Mark Chaplain - Mathematical modelling of cell cytoskeleton biomechanics and cell membrane deformations

Abstract: Understanding cell motility, namely the ability of a cell to deform and migrate is essential as it occurs in many important biological events such as embryogenesis, wound healing or the formation of tumour and metastasis. Cell membrane deformations, in particular, reflect the molecular and mechanical mechanisms involved inside the cell. Therefore the observations of the cell morphologies and their evolution wtih time (deformations) could reveal some cellular pathology. The ability of a cell to interact and to move in its environment to fulfil its functions, thus depends on the proper functionning of the internal cell machinery. This machinery implies the management and the distribution of energy for the generation and application of the forces required for the movements. This is realized in close relationship with the mechanisms of perception of the extracellular medium and the integration of the signals from the environment. The challenge of understanding accurately the mechanisms involved is to provide an efficient and reliable mean to control the cell behaviour and more especially the cell migration. In particular the selective inhibition of migration would have a considerable importance in cancerology (control of the angiogenesis phase and of the formation of metastasis). In this talk we will present a mathematical model of cell deformations, initially used to describe the dynamical behaviour of round-shaped cells such as keratinocytes or leukocytes, in order to take into account the dynamical behaviour of large membrane deformations such as observed in fibroblasts. The aim is to show that the same basic hypotheses for cell movements apply and allow to describe a wide variety of morphologies and behaviours. We first propose a simple membrane model to evaluate the potential morphologies that a cell might adopt as the result of two competing forces acting on the membrane, namely an hydrostatic protrusive force counterbalanced by a retraction force exerted by the actin filaments. The retraction force is described as a static function spatially modulated in the tangential direction and which simulates a stationary distribution of actin in the cell cortex. This is based on the assumption that the retraction force locally depends on the amount of F-actin. Protrusion and retraction forces are moreover modulated by an additional membrane curvature stress, whose influence on the resulting morphologies is evaluated for various value of the membrane stiffness coefficient. This simple membrane model is then coupled to the actin dynamics in the cortex described by a mecanochemical model. The simulations performed show that the model is able to reproduce the rotating waves of deformations of round-shaped cells such as kerotinocytes, but is also able to reproduce the pulsating behaviour of large membrane deformations which match the main features of fibroblast dynamics.