- Letter
- Open Access
Tuning of cytoplasmic effective viscosity via active noise
Phys. Rev. Research 7, L032052 – Published 9 September, 2025
DOI: https://doi.org/10.1103/3vm9-8k99
Abstract
The mechanical properties of cytoplasm are crucial for cellular functions. While active processes significantly alter cytoplasmic viscoelasticity, the physical mechanisms remain elusive. Here, we model the cytoplasm as a colloidal suspension subject to passive and active noise, quantified by an effective temperature. We demonstrate that a jammed cytoplasm undergoes a transition from solid to liquid phase at a critical effective temperature. Intriguingly, the simulated complex shear modulus at the critical state exhibits a power-law scaling with frequency and quantitatively matches the experimental data of live cells, given that the cytoplasmic volume fraction is slightly above the jamming transition. We further reveal the biological significance of the cytoplasm being slightly above jamming: It is a regime in which the effective viscosity, the magnitude of complex viscosity, is sensitive to changes in the effective temperature. Our results suggest that cells actively regulate their volume fraction into the sensitive regime, where they can efficiently tune cytoplasmic viscoelasticity through active processes.
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References (63)
- E. Elson, Cellular mechanics as an indicator of cytoskeletal structure and function, Annu. Rev. Biophys. Biophys. Chem. 17, 397 (1988).
- N. Wang, J. Butler, and D. Ingber, Mechanotransduction across the cell surface and through the cytoskeleton, Science 260, 1124 (1993).
- 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).
- P. Bursac, G. Lenormand, M. Oliver, D. Weitz, B. Fabry, and J. Fredberg, Cytoskeletal remodelling and slow dynamics in the living cell, Nat. Mater. 4, 557 (2005).
- X. Trepat, M. Wasserman, T. Angelini, E. Millet, D. Weitz, J. Butler, and J. Fredberg, Universal physical responses to stretch in the living cell, Nature (London) 447, 592 (2007).
- J. Dix and A. Verkman, Crowding effects on diffusion in solutions and cells, Annu. Rev. Biophys. 37, 247 (2008).
- B. Parry, I. Surovtsev, M. Cabeen, C. O'Hern, and C. Jacobs-Wagner, The bacterial cytoplasm has glass-like properties and is fluidized by metabolic activity, Cell 156, 183 (2014).
- E. Zhou, X. Trepat, C. Park, G. Lenormand, M. Oliver, S. Mijailovich, C. Hardin, D. Weitz, J. Butler, and J. Fredberg, Universal behavior of the osmotically compressed cell and its analogy to the colloidal glass transition, Proc. Natl. Acad. Sci. USA 106, 10632 (2009).
- J. Mattsson, H. M. Wyss, A. Fernández-Nieves, K. Miyazaki, Z. Hu, D. R. Reichman, and D. A. Weitz, Soft colloids make strong glasses, Nature (London) 462, 83 (2009).
- K. Nishizawa, K. Fujiwara, M. Ikenaga, N. Nakajo, M. Yanagisawa, and D. Mizuno, Universal glass-forming behavior of in vitro and living cytoplasm, Sci. Rep. 7, 15143 (2017).
- 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 68, 041914 (2003).
- G. Lenormand, E. Millet, B. Fabry, J. P. Butler, and J. J. Fredberg, Linearity and time-scale invariance of the creep function in living cells, J. R. Soc. Interface 1, 91 (2004).
- B. Hoffman, G. Massiera, K. Van Citters, and J. Crocker, The consensus mechanics of cultured mammalian cells, Proc. Natl. Acad. Sci. USA 103, 10259 (2006).
- P. Kollmannsberger, C. T. Mierke, and B. Fabry, Nonlinear viscoelasticity of adherent cells is controlled by cytoskeletal tension, Soft Matter 7, 3127 (2011).
- A. Rigato, A. Miyagi, and F. Rico, High-frequency microrheology reveals cytoskeleton dynamics in living cells, Nat. Phys. 13, 771 (2017).
- S. Hurst, B. Vos, and T. Betz, Intracellular softening and increased viscoelastic fluidity during division, Nat. Phys. 17, 1270 (2021).
- O. T. Cohen and A. G. Hendricks, Two dominant timescales of cytoskeletal crosslinking in the viscoelastic response of the cytoplasm, Phys. Rev. Res. 4, 043167 (2022).
- H. Ebata, K. Umeda, K. Nishizawa, W. Nagao, S. Inokuchi, Y. Sugino, T. Miyamoto, and D. Mizuno, Activity-dependent glassy cell mechanics I: Mechanical properties measured with active microrheology, Biophys. J. 122, 1781 (2023).
- K. Umeda, K. Nishizawa, W. Nagao, S. Inokuchi, Y. Sugino, H. Ebata, and D. Mizuno, Activity-dependent glassy cell mechanics II: Nonthermal fluctuations under metabolic activity, Biophys. J. 122, 4395 (2023).
- T. Muenker, G. Knotz, M. Krüger, and T. Betz, Accessing activity and viscoelastic properties of artificial and living systems from passive measurement, Nat. Mater. 23, 1283 (2024).
- K. Nishizawa, M. Bremerich, and D. Mizuno, Feedback-tracking microrheology in living cells, Sci. Adv. 3, e1700318 (2017).
- J.-T. Hang, Y. Kang, G.-K. Xu, and H. Gao, A hierarchical cellular structural model to unravel the universal power-law rheological behavior of living cells, Nat. Commun. 12, 6067 (2021).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/3vm9-8k99 for details on numerical simulations, additional analyses, and supplemental figures.
- C. S. O'Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel, Jamming at zero temperature and zero applied stress: The epitome of disorder, Phys. Rev. E 68, 011306 (2003).
- A. J. Liu and S. R. Nagel, The jamming transition and the marginally jammed solid, Annu. Rev. Condens. Matter Phys. 1, 347 (2010).
- D. Pan, Y. Wang, H. Yoshino, J. Zhang, and Y. Jin, A review on shear jamming, Phys. Rep. 1038, 1 (2023).
- B. Tighe, Relaxations and rheology near jamming, Phys. Rev. Lett. 107, 158303 (2011).
- K. Saitoh, T. Hatano, A. Ikeda, and B. P. Tighe, Stress relaxation above and below the jamming transition, Phys. Rev. Lett. 124, 118001 (2020).
- A. W. C. Lau, B. D. Hoffman, A. Davies, J. C. Crocker, and T. C. Lubensky, Microrheology, stress fluctuations, and active behavior of living cells, Phys. Rev. Lett. 91, 198101 (2003).
- M. Guo, A. Ehrlicher, and D. Weitz, Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy, Cell 158, 822 (2014).
- D. Koeze, D. Vågberg, B. Tjoa, and B. Tighe, Mapping the jamming transition of bidisperse mixtures, Europhys. Lett. 113, 54001 (2016).
- S. R. De Groot and P. Mazur, Non-Equilibrium Thermodynamics (Courier Corporation, North Chelmsford, MA, USA, 2013).
- This form of active noise is consistent with experimental data of E. coli [7]. It can be shown that a random force with a constant magnitude whose pointing direction diffuses due to thermal fluctuation has an autocorrelation function proportional to the cube of particle radius [49].
- T. Hatano, Growing length and time scales in a suspension of athermal particles, Phys. Rev. E 79, 050301 (2009).
- M. Doi, Soft Matter Physics (Oxford University Press, Oxford, UK, 2013).
- M. Rubinstein and R. H. Colby, Polymer Physics (Oxford University Press, Oxford, UK, 2003).
- M. Wyart, L. E. Silbert, S. R. Nagel, and T. A. Witten, Effects of compression on the vibrational modes of marginally jammed solids, Phys. Rev. E 72, 051306 (2005).
- A. Ikeda, T. Kawasaki, L. Berthier, K. Saitoh, and T. Hatano, Universal relaxation dynamics of sphere packings below jamming, Phys. Rev. Lett. 124, 058001 (2020).
- A. Ikeda, L. Berthier, and G. Biroli, Dynamic criticality at the jamming transition, J. Chem. Phys. 138, 124705 (2013).
- T. Bertrand, C. F. Schreck, C. S. O'Hern, and M. D. Shattuck, Hypocoordinated solids in particulate media, Phys. Rev. E 89, 062203 (2014).
- E. DeGiuli, E. Lerner, and M. Wyart, Theory of the jamming transition at finite temperature, J. Chem. Phys. 142, 164503 (2015).
- E. Flenner, G. Szamel, and L. Berthier, The nonequilibrium glassy dynamics of self-propelled particles, Soft Matter 12, 7136 (2016).
- D. Martin, J. O'Byrne, M. E. Cates, E. Fodor, C. Nardini, J. Tailleur, and F. van Wijland, Statistical mechanics of active Ornstein-Uhlenbeck particles, Phys. Rev. E 103, 032607 (2021).
- T. Kalwarczyk, N. Zibacz, A. Bielejewska, E. Zaboklicka, K. Koynov, J. Szymanski, A. Wilk, A. Patkowski, J. Gapinski, H.-J. Butt, and R. Holyst, Comparative analysis of viscosity of complex liquids and cytoplasm of mammalian cells at the nanoscale, Nano Lett. 11, 2157 (2011).
- W. P. Cox and E. H. Merz, Correlation of dynamic and steady flow viscosities, J. Polym. Sci. 28, 619 (1958).
- J. D. Ferry, Viscoelastic Properties of Polymers (John Wiley & Sons, New York, NY, USA, 1980).
- R. G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, Oxford, UK, 1999).
- A. Ikeda, L. Berthier, and P. Sollich, Unified study of glass and jamming rheology in soft particle systems, Phys. Rev. Lett. 109, 018301 (2012).
- L. Meng, Y. Jin, Y. Guan, J. Xu, and J. Lin, Diffusion enhancement in bacterial cytoplasm through an active random force, Phys. Rev. Res. 5, L032018 (2023).
- Y. Nematbakhsh, K. T. Pang, and C. T. Lim, Correlating the viscoelasticity of breast cancer cells with their malignancy, Convergent Sci. Phys. Oncol. 3, 034003 (2017).
- R. P. Joyner, J. H. Tang, J. Helenius, E. Dultz, C. Brune, L. J. Holt, S. Huet, D. J. Müller, and K. Weis, A glucose-starvation response regulates the diffusion of macromolecules, eLife 5, e09376 (2016).
- R. Wiese, K. Kroy, and D. Levis, Fluid-glass-jamming rheology of soft active Brownian particles, Phys. Rev. Lett. 131, 178302 (2023).
- L. Venkova, A. S. Vishen, S. Lembo, N. Srivastava, B. Duchamp, A. Ruppel, A. Williart, S. Vassilopoulos, A. Deslys, J. M. G. Arcos et al., A mechano-osmotic feedback couples cell volume to the rate of cell deformation, elife 11, e72381 (2022).
- G. Rivas and A. P. Minton, Influence of nonspecific interactions on protein associations: Implications for biochemistry in vivo, Annu. Rev. Biochem. 91, 321 (2022).
- J. Weng and W. Wang, Dynamic multivalent interactions of intrinsically disordered proteins, Curr. Opin. Struct. Biol. 62, 9 (2020).
- W. Zheng, H. Liu, and N. Xu, Shear-induced solidification of athermal systems with weak attraction, Phys. Rev. E 94, 062608 (2016).
- J. A. Owen, D. Osmanovic, and L. Mirny, Design principles of 3D epigenetic memory systems, Science 382, eadg3053 (2023).
- P.-G. De Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, USA, 1979).
- G. Tesei, A. I. Trolle, N. Jonsson, J. Betz, F. E. Knudsen, F. Pesce, K. E. Johansson, and K. Lindorff-Larsen, Conformational ensembles of the human intrinsically disordered proteome, Nature (London) 626, 897 (2024).
- M. Wyart, S. Nagel, and T. Witten, Geometric origin of excess low-frequency vibrational modes in amorphous solids, Europhys. Lett. 72, 486 (2005).
- J. Boschan, D. Vågberg, E. Somfai, and B. P. Tighe, Beyond linear elasticity: Jammed solids at finite shear strain and rate, Soft Matter 12, 5450 (2016).
- L. Persson, V. Ambati, and O. Brandman, Cellular control of viscosity counters changes in temperature and energy availability, Cell 183, 1572 (2020).
- https://github.com/thunder-skin/Tuning-of-cytoplasmic-effective-viscosity-via-active-noise.