Epithelia, quasi-two-dimensional sheets of cells, are important in molding organs into their correct final shape and size during animal development. Epithelia are active materials that are capable of both generating and reacting to mechanical forces, in a manner that depends on the organization of their cells. Cells in an epithelium may divide, exchange neighbors, or otherwise remodel their packing topology, thereby creating a complex feedback loop between tissue topology and mechanical forces. A full theory of the interplay between mechanical forces and cellular arrangement has not yet been developed. Here we work towards developing such a theory using a vertex model framework, which represents complex biological processes as an active network of cell-cell interactions. We consider several specific problems:
We carefully derive the forces acting on vertices, places where three or more cells meet, with special attention to fourfold vertices. This work results in a mathematical proof of the criterion for stabilizing fourfold vertices, which places theoretical limits on the types of tissues that can support stable fourfold vertices.
Continuous supra-cellular actomyosin cables are capable of generating large forces to either resist external stress or drive cell motion. These cables have been extensively studied in isolation, but there has been little work on the effect of multiple parallel cables on tissue mechanics. Here we show that these cables prevent cells from becoming elongated or misshapen under large stress anisotropies and can only arise in certain favorable topologies. We develop two measures of the favorability of a disordered packing to forming cables, a quality we call cableness, and show that passive cell flow reduces cableness whereas oriented cell divisions increase cableness.
A large anisotropic stress is applied to the Drosophila pupal notum for a few hours during its development, at which time it develops internal apical actomyosin fibers. We present a toy model incorporating these fibers into the network of cell-cell interactions, based on the assumption that these fibers form in order to resist the applied stress, and validate predictions of the model against experimental data.
We also summarize the computational methods that are the foundation of our scientific results. We present the design philosophy for our highly modular vertex model, as well as the algorithms we developed to correctly implement T1 transitions. We also discuss our use of automated image analysis techniques in the context of fluorescent imaging, including both morphological operations and machine learning algorithms.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149932/1/maspenc_1.pd
