Stochastic fluctuations in biophysical models of cell organization

Self-organization of living system is a fascinating process, interesting not only biologist, but also mathematicians and physicist. In the present work, the attention will focus on the spatial segregation between the primitive endoderm (PrE) and the epiblast (EPI) cells in mammals. The sorting of a mixture of two types of biological cells is already modelled by a modified version of the large-Q Potts model, an energy-based biophysical paradigm that, however, had progressed beyond being merely a proof of concept. Since this approach lacks a physical interpretation, there is a growing interest to develop more detailed dynamic methods to model relevant biophysical processes. The recent developments in the theory of non-equilibrium statistical physics allow to reformulate the sorting problem within stochastic thermodynamics frameworks. The stochastic kinetic approach used in the present work, provides a more sensible physical description of the dynamic characterizing the cell sorting phenomenon and still enables to study the energetics of the involved processes, their thermodynamic properties, as well as the role of dissipation and the response to perturbation. In order to test the equivalence of such kinetic approach with respect to the traditional Monte-Carlo sampling algorithm, their performances have been compered in the paradigmantic example of the Ising chain. Afterwards, the framework has been used to model lineage sorting characterizing the early development of mammals.