Theory of mechano-chemical patterning and optimal migration in cell monolayers

Abstract

Collective cell migration offers a rich field of study for non-equilibrium physics and cellular biology, revealing phenomena such as glassy dynamics [1], pattern formation [2] and active turbulence [3]. However, how mechanical and chemical signaling are integrated at the cellular level to give rise to such collective behaviors remains unclear. We address this by focusing on the highly conserved phenomenon of spatio-temporal waves of density [2,[4][5][6][7][8] and ERK/MAPK activation [9][10][11], which appear both in vitro and in vivo during collective cell migration and wound healing. First, we propose a biophysical theory, backed by mechanical and optogenetic perturbation experiments, showing that patterns can be quantitatively explained by a mechano-chemical coupling between three-dimensional active cellular tensions and the mechano-sensitive ERK/MAPK pathway. Next, we demonstrate how this biophysical mechanism can robustly induce migration in a desired orientation, and we determine a theoretically optimal pattern for inducing efficient collective migration fitting well with experimentally observed dynamics. We thereby provide a bridge between the biophysical origin of spatio-temporal instabilities and the design principles of robust and efficient long-ranged migration. ⇤ Equal contribution †

A free boundary mechanobiological model of epithelial tissues

“…The definition of f (ī, t) in Equation (14) contains arguments evaluated atī,ī − 1/N andī − 1/(2N ).…”

“…Substituting Equation (14) into Equations (15)- (17), and expanding all terms in a Taylor series aboutī gives,…”

“…Here we outline how Equations (24), (26) and (29) can be obtained using the factorised form of f (ī, t) in Equation (14). The equations of motion in Equations (15)- (17) are restated as,…”

“…The role of purely mechanical cell properties on tissue dynamics has been studied using mathematical and computational models [5][6][7][8][9][10]. Other models focus on intracellular signalling to examine how chemical signalling affects tissue dynamics [11][12][13][14][15]. We extend these studies by developing a model which couples mechanical cell properties to intracellular signalling.…”

Epithelial Tissues as Active Solids: From Nonlinear Contraction Pulses to Rupture Resistance

“…These evidence include contraction fronts in drosophila embryo during development [2] and density waves in MDCK cell monolayers in-vitro, either in confinement [3,4], during expansion [4,5] or under substrate-shear [6]. Theoretical works suggest models to explain the contractile patterns [7][8][9][10][11], models that include mechanical alongside chemical fields, diffusion or active transport. Note, that all these systems, and the suggested models, exhibit dynamics in time scales of minutes to hours.…”