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