A phenomenological multiscale framework for orientational interactions and viscoelasticity in migrating epithelial monolayer

Collective migration of epithelial monolayers emerges from the interplay between mechanical interactions and biochemical signalling on the cellular scale. Here, we provide a phenomenological mechanobiological framework with constitutive interpretation linking microscopic orientational interactions to tissue-scale mechanics. By distinguishing reversible from irreversible head-on and glancing interactions, we find that reversible interactions store orientational mechanical energy while preserving the collision angle between cells before and after contact, whereas irreversible interactions dissipate energy and alter the collision angle. Quantifying the storage and dissipation of orientational energy is crucial, as it governs how collective migration and mechanical feedback emerge in epithelial monolayers, ultimately influencing density-dependent outcomes such as cell jamming and live cell extrusion. These interactions modulate cell elasticity, contractility, and adhesion, thereby shaping the surface properties and effective viscoelastic response of the monolayer and influencing the efficiency of collective cell migration. Increasing cell packing density shifts the balance from energy storage to dissipation, inducing density-dependent changes in migration mechanisms, epithelial surface tension, and viscoelasticity. We quantify these effects using orientational potentials, an effective second virial coefficient, and dimensionless ratios capturing the relative fractions of energy stored or dissipated by orientational interactions. While these contributions are partial at intermediate densities (above the confluent cell packing density and below the jamming packing density), they become dominant near jamming. This framework provides a mechanobiological perspective linking cell-scale interaction dynamics and orientation changes to emergent tissue-scale rheological behavior. It suggests how collision-induced orientational energy may contribute to collective migration mechanics and how density-dependent interaction regimes may influence the epithelial viscoelastic response under varying cell packing conditions.