Mechanical design of fiber-wound hydraulic skeletons: The stiffening and straightening of embryonic notochords

Mechanical Design of Fiber-Wound Hydraulic Skeletons: The Stiffening and Straightening of Embryonic Notochords1

SYNOPSIS. 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 chi. 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 (Theta = angle of the fibers to long axis of the cylinder). Notochord models with Theta > 54 deg 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 Theta. In contrast, models with Theta

INTRODUCTION

The notochord plays a variety of important inductive and mechanical roles in the development of vertebrate embryos (reviewed in Adams et al., 1990; Koehl et al., 1990; Gilbert, 1985). One of its early mechanical functions is to elongate and straighten the anterior-posterior axis of the embryo between the late neurula and early tailbud stages. A number of studies of amphibian or chick embryos have shown that removal or disruption of the notochord by a variety of techniques greatly reduces the elongation of embryos during these stages (reviewed in Adams et al., 1990).

We studied the biomechanics of the elongation and straightening of the notochord of early frog embryos, focusing on Xenopus laevis embryos at stages 21 (late neurula) to 28 (early tailbud) (Adams et al., 1990; Koehl et al., 1990) (Fig. 1). The notochord is composed of a stack of flat cells surrounded by a connective tissue sheath. The density of the collagen fibers in the sheath increases and the osmotic activity of the vacuoles in the notochord cells rises during these stages. The swelling of the vacuoles is resisted by the sheath, so the internal pressure of the notochord rises 2- to 3-fold. The notochord elongates and straightens and its flexural stiffness increases by an order of magnitude during these stages of development. Removal of the sheath by collagenase digestion drastically reduces the flexural stiffness of the notochord. Such a floppy, sheathless notochord cannot push effectively on the surrounding embryonic tissues, but rather folds up like a wet noodle as it elongates relative to the surrounding embryo (Fig. 5 in Koehl et al., 1990). Thus, the early amphibian notochord is a hydraulic skeleton that uses osmotic inflation as a mechanism of force-generation and shapechange production, and the fibrous sheath is essential for its mechanical function. We found that the fibers in the sheath of X. laevus notochord during these stages of development are oriented at a mean angle of 54 deg with respect to the long axis of the notochord.

Hydraulic skeletons

A hydraulic skeleton is composed of a tension-resisting container inflated by compression-resisting fluid under pressure. The function of such skeletons, as well as many examples of their occurrence in the Plant and Animal Kingdoms, are reviewed by e.g., Chapman (1958, 1975), Clark (1964), Green (1980), Cosgrove (1987), and Wainwright (1988). Some of these hydraulic skeletons, such as notochords (e.g., Adams et al., 1990; Koehl et al., 1990; Koob et al., 1994; Fennaux, 1998) and plant cells (e.g., Green, 1980; Cosgrove, 1987) are inflated osmotically, whereas others, such as echinoderm tube feet (e.g., Woodley, 1967) and mammalian penises (e. g., Kelly, 1997), are inflated by muscle contractions elsewhere in the body that force fluid into the container. Most biological hydraulic skeletons are cylindrical and their walls are reinforced by relatively inextensible fibers (usually collagen or chitin in animals, and cellulose in plants). The shape changes that such hydraulic systems undergo when inflated are constrained by the orientation of the fibers reinforcing their walls (e.g., Clark and Cowey, 1958; Clark 1964). Fiber orientation is expressed as fiber angle (Theta), the angle between the fibers and the long axis of the cylinder.

Mathematical models have been developed for various pressurized, fiber-reinforced cylindrical systems (e.g., plant cells, worms, echinoderm tube feet, whales, manmade pressure vessels and hydraulic actuators) to predict the shape changes that occur when these structures are inflated, subjected to external loads, or deformed by contractions of muscles in their walls (e.g., Sherrer, 1967; Swanson, 1974; Hettiaratchi and O'Callaghan, 1978; Woodley, 1980; Alexander, 1987; Wadepuhl and Beyn, 1989; Tondu and Lopez, 1995; Chou and Hannaford, 1996; Skierczynski et al., 1996), but none of these address the issue of the forces exerted by inflating, curved, fiber-reinforced hydraulic systems like the embryonic notochord. A few measurements have been made of the flexural stiffness of various hydraulic cylinders in animals, such as the notochords of frog embryos (Adams et al., 1990; Koehl et al., 1990) and sturgeon adults (Long 1995), and of artificallyinflated armadillo penises (Kelly, 1999).