The cells and tissues that make up our body manage contradictory mechanical demands. It is crucial for their survival to be able to withstand large mechanical loads, but it is equally crucial for them to produce forces and actively change shape during biological processes such as tissue growth and repair. The mechanics of cells and tissues is determined by scaffolds of protein polymers known as the cytoskeleton and the extracellular matrix, respectively. Experiments on model systems reconstituted from purified components combined with polymer physics concepts have already uncovered some of the mechanisms that underlie the paradoxical mechanics of living matter. Initial work focused on explaining universal features, such as the nonlinear elasticity of cells and tissues, in terms of polymer network models. However, there is a growing recognition that living matter exhibits many advanced mechanical functionalities that are not captured by these coarse-grained theories. Here, we review recent experimental and theoretical insights that reveal how the porous structure, structural hierarchy, transient crosslinking and mechanochemical activity of biopolymers confer resilience combined with the ability to adapt and self-heal. These physical concepts increase our understanding of cell and tissue biology and provide inspiration for advanced synthetic materials.
Cells and tissues are supported by biopolymer scaffolds that are mechanically resilient yet dynamic. There is a growing realization that biopolymer networks acquire these unique features from their hierarchical structure combined with internal mechanochemical activity.
Biopolymer networks are embedded in water and therefore experience a strong coupling with the solvent, resulting in poroelastic effects.
Fibrous networks respond to cyclic mechanical loading with plastic effects, self-healing and fracture. These responses originate from all structural levels — from molecule to fibre to network.
Non-equilibrium activity causes biopolymer networks to undergo active stiffening, fluidization or self-driven flow, enabling a cell to deform.
Composite biopolymer systems, in which all these mechanisms act together, endow cells and tissues with their adaptive mechanical properties.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Strong, tough, rapid-recovery, and fatigue-resistant hydrogels made of picot peptide fibres
Nature Communications Open Access 04 May 2023
Four distinct network patterns of supramolecular/polymer composite hydrogels controlled by formation kinetics and interfiber interactions
Nature Communications Open Access 27 March 2023
Stretchable hydrogels with low hysteresis and anti-fatigue fracture based on polyprotein cross-linkers
Nature Communications Open Access 12 August 2020
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$99.00 per year
only $8.25 per issue
Rent or buy this article
Get just this article for as long as you need it
Prices may be subject to local taxes which are calculated during checkout
Freedman, B. R. et al. The (dys)functional extracellular matrix. Biochim. Biophys. Acta 1853, 3153–3164 (2015).
Fletcher, D. A. & Mullins, R. D. Cell mechanics and the cytoskeleton. Nature 463, 485–492 (2010).
Mouw, J. K., Ou, G. & Weaver, V. M. Extracellular matrix assembly: a multiscale deconstruction. Nat. Rev. Mol. Cell Biol. 15, 771–785 (2014).
Horton, E. R. et al. Definition of a consensus integrin adhesome and its dynamics during adhesion complex assembly and disassembly. Nat. Cell Biol. 17, 1577–1587 (2015).
Barriga, E. H., Franze, K., Charras, G. & Mayor, R. Tissue stiffening coordinates morphogenesis by triggering collective cell migration in vivo. Nature 554, 523–527 (2018).
Discher, D. E. et al. Matrix mechanosensing: from scaling concepts in ‘omics data to mechanisms in the nucleus, regeneration, and cancer. Annu. Rev. Biophys. 46, 295–315 (2017).
Roca-Cusachs, P., Conte, V. & Trepat, X. Quantifying forces in cell biology. Nat. Cell Biol. 19, 742–751 (2017).
Muncie, J. M. & Weaver, V. M. The physical and biochemical properties of the extracellular matrix regulate cell fate. Curr. Top. Dev. Biol. 130, 1–37 (2018).
Vogel, V. Unraveling the mechanobiology of extracellular matrix. Annu. Rev. Physiol. 80, 353–387 (2018).
Kirby, T. J. & Lammerding, J. Emerging views of the nucleus as a cellular mechanosensor. Nat. Cell Biol. 20, 373–381 (2018).
van Helvert, S., Storm, C. & Friedl, P. Mechanoreciprocity in cell migration. Nat. Cell Biol. 20, 8–20 (2018).
Fabry, B. et al. Scaling the microrheology of living cells. Phys. Rev. Lett. 87, 148102 (2001).
Fernandez, P., Pullarkat, P. A. & Ott, A. A master relation defines the nonlinear viscoelasticity of single fibroblasts. Biophys. J. 90, 3796–3805 (2006).
Trepat, X. et al. Universal physical responses to stretch in the living cell. Nature 447, 592–595 (2007).
Perepelyuk, M. et al. Normal and fibrotic rat livers demonstrate shear strain softening and compression stiffening: a model for soft tissue mechanics. PloS One 11, e0146588 (2016).
Ingber, D. E., Wang, N. & Stamenovic, D. Tensegrity, cellular biophysics, and the mechanics of living systems. Rep. Prog. Phys. 77, 046603 (2014).
Grinnell, F. Fibroblast biology in three-dimensional collagen matrices. Trends Cell Biol. 13, 264–269 (2003).
Lanir, Y. Mechanisms of residual stress in soft tissues. J. Biomech. Eng. 131, 044506 (2009).
Kreis, T. & Vale, R. (eds) Guidebook to the Cytoskeletal and Motor Proteins (Oxford Univ. Press, 1993).
Broedersz, C. P. & MacKintosh, F. C. Modeling semiflexible polymer networks. Rev. Mod. Phys. 86, 995 (2014).
Pritchard, R. H., Huang, Y. Y. & Terentjev, E. M. Mechanics of biological networks: from the cell cytoskeleton to connective tissue. Soft Matter 10, 1864–1884 (2014).
Kagan, H. M. & Li, W. Lysyl oxidase: properties, specificity, and biological roles inside and outside of the cell. J. Cell. Biochem. 88, 660–672 (2003).
van Mameren, J., Vermeulen, K. C., Gittes, F. & Schmidt, C. F. Leveraging single protein polymers to measure flexural rigidity. J. Phys. Chem. B 113, 3837–3844 (2009).
Bartsch, T. F., Kochanczyk, M. D., Lissek, E. N., Lange, J. R. & Florin, E. L. Nanoscopic imaging of thick heterogeneous soft-matter structures in aqueous solution. Nat. Commun. 7, 12729 (2016).
Block, J. et al. Nonlinear loading-rate-dependent force response of individual vimentin intermediate filaments to applied strain. Phys. Rev. Lett. 118, 048101 (2017). A pioneering experimental study of the stress–strain response of single intermediate filaments, demonstrating that monomer unfolding explains their remarkable extensibility.
Berezney, J. P. & Saleh, O. A. Electrostatic effects on the conformation and elasticity of hyaluronic acid, a moderately flexible polyelectrolyte. Macromolecules 50, 1085–1089 (2017).
De Gennes, P. G. Reptation of a polymer chain in the presence of fixed obstacles. J. Chem. Phys. 55, 572–579 (1971).
Doi, M. & Edwards, S. F. Dynamics of concentrated polymer systems. Part 1. — Brownian motion in the equilibrium state. J. Chem. Soc. Faraday Trans. 2 74, 1789–1801 (1978).
Kas, J., Strey, H. & Sackmann, E. Direct imaging of reptation for semiflexible actin filaments. Nature 368, 226–229 (1994).
Lang, P. & Frey, E. Disentangling entanglements in biopolymer solutions. Nat. Commun. 9, 494 (2018).
Blanchoin, L., Boujemaa-Paterski, R., Sykes, C. & Plastino, J. Actin dynamics, architecture, and mechanics in cell motility. Physiol. Rev. 94, 235–263 (2014).
Basnet, N. et al. Direct induction of microtubule branching by microtubule nucleation factor SSNA1. Nat. Cell Biol. 20, 1172–1180 (2018).
Lin, Y. C. et al. Divalent cations crosslink vimentin intermediate filament tail domains to regulate network mechanics. J. Mol. Biol. 399, 637–644 (2010).
Licup, A. J. et al. Stress controls the mechanics of collagen networks. Proc. Natl Acad. Sci. USA 112, 9573–9578 (2015).
Sharma, A. et al. Strain-controlled criticality governs the nonlinear mechanics of fibre networks. Nat. Phys. 12, 584–587 (2016). A combined experimental and theoretical study showing that the nonlinear elasticity of fibrous networks such as collagen corresponds to a strain-controlled continuous phase transition.
Holmes, D. F., Lu, Y., Starborg, T. & Kadler, K. E. Collagen fibril assembly and function. Curr. Top. Dev. Biol. 130, 107–142 (2018).
Gostynska, N. et al. 3D porous collagen scaffolds reinforced by glycation with ribose for tissue engineering application. Biomed. Mater. 12, 055002 (2017).
Valero, C., Amaveda, H., Mora, M. & Garcia-Aznar, J. M. Combined experimental and computational characterization of crosslinked collagen-based hydrogels. PloS One 13, e0195820 (2018).
Storm, C., Pastore, J. J., MacKintosh, F. C., Lubensky, T. C. & Janmey, P. A. Nonlinear elasticity in biological gels. Nature 435, 191–194 (2005).
Chaudhuri, O., Parekh, S. H. & Fletcher, D. A. Reversible stress softening of actin networks. Nature 445, 295–298 (2007).
Vos, B. E. et al. Programming the mechanics of cohesive fiber networks by compression. Soft Matter 13, 8886–8893 (2017).
van Oosten, A. S. et al. Uncoupling shear and uniaxial elastic moduli of semiflexible biopolymer networks: compression-softening and stretch-stiffening. Sci. Rep. 6, 19270 (2016).
Xu, X. & Safran, S. A. Compressive elasticity of polydisperse biopolymer gels. Phys. Rev. E 95, 052415 (2017).
MacKintosh, F. C., Kas, J. & Janmey, P. A. Elasticity of semiflexible biopolymer networks. Phys. Rev. Lett. 75, 4425–4428 (1995).
Liu, J., Koenderink, G. H., Kasza, K. E., Mackintosh, F. C. & Weitz, D. A. Visualizing the strain field in semiflexible polymer networks: strain fluctuations and nonlinear rheology of F-actin gels. Phys. Rev. Lett. 98, 198304 (2007).
Gardel, M. L. et al. Elastic behavior of cross-linked and bundled actin networks. Science 304, 1301–1305 (2004).
Lin, Y. C. et al. Origins of elasticity in intermediate filament networks. Phys. Rev. Lett. 104, 058101 (2010).
Kouwer, P. H. et al. Responsive biomimetic networks from polyisocyanopeptide hydrogels. Nature 493, 651–655 (2013).
Fernandez-Castano Romera, M. et al. Strain stiffening hydrogels through self-assembly and covalent fixation of semi-flexible fibers. Angew. Chem. Int. Ed. 56, 8771–8775 (2017).
Yan, B. et al. Duplicating dynamic strain-stiffening behavior and nanomechanics of biological tissues in a synthetic self-healing flexible network hydrogel. ACS Nano 11, 11074–11081 (2017).
Maxwell, J. C. L. On the calculation of the equilibrium and stiffness of frames. Lond. Edinb. Dublin Philos. Mag. J. Sci. 27, 294–299 (1864).
Broedersz, C. P., Xiaoming, M., Lubensky, T. C. & MacKintosh, F. C. Criticality and isostaticity in fibre networks. Nat. Phys. 7, 983–988 (2011).
Onck, P. R., Koeman, T., van Dillen, T. & van der Giessen, E. Alternative explanation of stiffening in cross-linked semiflexible networks. Phys. Rev. Lett. 95, 178102 (2005).
Licup, A. J., Sharma, A. & MacKintosh, F. C. Elastic regimes of subisostatic athermal fiber networks. Phys. Rev. E 93, 012407 (2016).
Jansen, K. A. et al. The role of network architecture in collagen mechanics. Biophys. J. 114, 2665–2678 (2018).
Han, Y. L. et al. Cell contraction induces long-ranged stress stiffening in the extracellular matrix. Proc. Natl Acad. Sci. USA 115, 4075–4080 (2018).
Biot, M. A. General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164 (1941).
Knapp, D. M. et al. Rheology of reconstituted type I collagen gel in confined compression. J. Rheol. 41, 971–993 (1997).
De Gennes, P. G. Dynamics of entangled polymer solutions (I&II). Macromolecules 9, 587–598 (1976).
de Cagny, H. C. et al. Porosity governs normal stresses in polymer gels. Phys. Rev. Lett. 117, 217802 (2016).
Nia, H. T., Han, L., Li, Y., Ortiz, C. & Grodzinsky, A. Poroelasticity of cartilage at the nanoscale. Biophys. J. 101, 2304–2313 (2011).
Charras, G. T., Yarrow, J. C., Horton, M. A., Mahadevan, L. & Mitchison, T. J. Non-equilibration of hydrostatic pressure in blebbing cells. Nature 435, 365–369 (2005).
Moeendarbary, E. et al. The cytoplasm of living cells behaves as a poroelastic material. Nat. Mater. 12, 253–261 (2013). A study providing direct evidence of the importance of poroelasticity in cell rheology on the basis of microindentation and microrheology experiments.
Hu, J. et al. Size- and speed-dependent mechanical behavior in living mammalian cytoplasm. Proc. Natl Acad. Sci. USA 114, 9529–9534 (2017).
Tao, J., Li, Y., Vig, D. K. & Sun, S. X. Cell mechanics: a dialogue. Rep. Prog. Phys. 80, 036601 (2017).
Maiuri, P. et al. Actin flows mediate a universal coupling between cell speed and cell persistence. Cell 161, 374–386 (2015).
Ruprecht, V. et al. Cortical contractility triggers a stochastic switch to fast amoeboid cell motility. Cell 160, 673–685 (2015).
Petrie, R. J., Koo, H. & Yamada, K. M. Generation of compartmentalized pressure by a nuclear piston governs cell motility in a 3D matrix. Science 345, 1062–1065 (2014).
Guo, M. et al. Cell volume change through water efflux impacts cell stiffness and stem cell fate. Proc. Natl Acad. Sci. USA 114, E8618–E8627 (2017).
Janmey, P. A. et al. Negative normal stress in semiflexible biopolymer gels. Nat. Mater. 6, 48–51 (2007).
Poynting, J. H. On pressure perpendicular to the shear planes in finite pure shears, and on the lengthening of loaded wires when twisted. Proc. R. Soc. A 82, 546–559 (1909).
Taber, L. A., Yang, M. & Podszus, W. W. Mechanics of ventricular torsion. J. Biomech. 29, 745–752 (1996).
Baumgarten, K. & Tighe, B. P. Normal stresses, contraction, and stiffening in sheared elastic networks. Phys. Rev. Lett. 120, 148004 (2018).
Taute, K. M., Pampaloni, F., Frey, E. & Florin, E. L. Microtubule dynamics depart from the wormlike chain model. Phys. Rev. Lett. 100, 028102 (2008).
Yang, L. et al. Mechanical properties of native and cross-linked type I collagen fibrils. Biophys. J. 94, 2204–2211 (2008).
Shen, Z. L., Dodge, M. R., Kahn, H., Ballarini, R. & Eppell, S. J. In vitro fracture testing of submicron diameter collagen fibril specimens. Biophys. J. 99, 1986–1995 (2010).
Wu, Y. T. & Adnan, A. Damage and failure of axonal microtubule under extreme high strain rate: an in-silico molecular dynamics study. Sci. Rep. 8, 12260 (2018).
Schnauss, J. et al. Transition from a linear to a harmonic potential in collective dynamics of a multifilament actin bundle. Phys. Rev. Lett. 116, 108102 (2016).
Ward, A. et al. Solid friction between soft filaments. Nat. Mater. 14, 583–588 (2015).
Kreplak, L., Herrmann, H. & Aebi, U. Tensile properties of single desmin intermediate filaments. Biophys. J. 94, 2790–2799 (2008).
Fudge, D. S., Gardner, K. H., Forsyth, V. T., Riekel, C. & Gosline, J. M. The mechanical properties of hydrated intermediate filaments: insights from hagfish slime threads. Biophys. J. 85, 2015–2027 (2003).
Kreplak, L., Doucet, J., Dumas, P. & Briki, F. New aspects of the alpha-helix to beta-sheet transition in stretched hard alpha-keratin fibers. Biophys. J. 87, 640–647 (2004).
Brown, A. E., Litvinov, R. I., Discher, D. E., Purohit, P. K. & Weisel, J. W. Multiscale mechanics of fibrin polymer: gel stretching with protein unfolding and loss of water. Science 325, 741–744 (2009). An impressive multiscale experimental study of the role of structural hierarchy in increasing the mechanical strength of fibrin.
Fleissner, F., Bonn, M. & Parekh, S. H. Microscale spatial heterogeneity of protein structural transitions in fibrin matrices. Sci. Adv. 2, e1501778 (2016).
Portale, G. & Torbet, J. Complex strain induced structural changes observed in fibrin assembled in human plasma. Nanoscale 10, 10063–10072 (2018).
Brown, A. E., Litvinov, R. I., Discher, D. E. & Weisel, J. W. Forced unfolding of coiled-coils in fibrinogen by single-molecule AFM. Biophys. J. 92, L39–41 (2007).
Zhmurov, A. et al. Mechanical transition from alpha-helical coiled coils to beta-sheets in fibrin(ogen). J. Am. Chem. Soc. 134, 20396–20402 (2012).
Protopopova, A. D. et al. Visualization of fibrinogen alphaC regions and their arrangement during fibrin network formation by high-resolution AFM. J. Thromb. Haemos. 13, 570–579 (2015).
Piechocka, I. K., Bacabac, R. G., Potters, M., Mackintosh, F. C. & Koenderink, G. H. Structural hierarchy governs fibrin gel mechanics. Biophys. J. 98, 2281–2289 (2010).
Houser, J. R. et al. Evidence that alphaC region is origin of low modulus, high extensibility, and strain stiffening in fibrin fibers. Biophys. J. 99, 3038–3047 (2010).
Hudson, N. E. et al. Submillisecond elastic recoil reveals molecular origins of fibrin fiber mechanics. Biophys. J. 104, 2671–2680 (2013).
Averett, R. D. et al. A modular fibrinogen model that captures the stress-strain behavior of fibrin fibers. Biophys. J. 103, 1537–1544 (2012).
Elvin, C. M. et al. Synthesis and properties of crosslinked recombinant pro-resilin. Nature 437, 999–1002 (2005).
Baldock, C. et al. Shape of tropoelastin, the highly extensible protein that controls human tissue elasticity. Proc. Natl Acad. Sci. USA 108, 4322–4327 (2011).
Reichheld, S. E., Muiznieks, L. D., Keeley, F. W. & Sharpe, S. Direct observation of structure and dynamics during phase separation of an elastomeric protein. Proc. Natl Acad. Sci. USA 114, E4408–E4415 (2017).
Amuasi, H. E. & Storm, C. Off-lattice Monte Carlo simulation of supramolecular polymer architectures. Phys. Rev. Lett. 105, 248105 (2010).
Giesa, T., Pugno, N. M. & Buehler, M. J. Natural stiffening increases flaw tolerance of biological fibers. Phys. Rev. E 86, 041902 (2012).
Aghaei-Ghareh-Bolagh, B., Mithieux, S. M. & Weiss, A. S. Elastic proteins and elastomeric protein alloys. Curr. Opin. Biotechnol. 39, 56–60 (2016).
Pinto, N. et al. Self-assembly enhances the strength of fibers made from vimentin intermediate filament proteins. Biomacromolecules 15, 574–581 (2014).
Rombouts, W. H., Giesbers, M., van Lent, J., de Wolf, F. A. & van der Gucht, J. Synergistic stiffening in double-fiber networks. Biomacromolecules 15, 1233–1239 (2014).
Wu, J. et al. Rationally designed synthetic protein hydrogels with predictable mechanical properties. Nat. Commun. 9, 620 (2018).
Schuldt, C. et al. Tuning synthetic semiflexible networks by bending stiffness. Phys. Rev. Lett. 117, 197801 (2016).
Bonakdar, N. et al. Mechanical plasticity of cells. Nat. Mater. 15, 1090–1094 (2016). A single-cell rheology study demonstrating that cells exhibit a reversible viscoelastic deformation response and additive plastic deformation that originates from bond ruptures within the cytoskeleton.
Fischer-Friedrich, E. et al. Rheology of the active cell cortex in mitosis. Biophys. J. 111, 589–600 (2016).
Clement, R., Dehapiot, B., Collinet, C., Lecuit, T. & Lenne, P. F. Viscoelastic dissipation stabilizes cell shape changes during tissue morphogenesis. Curr. Biol. 27, 3132–3142.e4 (2017).
Ferrer, J. M. et al. Measuring molecular rupture forces between single actin filaments and actin-binding proteins. Proc. Natl Acad. Sci. USA 105, 9221–9226 (2008).
Courson, D. S. & Rock, R. S. Actin cross-link assembly and disassembly mechanics for alpha-actinin and fascin. J. Biol. Chem. 285, 26350–26357 (2010).
Lieleg, O., Schmoller, K. M., Claessens, M. M. & Bausch, A. R. Cytoskeletal polymer networks: viscoelastic properties are determined by the microscopic interaction potential of cross-links. Biophys. J. 96, 4725–4732 (2009).
Broedersz, C. P. et al. Cross-link-governed dynamics of biopolymer networks. Phys. Rev. Lett. 105, 238101 (2010).
Muller, K. W. et al. Rheology of semiflexible bundle networks with transient linkers. Phys. Rev. Lett. 112, 238102 (2014).
Wolff, L., Fernandez, P. & Kroy, K. Resolving the stiffening-softening paradox in cell mechanics. PloS One 7, e40063 (2012).
Maier, M. et al. A single charge in the actin binding domain of fascin can independently tune the linear and non-linear response of an actin bundle network. Eur. Phys. J. E 38, 50 (2015).
Gralka, M. & Kroy, K. Inelastic mechanics: a unifying principle in biomechanics. Biochim. Biophys. Acta 1853, 3025–3037 (2015).
Ehrlicher, A. J., Nakamura, F., Hartwig, J. H., Weitz, D. A. & Stossel, T. P. Mechanical strain in actin networks regulates FilGAP and integrin binding to filamin A. Nature 478, 260–263 (2011).
Huang, D. L., Bax, N. A., Buckley, C. D., Weis, W. I. & Dunn, A. R. Vinculin forms a directionally asymmetric catch bond with F-actin. Science 357, 703–706 (2017).
Weins, A. et al. Disease-associated mutant alpha-actinin-4 reveals a mechanism for regulating its F-actin-binding affinity. Proc. Natl Acad. Sci. USA 104, 16080–16085 (2007).
Yao, N. Y. et al. Stress-enhanced gelation: a dynamic nonlinearity of elasticity. Phys. Rev. Lett. 110, 018103 (2013).
Falzone, T. T., Lenz, M., Kovar, D. R. & Gardel, M. L. Assembly kinetics determine the architecture of alpha-actinin crosslinked F-actin networks. Nat. Commun. 3, 861 (2012).
Foffano, G., Levernier, N. & Lenz, M. The dynamics of filament assembly define cytoskeletal network morphology. Nat. Commun. 7, 13827 (2016).
Schmoller, K. M., Lieleg, O. & Bausch, A. R. Internal stress in kinetically trapped actin bundle networks. Soft Matter 4, 2365–2367 (2008).
Lieleg, O., Kayser, J., Brambilla, G., Cipelletti, L. & Bausch, A. R. Slow dynamics and internal stress relaxation in bundled cytoskeletal networks. Nat. Mater. 10, 236–242 (2011).
Nam, S., Hu, K. H., Butte, M. J. & Chaudhuri, O. Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels. Proc. Natl Acad. Sci. USA 113, 5492–5497 (2016).
Lou, J., Stowers, R., Nam, S., Xia, Y. & Chaudhuri, O. Stress relaxing hyaluronic acid-collagen hydrogels promote cell spreading, fiber remodeling, and focal adhesion formation in 3D cell culture. Biomaterials 154, 213–222 (2018).
Gong, Z. et al. Matching material and cellular timescales maximizes cell spreading on viscoelastic substrates. Proc. Natl Acad. Sci. USA 115, E2686–E2695 (2018).
Bennett, M. et al. Molecular clutch drives cell response to surface viscosity. Proc. Natl Acad. Sci. USA 115, 1192–1197 (2018).
Schmoller, K. M., Fernandez, P., Arevalo, R. C., Blair, D. L. & Bausch, A. R. Cyclic hardening in bundled actin networks. Nat. Commun. 1, 134 (2010).
Majumdar, S., Foucard, L. C., Levine, A. J. & Gardel, M. L. Mechanical hysteresis in actin networks. Soft Matter 14, 2052–2058 (2018).
Kasza, K. E. et al. Actin filament length tunes elasticity of flexibly cross-linked actin networks. Biophys. J. 99, 1091–1100 (2010).
Wagner, B., Tharmann, R., Haase, I., Fischer, M. & Bausch, A. R. Cytoskeletal polymer networks: the molecular structure of cross-linkers determines macroscopic properties. Proc. Natl Acad. Sci. USA 103, 13974–13978 (2006).
Gardel, M. L. et al. Prestressed F-actin networks cross-linked by hinged filamins replicate mechanical properties of cells. Proc. Natl Acad. Sci. USA 103, 1762–1767 (2006).
Mulla, Y., Oliveri, G., Overvelde, J. T. B. & Koenderink, G. H. Crack initiation in viscoelastic materials. Phys. Rev. Lett. 120, 268002 (2018). Theoretical modelling reveals that transient networks are susceptible to spontaneous crack initiation, with a critical crack length that can be predicted from the nonlinear local bond dynamics.
Mulla, Y. & Koenderink, G.H. Crosslinker mobility weakens transient polymer networks. Phys. Rev. E. 6, 062503 (2018).
Sanchez, T., Chen, D. T., DeCamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).
Schaedel, L. et al. Microtubules self-repair in response to mechanical stress. Nat. Mater. 14, 1156–1163 (2015).
Noding, B., Herrmann, H. & Koster, S. Direct observation of subunit exchange along mature vimentin intermediate filaments. Biophys. J. 107, 2923–2931 (2014).
Sano, K. et al. Self-repairing filamentous actin hydrogel with hierarchical structure. Biomacromolecules 12, 4173–4177 (2011).
Jegou, A., Carlier, M. F. & Romet-Lemonne, G. Formin mDia1 senses and generates mechanical forces on actin filaments. Nat. Commun. 4, 1883 (2013).
Humphrey, J. D., Dufresne, E. R. & Schwartz, M. A. Mechanotransduction and extracellular matrix homeostasis. Nat. Rev. Mol. Cell Biol. 15, 802–812 (2014).
Yang, Y. & Urban, M. W. Self-healing polymeric materials. Chem. Soc. Rev. 42, 7446–7467 (2013).
Yanagisawa, Y., Nan, Y., Okuro, K. & Aida, T. Mechanically robust, readily repairable polymers via tailored noncovalent cross-linking. Science 359, 72–76 (2018).
Kurniawan, N. A. et al. Fibrin networks support recurring mechanical loads by adapting their structure across multiple scales. Biophys. J. 111, 1026–1034 (2016).
Ban, E. et al. Mechanisms of plastic deformation in collagen networks induced by cellular forces. Biophys. J. 114, 450–461 (2018).
Munster, S. et al. Strain history dependence of the nonlinear stress response of fibrin and collagen networks. Proc. Natl Acad. Sci. USA 110, 12197–12202 (2013). Confocal imaging directly reveals that fibrin and collagen networks exhibit plasticity owing to a combination of network-level and fibre-level remodelling in response to cyclic shear.
Kim, J. et al. Stress-induced plasticity of dynamic collagen networks. Nat. Commun. 8, 842 (2017).
Hall, M. S. et al. Fibrous nonlinear elasticity enables positive mechanical feedback between cells and ECMs. Proc. Natl Acad. Sci. USA 113, 14043–14048 (2016). A study highlighting the importance of nonlinear elasticity in cellular mechanosensing.
Gnesotto, F. S., Mura, F., Gladrow, J. & Broedersz, C. P. Broken detailed balance and non-equilibrium dynamics in living systems: a review. Rep. Prog. Phys. 81, 066601 (2018).
Kollmannsberger, P., Mierke, C. T. & Fabry, B. Nonlinear viscoelasticity of adherent cells is controlled by cytoskeletal tension. Soft Matter 7, 3127–3132 (2011).
Humphrey, D., Duggan, C., Saha, D., Smith, D. & Kas, J. Active fluidization of polymer networks through molecular motors. Nature 416, 413–416 (2002).
Chan, C. J. et al. Myosin II activity softens cells in suspension. Biophys. J. 108, 1856–1869 (2015).
Koenderink, G. H. et al. An active biopolymer network controlled by molecular motors. Proc. Natl Acad. Sci. USA 106, 15192–15197 (2009).
Alvarado, J., Sheinman, M., Abhinav, S., MacKintosh, F. C. & Koenderink, G. H. Molecular motors robustly drive active gels to a critically connected state. Nat. Phys. 9, 591–597 (2013).
Koenderink, G. H. & Paluch, E. K. Architecture shapes contractility in actomyosin networks. Curr. Opin. Cell Biol. 50, 79–85 (2018).
Murrell, M. P. & Gardel, M. L. F-actin buckling coordinates contractility and severing in a biomimetic actomyosin cortex. Proc. Natl Acad. Sci. USA 109, 20820–20825 (2012).
Ronceray, P., Broedersz, C. P. & Lenz, M. Fiber networks amplify active stress. Proc. Natl Acad. Sci. USA 113, 2827–2832 (2016).
Zemel, A., Bischofs, I. B. & Safran, S. A. Active elasticity of gels with contractile cells. Phys. Rev. Lett. 97, 128103 (2006).
Jansen, K. A., Bacabac, R. G., Piechocka, I. K. & Koenderink, G. H. Cells actively stiffen fibrin networks by generating contractile stress. Biophys. J. 105, 2240–2251 (2013).
Wollrab, V. et al. Polarity sorting drives remodeling of actin-myosin networks. J. Cell Sci. 132, 219717 (2018).
MacKintosh, F. C. & Levine, A. J. Nonequilibrium mechanics and dynamics of motor-activated gels. Phys. Rev. Lett. 100, 018104 (2008).
Sheinman, M., Broedersz, C. P. & MacKintosh, F. C. Actively stressed marginal networks. Phys. Rev. Lett. 109, 238101 (2012).
Mizuno, D., Tardin, C., Schmidt, C. F. & Mackintosh, F. C. Nonequilibrium mechanics of active cytoskeletal networks. Science 315, 370–373 (2007). A seminal study unveiling the effects of stresses generated by molecular motor activity on cytoskeletal mechanics.
Foster, P. J., Furthauer, S., Shelley, M. J. & Needleman, D. J. Active contraction of microtubule networks. eLife 4, e10837 (2015).
Gao, T., Blackwell, R., Glaser, M. A., Betterton, M. D. & Shelley, M. J. Multiscale polar theory of microtubule and motor-protein assemblies. Phys. Rev. Lett. 114, 048101 (2015).
Stam, S. et al. Filament rigidity and connectivity tune the deformation modes of active biopolymer networks. Proc. Natl Acad. Sci. USA 114, E10037–E10045 (2017).
Zenker, J. et al. Expanding actin rings zipper the mouse embryo for blastocyst formation. Cell 173, 776–791.e17 (2018).
Carlier, M. F. & Shekhar, S. Global treadmilling coordinates actin turnover and controls the size of actin networks. Nat. Rev. Mol. Cell Biol. 18, 389–401 (2017).
Brouhard, G. J. & Rice, L. M. Microtubule dynamics: an interplay of biochemistry and mechanics. Nat. Rev. Mol. Cell Biol. 19, 451–463 (2018).
Wioland, H. et al. ADF/cofilin accelerates actin dynamics by severing filaments and promoting their depolymerization at both ends. Curr. Biol. 27, 1956–1967 (2017).
Hiraiwa, T. & Salbreux, G. Role of turnover in active stress generation in a filament network. Phys. Rev. Lett. 116, 188101 (2016).
Mak, M., Zaman, M. H., Kamm, R. D. & Kim, T. Interplay of active processes modulates tension and drives phase transition in self-renewing, motor-driven cytoskeletal networks. Nat. Commun. 7, 10323 (2016).
McFadden, W. M., McCall, P. M., Gardel, M. L. & Munro, E. M. Filament turnover tunes both force generation and dissipation to control long-range flows in a model actomyosin cortex. PLoS Comput. Biol. 13, e1005811 (2017).
McCall, P. M., MacKintosh, F. C., Kovar, D. R. & Gardel, M. L. Cofilin drives rapid turnover and fluidization of entangled F-actin. Preprint at biorXiv https://www.biorxiv.org/content/10.1101/156224v1 (2017)..
Tan, T. H. et al. Self-organized stress patterns drive state transitions in actin cortices. Sci. Adv. 4, eaar2847 (2018).
Wuhr, M. et al. Deep proteomics of the Xenopus laevis egg using an mRNA-derived reference database. Curr. Biol. 24, 1467–1475 (2014).
Boekhoven, J., Hendriksen, W. E., Koper, G. J., Eelkema, R. & van Esch, J. H. Transient assembly of active materials fueled by a chemical reaction. Science 349, 1075–1079 (2015).
Li, Q. et al. Macroscopic contraction of a gel induced by the integrated motion of light-driven molecular motors. Nat. Nanotechnol. 10, 161–165 (2015).
Bertrand, O. J., Fygenson, D. K. & Saleh, O. A. Active, motor-driven mechanics in a DNA gel. Proc. Natl Acad. Sci. USA 109, 17342–17347 (2012).
Han, E. H., Chen, S. S., Klisch, S. M. & Sah, R. L. Contribution of proteoglycan osmotic swelling pressure to the compressive properties of articular cartilage. Biophys. J. 101, 916–924 (2011).
Huber, F., Boire, A., Lopez, M. P. & Koenderink, G. H. Cytoskeletal crosstalk: when three different personalities team up. Curr. Opin. Cell Biol. 32, 39–47 (2015).
van Doorn, J. M., Lageschaar, L., Sprakel, J. & van der Gucht, J. Criticality and mechanical enhancement in composite fiber networks. Phys. Rev. E 95, 042503 (2017).
Das, M. & Mackintosh, F. C. Poisson’s ratio in composite elastic media with rigid rods. Phys. Rev. Lett. 105, 138102 (2010).
Esue, O., Carson, A. A., Tseng, Y. & Wirtz, D. A direct interaction between actin and vimentin filaments mediated by the tail domain of vimentin. J. Biol. Chem. 281, 30393–30399 (2006).
Golde, T. et al. Glassy dynamics in composite biopolymer networks. Soft Matter 14, 7970–7978 (2018).
Brangwynne, C. P. et al. Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement. J. Cell Biol. 173, 733–741 (2006). A combined in vivo and in vitro study showing the importance of the composite architecture of the cytoskeleton for cell mechanics.
Bouchet, B. P. et al. Mesenchymal cell invasion requires cooperative regulation of persistent microtubule growth by SLAIN2 and CLASP1. Dev. Cell 39, 708–723 (2016).
Latorre, E. et al. Active superelasticity in three-dimensional epithelia of controlled shape. Nature 563, 203–208 (2018).
Kreger, S. T. & Voytik-Harbin, S. L. Hyaluronan concentration within a 3D collagen matrix modulates matrix viscoelasticity, but not fibroblast response. Matrix Biol. 28, 336–346 (2009).
Lai, V. K. et al. Swelling of collagen-hyaluronic acid co-gels: an in vitro residual stress model. Ann. Biomed. Eng. 44, 2984–2993 (2016).
Burla, F., Tauber, J., Dussi, S., van der Gucht, J. & Koenderink, G.H. Stress management in composite biopolymer networks. Nat. Phys. https://doi.org/10.1038/s41567-019-0443-6 (2019).
Huisman, E. M., Heussinger, C., Storm, C. & Barkema, G. T. Semiflexible filamentous composites. Phys. Rev. Lett. 105, 118101 (2010).
Wada, H. & Tanaka, Y. Mechanics and size-dependent elasticity of composite networks. Europhys. Lett. 87, 58001 (2009).
Bai, M., Missel, A. R., Klug, W. S. & Levine, A. J. The mechanics and affine-nonaffine transition in polydisperse semiflexible networks. Soft Matter 7, 907–914 (2011).
Shahsavari, A. S. & Picu, R. C. Exceptional stiffening in composite fiber networks. Phys. Rev. E 92, 012401 (2015).
Lin, Y.-C., Koenderink, G. H., MacKintosh, F. C. & Weitz, D. A. Control of non-linear elasticity in F-actin networks with microtubules. Soft Matter 7, 902–906 (2011).
Ricketts, S. N., Ross, J. L. & Robertson-Anderson, R. M. Co-entangled actin-microtubule composites exhibit tunable stiffness and power-law stress relaxation. Biophys. J. 115, 1055–1067 (2018).
Das, M. & MacKintosh, F. C. Mechanics of soft composites of rods in elastic gels. Phys. Rev. E 84, 061906 (2011).
Pelletier, V., Gal, N., Fournier, P. & Kilfoil, M. L. Microrheology of microtubule solutions and actin-microtubule composite networks. Phys. Rev. Lett. 102, 188303 (2009).
Broedersz, C. P., Storm, C. & MacKintosh, F. C. Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers. Phys. Rev. Lett. 101, 118103 (2008).
Das, M., Quint, D. A. & Schwarz, J. M. Redundancy and cooperativity in the mechanics of compositely crosslinked filamentous networks. PloS One 7, e35939 (2012).
Schmoller, K. M., Lieleg, O. & Bausch, A. R. Cross-linking molecules modify composite actin networks independently. Phys. Rev. Lett. 101, 118102 (2008).
Jensen, M. H., Morris, E. J., Goldman, R. D. & Weitz, D. A. Emergent properties of composite semiflexible biopolymer networks. Bioarchitecture 4, 138–143 (2014).
Deek, J., Maan, R., Loiseau, E. & Bausch, A. R. Reconstitution of composite actin and keratin networks in vesicles. Soft Matter 14, 1897–1902 (2018).
Yang, Y. L. et al. Influence of chondroitin sulfate and hyaluronic acid on structure, mechanical properties, and glioma invasion of collagen I gels. Biomaterials 32, 7932–7940 (2011).
Jaspers, M. et al. Nonlinear mechanics of hybrid polymer networks that mimic the complex mechanical environment of cells. Nat. Commun. 8, 15478 (2017).
Schiffhauer, E. S. et al. Mechanoaccumulative elements of the mammalian actin cytoskeleton. Curr. Biol. 26, 1473–1479 (2016).
Gan, Z. et al. Vimentin intermediate filaments template microtubule networks to enhance persistence in cell polarity and directed migration. Cell Syst. 3, 500–501 (2016).
Costigliola, N. et al. Vimentin fibers orient traction stress. Proc. Natl Acad. Sci. USA 114, 5195–5200 (2017).
Preciado Lopez, M. et al. Actin–microtubule coordination at growing microtubule ends. Nat. Commun. 5, 4778 (2014).
Gautieri, A., Vesentini, S., Redaelli, A. & Buehler, M. Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up. Nano Lett. 11, 757–766 (2011).
Valon, L., Marin-Llaurado, A., Wyatt, T., Charras, G. & Trepat, X. Optogenetic control of cellular forces and mechanotransduction. Nat. Commun. 8, 14396 (2017).
Oakes, P. W. et al. Optogenetic control of RhoA reveals zyxin-mediated elasticity of stress fibres. Nat. Commun. 8, 15817 (2017).
Bonnans, C., Chou, J. & Werb, Z. Remodelling the extracellular matrix in development and disease. Nat. Rev. Cell Biol. 15, 786–801 (2014).
Chang, S. W., Flynn, B. P., Ruberti, J. W. & Buehler, M. J. Molecular mechanism of force induced stabilization of collagen against enzymatic breakdown. Biomaterials 33, 3852–3859 (2012).
Bouameur, J. E. & Magin, T. M. Lessons from animal models of cytoplasmic intermediate filament proteins. Subcell. Biochem. 82, 171–230 (2017).
Arseni, L., Lombardi, A. & Orioli, D. From structure to phenotype: impact of collagen alterations on human health. Int. J. Mol. Sci. 19, 1407 (2018).
Needleman, D. & Dogic, Z. Active matter at the interface between materials science and cell biology. Nat. Rev. Mater. 2, 17048 (2017).
The authors thank K. Ganzinger for critically reading the manuscript, C. Martinez-Torres for help in acquiring the confocal microscopy image in Fig. 1c and F. C. MacKintosh and C. Broedersz for stimulating discussions about many of the topics covered in this Review. The authors gratefully acknowledge financial support from the European Research Council (Starting Grant no. 335672-MINICELL) and from the Industrial Partnership Programme Hybrid Soft Materials, which is carried out under an agreement between Unilever Research and Development B.V. and the Netherlands Organisation for Scientific Research (NWO).
The authors declare no competing interests.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Burla, F., Mulla, Y., Vos, B.E. et al. From mechanical resilience to active material properties in biopolymer networks. Nat Rev Phys 1, 249–263 (2019). https://doi.org/10.1038/s42254-019-0036-4
This article is cited by
Strong, tough, rapid-recovery, and fatigue-resistant hydrogels made of picot peptide fibres
Nature Communications (2023)
Four distinct network patterns of supramolecular/polymer composite hydrogels controlled by formation kinetics and interfiber interactions
Nature Communications (2023)
The hidden hierarchical nature of soft particulate gels
Nature Physics (2023)
Metabolic labeling of secreted matrix to investigate cell–material interactions in tissue engineering and mechanobiology
Nature Protocols (2022)
Interfacial friction and substrate deformation mediate long-range signal propagation in tissues
Biomechanics and Modeling in Mechanobiology (2022)