Lecture 8, Oct 1hydrostatic>hydraulic> hydrodynamic (continued)

Finishing echinoderm tube feet

Moving on to squids and jetting

Sources:Kier W.M. 2012. The diversity of hydrostatic skeletons. J. exp. Biol. 215… [continuing].

McCurley R.S. & Kier W.M. 1995. The functional morphology of starfish tube feet: the role of a crossed-fiber helical array in movement. Biological Bulletin 188: 197-209. (Kier’s Fig. 7 in ‘The Diversity of Hydrostatic Skeletons’ paper arises here.)

Santos, R. et al. 2005. Adhesion of echinoderm tube feet to rough surfaces. J. exp. Biol. 208: 2555-2567.

• …water vascular system of asteroids* serves crucial roles in locomotion, food handling, respiration and, in many species, burrowing. The major components of the system are the circumoral ring canal, the radial canals extending from the ring canal down each arm, and the tube feet with their associated ampullae that are connected to the radial canal by the lateral canals” (McCurley & Kier 1995).

Virginia Living Museum‘off the beaten path’

Gas exchange in a marine animalis always a possible role where large surface areas contact the sea: in one ambulacral groove there may be >100 tube feet, affording in total lots of surface area for gas exchange; and perhaps papulae are important too (see next slide).

Tube foot functioning in predation: pulling with tube feet to open the valves of shellfish.

*asteroid – among the Phylum Echinodermatathese are the starfishes.

Fig. from Frank Brown, Selected InvertebrateTypes.

Transverse section of starfish arm

papulae

pedicellariae

Pedicellariaefunction to clean the surface of the skin.

One-way valve can isolate each ampulla & tube foot functionally.Ampulla is squeezed by contraction of ampullar (protractor) muscles; (incompressible) fluid is displaced into the lumen of the tube foot; the annular rings in the tube-foot wall (not drawn) disappear as the foot protracts, reappear as it retracts.

HydraulicSystem

lumen: term for innerspace of an organ, e.g.,lumen of gut, of bladder, etc., it’s a space but not necessarily empty, fluid can be present as here. Because of the crossed fibre helical connective

tissue array in the wall of the tube foot (CFHCTA) -- the foot protracts – lengthens.

Fibre angle is ~67 degrees; angle made by collagen fibres with long axis of tube foot.

PEDAL DISCS Santos, R. et al. 2005. Adhesion of echinoderm tube feet to rough surfaces. J. exp. Biol. 208: 2555-2567.

Fig. 6 external morphology of unattached pedal discs of Paracentrotus lividus (left) [sea urchin] and Asterias rubens [starfish] (right) .

End of extensible cylinder is called the pedal disc, larger in diameter than the stem. There is a central depression provided with secretory epithelium.

Temporary adhesion: the epidermis of the pedal disc contains glands which produce secretions: a glue and an unglue secretion, i.e., bonder and de-bonder. The glue is secreted onto the shell of a bivalve from the disc epithelium where it forms a thin bonding film. The debonding secretions are placed later, enzymes that detach the upper coat of the glue and leave the rest of the adhesive material behind attached as a ‘tubefoot-foot-print’.Recalls the viscoelastic composite material used by slugs.

“The tube foot is equipped with longitudinal muscle fibres that can be contracted selectively on one side of the foot to create bending movements or can contract simultaneously to shorten the tube foot, forcing the water back into the ampulla” (Kier 2012).

Equation 4 of Kier: ‘Kier’s Law’, p. 1250:For a cylindrical pressurized fluid chamber circumferential stress equals 2 times the longitudinal stress.“…at a given pressure the stresses in the circumferential direction are twice those in the longitudinal direction.

“Without reinforcement of the tube foot wall [by the helix of connective tissue] the pressure generated by the ampulla will cause an increase in diameter rather than elongation of the tube foot.”

• The fluid cavity of a nematode can evolve to an adaptive range of extensibility that depends upon the relationship between the possible range of helical fibre angles and the fixed volume of the species. Pick a particular fixed volume (up the y axis) – a larger volume – and the range of helix angles available for shape change (involving flattening as the circular body goes to an elliptical cross section) is more constrained. More extensible species (e.g., Lineus) will evolve to use a volume that is giving the helix a greater range of angles.

The relationship between volume and fibre angle θ as in Fig. 1C, on which are superimposed the actual volumes of various nemerteans and turbellarians (fine horizontal lines).

Shadwick R E J Exp Biol 2008;211:289-291

©2008 by The Company of Biologists Ltd

“By examining Fig. 4 , it should be clear that an increase in volume of the tube foot will cause elongation only if the fiber angle of the connective tissue fibers is greater than 54 deg 44 min. This is indeed the case for brittlestar and starfish tube feet” (Kier 2012).

Fig. 4 Kier 2012

Recall this slide from an earlier lecture

54deg44min

• “The deformation of the cylinder that results from inflation with fluid depends on the initial fibre angle: if this is less than 54deg44min, an increase in volume will result in shortening rather than elongation, and no length change will occur at a fibre angle of 54deg44min.”

McCurley R.S. & Kier W.M. 1995. The functional morphology of starfish tube feet: the role of a crossed-fiber helical array in movement. Biological Bulletin 188: 197-209.

Luidia

Kier p.1252 Tongues, tentacles, trunks: “lack the fluid-filled cavities and fibre-reinforced containers that characterize ... hydrostatic skeletal support systems” rather they are:

“a densely packed, three-dimensional array of muscle and connective tissue fibres”

Muscular hydrostats

Transverse sections showing the muscular arrangement of three examples of muscular hydrostats.

Kier W M J Exp Biol 2012;215:1247-1257

©2012 by The Company of Biologists Ltd

A. Squid tentacle: T, transverse muscle fibres; L , longitudinal; transverse in the tentacle core, “and extend to interdigitate with bundles of longitudinal muscle fibres, notice the suckers.

Transverse sections showing the muscular arrangement of three examples of muscular hydrostats.

Kier W M J Exp Biol 2012;215:1247-1257

©2012 by The Company of Biologists Ltd

B. Elephant Trunk: R, radials ‘extend from centre of the trunk between bundles of longitudinal muscle that are more superficial, notice nasal passages.

C. Monitor lizard tongue. Circular muscle fibres surround two large bundles of longitudinal fibres.

• “The muscle fibers are typically arranged so that all three dimensions of the structure can be actively controlled, but in several cases such as the mantle of the squid [of which more later] and some frog tongues, one of the dimensions is constrained by connective tissue fibers.” Here again: crossed fibre helical connective tissue array: CFHCTA.

• “Because muscle tissue …has a high bulk modulus, selective muscle contraction that decreases one dimension of the structure must result in an increase in another dimension. This simple principle serves as the basis upon which diverse deformations and movement of the structure can be achieved” (Kier 2012).

*bulk modulus of a substance [an index] measures [the substance’s resistance to uniform compression Wikki

Muscular hydrostats (Kier contin.)

• Selective contraction: “This simultaneous contractile activity is necessary to prevent the compressional forces generated by the longitudinal muscle from simply shortening the structure, rather than bending it, and can actually augment the bending by elongating the structure along the outside radius of the bend.”

• “The longitudinal muscle bundles are frequently located near the surface of the structure, as this placement away from the neutral plane increases the bending moment.”

• Helically arranged muscle fibres can be present and generate torsion.

Now we turn to jetting: locomotion where the incompressibility of water, combines with a vented cavity to create reaction force displacement.

Snail body, visceral mass and foot almost amorphous: excepting the shell the variability of body’s shape is its dominant feature: octopus are reknowned for escaping cages through cracks (coral head story): versatility in body shape change marks the importance of its hydraulic skeleton: its use of fluid force translocation in moving about: changing body shape by the interaction of fluid and muscle and collagen fibres.

Land snailMembers of this phylum (snails, octopus, squid, cuttlefish, Nautilus, bivalves, slugs etc.) show no body segmentation. Strong cephalization but not much neck. Thick muscular body wall: visceral mass atop a muscular foot. Outfolds of visceral mass secrete protective shell. . Mantle: dorsal body wall extended as folds. as a ‘skirt’ about the body, this skirt creating a mantle cavity containing gills. Mantle secretes a shell.

Cartoon to illustrate body form of the generalized molluscan ancestor. (The closest modern group of molluscs are limpets.) A visceral mass sits atop a muscular ventral foot. The body and especially the foot contain blood sinuses that interconnect with the closed part of the circulatory system, residing in a remnant coelom. Blood sinuses surrounded by muscle provide the basis for hyraulic shape change in the mollusc foot. Note the bottom right section shows the skirt overhang on the visceral mass that delimits the mantle cavity and contains and protects the ctenidia (gills).

streamliningdorsal view

Upper left a squid drawn oriented in the primitive fashion: the ancestral foot relates to the tentacles, the pen (remnant of the shell of the ancestor) lies within the tissue, but still gives support, an exoskeleton become endo.

Squid body form has come a long way from its ‘snail’-like ancestor.

Hypostome,Siphon,Funnel,Spigot,Nozzle: all the same thing: directing jet.

• Funnel (siphon) (not visible in this photo) developed from posterior of primitive foot.

• Primitive ventral surface of ancestor became functional anterior end.

Chromatophores are pigment cells in skin, circlet of smooth muscle cells, disperse concentrate.

Class Cephalopoda includessquid, octopus, cuttlefish, Nautilus

primitive dorsum

Fins set up waves; posterior lateralfins act as stabilizers and rudders; squids achieve greatest swimming speeds of any aquatic invertebrate, up to 40 kmph.

Assigned reading: Gosline J.M., & Demont M.E. 1984. Jet-propelled swimming in squids. Scientific American 252: 96-103.

A swimming squid takes up and expels water by contracting radial and circular muscles in its mantle wall. It makes the mantle thick or thin in order to change mantle cavity volume. Radial and circular muscles are antagonists. There are collagen fibres whose purpose is to keep the body from lengthening. This is critical in making the muscles antagonists.

Beware potential confusion: squids jet-propel themselves and of course there is a fluid-filled cavity involved – the mantle cavity. The seawater in this cavity functions in locomotion by virtue of its high bulk modulus; if the seawater were not incompressible the jetting wouldn’t work. But the mantle cavity is NOT functioning as a hydrostatic skeleton antagonizing mantle muscles. Rather the mantle wall itself is a muscular hydrostat.

The three (transverse) body diagrams follow one cycle from maximum seawater intake to maximum seawater expulsion. They are drawn to show how the muscular mantle changes its thickness during the cycle. (Only the radial muscles are shown based upon the fibre ‘lines’; you have to imagine the circulars as being present too.

The squid jets water out of its mantle cavity via the siphon/funnel. It does this by contracting muscles of two sorts: radial and circular.

The seawater within the mantle cavity of the squid is not functioning as a hydrostatic skeleton. But it is the basis of the animal's jet propulsion, which in turn depends upon the incompressibility of seawater. When the radial muscles of the mantle contract, the volume of the mantle cavity is increased and seawater is drawn in. When the circular muscles of the mantle contract, the volume of the mantle cavity is decreased and seawater is squirted out.  The action-force of the jetted seawater creates a reaction force that pushes the squid in the opposite direction: opposite to whatever direction the funnel is pointing.

One-way valves* control intake of water into mantle

cavity at sides.Pressure build up in

seawater inside mantle cavity (circulars contract)

forces the inner flaps of the funnel against the mantle

wallwater jets out funnel

(hypostome).[*recall starfish canals]

The animal has great flexibility in directing the funnel.

Mantle structures interact: 1) helical collagen fibres act as a tunic that prevents longitudinal dimension change [see cross-hatch] 2) radial muscles contract to thin the

mantle wall and 3) circular muscles of the mantle contract to thicken the wall. Circulars and radials are antagonists.

The mantle (the actual wall) is a muscular hydrostat and its volume must stay constant (just as if it were a fluid-filled cavity).

But (per Kier) the fibres are very critical: because of the collagen ‘tunic’ the mantle cannot get longer in the A to B dimension: it can change in girth.

[Imagine it as it isn’t: no tunic: it would lengthen in response to circulars rather than affecting mantle cavity volume and stretching radials.]

AB

1. Radial muscles contract to cause: hyperinflation: seawater intake into mantle cavity: outside diameter of mantle increases by approximately 10% over resting diameter (girth increase); cavity volume increases 22% re relaxed volume, wall thins.

2. Circular muscles contract to bring mantle to about 75% of its relaxed diameter, radials restored to precontracted length (girth decrease): volume drops & pressure rises sharply , forcing the inlet valves against the mantle wall and leaving only the funnel as exit.

relaxed

relaxed

Mantlewall

Escape JetCycle of squid

Internal organs

contracted

• The mantle wall functions as a muscular hydrostat – a skeleton acting without a special fluid chamber, but making use of the incompressibility of muscle tissue (which has the necessary high bulk modulus). Mantle wall acting as hydrostat contains radial and circular muscles: contraction of the one muscle type restores the other type to its relaxed state. The radial and circular muscles become coupled as antagonists because the mantle cannot lengthen.

• Because the mantle muscle is incompressible it must retain an overall constant volume; and it cannot get longer as mantle muscles contract because of the collagen fibre tunic that prevents any longitudinal movement. It can only increase or decrease in thickness – at the same time changing its overall diameter and the capacity of the mantle cavity. When the radials contract the mantle walls must get thinner and the walls move apart -- to maintain hydrostat volume. Conversely when the circulars contract the mantle wall must get thicker as the overall outside diameter of the mantle decreases. If there were no inextensible fibres, if the animal’s mantle was not in a jacket of fibres preventing it from lengthening, then the radials and the circulars could not have an antagonistic effect on each other.