The actin cortex is a thin, approximately 1μm-thick layer of actin gel attached to the cell lipid bilayer. The gel is made a network of actin filaments, connected by crosslinking proteins. Actin filaments treadmill in the cortex, being constantly polymerized at the membrane and depolymerized in the bulk. Myosin molecular motors interact with actin filaments, generating internal stresses in the gel and putting the actin cortex under tension. The cortex thus gives the cell its mechanical resistance and controls its shape changes. In our work we use an hydrodynamical model of actomyosin interaction to explore some properties of the actin cortex. The actomyosin system is described at the mesoscopic scale as a viscoelastic material, with nematic or polar order, in which myosins use the energy provided by ATP hydrolysis to produce active stresses, active meaning out of thermodynamical equilibrium. In this seminar we will first discuss the onset of active instabilities in the layer, and show how those instabilities can explain experimental observation of fibroblast shape oscillations, where the cortex is coupled to mechanosensitive calcium channels. We will then propose an application of our model to the beginning of cytokinesis, during which a contractile ring forms in the equatorial plane of the cortex, before contracting and separating the cell into two daughter cells. By including a nematic order parameter in our description, we show that submitting the cortex to an inhomogeneous distribution of myosins should lead to the appearance of a cortical flow and the formation of a ring, as observed in different experimental systems.
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