Functional design of tentacles in squid: linking sarcomere ultrastructure to gross morphological dynamics

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Abstract
This paper offers a quantitative analysis of tentacle extension in squid that integrates several levels of structural organization. The muscular stalks of the two tentacles of squid are rapidly elongated by 70 per cent of resting length during prey capture. A typical duration of the extension is 30 ms in Loligo pealei (with a contracted tentacle length of 93 mm and a strike distance of about 37 mm). In a successful strike, the terminal clubs hit the prey and attach to it via arrays of suckers. A forward dynamics model is proposed for the extension of the tentacular stalk and the forward motion of the terminal club. The stalk is modelled as a longitudinal array of thin muscular discs with extensor muscle fibres oriented parallel to the disc planes. As a disc contracts radially, it lengthens because its volume is constant. The equations of motion for the linked system of discs were formulated and solved numerically. The inputs of the model are the dimensions of the tentacle, passive and active muscle properties such as Hill's force–velocity relationship, myofilament lengths and activation of the muscle fibres. The model predicts the changing geometry of the tentacle, the pressure and stress distribution inside the tentacle and the velocity and kinetic energy distribution of the stalk and club. These predictions are in agreement with kinematic observations from high–speed films of prey capture. The model demonstrates also that the unusually short myosin filaments (reported range 0.5–0.9 micrometre) that characterize the extensor muscles are necessary for the observed extension performance. Myosin filament lengths typical for vertebrate sarcomeres (1.58 micrometre) would lead to a significant reduction in performance. In addition, the model predicts that, to maximize peak velocity of the terminal club, the myosin filaments should be longer at the base and shorter at the tip of the stalk (0.97 micrometre at the base and 0.50 micrometre at the tip for the tentacle size above). This results from differences in dynamic loading along the stalk. Finally, the model allows exploration of the effects of changes in the dimensions and mass of the tentacle and intrinsic speed of the myofilaments on the optimum myosin filament lengths.