- Open Access
Two dominant timescales of cytoskeletal crosslinking in the viscoelastic response of the cytoplasm
Phys. Rev. Research 4, 043167 – Published 6 December, 2022
DOI: https://doi.org/10.1103/PhysRevResearch.4.043167
Abstract
Cells precisely regulate their frequency-dependent viscoelastic properties in response to chemical and mechanical cues. We use optical trap-based active microrheology using intracellular probes to measure the cytoplasmic mechanical response of fibroblast and macrophage cells over a broad frequency range ( Hz). Both cell types show similar frequency-dependent behavior, suggesting that the mechanisms that control the cell's mechanical response are general to many cell types. At frequencies above 1 Hz, the cytoplasmic mechanical behavior shows a broad distribution of relaxation timescales consistent with power-law mechanics. At low frequencies ( Hz), cells exhibit fluidlike behavior with distinct relaxation timescales, similar to that observed in reconstituted networks of transiently crosslinked actin filaments. The response across all frequencies can be captured by a mathematical model combining a power-law term with two crosslinker-unbinding terms. The two unbinding rates required to describe the low-frequency response suggest that the viscoelastic relaxation of the cytoplasm is governed either by multiple dominant crosslinkers or by a single crosslinker with multiple states.
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References (87)
- G. B. Nash, E. O'Brien, E. C. Gordon-Smith, and J. A. Dormandy, Abnormalities in the mechanical properties of red blood cells caused by Plasmodium falciparum, Blood 74, 855 (1989).
- J. Jaffar, S.-H. Yang, S. Y. Kim, H.-W. Kim, A. Faiz, W. Chrzanowski, and J. K. Burgess, Greater cellular stiffness in fibroblasts from patients with idiopathic pulmonary fibrosis, Am. J. Physiol.-Lung Cell. Mol. Physiol. 315, L59 (2018).
- N. L. Sehgel, S. F. Vatner, and G. A. Meininger, Smooth muscle cell stiffness syndrome-revisiting the structural basis of arterial stiffness, Front. Physiol. 6, 335 (2015).
- F. Lautenschläger, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, The regulatory role of cell mechanics for migration of differentiating myeloid cells, Proc. Natl. Acad. Sci. USA 106, 15696 (2009).
- R. R. Chaturvedi, T. Herron, R. Simmons, D. Shore, P. Kumar, B. Sethia, F. Chua, E. Vassiliadis, and J. C. Kentish, Passive stiffness of myocardium from congenital heart disease and implications for diastole, Circulation 121, 979 (2010).
- K. A. Ward, W. I. Li, S. Zimmer, and T. Davis, Viscoelastic properties of transformed cells: Role in tumor cell progression and metastasis formation, Biorheology 28, 301 (1991).
- J. H. Dangaria and P. J. Butler, Macrorheology and adaptive microrheology of endothelial cells subjected to fluid shear stress, Am. J. Physiol.-Cell Physiology 293, C1568 (2007).
- R. Matzke, K. Jacobson, and M. Radmacher, Direct, high-resolution measurement of furrow stiffening during division of adherent cells, Nat. Cell Biol. 3, 607 (2001).
- G. S. Worthen, B. Schwab, E. L. Elson, and G. P. Downey, Mechanics of stimulated neutrophils: Cell stiffening induces retention in capillaries, Science 245, 183 (1989).
- H. Yu, C. Y. Tay, W. S. Leong, S. C. W. Tan, K. Liao, and L. P. Tan, Mechanical behavior of human mesenchymal stem cells during adipogenic and osteogenic differentiation, Biochem. Biophys. Res. Commun. 393, 150 (2010).
- J. Hu, S. Jafari, Y. Han, A. J. Grodzinsky, S. Cai, and M. Guo, Size- and speed-dependent mechanical behavior in living mammalian cytoplasm, Proc. Natl. Acad. Sci. USA 114, 9529 (2017).
- O. Thoumine and A. Ott, Time scale dependent viscoelastic and contractile regimes in fibroblasts probed by microplate manipulation, J. Cell Sci. 110, 2109 (1997).
- T. L. Nguyen, E. R. Polanco, A. N. Patananan, T. A. Zangle, and M. A. Teitell, Cell viscoelasticity is linked to fluctuations in cell biomass distributions, Sci. Rep. 10, 7403 (2020).
- E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, The cytoplasm of living cells behaves as a poroelastic material, Nat. Mater. 12, 253 (2013).
- A. Cartagena and A. Raman, Local viscoelastic properties of live cells investigated using dynamic and quasi-static atomic force microscopy methods, Biophys. J. 106, 1033 (2014).
- N. Wang, K. Naruse, D. Stamenović, J. J. Fredberg, S. M. Mijailovich, I. M. Tolić-Nørrelykke, T. Polte, R. Mannix, and D. E. Ingber, Mechanical behavior in living cells consistent with the tensegrity model, Proc. Natl. Acad. Sci. USA 98, 7765 (2001).
- B. D. Hoffman, G. Massiera, K. M. Van Citters, and J. C. Crocker, The consensus mechanics of cultured mammalian cells, Proc. Natl. Acad. Sci. USA 103, 10259 (2006).
- Y. Bu, L. Li, and J. Wang, Power law creep and relaxation with the atomic force microscope: Determining viscoelastic property of living cells, Sci. China: Technol. Sci. 62, 781 (2019).
- M. Balland, N. Desprat, D. Icard, S. Féréol, A. Asnacios, J. Browaeys, S. Hénon, and F. Gallet, Power laws in microrheology experiments on living cells: Comparative analysis and modeling, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 021911 (2006).
- E. H. Zhou, S. T. Quek, and C. T. Lim, Power-law rheology analysis of cells undergoing micropipette aspiration, Biomech. Model. Mechanobiol. 9, 563 (2010).
- B. Fabry, G. N. Maksym, J. P. Butler, M. Glogauer, D. Navajas, and J. J. Fredberg, Scaling the Microrheology of Living Cells, Phys. Rev. Lett. 87, 148102 (2001).
- S. Hurst, B. E. Vos, M. Brandt, and T. Betz, Intracellular softening and increased viscoelastic fluidity during division, Nat. Phys. 17, 1270 (2021).
- C. P. Broedersz, M. Depken, N. Y. Yao, M. R. Pollak, D. A. Weitz, and F. C. MacKintosh, Cross-Link-Governed Dynamics of Biopolymer Networks, Phys. Rev. Lett. 105, 238101 (2010).
- L. Deng, X. Trepat, J. P. Butler, E. Millet, K. G. Morgan, D. A. Weitz, and J. J. Fredberg, Fast and slow dynamics of the cytoskeleton, Nat. Mater. 5, 636 (2006).
- K. K. Mandadapu, S. Govindjee, and M. R. K. Mofrad, On the cytoskeleton and soft glassy rheology, J. Biomech. 41, 1467 (2008).
- O. Lieleg, K. M. Schmoller, M. M. A. E. Claessens, and A. R. Bausch, Cytoskeletal polymer networks: Viscoelastic properties are determined by the microscopic interaction potential of cross-links, Biophys. J. 96, 4725 (2009).
- D. H. Wachsstock, W. H. Schwarz, and T. D. Pollard, Cross-linker dynamics determine the mechanical properties of actin gels, Biophys. J. 66, 801 (1994).
- S. M. V. Ward, A. Weins, M. R. Pollak, and D. A. Weitz, Dynamic viscoelasticity of actin cross-linked with wild-type and disease-causing mutant α-Actinin-4, Biophys. J. 95, 4915 (2008).
- J. Xu, D. Wirtz, and T. D. Pollard, Dynamic cross-linking by α-Actinin determines the mechanical properties of actin filament networks, J. Biol. Chem. 273, 9570 (1998).
- N. Y. Yao, C. P. Broedersz, M. Depken, D. J. Becker, M. R. Pollak, F. C. MacKintosh, and D. A. Weitz, Stress-Enhanced Gelation: A Dynamic Nonlinearity of Elasticity, Phys. Rev. Lett. 110, 018103 (2013).
- O. Lieleg, M. M. A. E. Claessens, Y. Luan, and A. R. Bausch, Transient Binding and Dissipation in Cross-Linked Actin Networks, Phys. Rev. Lett. 101, 108101 (2008).
- M. Atakhorrami, G. H. Koenderink, J. F. Palierne, F. C. MacKintosh, and C. F. Schmidt, Scale-Dependent Nonaffine Elasticity of Semiflexible Polymer Networks, Phys. Rev. Lett. 112, 088101 (2014).
- F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt, Microscopic Viscoelasticity: Shear Moduli of Soft Materials Determined from Thermal Fluctuations, Phys. Rev. Lett. 79, 3286 (1997).
- T. Golde, M. Glaser, C. Tutmarc, I. Elbalasy, C. Huster, G. Busteros, D. M. Smith, H. Herrmann, J. A. Käs, and J. Schnauß, The role of stickiness in the rheology of semiflexible polymers, Soft Matter 15, 4865 (2019).
- T. G. Mason, T. Gisler, K. Kroy, E. Frey, and D. A. Weitz, Rheology of F-actin solutions determined from thermally driven tracer motion, J. Rheol. 44, 917 (2000).
- D. Mizuno, D. A. Head, F. C. MacKintosh, and C. F. Schmidt, Active and passive microrheology in equilibrium and nonequilibrium systems, Macromolecules 41, 7194 (2008).
- F. Wottawah, S. Schinkinger, B. Lincoln, R. Ananthakrishnan, M. Romeyke, J. Guck, and J. Käs, Optical Rheology of Biological Cells, Phys. Rev. Lett. 94, 098103 (2005).
- L. Chaubet, A. R. Chaudhary, H. K. Heris, A. J. Ehrlicher, and A. G. Hendricks, Dynamic actin cross-linking governs the cytoplasm's transition to fluid-like behavior, Mol. Biol. Cell 31, 1744 (2020).
- A. J. Ehrlicher, R. Krishnan, M. Guo, C. M. Bidan, D. A. Weitz, and M. R. Pollak, Alpha-actinin binding kinetics modulate cellular dynamics and force generation, Proc. Natl. Acad. Sci. 112, 6619 (2015).
- M. T. Valentine, Z. E. Perlman, M. L. Gardel, J. H. Shin, P. Matsudaira, T. J. Mitchison, and D. A. Weitz, Colloid surface chemistry critically affects multiple particle tracking measurements of biomaterials, Biophys. J. 86, 4004 (2004).
- D. Mizuno, R. Bacabac, C. Tardin, D. Head, and C. F. Schmidt, High-Resolution Probing of Cellular Force Transmission, Phys. Rev. Lett. 102, 168102 (2009).
- A. G. Hendricks, E. L. F. Holzbaur, and Y. E. Goldman, Force measurements on cargoes in living cells reveal collective dynamics of microtubule motors, Proc. Natl. Acad. Sci. USA 109, 18447 (2012).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.043167 for supplemental methods and figures.
- J. R. Staunton, B. Blehm, A. Devine, and K. Tanner, In situ calibration of position detection in an optical trap for active microrheology in viscous materials, Opt. Express 25, 1746 (2017).
- D. Stamenović, N. Rosenblatt, M. Montoya-Zavala, B. D. Matthews, S. Hu, B. Suki, N. Wang, and D. E. Ingber, Rheological behavior of living cells is timescale-dependent, Biophys. J. 93, L39 (2007).
- J. Alcaraz, L. Buscemi, M. Grabulosa, X. Trepat, B. Fabry, R. Farré, and D. Navajas, Microrheology of human lung epithelial cells measured by atomic force microscopy, Biophys. J. 84, 2071 (2003).
- B. Fabry, G. N. Maksym, J. P. Butler, M. Glogauer, D. Navajas, N. A. Taback, E. J. Millet, and J. J. Fredberg, Time scale and other invariants of integrative mechanical behavior in living cells, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68, 041914 (2003).
- G. Fläschner, C. I. Roman, N. Strohmeyer, D. Martinez-Martin, and D. J. Müller, Rheology of rounded mammalian cells over continuous high-frequencies, Nat. Commun. 12, 2922 (2021).
- A. Rigato, A. Miyagi, S. Scheuring, and F. Rico, High-frequency microrheology reveals cytoskeleton dynamics in living cells, Nat. Phys. 13, 771 (2017).
- J. R. Staunton, W. Y. So, C. D. Paul, and K. Tanner, High-frequency microrheology in 3D reveals mismatch between cytoskeletal and extracellular matrix mechanics, Proc. Natl. Acad. Sci. 116, 14448 (2019).
- G. Schwarz, Estimating the dimension of a model, Ann. Stat. 6, 461 (1978).
- C. Arbore, L. Perego, M. Sergides, and M. Capitanio, Probing force in living cells with optical tweezers: From single-molecule mechanics to cell mechanotransduction, Biophys. Rev. 11, 765 (2019).
- A. G. Hendricks and Y. E. Goldman, Measuring molecular forces using calibrated optical tweezers in living cells, Methods Mol. Biol. 1486, 537 (2017).
- C. Aermes, A. Hayn, T. Fischer, and C. T. Mierke, Cell mechanical properties of human breast carcinoma cells depend on temperature, Sci. Rep. 11, 10771 (2021).
- C. J. Chan, G. Whyte, L. Boyde, G. Salbreux, and J. Guck, Impact of heating on passive and active biomechanics of suspended cells, Interface Focus 4, 20130069 (2014).
- S. Ebert, K. Travis, B. Lincoln, and J. Guck, Fluorescence ratio thermometry in a microfluidic dual-beam laser trap, Opt. Express. 15, 15493 (2007).
- T. R. Kießling, R. Stange, J. A. Käs, and A. W. Fritsch, Thermorheology of living cells—impact of temperature variations on cell mechanics, New J. Phys. 15, 045026 (2013).
- J. Bixler, B. Hokr, M. Denton, G. Noojin, A. Shingledecker, H. Beier, R. Thomas, B. Rockwell, and V. Yakovlev, Assessment of tissue heating under tunable near-infrared radiation, J. Biomed. Opt. 19, 70501 (2014).
- C. G. D. Remedios, D. Chhabra, M. Kekic, I. V. Dedova, M. Tsubakihara, D. A. Berry, and N. J. Nosworthy, Actin binding proteins: Regulation of cytoskeletal microfilaments, Physiol. Rev. 83, 433 (2003).
- R. Mohan and A. John, Microtubule-associated proteins as direct crosslinkers of actin filaments and microtubules, IUBMB Life 67, 395 (2015).
- Y. Yang, J. Dowling, Q. C. Yu, P. Kouklis, D. W. Cleveland, and E. Fuchs, An essential cytoskeletal linker protein connecting actin microfilaments to intermediate filaments, Cell 86, 655 (1996).
- A. Bretscher, Fimbrin is a cytoskeletal protein that crosslinks F-actin in vitro, Proc. Natl. Acad. Sci. USA 78, 6849 (1981).
- T. E. Kreis and R. E. Vale, Guidebook to Cytoskeletal and Motor Proteins, 2nd ed. (Oxford University Press, Oxford, 1999).
- J. M. Ferrer, H. Lee, J. Chen, B. Pelz, F. Nakamura, R. D. Kamm, and M. J. Lang, Measuring molecular rupture forces between single actin filaments and actin-binding proteins, Proc. Natl. Acad. Sci. 105, 9221 (2008).
- W. H. Goldmann and G. Isenberg, Analysis of filamin and alpha-actinin binding to actin by the stopped flow method, FEBS Lett. 336, 408 (1993).
- Y. Mulla, H. Wierenga, C. Alkemade, P. R. ten Wolde, and G. H. Koenderink, Frustrated binding of biopolymer crosslinkers, Soft Matter 15, 3036 (2019).
- Z. Lansky, M. Braun, A. Lüdecke, M. Schlierf, P. R. ten Wolde, M. E. Janson, and S. Diez, Diffusible crosslinkers generate directed forces in microtubule networks, Cell 160, 1159 (2015).
- Y. S. Aratyn, T. E. Schaus, E. W. Taylor, and G. G. Borisy, Intrinsic dynamic behavior of fascin in filopodia, Mol. Biol. Cell 18, 3928 (2007).
- C. T. Skau, D. S. Courson, A. J. Bestul, J. D. Winkelman, R. S. Rock, V. Sirotkin, and D. R. Kovar, Actin filament bundling by fimbrin is important for endocytosis, cytokinesis, and polarization in fission yeast, J. Biol. Chem. 286, 26964 (2011).
- T. P. Lele, J. Pendse, S. Kumar, M. Salanga, J. Karavitis, and D. E. Ingber, Mechanical forces alter zyxin unbinding kinetics within focal adhesions of living cells, J. Cell. Physiol. 207, 187 (2006).
- Y. Tseng, T. P. Kole, J. S. Lee, E. Fedorov, S. C. Almo, B. W. Schafer, and D. Wirtz, How actin crosslinking and bundling proteins cooperate to generate an enhanced cell mechanical response, Biochem. Biophys. Res. Commun. 334, 183 (2005).
- E. M. Reichl, Y. Ren, M. K. Morphew, M. Delannoy, J. C. Effler, K. D. Girard, S. Divi, P. A. Iglesias, S. C. Kuo, and D. N. Robinson, Interactions between myosin and actin crosslinkers control cytokinesis contractility dynamics and mechanics, Curr. Biol. 18, 471 (2008).
- M. L. Gardel, K. E. Kasza, C. P. Brangwynne, J. Liu, and D. A. Weitz, Chapter 19: Mechanical response of cytoskeletal networks, Methods Cell Biol. 89, 487 (2008).
- E. Fuchs and I. Karakesisoglou, Bridging cytoskeletal intersections, Genes Dev. 15, 1 (2001).
- L. Rognoni, J. Stigler, B. Pelz, J. Ylänne, and M. Rief, Dynamic force sensing of filamin revealed in single-molecule experiments, Proc. Natl. Acad. Sci. USA 109, 19679 (2012).
- E. S. Schiffhauer, T. Luo, K. Mohan, V. Srivastava, X. Qian, E. R. Griffis, P. A. Iglesias, and D. N. Robinson, Mechanoaccumulative elements of the mammalian actin cytoskeleton, Curr. Biol. 26, 1473 (2016).
- S. Le, X. Hu, M. Yao, H. Chen, M. Yu, X. Xu, N. Nakazawa, F. M. Margadant, M. P. Sheetz, and J. Yan, Mechanotransmission and mechanosensing of human alpha-Actinin 1, Cell Rep. 21, 2714 (2017).
- K. Hosseini, L. Sbosny, I. Poser, and E. Fischer-Friedrich, Binding dynamics of α-Actinin-4 in dependence of actin cortex tension, Biophys. J. 119, 1091 (2020).
- D. L. Huang, N. A. Bax, C. D. Buckley, W. I. Weis, and A. R. Dunn, Vinculin forms a directionally asymmetric catch bond with F-actin, Science 357, 703 (2017).
- M. G. Mendez, D. Restle, and P. A. Janmey, Vimentin enhances cell elastic behavior and protects against compressive stress, Biophys. J. 107, 314 (2014).
- H. Ahmadzadeh, D. H. Smith, and V. B. Shenoy, Viscoelasticity of tau proteins leads to strain rate-dependent breaking of microtubules during axonal stretch injury: Predictions from a mathematical model, Biophys. J. 106, 1123 (2014).
- M. Balland, A. Richert, and F. Gallet, The dissipative contribution of myosin II in the cytoskeleton dynamics of myoblasts, Eur. Biophys. J. 34, 255 (2005).
- J. Hu, Y. Li, Y. Hao, T. Zheng, S. K. Gupta, G. A. Parada, H. Wu, S. Lin, S. Wang, X. Zhao, R. D. Goldman, S. Cai, and M. Guo, High stretchability, strength, and toughness of living cells enabled by hyperelastic vimentin intermediate filaments, Proc. Natl. Acad. Sci. 116, 17175 (2019).
- Y.-C. Lin, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, Control of non-linear elasticity in F-actin networks with microtubules, Soft Matter 7, 902 (2011).
- S. N. Ricketts, M. L. Francis, L. Farhadi, M. J. Rust, M. Das, J. L. Ross, and R. M. Robertson-Anderson, Varying crosslinking motifs drive the mesoscale mechanics of actin-microtubule composites, Sci. Rep. 9, 12831 (2019).
- M. H. Jensen, E. J. Morris, and D. A. Weitz, Mechanics and dynamics of reconstituted cytoskeletal systems, Biochim. Biophys. Acta 1853, 3038 (2015).
- M. H. Jensen, E. J. Morris, R. D. Goldman, and D. A. Weitz, Emergent properties of composite semiflexible biopolymer networks, Bioarchitecture 4, 138 (2014).