Onset of Mechanochemical Pattern Formation in Poroviscoelastic Models of Active Cytoplasm

  • Sergio AlonsoEmail author
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 20)


The cytoplasm of living cells is a complex structure formed by a fluid phase composed by water and small molecules and a second phase composed by the filaments of the cytoskeleton forming a viscoelastic gel. The interaction between the two phases gives rise to a poroviscoelastic structure which combines elastic and viscous responses to external stimuli. On the other hand, the cytoplasm is active, and molecular motors perform active stress. Different molecules regulate the activity of the motors. In the cytoplasm the biochemistry and the mechanics are interconnected, while motors and biochemical regulators are transported by flows in the two phases, the motors produce active stresses into the cytoskeleton and generate active flows. Here, we compare two active poroviscoelastic models with different viscoelastic properties, which can produce oscillations and the polarization of a living cell. The main features of the different mechanisms of pattern formation are studied by linear stability analysis of the homogeneous steady state and by numerical simulations.



I acknowledge fruitful discussions with Markus Bär, Markus Radszuweit, Harald Engel and Marcus J.B. Hauser. I thank financial support by MINECO of Spain under the Ramon y Cajal program with the grant number RYC-2012-11265 and FIS2014-55365-P.


  1. 1.
    Alonso, S., Stange, M., Beta, C.: Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells. PLos ONE 13, e0201977 (2018)CrossRefGoogle Scholar
  2. 2.
    Alonso, S., Strachauer, U., Radszuweit, M., Bär, M., Hauser, M.J.: Oscillations and uniaxial mechanochemical waves in a model of an active poroelastic medium: application to deformation patterns in protoplasmic droplets of Physarum polycephalum. Phys. D 318, 58–69 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Alonso, S., Radszuweit, M., Engel, H., Bär, M.: Mechanochemical pattern formation in simple models of active viscoelastic fluids and solids. J. Phys. D: Appl. Phys. 50, 434004 (2017)CrossRefGoogle Scholar
  4. 4.
    Alt, W., Dembo, M.: Cytoplasm dynamics and cell motion: two-phase flow models. Math. Biosci. 156, 207–228 (1999)CrossRefGoogle Scholar
  5. 5.
    Banerjee, S., Liverpool, T.B., Marchetti, M.C.: Generic phases of cross-linked active gels: relaxation, oscillation and contractility. Europhys. Lett. 96, 58004 (2011)CrossRefGoogle Scholar
  6. 6.
    Beta, C., Kruse, K.: Intracellular oscillations and waves. Annu. Rev. Condes. Matter Phys. 8 (2017)CrossRefGoogle Scholar
  7. 7.
    Bois, J.S., Jülicher, F., Grill, S.W.: Pattern formation in active fluids. Phys. Rev. Lett. 106, 028103 (2011)CrossRefGoogle Scholar
  8. 8.
    Bressloff, P.C., Newby, J.M.: Stochastic models of intracellular transport. Rev. Mod. Phys. 85, 135 (2013)CrossRefGoogle Scholar
  9. 9.
    Callan-Jones, A.C., Jlicher, F.: Hydrodynamics of active permeating gels. New J. Phys. 13, 093027 (2011)CrossRefGoogle Scholar
  10. 10.
    Charras, G.T., Mitchison, T.J., Mahadevan, L.: Animal cell hydraulics. J. Cell Sci. 122, 3233–3241 (2009)CrossRefGoogle Scholar
  11. 11.
    Cross, M.C., Hohenberg, P.C.: Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851 (1993)CrossRefGoogle Scholar
  12. 12.
    Goehring, N.W., Grill, S.W.: Cell polarity: mechanochemical patterning. Trends Cell Biol. 23, 72–80 (2013)CrossRefGoogle Scholar
  13. 13.
    Howard, J., Grill, S.W., Bois, J.S.: Turing’s next steps: the mechanochemical basis of morphogenesis. Nat. Rev. Mol. Cell Biol. 12, 392–398 (2011)CrossRefGoogle Scholar
  14. 14.
    Huber, F., Schnauss, J., Rönicke, S., Rauch, P., Müller, K., Fütterer, C., Käs, J.: Emergent complexity of the cytoskeleton: from single filaments to tissue. Adv. Phys. 62, 1–112 (2013)CrossRefGoogle Scholar
  15. 15.
    Ingber, D.E., Wang, N., Stamenovic, D.: Tensegrity, cellular biophysics, and the mechanics of living systems. Rep. Prog. Phys. 77, 046603 (2014)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Joanny, J.F., Kruse, K., Prost, J., Ramaswamy, S.: The actin cortex as an active wetting layer. Eur. Phys. J. E Soft Matter 36, 1–6 (2013)CrossRefGoogle Scholar
  17. 17.
    Karcher, H., Lammerding, J., Huang, H., Lee, R.T., Kamm, R.D., Kaazempur-Mofrad, M.R.: A three-dimensional viscoelastic model for cell deformation with experimental verification. Biophys. J. 85, 3336–3349 (2003)CrossRefGoogle Scholar
  18. 18.
    Keener, J.P., Sneyd, J.: Mathematical Physiology. Springer, New York (2009)CrossRefGoogle Scholar
  19. 19.
    Kollmannsberger, P., Fabry, B.: Linear and nonlinear rheology of living cells. Annu. Rev. Mater. Res. 41, 75–97 (2011)CrossRefGoogle Scholar
  20. 20.
    Kumar, K.V., Bois, J.S., Jülicher, F., Grill, S.W.: Pulsatory patterns in active fluids. Phys. Rev. Lett. 112, 208101 (2014)CrossRefGoogle Scholar
  21. 21.
    Lim, C.T., Zhou, E.H., Quek, S.T.: Mechanical models for living cells—a review. J. Biomech. 39, 195–216 (2006)CrossRefGoogle Scholar
  22. 22.
    Luby-Phelps, K.: Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intracellular surface area. Int. Rev. Cytol. 192, 189–221 (1999)CrossRefGoogle Scholar
  23. 23.
    MacKintosh, F.C., Levine, A.J.: Nonequilibrium mechanics and dynamics of motor-activated gels. Phys. Rev. Lett. 100, 018104 (2008)CrossRefGoogle Scholar
  24. 24.
    Mitchison, T.J., Charras, G.T., Mahadevan, L.: Implications of a poroelastic cytoplasm for the dynamics of animal cell shape. Semin. Cell Dev. Biol. 19, 215–223 (2008)CrossRefGoogle Scholar
  25. 25.
    Moeendarbary, E., Valon, L., Fritzsche, M., Harris, A.R., Moulding, D.A., Thrasher, A.J., Stride, E., Mahadevan, L., Charras, G.T.: The cytoplasm of living cells behaves as a poroelastic material. Nat. Mater. 12, 253–261 (2013)CrossRefGoogle Scholar
  26. 26.
    Mogilner, A., Allard, J., Wollman, R.: Cell polarity: quantitative modeling as a tool in cell biology. Science 336, 175–179 (2012)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Murray, J.D.: Mathematical Biology. II Spatial Models and Biomedical Applications. Springer, New York (2001)Google Scholar
  28. 28.
    Radszuweit, M., Alonso, S., Engel, H., Bär, M.: Intracellular mechanochemical waves in an active poroelastic model. Phys. Rev. Lett. 110, 138102 (2013)CrossRefGoogle Scholar
  29. 29.
    Radszuweit, M., Engel, H., Bär, M.: An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum. PloS One 9, e99220 (2014)CrossRefGoogle Scholar
  30. 30.
    Rodriguez, M.L., McGarry, P.J., Sniadecki, N.J.: Review on cell mechanics: experimental and modeling approaches. Appl. Mech. Rev. 65, 060801 (2013)CrossRefGoogle Scholar
  31. 31.
    Salbreux, G., Charras, G., Paluch, E.: Actin cortex mechanics and cellular morphogenesis. Trends Cell Biol. 22, 536–545 (2012)CrossRefGoogle Scholar
  32. 32.
    Turing, A.M.: The chemical basis of morphogenesis. Philos. Trans. R. Soc. B 237, 37 (1952)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversitat Politècnica de CatalunyaBarcelonaSpain

Personalised recommendations