chemical Physics,2002,117(8): 4030-4041.

[73]PETERA D, MUTHUKUMAR M. Brownian dynamics simulation of bead-rod chains under shear with hydrodynamic interaction[J]. The Journal of Chemical Physics,1999,111(16): 7614-7623.

[74]AGARWAL U. Effect of initial conformation, flow strength, and hydrodynamic interaction on polymer molecules in extensional flows[J]. The Journal of Chemical Physics,2000,113(8): 3397-3403.

[75]AGARWAL U, BHARGAVA R, MASHELKAR R. Brownian dynamics simulation of a polymer molecule in solution under elongational flow[J]. The Journal of Chemical Physics,1998,108(4): 1610-1617.

[76]WANG J, GAO H. Brownian dynamics simulations of charged semiflexible polymers confined to curved surfaces[J]. Journal of the Mechanical Behavior of Biomedical Materials,2011,4(2): 174-179.

[77]HESS B, BEKKER H, BERENDSEN H J, et al. LINCS: a linear constraint solver for molecular simulations[J]. Journal of Computational Chemistry, 1997,18(12): 1463-1472.

[78]BEHRINGER H, EICHHORN R. Brownian dynamics simulations with hard-body interactions: spherical particles[J]. The Journal of Chemical Physics,2012,137(16): 164108.

[79]PAMIES R, CIFRE J H, DE LA TORRE J G. Brownian dynamics simulation of polyelectrolyte dilute solutions under shear flow[J]. Journal of Polymer Science Part B: Polymer Physics,2007,45(1): 1-9.

[80]MONTESI A, MORSE D C, PASQUALI M. Brownian dynamics algorithm for bead-rod semiflexible chain with anisotropic friction[J]. The Journal of Chemical Physics,2005,122(8): 084903.

[81]LANG P S, OBERMAYER B, FREY E. Dynamics of a semiflexible polymer or polymer ring in shear flow[J]. Physical Review E,2014,89(2): 022606.

[82]HSU H P, GRASSBERGER P. A review of Monte Carlo simulations of polymers with PERM[J]. Journal of Statistical Physics,2011,144(3): 597-637.

[83]HSU H P, BINDER K. Semi-flexible polymer chains in quasi-one-dimensional confinement: a Monte Carlo study on the square lattice[J]. Soft Matter,2013,9(44): 10512-10521.

[84]HSU H P, GRASSBERGER P. Polymers confined between two parallel plane walls[J]. The Journal of Chemical Physics,2004,120(4): 2034-2041.

[85]MURALIDHAR A, TREE D R, WANG Y, et al. Interplay between chain stiffness and excluded volume of semiflexible polymers confined in nanochannels[J]. The Journal of Chemical Physics,2014,140(8): 084905.

[86]LI X, DORFMAN K D. Effect of excluded volume on the force-extension of wormlike chains in slit confinement[J]. The Journal of Chemical Physics,2016,144(10): 104902.

[87]JUN S, THIRUMALAI D, HA B Y. Compression and stretching of a self-avoiding chain in cylindrical nanopores[J]. Physical Review Letters,2008,101(13): 138101.

[88]JUNG Y, JUN S, HA B Y. Self-avoiding polymer trapped inside a cylindrical pore: Flory free energy and unexpected dynamics[J]. Physical Review E,2009,79(6): 061912.

施引文献

资源附件(0)

访问统计