Multi-scale nature of the tissue surface tension: Theoretical consideration on tissue model systems.

Tissue surface tension is one of the key parameters that govern tissue rearrangement, shaping, and segregation within various compartments during organogenesis, wound healing, and cancer diseases. Deeper insight into the relationship between tissue surface tension and cell residual stress accumulation caused by collective cell migration can help us to understand the multi-scale nature of cell rearrangement with pronounced oscillatory trend. Oscillatory change of cell velocity that caused strain and generated cell residual stress were discussed in the context of mechanical waves. The tissue surface tension also showed oscillatory behaviour. The main goal of this theoretical consideration is to emphasize an inter-relation between various scenarios of cell rearrangement and tissue surface tension by distinguishing liquid-like and solid-like surfaces. This complex phenomenon is discussed in the context of an artificial tissue model system, namely cell aggregate rounding after uni-axial compression between parallel plates. Experimentally obtained oscillatory changes in the cell aggregate shape during the aggregate rounding, which is accompanied by oscillatory decrease in the aggregate surface area, points to oscillatory changes in the tissue surface tension. Besides long-time oscillations, cell surface tension can perform short time relaxation cycles. This behaviour of the tissue surface tension distinguishes living matter from other soft matter systems. This complex phenomenon is discussed based on dilatational viscoelasticity and thermodynamic approach.