Rens, E. G. | bioRxiv Science

bioRxiv2020

Autocrine inhibition of cell motility can drive epithelial branching morphogenesis in absence of growth

Epithelial branching morphogenesis drives the development of organs such as the lung, salivary gland, kidney and the mammary gland. It involves cell proliferation, cell differentiation and cell migration. An elaborate network of chemical and mechanical signals between the epithelium and the surrounding mesenchymal tissues regulates the formation and growth of branching organs. Surprisingly, when cultured in isolation from mesenchymal tissues, many epithelial tissues retain the ability to exhibit branching morphogenesis even in absence of proliferation. In this work, we propose a simple, experimentally-plausible mechanism that can drive branching morphogenesis in absence of proliferation and cross-talk with the surrounding mesenchymal tissue. The assumptions of our mathematical model derive from in vitro observations of the behavior of mammary epithelial cells. These data show that autocrine secretion of the growth factor TGF{beta}1 inhibits the formation of cell protrusions, leading to curvature dependent inhibition of sprouting. Our hybrid cellular Potts and partial-differential equation model correctly reproduces the experimentally observed tissue-geometry dependent determination of the sites of branching, and it suffices for the formation of self-avoiding branching structures in absence and also in presence of cell proliferation.

biophysics↗

bioRxiv2019

From Energy to Cellular Force in the Cellular Potts Model

Single and collective cell dynamics, cell shape changes, and cell migration can be conveniently represented by the Cellular Potts Model, a computational platform based on minimization of a Hamiltonian while permitting stochastic fluctuations. Using the fact that a force field is easily derived from a scalar energy (F = -{nabla}H), we develop a simple algorithm to associate effective forces with cell shapes in the CPM. We display the predicted forces for single cells of various shapes and sizes (relative to cell rest-area and cell rest-perimeter). While CPM forces are specified directly from the Hamiltonian on the cell perimeter, we infer internal forces using interpolation, and refine the results with smoothing. Predicted forces compare favorably with experimentally measured cellular traction forces. We show that a CPM model with internal signaling (such as Rho-GTPase-related contractility) can be associated with retraction-protrusion forces that accompany cell shape changes and migration. We adapt the computations to multicellular systems, showing, for example, the forces that a pair of swirling cells exert on one another, demonstrating that our algorithm works equally well for interacting cells. Finally, we show forces associated with the dynamics of classic cell-sorting experiments in larger clusters of model cells.\n\nAuthor summaryCells exert forces on their surroundings and on one another. In simulations of cell shape using the Cellular Potts Model (CPM), the dynamics of deforming cell shapes is traditionally represented by an energy-minimization method. We use this CPM energy, the Hamiltonian, to derive and visualize the corresponding forces exerted by the cells. We use the fact that force is the negative gradient of energy to assign forces to the CPM cell edges, and then extend the results to interior forces by interpolation. We show that this method works for single as well as multiple interacting model cells, both static and motile. Finally, we show favorable comparison between predicted forces and real forces measured experimentally.

cell biology↗