Mechanical Responses of Crosslinked Biopolymer Networks
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摘要: 生物聚合物交联网络(crosslinked biopolymer networks)是由肌动蛋白微丝等生物纤维相互交联形成的复杂网络结构,它广泛存在于细胞骨架和生物凝胶等系统中,对维持细胞完整性、使细胞具有主动变形和抵抗被动变形能力起着不可或缺的作用,其力学响应及工作机理对细胞工程、组织工程的发展非常重要.生物聚合物交联网络中交联蛋白的结合能量通常较低,其解离和重连过程容易受到网络结构变形和环境热涨落等因素的影响.实验中发现生物聚合物交联网络在小变形时刚度较低,但随着变形的增加,网络整体刚度会呈现数量级的增加,如果变形继续增加并超过一定阈值,网络刚度将急剧下降,这种应变硬化到软化的现象引起了研究者的广泛关注.已有理论模型和数值模拟发现,生物聚合物交联网络的硬化主要来源于纤维变形模式从弯曲到拉伸的转化,而软化则是由于网络中交联蛋白解离导致结构弱化和应力松弛.从生物聚合物交联网络的微观组成和结构出发,综述了生物聚合物纤维的力学模型、交联蛋白的力学属性和交联方式、交联网络的主要构型以及测量网络力学响应的实验方法,重点讨论了理论建模、有限元模拟、分子动力学等方法在研究生物聚合物交联网络非线性力学行为的进展,旨在为具有不同专业背景的研究者了解并开展生物聚合物交联网络力学响应的相关研究提供参考,也有助于机理化、定量化地理解细胞骨架中蕴含的结构-功能关系.Abstract: Crosslinked biopolymer networks are composed of filaments randomly distributed and crosslinked by specific binders, and are widespread in cytoskeletons of cells, biological gels and other natural materials. The binding energy of typical crosslinks in such biopolymer networks is relatively low and close to thermal energy, so that the binding status of the interaction is strongly influenced by the deformation of networks and thermal excitations from the environment. Experiments on different types of crosslinked biopolymer networks have demonstrated that these networks exhibit a linear response with low modulus in small deformation, and can be stiffened by more than two orders of magnitude in large strain. However, the network stiffness decreases dramatically when the applied strain exceeds a threshold value. This phenomenon is known as the transition from strain hardening to softening, and draws great attention from many researchers. Theoretical and numerical studies have indicated that such strain hardening is mainly caused by a transition from bending-dominated filament deformation in small strain to stretching-dominated response in large strain, and the strain softening is due to the microscopic unbinding of crosslinks, leading to weakened networks. This paper overviews the key components and representative architectures of crosslinked biopolymer networks, stretching behaviors of biopolymers, types and properties of crosslinks, and experimental methods used to measure the mechanical responses of network structures, with an emphasis on the theoretical, finite element and molecular dynamics models that pave the way to the understanding of the structure-function relations in crosslinked biopolymer networks.
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Key words:
- crosslinked biopolymer network /
- mechanical response /
- filament /
- crosslink /
- hardeningsoftening /
- nonlinear behavior
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[1] Alberts B, Johnson A, Lewis J, Roberts M R K, Walter P.Molecular Biology of the Cell[M]. 4th ed. New York: Garland Science Press, 2002. [2] Desprat N, Guiroy A, Asnacios A. Microplates-based rheometer for a single living cell[J].Review of Scientific Instruments,2006,77(5): 055111-055119. [3] Kollmannsberger P, Fabry B. High-force magnetic tweezers with force feedback for biological applications[J].Review of Scientific Instruments,2007,78(11): 114301-114306. [4] Crick F H C, Hughes A F W. The physical properties of cytoplasm: a study by means of the magnetic particle method—part I: experimental[J].Experimental Cell Research,1950,1(1): 37-80. [5] Howard J, Clark R L.Mechanics of Motor Proteins and the Cytoskeleton [M]. Sunderland M A: Sinauer Press, 2001. [6] Jackson W M, Jaasma M J, Tang R Y, Keaveny T M. Mechanical loading by fluid shear is sufficient to alter the cytoskeletal composition of osteoblastic cells[J].American Journal of Physiology Cell Physiology,2008,295(4): C1007-C1015. [7] 苗龙. 细胞运动、细胞迁移与细胞骨架研究进展[J]. 生物物理学报, 2007,23(4): 281-289. (MIAO Long. Recent progresses on the cellular motility, cell migration and cytoskeleton[J].Acta Biophysica Sinca,2007,23(4): 281-289.(in Chinese)) [8] 邓林红, 陈诚. 细胞骨架的普遍性动力学行为[J]. 医用生物力学, 2011,26(3): 193-200.(DENG Lin-hong, CHEN Cheng. Universal dynamics behaviors of the cytoskeleton[J].Journal of Medical Biomechanics,2011,26(3): 193-200.(in Chinese)) [9] Hatami-Marbini H, Mofrad M R K.Rheology and Mechanics of the Cytoskeleton [M]. New York: Springer, 2015. [10] Lieleg O, Claessens M M A E, Bausch A R. Structure and dynamics of cross-linked actin networks[J].Soft Matter,2010,6(2): 218-225. [11] Unterberger M J, Holzapfel G A. Advances in the mechanical modeling of filamentous actin and its cross-linked networks on multiple scales[J].Biomechanics and Modeling in Mechanobiology,2014,13(6): 1155-1174. [12] De La Cruz E M, Gardel M L. Actin mechanics and fragmentation[J].Journal of Biological Chemistry,2015,290(28): 17137-17144. [13] WANG Ning, Ingber D E. Probing transmembrane mechanical coupling and cytomechanics using magnetic twisting cytometry[J].Biochemistry and Cell Biology,1995,73(7/8): 327-335. [14] Gardel M L, Shin J H, MacKintosh F C, Mahadevan L, Matsudaira P, Weitz D A. Elastic behavior of cross-linked and bundled actin networks[J].Science,2004,304(5675): 1301-1305. [15] Storm C, Pastore J J, MacKintosh F C, Lubensky T C, Janmey P A. Nonlinear elasticity in biological gels[J].Nature,2005,435(7039): 191-194. [16] Trepat X, DENG Lin-hong, An S S, Navajas D, Tschumperlin D J, Gerthoffer W T, Butler J P, Fredberg J J. Universal physical responses to stretch in the living cell[J].Nature,2007,447(7144): 592-595. [17] Kang H, WEN Qi, Janmey P A, Tang J X, Conti E, Mackintosh F C. Nonlinear elasticity of stiff filament networks: strain stiffening, negative normal stress, and filament alignment in fibrin gels[J].Journal of Physical Chemistry B,2009,113(12): 3799-3805. [18] Kasza K E, Broedersz C P, Koenderink G H, Lin Y C, Messner W, Millman E A, Nakamura F, Stossel T P, Mackintosh F C, Weitz D A. Actin filament length tunes elasticity of flexibly cross-linked actin networks[J].Biophysical Journal,2010,99(4): 1091-1100. [19] Broedersz C P, Kasza K E, Jawerth L M, Münster S, Weitz D A, Mackintosh F C. Measurement of nonlinear rheology of cross-linked biopolymer gels[J].Soft Matter,2010,6(17): 4120-4127. [20] Chaudhuri O, Parekh S H, Fletcher D A. Reversible stress softening of actin networks[J].Nature,2007,445(7125): 295-298. [21] DiDonna B A, Levine A J. Unfolding cross-linkers as rheology regulators in F-actin networks[J].Physical Review E,2007,75(4): 041909. [22] Wolff L, Fernandez P, Kroy K. Resolving the stiffening-softening paradox in cell mechanics[J].Plos One,2012,7(7): e40063. [23] LIN Yuan, Wei X, Qian J, Sze K Y, Shenoy V B. A combined finite element-Langevin dynamics (FEM-LD) approach for analyzing the mechanical response of bio-polymer networks[J].Journal of the Mechanics and Physics of Solids,2014,62: 2-18. [24] WEI Xi, ZHU Qian, QIAN Jin, LIN Yuan, Shenoy V B. Response of biopolymer networks governed by the physical properties of cross-linking molecules[J].Soft Matter,2016,12: 2537-2541. [25] Machesky L M, Mullins R D, Higgs H N, Kaiser D A, Blanchoin L, May R C, Hall M E, Pollard T D. Scar, a WASp-related protein, activates nucleation of actin filaments by the Arp2/3 complex[J].Proceedings of the National Academy of Sciences,1999,96(7): 3739-3744. [26] Remedios C G D, Chhabra D, Dedova I V, Berry D A, Kekic M, Tsubakihara M, Nosworthy N J. Actin binding proteins: regulation of cytoskeletal microfilaments[J].Physiological Reviews,2003,83(2): 433-473. [27] Gunning P W, Ghoshdastider U, Whitaker S, Popp D, Robinson R C. The evolution of compositionally and functionally distinct actin filaments[J].Journal of Cell Science,2015,128(11): 2009-2019. [28] Mücke N, Kreplak L, Kirmse R, Wedig T, Herrmann H, Aebi U, Langowski J. Assessing the flexibility of intermediate filaments by atomic force microscopy[J].Journal of Molecular Biology,2004,335(5): 1241-1250. [29] JI Xiang-ying, FENG Xi-qiao. Coarse-grained mechanochemical model for simulating the dynamic behavior of microtubules[J].Physical Review E,2011,84(3): 031933. [30] 穆罕默德·塔杰, 张俊乾. 弹性介质中正交各向异性微管的屈曲分析[J]. 应用数学和力学, 2011,32(3): 279-285.(Muhammad T, ZHANG Jun-qian. Buckling of embedded microtubules in elastic medium[J].Applied Mathematics and Mechanics,2011,32(3): 279-285.(in Chinese)). [31] Gittes F, Mickey B, Nettleton J, Howard J. Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape[J].Journal of Cell Biology,1993,120(4): 923-934. [32] Isambert H, Venier P, Maggs A C, Fattoum A, Kassab R, Pantaloni D, Carlier M F. Flexibility of actin filaments derived from thermal fluctuations: effect of bound nucleotide, phalloidin and regulatory proteins[J].The Journal of Biological Chemistry,1995,270(19): 11437-11444. [33] Van Dillen T, Onck P R, Van der Giessen E. Models for stiffening in cross-linked biopolymer networks: a comparative study[J].〖QX(Y12#〗 Journal of the Mechanics and Physics of Solids〖QX)〗, 2008,56(6): 2240-2264. [34] Fallqvist B, Kulachenko A, Kroon M. Modelling of cross-linked actin networks—influence of geometrical parameters and cross-link compliance[J].Journal of Theoretical Biology,2014,350: 57-69. [35] Marko J F, Siggia E D. Statistical mechanics of supercoiled DNA[J].Physical Review E,1995,52(3): 2912-2938. [36] Ferrer J M, Hyungsuk L, Jiong C, Benjamin P, Fumihiko N, Kamm R D, Lang M J. Measuring molecular rupture forces between single actin filaments and actin-binding proteins[J].Proceedings of the National Academy of Sciences of the United States of America,2008,105(27): 9221-9226. [37] Sharma A, Sheinman M, Heidemann K M, MacKintosh F C. Elastic response of filamentous networks with compliant crosslinks[J].Physical Review E,2013,88(5): 052705. [38] Abhilash A S, Purohit P K, Joshi S P. Stochastic rate-dependent elasticity and failure of soft fibrous networks[J].Soft Matter,2012,8(26): 7004-7016. [39] 曲东明, 韩梅, 温进坤. 肌动蛋白结合蛋白[J]. 中国细胞生物学学报, 2007,29(2): 219-224.(QU Dong-ming, HAN Mei, WEN Jin-kun. Actin binding protein[J].Chinese Journal of Cell Biology,2007,29(2): 219-224.(in Chinese)) [40] Chen P, Shenoy V B. Strain stiffening induced by molecular motors in active crosslinked biopolymer networks[J].Soft Matter,2011,7(2): 355-358. [41] Plaza G R, Uyeda T Q P, Mirzaei Z, Simmons C A. Study of the influence of actin-binding proteins using linear analyses of cell deformability[J].Soft Matter,2015,11(27): 5435-5446. [42] Uyeda T Q P, Iwadate Y, Umeki N, Nagasaki A, Yumura S. Stretching actin filaments within cells enhances their affinity for the myosin II motor domain[J].Plos One,2011,6(10): e26200. [43] Mizuno D, Tardin C, Schmidt C F, Mackintosh F C. Nonequilibrium mechanics of active cytoskeletal networks[J].Science,2007,315(5810): 370-373. [44] Fletcher D A, Müllins D. Cell mechanics and the cytoskeleton[J].Nature,2010,463(7280): 485-492. [45] Pritchard R H, Huang Y Y S, Terentjev E M. Mechanics of biological networks: from the cell cytoskeleton to connective tissue[J].Soft Matter,2014,10(12): 1864-1884. [46] Lieleg O, Claessens M M A E, Luan Y, Bausch A R. Transient binding and dissipation in cross-linked actin networks[J].Physical Review Letters,2008,101(10): 108101. [47] Müller K W, Bruinsma R F, Lieleg O, Bausch A R, Wall W A, Levine A J. Rheology of semiflexible bundle networks with transient linkers[J].Physical Review Letters,2014,112(23): 238102. [48] Lee H, Pelz B, Ferrer J M, Kim T, Lang M J, Kamm R D. Cytoskeletal deformation at high strains and the role of cross-link unfolding or unbinding[J].Cellular and Molecular Bioengineering,2009,2(1): 28-38. [49] Koenderink G H, Dogic Z, Nakamura F, Bendix P M, MacKintosh F C, Hartwig J H, Stossel T P, Weitz D A. An active biopolymer network controlled by molecular motors[J].Proceedings of the National Academy of Sciences of the United States of America,2009,106(36): 15192-15197. [50] Kollmannsberger P, Fabry B. Linear and nonlinear rheology of living cells[J].Annual Review of Materials Research,2011,41(1): 75-97. [51] Palierne J F. Scale-dependent nonaffine elasticity of semiflexible polymer networks[J].Physical Review Letters,2014,112(8): 195-201. [52] FENG She-chao, Thorpe M F, Garboczi E. Effective-medium theory of percolation on central-force elastic networks[J].Physical Review B,1985,31(1): 276-280. [53] Broedersz C P, Storm C, MacKintosh F C. Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers[J].Physical Review Letters,2008,101(11): 118103. [54] Broedersz C P, MacKintosh F C. Modeling semiflexible polymer networks[J].Review of Modern Physics,2014,86(3): 995-1036. [55] Onck P R, Koeman T, Van Dillen T, Van der Giessen E. Alternative explanation of stiffening in cross-linked semiflexible networks[J].Physical Review Letters,2005,95(17): 178102. [56] Lindstrm S B, Kulachenko A, Jawerth L M, Vader D A. Finite-strain, finite-size mechanics of rigidly cross-linked biopolymer networks[J].Soft Matter,2013,9(30): 7302-7313. [57] Kurniawan N A, Enemark S, Rajagopalan R. The role of structure in the nonlinear mechanics of cross-linked semiflexible polymer networks[J].Journal of Chemical Physics,2012,136(6): 065101. [58] Yang Y, Bai M, Klug W S, Levine A J, Valentine M T. Microrheology of highly crosslinked microtubule networks is dominated by force-induced crosslinker unbinding[J].Soft Matter,2013,9(2): 383-393. [59] Vaca C, Shlomovitz R, Yang Y L, Valentine M T, Levine A J. Bond breaking dynamics in semiflexible networks under load[J].Soft Matter,2015,11(24): 4899-4911. [60] Wilhelm J, Frey E. Elasticity of stiff polymer networks[J].Physical Review Letters,2003,91(10): 108103. [61] Head D A, Levine A J, MacKintosh F C. Deformation of cross-linked semiflexible polymer networks[J].Physical Review Letters,2003,91(10): 108102. [62] Head D A, Levine A J, Mackintosh F C. Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks[J].Physical Review E,2003,68(6): 061907. [63] Levine A J, Head D A, Mackintosh F C. The deformation field in semiflexible networks[J].Journal of Physics Condensed Matter,2004,16(22): 2079-2088. [64] Huisman E M, Van Dillen T, Onck P R, Van der Giessen E. Three-dimensional cross-linked F-actin networks: relation between network architecture and mechanical behavior[J].Physical Review Letters,2007,99(20): 208103. [65] Zagar G, Onck P R, Van der Giessen E. Two fundamental mechanisms govern the stiffening of cross-linked networks[J].Biophysical Journal,2015,108(6): 1470-1479. [66] Bell G I. Models for specific adhesion of cells to cells[J].Science,1978,200(4342): 618-627. [67] Bell G I, Dembo M, Bongrand P. Cell-adhesion. Competition between nonspecific repulsion and specific bonding[J].Biophysical Journal,1984,45(6): 1051-1064. [68] Abhilash A S, ZHANG Liang, Stiefel J, Purohit P K, Joshi S P. Predictive maps for stochastic nonaffine stiffening and damage in fibrous networks[J].Physical Review E,2014,89(2): 022607-1-022607-9. [69] Yamazaki M, Shou F, Ito T. Mechanical response of single filamin A (ABP-280) molecules and its role in the actin cytoskeleton[J].Journal of Muscle Research and Cell Motility,2003,23(5/6): 525-534. [70] Chen P. Anomalous normal stresses in biopolymer networks with compliant cross-links[J].Europhysics Letters,2014,105(3): 38003. [71] JIN Tao, Stanciulescu I. Numerical simulation of fibrous biomaterials with randomly distributed fiber network structure[J].Biomechanics and Modeling in Mechanobiology,2015: 1-14.doi: 10.1007/s10237-015-0725-6. [72] Matsushita S, Adachi T, Inoue Y, Hojo M, Sokabe M. Evaluation of extensional and torsional stiffness of single actin filaments by molecular dynamics analysis[J].Journal of Biomechanics,2010,43(16): 3162-3167. [73] Matsushita S, Inoue Y, Hojo M, Sokabe M, Adachi T. Effect of tensile force on the mechanical behavior of actin filaments[J].Journal of Biomechanics,2011,44(9): 1776-1781. [74] Matsushita S, Inoue Y, Adachi T. Quantitative analysis of extension-torsion coupling of actin filaments[J].Biochemical and Biophysical Research Communications,2012,420(4): 710-713. [75] Chu J W, Voth G A. Coarse-grained modeling of the actin filament derived from atomistic-scale simulations[J].Biophysical Journal,2006,90(5): 1572-1582. [76] Li T, Gu Y T, Feng X Q, Yarlagadda P K D V, Oloyede A. Hierarchical multiscale model for biomechanics analysis of microfilament networks[J].Journal of Applied Physics,2013,113(19): 320-324. [77] Astrm J A, Kumar P B S, Vattulainen I, Karttunen M. Strain hardening, avalanches, and strain softening in dense cross-linked actin networks[J].Physical Review E,2008,77(5): 051913. [78] Hoffmann C, Moes D, Dieterle M, Neumann K, Moreau F, Tavares F A, Dumas D, Steinmetz A, Thomas C. Live cell imaging reveals actin-cytoskeleton-induced self-association of the actin-bundling protein WLIM1[J].Journal of Cell Science,2014,127(3): 583-598. [79] Weichsel J, Schwarz U S. Two competing orientation patterns explain experimentally observed anomalies in growing actin networks[J].Proceedings of the National Academy of Sciences of the United States of America,2010,107(14): 6304-6309. [80] Weichsel J, Schwarz U S. Mesoscopic model for filament orientation in growing actin networks: the role of obstacle geometry[J].New Journal of Physics,2013,15(10): 35006-35031.
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