A free-boundary model of a motile cell explains turning behavior

Abstract

To understand shapes and movements of cells undergoing lamellipodial motility, we systematically explore minimal free-boundary models of actin-myosin contractility consisting of the force-balance and myosin transport equations. The models account for isotropic contraction proportional to myosin density, viscous stresses in the actin network, and constant-strength viscous-like adhesion. The contraction generates a spatially graded centripetal actin flow, which in turn reinforces the contraction via myosin redistribution and causes retraction of the lamellipodial boundary. Actin protrusion at the boundary counters the retraction, and the balance of the protrusion and retraction shapes the lamellipodium. The model analysis shows that initiation of motility critically depends on three dimensionless parameter combinations, which represent myosin-dependent contractility, a characteristic viscosity-adhesion length, and a rate of actin protrusion. When the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectories, and the motile behavior is sensitive to conditions at the cell boundary. Scanning of a model parameter space shows that the contractile mechanism of motility supports robust cell turning in conditions where short viscosity-adhesion lengths and fast protrusion cause an accumulation of myosin in a small region at the cell rear, destabilizing the axial symmetry of a moving cell.

Vesicles with internal active filaments: self-organized propulsion controls shape, motility, and dynamical response

“…Biological cells are model systems where self-organization of the internal active processes has been studied in detail experimentally [11]. Motility is controlled mainly by actin polymerization and actomyosin contractility [12,13]; it is challenging to study cell motility theoretically because of the large length-scale gap between single filaments and entire cells. Therefore, generic continuum models have been developed to predict cell shape and motility on homogenous substrates [12,[14][15][16][17], on striped substrates substrates and at interfaces [18][19][20], as well as for cell-cell collisions [21].…”

Simulation of the mechanics of actin assembly during endocytosis in yeast

“…Hydrostatic pressure is not included in the force-balance equation in our model, because the mechanics of the actin filament network decouples from mechanics of the cytoplasm. Indeed, the viscous drag exerted on actin filaments by the cytoplasm is much weaker than the intrinsic viscous forces due to direct contacts of the filaments and can thus be ignored (Nickaeen et al, 2017). Technically, the repulsive active stress can be viewed as playing a role of pressure in our model.…”

Mechanistic and experimental models of cell migration reveal the importance of intercellular interactions in cell invasion

“…Cell motility is a complicated process involving both the interplay and competition between various individual-level mechanisms [14, 15, 16, ?]. One of the most well-studied individual-level cell motility mechanisms is lamellipodial cell migration where cells undergo undirected movement due to myosin-powered contractions of the actin network under the cytoplasmic membrane [17]. Since this process is observed in many cell types, it remains prevalent in many mathematical modelling frameworks.…”