A central goal of developmental biology is to understand how an organism shapes itself, a process referred to as morphogenesis. While the molecular components critical to determining the initial body plan have been well characterized, the control of the subsequent dynamics of cellular rearrangements which ultimately shape the organism are far less understood. A major roadblock to a more complete picture of morphogenesis is the inability to measure tissue-scale mechanics throughout development and thus answer fundamental questions: How is the mechanical state of the cell regulated by local protein expression and global pattering? In what way does stress feedback onto the larger developmental program?
In this dissertation, we begin to approach these questions through the introduction and analysis of a multi-scale model of epithelial mechanics which explicitly connects cytoskeletal protein activity to tissue-level stress. In Chapter 2, we introduce the discrete Active Tension Network (ATN) model of cellular mechanics. ATNs are tissues that satisfy two primary assumptions: that the mechanical balance of cells is dominated by cortical tension and that myosin actively remodels the actin cytoskeleton in a stress-dependent manner. Remarkably, the interplay of these features allows for angle-preserving, i.e. `isogonal', dilations or contractions of local cell geometry that do not generate stress. Asymptotically this model is stabilized provided there is mechanical feedback on expression of myosin within the cell; we take this to be a strong prediction to be tested.
The ATN model exposes a fundamental connection between equilibrium cell geometry and its underlying force network. In Chapter 3, we relax the tension-net approximation and demonstrate that at equilibrium, epithelial tissues with non-uniform pressure have non-trivial geometric constraints that imply the network is described by a weighted `dual' triangulation. We show that the dual triangulation encodes all information about the mechanical state of an epithelial tissue. Utilizing the stress-geometry ‘duality’, we formulate a local "Mechanical Inference" of cellular-level stress using solely cell geometry that dramatically improves over past image-based inference techniques.
In Chapter 4, we generalize the ATN model to explore the controlled re-arrangement of cells within epithelial tissues. This requires us to explicitly consider the effects of cadherin mediated adhesion, and its regulation, on tissue morphogenesis. We find that positive feedback between myosin and cortical tension, along with traction-dependent depletion of cytoskeletal cadherin is sufficient to recapitulate the morphogenetic movement of cells observed during convergent extension of the lateral ectoderm during Drosophila embryogenesis. Statistical analyses of live-imaging data supports the fundamentals of the model.
Chapter 5 focuses on morphogenesis at a mesoscopic scale by coarse-graining the cellular ATN model. Under this limit, we expect an epithelial tissue should behave as an effective viscous, compressible fluid driven by myosin gradients on intermediate time-scales. Theoretical predictions are empirically tested against in-toto microscopy data obtained during early Drosophila embryogenesis.
