The problem of understanding the complex sequence of morphogenetic processes that transform a single cell zygote into a fully formed and functional organism is at the heart of the field of developmental biology. Early progress in the field relied on detailed observations of the developing embryo to produce qualitative descriptions of the various morphogenetic processes, establishing a rough timeline for development and the relative sequence of events. Later, extensive genetic screens allowed researchers to identify critical genes in morphogenetic processes based on the observed defects, and with many iterations carefully piece together the genetic cascades that direct development. Nevertheless, shape is inherently a problem of mechanics, and therefore a thorough view of morphogenesis requires an understanding of the intimate interplay between genetics and mechanics. Although an appreciation for this role of the physical aspects of developmental biology predate our knowledge of genetics, its characterization has been much slower that its genetic counterpart. Perhaps best characterized genetically is the example of the embryogenesis of Drosophila melanogaster, which therefore offers an ideal context within which to study the role of mechanics. In this dissertation, we aim to take advantage of the detailed genetic foundation to better understand the role of mechanics in development, in particular during the period of early gastrulation in the fruit fly. Extensive studies of the genetics and preliminary characterization of the mechanics have been undertaken for the morphogenetic processes associated with this developmental stage, namely ventral furrow formation and germ-band extension. We aim to build off this previous work utilizing in toto multi-view light sheet microscopy to image global dynamics of the developing embryo and take advantage of image processing techniques to allow rigorous quantitative analysis of strain and myosin rates. With these methods, we identify a strong correlation between strain and myosin dynamics across the embryo surface. We confirm the relationship at the level of single junctions with high spatiotemporal resolution confocal microscopy and demonstrate that a simple physical model with mechanical feedback as a key feature recapitulates the single junction observations. We next utilize an optogenetic construct to pattern actomyosin contractility in order to induce physiologically relevant and minimally invasive ectopic strain rates and measure the resulting changes to the myosin dynamics. By altering the pattern of activation, we show that not only does a strain based mechanical feedback mechanism recruit myosin in vivo, but we further show that this mechanism is isotropic within the cell but spatially modulated along the D-V axis. We then adapt our model to predict the myosin distribution at the tissue scale and show that incorporating this D-V modulation of feedback strength provides an accurate prediction of the myosin profile. Finally, we demonstrate the importance of this feedback mechanism for normal development by analyzing genetic mutants defective for a major strain generating process: ventral furrow formation. We find that these mutants have significantly reduced strain rates and proportional reductions in the myosin distribution. Notably, these embryos have an equivalent reduction in the rate of germ-band extension, which is known to depend on the myosin distribution, indicating the developmental relevance of this mechanism.

In plants and animals, developmental programs transform single-celled zygotes intofully formed and functional organisms. Understanding morphogenesis, the collective set of mechanisms that transduce discrete genetic information into the 3D form of tissues, organs, and appendages, is a foundational problem at the interface of biology and physics. While great progress has been made characterizing the molecular components that deter- mine the initial body plan, the subsequent dynamics of cellular rearrangements and tissue deformations that ultimately shape the organism are far less understood. A thorough de- scription of morphogenesis necessitates an understanding of the intricate interplay among genetics, mechanics, and geometry.

This dissertation presents a body of work aimed at understanding how mechanics andgeometry sculpt thin tissues into complex shapes during development. We apply a com- bination of theoretical, computational, and experimental methods to build quantitative descriptions of a variety of morphogenetic processes, including germband organization, organogenesis, and limb growth. In each setting, careful analysis reveals how physical mechanisms dynamically coordinate the self-organization of shape and form across mul- tiple scales, from the cellular to the organismal. The synthesis of these various results contributes towards building a quantitative and predictive understanding of morphogen- esis.

In Chapter 2, we present set of computational methods for the characterization andanalysis of tissue deformation in tubelike surfaces. These methods, contained within our open-source TubULAR package, enable users to extract dynamic surfaces, construct 2D parameterizations optimized for tracking tissue parcels, measure whole-organ tissue deformation, and compute signatures of 3D motion. We showcase the power of these methods by quantifying tissue flow during the development of the Drosophila midgut and the zebrafish heart. Decomposition of complicated flow fields in to simple components with straightforward physical interpretations enable novel insights that would be difficult or impossible to find with exisiting methodologies.

In Chapter 3, we demonstrate how actively oriented cell divisions organize the ecto-dermal germband in Parhyale hawaiensis. Live imaging and computer vision reveal that waves of cell proliferation sweep across the embryo in such a way that the initially fluid germband flows towards a fourfold orientationally ordered state. We develop a hydrody- namic model that can predict coarse-grained flow fields from division events, bridging the gap between cell-scale and tissue-scale dynamics. Vertex model simulations demonstrate that oriented cell divisions constitute a robust mechanism for generating orientational order in living tissues far from thermal equilibrium.

In Chapter 4, we study the transformation of the Drosophila midgut from a simpletube into a complex, coiling configuration of folds and compartments. We demonstrate that tissue shape is controlled by gene expression via mechanical interactions between heterologous tissue layers. Hox genes mediate calcium signaling that regulates muscle contractions at precise locations along the length of the gut. These muscle contractions induce sharp folds and convergent extenstion in the gut endoderm, which is strongly con- strained by tissue incompressibility. We show that the tissue scale flow is mediated by anisotropic cell shape change resulting from the mechanical coupling to muscle contractil- ity. Taken together, these results form a concrete link from genes to cell-scale mechanics to tissue morphodynamics via active forces.

In Chapter 5, we present a theoretical and computational framework for tacklingthe problem of growth pattern selection in epithelial morphogenesis. We show that de- velopmental programs can be quantified in terms of anistropy and areal growth rates. Arbitrarily complicated growth patterns can be built up by composing simple infinites- imal updates to the system’s intrinsic geometry. We proposed an action principle that selects for simple growth patterns that minimize spatiotemporal variation in these quan- tities. We then applied this formalism to seveal synthetic and experimental systems, including limb morphogenesis in Parhyale.