Forces and flows in cells and tissues. Blebs, active gels, and collective cell migration

Abstract

In this thesis, we have studied mechanical aspects of some biological processes in cells and tissues, which we addressed by developing theoretical models based on the physics of soft active matter. The thesis contains three parts that focus on different biological systems. In Part I, we study the adhesion between the plasma membrane and the actin cortex of eukaryotic cells. We propose a continuum model for membrane-cortex adhesion that couples the mechanics and hydrodynamics of the membrane to the force-dependent binding kinetics of the linker proteins. We predict the critical pressure difference that causes membrane-cortex detachment, and we discuss how cortical tension can be inferred from micropipette suction experiments. Then, we study the fluctuations of an adhered membrane, and suggest ways in which our predictions could allow probing membrane-cortex adhesion in fluctuation spectroscopy experiments. Then, we employ the proposed model to study the nucleation of blebs, which are balloon-like membrane protrusions arising from a local membrane-cortex detachment. We show that bleb nucleation is governed by membrane peeling, the fracture propagation process whereby adjacent membrane-cortex bonds break sequentially. Through this mechanism, bleb nucleation is not determined by the energy of a local detachment like in the classical nucleation picture, but rather by the kinetics of membrane-cortex linkers. We predict the critical radius for bleb nucleation through membrane peeling and the corresponding effective energy barrier. Finally, we simulate a fluctuating adhered membrane to obtain the probability distribution of bleb nucleation times. In Part II, we study the dynamics of active polar gels, which are soft materials, usually transiently-crosslinked polymeric networks, that are maintained out of equilibrium by internal processes that continuously transduce energy. We derive the constitutive equations of an active polar gel from a mesoscopic model for the dynamics of the molecules that crosslink the polar elements of the system. This way, we establish a connection between the molecular properties and the macroscopic behaviour of active polar gels. Specifically, we explicitly obtain the transport coefficients in terms of molecular parameters, showing that all transport coefficients have an active contribution that stems from breaking detailed balance for the crosslinker binding kinetics. In Part III, we study cell colonies and tissues, focusing in collective cell migration and tissue morphology. First, we propose a particle-based description of cell colonies to study how the different organizations of cells in tissues emerge from intercellular interactions. The model intends to capture generic cellular behaviours such as cell migration, adhesion, and cell-cell overlapping. In addition, it models the so-called contact inhibition of locomotion (CIL), which repolarizes cell migration away from cell-cell contacts, as a torque on the migration direction. We show how CIL yields an effective repulsion between cells, which allows to predict transitions between non-cohesive, cohesive, and 3D tissues. We conclude that, at low cell-cell adhesion, CIL hinders the formation of cohesive tissues. Yet, in continuous cell monolayers, CIL gives rise to self-organized collective motion, ensures tensile stresses in the monolayer, and opposes cell extrusion, thereby hindering the collapse of the monolayer into a 3D aggregate. Then, we focus on the spreading of epithelial monolayers, which we address by means of a continuum model based on the theory of active polar gels. First, we concentrate on the wetting transition of epithelial tissues, which separates monolayer spreading from retraction towards a 3D aggregate — namely the equivalent of a fluid droplet. We show that a critical radius exists for the wetting transition, which does not exist in the classical wetting picture. Thus, we show how the wetting properties of tissues emerge from active cellular forces, evidencing that the wetting transition has an active nature. Finally, we study the morphological stability of the front of a spreading monolayer. The model predicts that traction forces cause a long-wavelength instability of the monolayer front, whereas tissue contractility has a stabilizing effect. The predicted instability can explain the formation of finger-like multicellular protrusions observed during epithelial spreading. It can also explain the symmetry breaking of tissue shape observed during monolayer dewetting. By fitting the predictions to experimental data, we infer the monolayer viscosity and the noise intensity of tissue shape fluctuations, which we suggest to have an active origin.

En aquesta tesi hem estudiat aspectes mecànics d'alguns processos biològics en cèl·lules i teixits, que hem abordat desenvolupant models teòrics basats en la física de la matèria tova activa. La tesi té tres parts centrades en sistemes biològics diferents. En la primera part s'estudia l'adhesió entre la membrana plasmàtica i el còrtex d'actina de les cèl·lules eucariotes. Proposem un model continu per l'adhesió membrana-còrtex que acobla la mecànica i la hidrodinàmica de la membrana amb la cinètica de les proteïnes que ancoren la membrana al còrtex. Prediem la pressió crítica pel desenganxament i estudiem les fluctuacions de la membrana adherida. Després, ens centrem en la nucleació de butllofes cel·lulars, que són protrusions degudes a desenganxaments locals de la membrana. Mostrem que la nucleació de butllofes cel·lulars està governada pel procés de pelat de la membrana, pel qual proteïnes connectores adjacents es desenganxen seqüencialment. Per aquest mecanisme, la nucleació de butllofes no està determinada per l'energia com en l'escenari clàssic sinó per la cinètica dels connectors. A la segona part es deriven les equacions constitutives d'un gel polar actiu a partir d'un model mesoscòpic per la dinàmica de les molècules entrellaçadores. Així, prediem explícitament els coeficients de transport dels gels polars actius en termes de paràmetres moleculars. Tots els coeficients de transport tenen una contribució activa, provinent del trencament de balanç detallat per la cinètica dels entrellaçadors. A la tercera part estudiem colònies cel·lulars i teixits. Primer, proposem un model de partícules per estudiar com les diferents organitzacions dels teixits emergeixen de les interaccions intercel·lulars. El model captura comportaments cel·lulars genèrics i, en particular, la inhibició de la motilitat per contacte. Es mostra com aquesta interacció dóna una repulsió efectiva entre cèl·lules. Després, s'estudia l'escampament de monocapes epitelials en base a un model continu basat en la teoria dels gels polars actius. Primer es mostra que, a diferència del que passa en l'escenari clàssic, la transició de mullat d'un teixit té un radi crític determinat per les forces cel·lulars actives. Finalment, es prediu que, a causa de les forces de tracció, el front d'una monocapa en expansió, fet que explica observacions experimentals.