Mechanics of motility initiation and motility arrest in crawling cells

Abstract

Motility initiation in crawling cells requires transformation of a symmetric state into a polarized state. In contrast, motility arrest is associated with re-symmetrization of the internal configuration of a cell. Experiments on keratocytes suggest that polarization is triggered by the increased contractility of motor proteins but the conditions of re-symmetrization remain unknown. In this paper we show that if adhesion with the extra-cellular substrate is sufficiently low, the progressive intensification of motor-induced contraction may be responsible for both transitions: from static (symmetric) to motile (polarized) at a lower contractility threshold and from motile (polarized) back to static (symmetric) at a higher contractility threshold. Our model of lamellipodial cell motility is based on a 1D projection of the complex intra-cellular dynamics on the direction of locomotion. In the interest of analytical transparency we also neglect active protrusion and view adhesion as passive. Despite the unavoidable oversimplifications associated with these assumptions, the model reproduces quantitatively the motility initiation pattern in fish keratocytes and reveals a crucial role played in cell motility by the nonlocal feedback between the mechanics and the transport of active agents. A prediction of the model that a crawling cell can stop and re-symmetrize when contractility increases sufficiently far beyond the motility initiation threshold still awaits experimental verification.

Prediction of traction forces of motile cells

“…This rheology is in line with early models of actomyosin [39] and active gels models [40]. We do not supplement this contractile liquid behaviour with an elastic resistance term of the cell, contrarily to what is done in mechanosensing [41,42] and migration models [17]. Other models have also considered the same rheology for cell migration, with an additional inertial term used for numerical stabilization [4].…”

“…Important modelling efforts have been made to understand the initiation and maintenance of motility [13][14][15][16][17]. These works are using the simple and stable shape of keratocyte cells, or a one-dimensional (1D) simplification.…”

“…This is assumed in many modelling approaches, including [17,28] where c f is taken constant, and in [43] where position-dependent and dissymmetric adhesion is implemented. However, experiments show that although local traction force and actin velocity are positively correlated on the whole, above some critical velocity, the traction forces drop by several folds [16,30], indicating that c f is not uniformly constant.…”

Force-induced repolarization of an active crawler

“…The associated size-control mechanisms are discussed in [40]. While length changes are known to be involved in oscillatory motion of cells [41] and may play some role during the initiation of motility [42], we have chosen to…”

Joint Motion Estimation and Source Identification using Convective Regularisation with an Application to the Analysis of Laser Nanoablations

“…We refer to [45] for a derivation of this model. Briefly, (29) is an advection-reaction equation modelling mass conservation of myosin molecules m, subject to rates of adsorption k on > 0 and desorbtion k off > 0, Fig.…”