Feb 5 Cuticle transmits forces In preparing for the test Thursday be sure to include the opening lecture on Membracidae. There is a course ‘theme’ and it governs the sort of questions asked. The course is also about the form of structures and their behaviour; about what form a structure takes and why. Why have certain features: shape, size, elasticity, colour, etc. evolved and not some others? Look at animals functionally. Think about adaptive consequence.

For more information on cuticle see Vincent J.F.V., Wegst U.GK Design and mechanical properties of insect cuticle. Arthropod Structure & Development 33: Section of chitin nanofibre looking along the chitin chains. Chitin is a polysaccharide akin to cellulose. Nanofibre is 3 nm in diameter, 0.3 micrometeres long with 19 molecular chains Insect cuticle/exoskeleton is a composite material of crystalline chitin nanofibres embedded in a protein matrix.

“...control of [cuticle] stiffness is in general a matter of manipulating the water content” (Vincent& Wegst 2004). Stiffness and strength of cuticle are due in part to their hydration. Compliant (soft) cuticle contains equal weight fractions of chitin and protein and 40-75% water. Hard (stiff) cuticles contatin 15-30% dry weight chitin and only 12% water. Cuticle is a unidirectional composite, i.e., it has a grain of fibre vs matrix. Tensile and shear stiffnesses and strengths are much larger when chitin fibres are alligned parallel to the applied load (Fig. 4). “When the fibres are alligned perpendicular to the applied load the properties are dominated by the modulus of the matrix.” If stiffness in more than one direction is required cuticle can be laminated. becoming ‘platey’ or multilayered with a plywood-like structure. The grain can change in successive layers to resiste pull (tension) or push (compression) from different directions.

The cat flea Ctenocephalides felis Morphological features form of the flea: no wings, it’s flightless (its ancestors had wings); body extremely laterally compressed; greatly enlarged metathoracic legs; unidirected body spines. Apply the course theme to this insect thinking about where and how the animal lives. Course theme: the course is about the form of structures and their behaviour; about what form a structure takes and why. Why have certain features: shape, size, elasticity, colour, etc. evolved and not some others? Look at animals functionally. Think about adaptive consequence.

Jumping is by power amplification. Energy is loaded (relatively slowly by isometric contraction of antagonistic muscles) into a pleural arch (the site of the wing-hinge in its flying insect ancestors) and stored there in the rubbery protein resilin (insect rubber: matrix between the chitin nanofibres is now this particular protein). Once loaded the energy is held there as potential energy by latching sclerites, so no ongoing effort needed by the flea. Release is by body width change. The leg segments extend pushing down on the substrate and because of the stored energy they do this very very fast. So the ‘engine amplifier tool’ arrangement of Patek is: leg muscles as engine, resilin of pleural arch as amplifier, flea hind leg as tool. A flea only 2 mm long can jump 200 mm, 100 times its own body length, equivalent for a 6’ human of 600 feet! Accelerates from rest to 1 metre/sec in a distance of 0.4 mm; by extending its legs in about 8/1000 th of a second.

The muscle depressor of the trochanter (green here) is a relatively long way from the trochanter; it originates on the notum, it inserts on the trochanter. The insertion is via a massive apodeme which tapers down to attach anterior to the (dicondylic) axis of the trochanteral rotation (see blue dots). So the contraction of the trochanteral depressor pulls the trochanter, rotating it forward on the coxa and extending it (= depressing it).

An antagonist of the trochanteral depressor is the levator of the trochanter. It originates on the inner wall of the coxa and inserts on the trochanter posterior to the axis. And another muscle antagonistic to the trochanteral depressor is the epipleural muscle: this inserts on the base of the coxa; on its contraction, as with the levator, it pulls behind the axis of rotation of the trochanter on the coxa. Both the epipleural muscle and the levator of the trochanter have the effect of flexing (levating) the limb, i.e., raising it from the substratum.

Under normal walking movement either the levator or the depressor contracts: they are not shortening at the same time. But in preparing itself in the jumping position, the flea eventually contracts all three muscles simultaneously: isometrically: no movement at the joints: hence distortion.

Flea begins its jump by flexing the limb (the levator and epipleural muscles playing an appropriate part in this). Then all three muscles [levator of trochanter, epipleural muscle and depressor of the trochanter] contract simultaneously. Since the depressor opposes the action of the other two, nothing happens now to change the relation of the segments of the flexed hind limb [isometric]. Rather the force expended by the muscles is "loaded into the pleural arch", i.e., it goes to compress the resilin pad located above the pleural plate, squeezing the resilin between the plate and the notum.

Sutton G.P., Burrows M Biomechanics of jumping in the flea. J. of exp. Biol 214: In this paper the authors present arguments between two hypotheses of how the flea jump works: 1) Rothschild Hypothesis 2) Bennet-Clark Hypothesis. Their arguments are all in favour of the latter: the trochanters do not drive into the ground, rather that “expansion of the spring applied a torque about the coxotrochanteral joint that (is) carried through the femur and tibia and finally resulted in a force applied to the ground by the hind tibia and tarsus. Driving down the trochanters into the ground has some obvious arguments against: animal would be propelled vertically and could have trouble jumping and making horizontal distance (of course to reach a passing dog vertical might be rather good).

Patek S.N., Dudek D.M., Rosario M.V From bouncy legs to poisoned arrows: elastic movements in invertebrates. [Superficial broad treatment but worthwhile as an overview of Power Amplification.] Fundamental principles underlying the diverse elastic mechanisms that speed up biological movements, i.e. inserting a spring’ into a movment system. Three components: engine, amplifier, tool [effector]. Patek makes an analogy with an archer shooting a bow: ENGINE is the archer’s muscle supplying energy, the bow is the AMPLIFIER which, as it is bent, stores energy from the archer’s muscle; this energy storage is relatively slow [so low power]; the ‘tool’ (I like effector better) is the structure/appendage, the arrow, whose movement is speeded up by the relatively fast release of the stored energy. Power is defined as the rate of supplying energy/doing work. A rate is division by time. Store at a low rate – at low power; release at a high rate -- at high power. Power is amplified by reducing the time of work/energy delivery. Patek the author of this paper on bouncy legs, has worked largely on mantis shrimp.

Odontodactylus scyllarus, peacock mantis shrimp Mantis shrimp are Crustacea: a major group of Phylum Arthropoda, the Order Stomatopoda ~300 species. All are marine predators of fish, crabs, shrimps molluscs. Very great range of species sizes 5-36 cm; they have the most highly developed compound eyes among crustaceans

Gonodactylaceus falcatus (A) uses its raptorial appendages to smash hard-shelled prey. Zack T I et al. J Exp Biol 2009;212: ©2009 by The Company of Biologists Ltd Second pair of appendages on thorax are raptorial extended at high speed they smash into the prey. Power amplification of this strike is achieved by latches that brace the metacarpal joint during extensor muscle contraction. With the latches engaged, the extensor contracts relatively slowly and compresses the merus along its long axis. When these two latches are suddenly released the merus springs back to its normal shape which forces the carpus, prodopus and dactyl to rotate with high acceleration. Segments of the raptorial limb merus distad: m – merus, v – meral V, c – carpus, p- propodus, d - dactyl

During preparation for a strike, the merus moves from its resting position (solid outline) to a compressed state (overlaid colors) that was mimicked by our materials testing apparatus. Zack T I et al. J Exp Biol 2009;212: ©2009 by The Company of Biologists Ltd

Cercopidae: froghoppers Philaenus spumarius Spittlebugs Cosmos Ask Nature Burrows M Froghopper insects leap to new heights. Nature 424: 509. See also Patek et al From bouncy legs... Burrows M Morphology and action of the hind leg joints controlling jumping in froghopper insects J. exp. Biol. 209: Sap-feeding animals that have adapted their excretion of excess fluid as a bubble defense of their larvae.

Trochanteral depressor (extensor) muscles provide energy for the jump, apparently on their own (i.e., not via opposition from an antagonist). For jumping first the hind leg is flexed at all joints and latched in place by the interposing of two protrusions: one on the coxa and one on the femur. Latched in this way, the contraction of the depressor is ‘almost isometric’ and stores energy in the sides of the animal’s body – in right and left stiff cuticular ridges, the pleural arches. At some point the accumulated energy exceeds the capacity of the latch and the insect jumps by leg extension. This is another case of power amplification: energy stored slowly from muscles that is then released in a tiny fraction of the time.

coxal protrusion On the dorsal face of the femur opposite to where the blue oval is placed is a swelling that engages with the coxal protrusion to create the latch. Ventral view of froghopper hind leg coxa femur trochanter

pleural arch