The developing vertebrate gut tube forms a reproducible looped pattern as it grows into the body cavity. Here we use developmental experiments to eliminate alternative models and show that gut looping morphogenesis is driven by the homogeneous and isotropic forces that arise from the relative growth between the gut tube and the anchoring dorsal mesenteric sheet, tissues that grow at different rates. A simple physical mimic, using a differentially strained composite of a pliable rubber tube and a soft latex sheet is consistent with this mechanism and produces similar patterns. We devise a mathematical theory and a computational model for the number, size and shape of intestinal loops based solely on the measurable geometry, elasticity and relative growth of the tissues. The predictions of our theory are quantitatively consistent with observations of intestinal loops at different stages of development in the chick embryo. Our model also accounts for the qualitative and quantitative variation in the distinct gut looping patterns seen in a variety of species including quail, finch and mouse, illuminating how the simple macroscopic mechanics of differential growth drives the morphology of the developing gut.
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We thank R. Prum for pointing out to us the literature on avian intestines, and the Harvard NSF MRSEC, the MacArthur Foundation (L.M.) and NIH RO1 HD047360 (C.J.T.) for support.
This movie shows gut looping simulations. Numerically computed equilibrium configurations of the gut-mesentery composite as a function of the differential growth strain between the gut and the mesentery for three representative values of the geometrical and mechanical parameters that characterize the system (see text, esp. Eq. (1)-(4) and SI for details). The top right sequence shows the length of the loops, while the bottom right sequence below shows the radius of the loops. We observe that the length of the loops does not change as a function of the differential strain (once past a threshold for the onset of the instability), but the radius decreases, as expected.
This movie shows the measuring of the mechanical properties of tissues. The movie on the left shows a sequence of displacements induced by a magnet on a bead that is glued to the tissue. Following calibration, this assay is used to measure the force-extension relation (shown on the right) for a piece of the mesentery, and thence its modulus.