Motivated by cytoskeletal networks, such the mitotic spindle or the actomyosin cortex, we used a physical model of an active gel as a network of elastic elements connected by transient crosslinks. The crosslinkers bind and unbind at rates that break the detailed balance condition, which introduces activity at the molecular level. We then coarse-grained this model to derive hydrodynamic equations including a noise term, which includes an active contribution that explicitly emerges from the breaking of detailed balance. We also obtained predictions for how this noise would impact the motion of a tracer particle, like the ones used in microrheology experiments to reveal the presence of active fluctuations. These results therefore facilitate the comparison of our prediction to experimental measurements, both in synthetic active gels and in cells.
At the tissue scale, we considered discrete stochastic processes of cell division and death with four different scenarios, corresponding to four different ways in which the environment affects cellular proliferation: uniform growth (independent of the environment), logistic growth (which saturates at high cell densities), contact-inhibited growth (which either arrests cell division or promotes cell death at high cell densities), and growth coupled to a fluctuating resource, such as a nutrient. We then derived the equations that govern the cell-density fluctuations in each of these scenarios. In each case, we analysed the amplitude and the spatiotemporal correlations of the density fluctuations, and identified cases of short-ranged and scale-free long-ranged correlations.
We also studied the impact of stochastic events of cell division on the collective migration of cell clusters. We derived a stochastic equation for the motion of a cell cluster in which the noise term emerges from the cell division events.
