Abstract This study attempts to correlate mechanical characteristics of the tube feet and ampullae in Pycnopodia helianthoides with filmed behaviour of the tube foot-ampulla system in operation. The tube foot-ampulla system is an isovolumetric system. Tube foot wall thickness increases during contraction (£ = 0.5 at 54% extensjon). lube feet at maximum contraction lose about 88% of their extended volume. The ampullae simultaneously expand in volume by roughly 1110%. Longitudinal and circular fibers were found in the ampulla. The maximum strain for these fibers is as yet undetermined, but what limits tube foot contraction is more likely the maximum contractility of tube foot longitudinal muscles. Tube foot extension is limited by contraction of the ampulla (i.e. restricted by total internal volume of the system). Helically unmapped fibers in the tube foot greatly enhance its extensile capability. Introduction The tube feet and ampullae are the extremities of the water vascular system in Echinoderms. Water enters the system through a madrepore on the dorsal side of the oral disc. Some of this water is channeled out the arms of the organism through radial canals. These canals are the common ducts to which all of the tube feet and ampullae are connected. The tube feet-ampullae systems of Asteroids are reported to be isovolumetric. A muscularly controlléd, one-way valve (Smith, 1946) allows water to enter from the radial canal to compensate for diffusion. This valve then closes, trapping a finite volume inside, Physical properties of the tube foot have received much attention lately, but the morphology of the ampullae and how it coordinates activity with the tube foot de¬ serves further examination. This study attempts to correlate physical characteri¬ stics of the ampullae and tube foot in Pycnapodja heljan¬ thoides with actual behaviour of the tube foot-ampulla system in operation. Studjes recently undertaken by others at the Hopkins Marine Station: Tang (unpub. 1983), Shibata (unpub. 1983), as well as by Smith (1946) and Woodley (1979) will be analyzed as they relate to findings in this study. -4- Materials and Methods I. Filming To observe the tube foot and ampulla in operation, am¬ bulacra of Pycnapodia were amputated and a viewing window was cut into the side (figure 1). Video films were recorded and three events showing clear and dramatic contraction and extension were chosen for analysis. The tube foot and its associated ampulla were care¬ fully traced after stopping the film every thirty to sixty frames (0.5 - 1.0 seconds). These tracings were then projected and retraced onto paper. The paper tracings were retraced a third time onto an Apple II graphics tablet digitizer. Area data of both the tube foot and ampulla as well as the length and width of the tube foot at intervals during contraction and extension were recorded. The accuracy of the above measurements was determined by first retracing the minimum possible outline of both the tube foot and ampulla and then tracing a maximum possible outline for the same events. Averaging the maxi¬ mum and minimum values separately gave the individual high and low boundaries of error for areas, length, and width. II. Volume In order to ascertain relative volumes of the tube foot and ampulla, ambulacra were first fixed in 37% formalin for two days, then decalcified in a solution of 3% HCI in 70% ethanol for seven to fourteen days. Neutralization in 70% alcohol with KCO, added as needed was accomplished within two more days. (Kozloff, 1971) In preparation for sectioning the arms in the cryostat, they were slowly taken up into distilled water by a Magruder osmotic gradient apparatus and then soaked in a solution of 10% gum arabic in 50% saturated sugar solution. (Kozloff, 1971) The arms were frozen at -25° C. in the microtome for twelve hours before sectioning. Sections were made longitudinally through the tube foot and ampulla (figure 3). Measurements of their internal geometry were made by using an ocular ruler. Volumes were then calculated. III. Volume Exchange In determining how water volume is exchanged throughout contraction and extension, I needed to obtain similar sections from tube feet in their most extended and contracted states. This was accomplished by instantly freezing amputated ambulacra in liquid nitrogen. Fixation was done at -20°C. in a solution of 37% formalin in 70% alcohol. Decalcification and preparation were repeated as before. in the microtome proved difficult so Sectioning tube feet of various lengths were cut radially by hand with fine micro scissors. Hall thicknesses were measured at 100%, 75%, and 54% longitudinal extension of the tube foot. Strain W- values were calculated by the formula £ - where g is strain (a percentage change value), W is new wall width and W. is the wall width at maximum tube foot extension. Area measurements of the model section used for the volume calculations in Part II above were matched with a tube foot and ampulla from one of the three filmed events. The model fit tube foot 1878 in its most extended state, so using the wall strain data, total wall thickness at 54% extension could be calculated. Hall thickness was then subtracted from the observed tube foot total width at 54% contraction to give average internal width. The internal tube foot volume was cal¬ culated as Irl, where r - lumen radius, and L = tube foot length. IV. Ampulla Morphology The morphology of the ampulla was studied. Tts muscu¬ lature could easily be determined by direct observation. These muscles were then separated from the ampullae with fine forceps after briefly soaking them in a 1:1 solution of IM KOH and glycerol (Woodley, 1967). The remaining tissue was then observed with an Aus Jena polarizing light microscope. Results Relative areas, which are proportional to volumes, of three distinct tube foot-ampulla systems during contraction and extension are depicted in figure 2 (time intervals are roughly the same between each point: 0.5 - 1.0 seconds). The data from each of the three filmed events fit lines of similar slope (-0.54, -0.81, -0.88 with linear regressions of -0.68, -0.92, -0.88 respectively) indicating that volume is immediately and directly displaced from the tube foot to the ampulla and back during contraction and extension. This proves that the system is isovolumetric, which adds confirmation to the existence of a one-way valve reported by Smith (1946). To determine how volume in the tube foot changed during contraction, areas of the model in figure 3 were matched to those of the filmed event f878 in its most extended condition. For the model: Ampulla area - 2.3 mm + 10%) Tube foot area = 9.9 mm (+ 10%) For 1878 (at maximum extension): Ampulla area - 2.3 mm° (49.4%, -4,3%) Tube foot area = 9.22 mm (+10.3%, -5.6%) Ampulla areas are identical and tube foot areas agree within 95% confidence intervals. Volumes are therefore assumed to be identical. Wall thickness of the tube feet from arms frozen in liquid nitrogen was found to increase during tube foot contraction. The strain value at 53% (minimum) extension is 0.5 (+ 0.07). The wall strain at 53% extension being known, the thickness of the walls of 1878 at 53% extensjon could be calculated. Subtracting this figure from the obseryed tube foot total width at 53% extension of 1878 gave the Jumen width, and finally its volume was calculated. At 53% extension, the tube foot lumen volume of 1878 has decreased by 88% from full extension. The ampulla at 53% tube foot extension has increased in volume by 1110%, Study of ampulla morphology reveals only longitudinal and circular fibers oriented at 902 to each other (figure 44 and B). No helically wound fibers were found. During ampulla contraction, the outer longitudinal fibers become crimped into waves and the inner circular fibers arrange themselves in the troughs of these waves. The innermost layer of tissue is muscle bundles. Separate bands of muscle radiate from the top of the ampulla until they form a continuous sheath about half-way down (figure 4C and D). Presumably this is to allow for greater ampulla expansion by reducing the limitations of diametric muscle stretch. Discussion From the value of 1110% increase in ampulla volume at maximum tube foot contraction, it is obvious that the ampulla is capable of withstanding a very great strain (£ - 9.2). Maximum strains in the longitudinal and circular fibers are unknown but are probably not the limiting factors in tube foot contraction. Since the tube foot volume at maximum contraction was reduced to 12% of that at full extension, very little more could be realistically squeezed out without collapsing the tube foot altogether. What seems more probable as the limiting factor in tube foot contraction is the maximum contractility of the longitudinal muscles in the tube foot. This hypothesis, however, requires verification. The tube feet can be physically stretched to much greater than their maximally observed extension of 254%, and afterward retürn to normal operation. This then rules out the maximum strain of the longitudinal fibers limiting extension as is hypo¬ thesized for ophiuroid tube feet by Woodley (Wainwright et al, 1976). When one observes the ampulla in figure 3 at 8.5% its maximal ly expanded volume, it appears that it must be approach- ing very closely its maximum contraction. What seems most likely then, is that maximum tube foot extension is limited by the contractility of muscles in the ampulla, or more precisely, the finite volume of the system. If the model tube foot in figure 3 is at very near maximum extension (200%), how is it that a tube foot can attain extensions of 254% as was recorded for one of the three filmed events? This is explained in figure 5. A tube foot at minimum extension with dimensions 2 mm. x 1.5 mm. is increased in volume by 88%. If its walls were constructed of an ISOTROPIC material,the stress would be twice as high in the hoop direction as in the longitudinal direction. Thus it would increase in the circumference twice as much as it does in length (Wainwright et al, 1976). If the tube foot were to remain a RIGID HOOP as vôlume increased, it would attain a two-fold increase in length as was observed for two of the three filmed events. The third event, however, (MAXIMUM OBSERVED, figure 5), revealed a further extension of up to 254%, and a discernible decrease in width to 78% (+3,8%, -9.3%). Tang (1983) and Shibata (1983) have both recorded helically wound fibers in the tube feet of Asteroids. Shibata's work was done on Pycnapodia tube feet. These helically wrapped fibers are depicted in figure 4 and probably allow the tube foot to attain further extension by constricting the tube foot in width. To better understand this concept one must recognize that these helical fibers become packed together so that they lie nearly horizontal at maximum tube foot contraction. As the tube foot extends, the angles between the fibers and the longitudinal axis of the tube foot decrease. Tang (1983) has reported helical fibers in Pisaster ochraceous, to be oriented at 76° at minimum extension and 6° at maximum extension. If we assume similar angles of 80° and 10° for Pycnapodia, percent decreases in width during extension would be as follows: At 80°, width = 100% At 45°, width = 72% (Denny, pers. comm.) At 10°, width - 17.3% One can see that widths change very little during at least the first half of extension, but much more noticeably during the second half. This reflects the observation that below about a 200% increase in length, no discernible change in width was recorded. From 200% to 254% however, tube foot width is seen to decrease. This simple but illustrative exercise fails to account for strains in the helical fibers. No doubt stretching goes on during extension and this must be taken into consideration. Nonetheless, this concept plays a major role in explaining the observed strains in tube foot width during extension. Conclusion 1. A direct tube foot to ampulla volume displacement supports the existence of a one-way valve (Smith, 1946). The tube foot¬ ampulla system is isovolumetric. 2. Tube foot wall thicknesses increase with contraction. £ = 0.5 at 54% extension. 3. Tube feet at maximum contraction lose about 88% of their extended volume. Ampullae can increase in volume to roughly 1110%. 4. The ampulla has longitudinal and circular fibers but none helically wrapped. 5. The limit of tube foot contraction is probably due to maximum contractility of its longitudinal muscles, Extensjon is limited by muscular contraction of the ampulla (j.e. restricted by total internal volume). 6. Extensile capabilities of the tube feet are greatly enhanced by helically wrapped fibers, Acknowledgements Thanks to my advisor Mark Denny for all his help and in¬ spiration. Thanks to Freya Sonner for her sound advice and selfless sistance. Finally, thanks to Sushma Govindarajulu for her spiritual encouragement and typing this manuscript. -14- Literature Cited Kozloff, E.N., Galigher, A.G., (1971) Essentials of Practical Microtechnique. London. Henry Kimpton Smith, J.E. (1946) The mechnaics and innervation of the starfish tube foot-ampulla system. Phil. Trans. R. Soc. B 232:270-310 Wainwright, S.A., W.D. Biggs, J.D. Currey and M.M. Gosline (1976) Mechanical Design in Organisms. New York : John Wiley Woodley, J.D. (1967) Problems in the ophiuroid water-vascular system. Symp. zool. Soc. Lond. 20: 75-104 Woodley, J.D. (1979) The biomechanics of ophiuroid tube feet. In: Echinoderms: Present and Past, (M. Jangoux, ed.), pp. 293-299. Figure Legends Figure 1: The viewing window cut into the side of a Pycna¬ podia ambulacrum to facilitate filming of the entire tube foot¬ ampulla system in operation. Figure 2: Graph of tube foot vs. ampulla areas during tube foot contraction and extension. Tube foot area per¬ centage errors are +10.3%, -5.6%; ampulla area percentage errors are +9.4%, -4.3%. Figure 3: Cross-section of the model tube foot-ampulla system. Figure 4: Morphology of the Ampulla. Figure 5: Tube foot extension for tube feet of different physical characteristics given an internal volume increase of 88% from the ORIGINAL volume. Helically wound fibers are responsible for the MAXIMUM OBSERVED tube foot as illustrated. fgne ambulacrum 39 C -16- VIE WING WINDOw ampulla DORSAL 2 ji N C D VENTRAL tube foot fm 2 100 80 — —— 60 ---- —. 7 40 -17- 40 60 80 tube foot (% extension) 7878 —— - 1834 —. —. — 7868 — — :— — --- ) — — —-—- ... ... 100 - -.. fgu -18- Pegvr 4 . AMPULLA MORPHOLOGY —--— — outer long. fibers inner circ. fibers - muscle Iny innermost muscle bands muscle bands (top view) -20- .. —-—— — — . : —:—— EXTENSION TUBE FOOT - - — —: —.— -.— —1. -— -.- —1 — — ORGNAL 1 — — ISOTROPIO — — - -:— — — — „ 4 - —--:—- 2 â RDGED HOOP. --— A —.—— L —1— I â — — ÖBSERVED — MAX. 1 — — 3 8-1 D . 1 — ---- -- ——— ——.— ———— + -- —.— —-- — :. — —— — —-- —--- ---- 1 ka- — —— S — — —+ —- —- —-- - — WIDTH Cin mm.) — —- -.-— ——— -------- ———