Factors Controlling the Change of Shape of Certain Nemertean and Turbellarian Worms

INTRODUCTION Two groups of free-living, acoelomate worms, the nemerteans and turbellarians, are noted for their ability to change their shape. The role of circular and longitudinal muscles in producing these changes are well known, but since these worms are not invested by a cuticle, it is not immediately apparent what limits the changes of shape. Obviously the worms are not indefinitely extensible and compressible. Cowey (1952) discovered that the epidermal basement membrane of the nemertean Amphiporus is composed of regularly disposed, inextensible fibres arranged in alternate left-and right-handed geodesic helices running around the body of the animal (Text-figs. iA; PI. 12, figs. B, C and D). Although the fibres themselves are inextensible, changes of length of the body, or parts of the body, of the worm are permitted by a change in the angle between intersecting elements in the lattice formed by the fibres, just as in the extension and retraction of lazy tongs or a garden trellis. Cowey demonstrated the way in which these fibres set limits to the change in length of Amphiporus. A similar arrangement of fibrillar structures occurs in the cuticle of nematodes and functions in fundamentally the same way, although the nematode system is a highly specialized one (Harris & Crofton, 1957). In this paper we have considered the potentialities of this fibre system and the way it operates in a variety of turbellarians and nemerteans. In considering the fibre system alone there is a simple relationship between the inclination of the fibres to the longitudinal axis and the length of the system. So for any particular orientation of the fibres the volume depends upon the cross-sectional area. This is greatest when the cross-section is circular, though it may be less if the cross-section is flattened to an ellipse and this can happen without any change in the length of the system, the orientation of the fibres, or the length of the perimeter of the cross-section. As the inclination of the fibres changes, so does the total volume the system can contain. Assuming a circular cross-section throughout , the volume varies as & sin* 8 cos 6 , _. V = , (see bqn. 2, Appendix)