Collections of cells must be patterned spatially during embryonic development to generate the intricate architectures of mature tissues. In several cases, including the formation of the branched airways of the lung, reciprocal signaling between an epithelium and its surrounding mesenchyme helps generate these spatial patterns. Several molecular signals are thought to interact via reactiondiffusion kinetics to create distinct biochemical patterns, which act as molecular precursors to actual, physical patterns of biological structure and function. Here, however, we show that purely physical mechanisms can drive spatial patterning within embryonic epithelia. Specifically, we find that a growth-induced physical instability defines the relative locations of branches within the developing murine airway epithelium in the absence of mesenchyme. The dominant wavelength of this instability determines the branching pattern and is controlled by epithelial growth rates. These data suggest that physical mechanisms can create the biological patterns that underlie tissue morphogenesis in the embryo.buckling | instability | mechanical stress | morphodynamics | morphogenesis S pace-filling, branched networks form the basic architecture of several organs, including the lung, kidney, and mammary gland. In the developing embryo, these complex structures originate as simple epithelial tubes. To form a ramified network, the initial tubular geometry is molded by a series of branching events, patterned in both space and time (1-3). In most cases, branching involves reciprocal signaling between adjacent tissues (4, 5), but it remains unclear how the locations of new branches are determined.Airway branching is highly stereotyped in the developing mouse lung (6) and regulated in part by fibroblast growth factors (FGFs) (7). New epithelial branches are thought to emerge at locations adjacent to a prepattern of focal expression of FGF10 in the neighboring mesenchyme (8, 9) (Fig. 1A), a molecular mechanism with remarkable similarity to the induction of Drosophila tracheal branching by the FGF homolog Branchless (10). Moreover, the prepattern of FGF10 is regulated by reciprocal feedback between core signaling pathways, including those downstream of sonic hedgehog, bone morphogenetic protein, Wnt, and Notch (5, 11-13). These molecular signals are thought to interact via a reaction-diffusion mechanism (14, 15) to generate the spatial template of FGF10 (16) and are typically assumed to be sufficient to pattern branch locations along the airway epithelium (5, 10). This rich molecular description, however, overlooks the role that mechanical cues might play in establishing biological patterns. The pattern of villi in the developing gut, for instance, is determined by physical buckling (17,18).When the mesenchyme is removed, thus disrupting reciprocal signaling, isolated epithelia still branch in response to FGF1 or FGF10 (19,20). In these culture models, the exogenous growth factors are present ubiquitously, with no apparent spatial pattern (Fig. 1...