Viscoelasticity of multicellular surfaces

Various modeling approaches have been applied to describe viscoelasticity of multicellular surfaces. The viscoelasticity is considered within three time regimes: (1) short time regime for milliseconds to seconds time scale which corresponds to sub-cellular level; (2) middle time regime for several tens of seconds to several minutes time scale which corresponds to cellular level; and (3) long time regime for several tens of minutes to several hours time scale which corresponds to supra-celltilar level. Short and middle time regimes have been successfully elaborated in the literature, whereas long time viscoelasticity remains unclear. Long time regime accounts for collective cell migration. Collective cell migration could induce uncorrelated motility which has an impact to energy storage and dissipation during cell surface rearrangement. Uncorrelated motility influences: (1) volume fraction of migrating cells, (2) distribution of migrating cells, (3) shapes of migrating cell groups. These parameters influence mechanical coupling between migrating and resting subpopulations and consequently the constitutive model for long time regime. This modeling consideration indicates that additional experimental work is needed to confirm the feasibility of constitutive models which have been applied in literature for long time regime as: (1) relaxation of stress and strain, (2) storage and loss moduli as the function of time, (3) distribution of migrating cells