Long-time viscoelasticity of multicellular surfaces caused by collective cell migration - Multi-scale modeling considerations

Abstract

Long-time viscoelasticity of multicellular surfaces caused by collective cell migration depends on: (1) the volume fraction and configuration of migrating cells and the rate of its change, (2) the viscoelasticity of migrating cell groups, and (3) the viscoelasticity of surrounding resting cells. The key parameter that influences the viscoelasticity is the size, shape, and thickness of the biointerface between migrating and resting cell sub-populations. The mull-scale nature of the biointerface dynamics represents the product of: (1) the local changes of the size and shape of migrating cell groups, (2) the local accumulation of resistance stress within the core regions of migrating cell groups (internal effects), (3) the collision of the velocity fronts (external effects). The local changes of the size and shape of migrating cell groups induces additional energy dissipation. The accumulated stress could induce disordering of migrating cell groups and consequently migrating-to-resting cell state transition. The collision of the velocity fronts could lead to stagnant zone formation and local increase of the volume fraction of resting cells. Herein, an attempt is made to discuss and connect various modeling approaches from the stand point of thermodynamics and rheology obtained at (1) cellular level, (2) biointerface between migrating cell group and surrounding resting cells, and (3) a part of multicellular surfaces. These complex phenomena are discussed on the model system such as cell aggregate rounding after uni-axial compression under in vitro conditions at characteristic times such as: (1) cell shape relaxation time under stretching/compression, (2) contact time between migrating cell group and surrounding resting cells, (3) cell persistence time, (4) the lifetime of migrating cell groups, (5) cell rearrangement time (i.e. the process time), and (6) the stress and strain relaxation times of perturbed multicellular surface parts. The results of this theoretical analysis point to the relationship between interfacial size, mechanical coupling mode and rheological behavior of multicellular surfaces. Multi scale dynamics at the biointerface is a key parameter which influences mechanical behavior of multicellular surfaces. Consequently, the shape of migrating cell groups and their distribution are not random characteristics of the multicellular surface but rather influenced by cause-consequence relations between biochemical processes at the cellular level and surface stiffness distribution at the mesoscopic level.