  While it is commonly observed that the shape dynamics of mammalian cells can
undergo large random fluctuations, theoretical models aiming at capturing cell
mechanics often focus on the deterministic part of the motion. In this paper,
we present a framework that couples an active gel model of the cell mechanical
scaffold with the complex cell metabolic system stochastically delivering the
chemical energy needed to sustain an active stress in the scaffold. Our closure
assumption setting the magnitude of the fluctuations is that the
chemo-mechanical free energy of the cell is controlled at a target homeostatic
value. Our model rationalizes the experimental observation that the cell shape
fluctuations depend on the mechanical environment that constraints the cell. We
apply our framework to the simple case of a cell migrating on a one dimensional
track to successfully capture the different regimes of the cell mean square
displacement along the track as well as the magnitude of the long time scale
effective diffusive motion of the cell.
