Lumens in small-size and intermediate-size MDCK spheroids are irregularly shaped Our results support a unifying physical mechanism for the formation of luminal openings in a variety of physiological contexts. Motivated by these observations, we developed a biophysical model in which lumen shape is determined by the combined influence of intraluminal pressure and basic geometric considerations. Instead, we find that, in our model system, lumen shape is determined primarily by geometrical constraints arising from the creation of distinct, lumen-facing apical domains. Our experiments revealed that neither lumen pressure nor the actomyosin cytoskeleton were required to maintain the stability of lumen shape. We examined the mechanics of lumen formation and expansion in MDCK cell spheroids, an archetypal cell culture model for studying lumenogenesis. In this study, we sought to understand the physical forces maintaining lumen shape in the context of de novo lumen formation. These observations suggest that a positive pressure gradient may not be the dominant contributor to the growth of all lumens. However, published images of some model systems, for example MDCK cell spheroids and various in vivo examples of lumens such as liver bile ducts, blood vessels, and pro-amniotic cavities, demonstrate areas of concave lumen curvature, where cell apical faces are bowed into the lumen 1, 2, 3, 5, 17, 18, 19, 20, 21, 22. In model systems such as the developing mouse blastocyst and the bile canaliculus this convex surface curvature is well-documented 11, 16. Importantly, a positive luminal pressure should produce convex lumen surfaces that bow outwards toward the surrounding cells. The presence of a luminal pressure is motivated by work that showed ion channels are critical for lumen formation and expansion in vitro and in vivo 14, 15, and by pressure-driven fluctuations in lumen size in some model systems 10, 13.
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