D'Arcy Thompson was a proponent of applying mathematical and physical principles to biological systems, an approach that is becoming increasingly common in developmental biology. Indeed, the recent integration of quantitative experimental data, force measurements and mathematical modeling has changed our understanding of morphogenesis - the shaping of an organism during development. Emerging evidence suggests that the subcellular organization of contractile cytoskeletal networks plays a key role in force generation, while on the tissue level the spatial organization of forces determines the morphogenetic output. Inspired by D'Arcy Thompson's , we review our current understanding of how biological forms are created and maintained by the generation and organization of contractile forces at the cell and tissue levels. We focus on recent advances in our understanding of how cells actively sculpt tissues and how forces are involved in specific morphogenetic processes.

Tissue folding promotes three-dimensional (3D) form during development. In many cases, folding is associated with myosin accumulation at the apical surface of epithelial cells, as seen in the vertebrate neural tube and the Drosophila ventral furrow. This type of folding is characterized by constriction of apical cell surfaces, and the resulting cell shape change is thought to cause tissue folding. Here, we use quantitative microscopy to measure the pattern of transcription, signaling, myosin activation and cell shape in the Drosophila mesoderm. We found that cells within the ventral domain accumulate different amounts of active apical non-muscle myosin 2 depending on the distance from the ventral midline. This gradient in active myosin depends on a newly quantified gradient in upstream signaling proteins. A 3D continuum model of the embryo with induced contractility demonstrates that contractility gradients, but not contractility per se, promote changes to surface curvature and folding. As predicted by the model, experimental broadening of the myosin domain in vivo disrupts tissue curvature where myosin is uniform. Our data argue that apical contractility gradients are important for tissue folding.

During development, gene expression regulates cell mechanics and shape to sculpt tissues. Epithelial folding proceeds through distinct cell shape changes that occur simultaneously in different regions of a tissue. Here, using quantitative imaging in Drosophila melanogaster, we investigate how patterned cell shape changes promote tissue bending during early embryogenesis. We find that the transcription factors Twist and Snail combinatorially regulate a multicellular pattern of lateral F-actin density that differs from the previously described myosin-2 gradient. This F-actin pattern correlates with whether cells apically constrict, stretch, or maintain their shape. We show that the myosin-2 gradient and F-actin depletion do not depend on force transmission, suggesting that transcriptional activity is required to create these patterns. The myosin-2 gradient width results from a gradient in RhoA activation that is refined through the balance between RhoGEF2 and the RhoGAP C-GAP. Our experimental results and simulations of a 3D elastic shell model show that tuning gradient width regulates tissue curvature.

Tissue folding promotes three-dimensional (3D) form during development. In many cases, folding is associated with myosin accumulation at the apical surface of epithelial cells, as seen in the vertebrate neural tube and the Drosophila ventral furrow. This type of folding is characterized by constriction of apical cell surfaces, and the resulting cell shape change is thought to cause tissue folding. Here, we use quantitative microscopy to measure the pattern of transcription, signaling, myosin activation and cell shape in the Drosophila mesoderm. We found that cells within the ventral domain accumulate different amounts of active apical non-muscle myosin 2 depending on the distance from the ventral midline. This gradient in active myosin depends on a newly quantified gradient in upstream signaling proteins. A 3D continuum model of the embryo with induced contractility demonstrates that contractility gradients, but not contractility per se, promote changes to surface curvature and folding. As predicted by the model, experimental broadening of the myosin domain in vivo disrupts tissue curvature where myosin is uniform. Our data argue that apical contractility gradients are important for tissue folding.

10During development, gene expression regulates cell mechanics and shape to sculpt tissues. 11One example is epithelial folding, which proceeds through distinct cell shape changes that 12 occur in different regions of the tissue. How transcription factors combinatorially coordinate 13 cell shape across a tissue is poorly understood. Here, using Drosophila melanogaster as a 14 model, we investigate how cell shape changes are coordinated to promote tissue bending 15 during gastrulation. By quantifying the multicellular patterns of RhoA activation, F-actin, and 16 myosin-2 and perturbing RhoA activation, we find that Snail and Twist regulate distinct 17 patterns of graded F-actin accumulation and uniform F-actin depletion, which synergize to 18 create zones of high and low F-actin levels within the Drosophila mesoderm. Graded 19 actomyosin results from a gradient in RhoA activation and the width of this zone regulates 20 tissue curvature. Thus, changes in tissue shape are regulated through the choreographed 21 interplay of distinct gene expression patterns.94 actomyosin gradient is tuned by the activity of the RhoA pathway, which regulates tissue 95 curvature and lumen size in the mesodermal tube structure that results from this fold. Our 96 results show how the combination of overlapping transcriptional pre-patterns coordinates cell 97 shapes across the mesoderm to promote proper tissue curvature.