Abstract

Complex bio-chemical processes attempt to maintain constant time-averaged concentrations of a range of proteins within cells in a process commonly referred to as cellular homeostasis. These chemical processes cause fluctuations of the state of cells that depends on the extra-cellular environment. A statistical mechanics view to model these fluctuations will be presented which will enable a unifying treatment of range of disparate cellular phenomena. First the probability of observing a cell in a so-called spread micro-state is estimated in terms of the free-energy of that state using the basic idea of Gibbs entropy. Next a model is presented to estimate this free-energy. The model includes stress-fiber reorganisation and the associated contractility by considering the energetics of the actin/myosin functional units that constitute the stress-fibers. This model then used to elucidate the range of states over which the cell can fluctuate in a particular environment and the probability of observing each of those states. Finally some initial predictions are presented for a range of experimentally observed phenomena using this approach. This includes: (i) the spreading and shape of cells as a function of the stiffness of the substrate; (ii) durotaxis whereby cells tends to migrate guided by rigidity gradients on substrates and (iii) differentiation of stem cells guided by the stiffness of substrates and as well as cell shape as controlled by the chemical environment.