Mechanical Design of Fiber-Wound Hydraulic Skeletons: The Stiffening and Straightening of Embryonic Notochords

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The notochord can play an important mechanical role in shape changes during early morphogenesis of vertebrates. For example, osmotic inflation of notochords elongates and straightens the axis of frog early tail-bud embryos. In Xenopus laevis, the sheath of cross-helically arranged fibers around the notochord limits the shape changes it undergoes when inflating, causing the notochord to stiffen and straighten (Adams et al., 1990; Koehl et al., 1990). We used physical models of stage 24 X. laevis notochords to explore the mechanical consequences of different arrangements of the sheath fibers on the behavior of such curved hydraulic cylinders. All the models straightened upon inflation regardless of initial fiber angle (𝛉 = angle of the fibers to long axis of the cylinder). Notochord models with 𝛉 > 54° lengthened and narrowed as they straightened; although they could push, the forces they exerted were limited by their tendency to buckle, which increased the greater the 𝛉. In contrast, models with 𝛉 < 54° shortened and widened as they straightened and showed pronounced increases in flexural stiffness. The mean 𝛉 of X. laevis early tail-bud notochords is 54°, a fiber angle that permits an increase in the end-to-end distance of the model (along the anterior-posterior axis of the embryo) as it straightens and pushes when pressurized, but that is less prone to Euler and local buckling than are models with higher 𝛉's. Nonetheless, a 𝛉 of 54° in notochords may simply be the result of osmotic swelling.