Lecture 14 BIO 325 Levers Insect Flight Elastic recoil: subalar arm Elastic storage for power amplification: flea jump Assigned reading: Sutton G.P., Burrows M. 2011. Biomechanics of jumping in the flea. J. of exp. Biol 214: 836-847. Patek S.N. et al. 2011. From bouncy legs to poisoned arrows: elastic movements in invertebrates. J. exp. Biol. 214: 1973- Rothschild, M. et al. 1973. The flying leap of the flea. Scientific American 222: 92-101. Roberts T.J., Azizi E. 2011. Flexible mechanisms: the diverse roles of biological springs in vertebrate movement. J. exp. Biol. 214: 353-

Levers A lever is a machine that moves (translocates) forces from one place to another, at the same time changing the force magnitude and direction. Lever arm of the force-in is the shortest distance from the axis of rotation to the load. Lever arm of the force-out is the shortest distance from the axis of rotation to where the load is considered to act (i.e., it’s centre of gravity). Force advantage of a lever: the factor by which the force in is changed: FORCE OUT/FORCE IN. Distance advantage of a lever: the factor by which the distance moved is changed: DISTANCE OUT/DISTANCE (speed) IN [Since both effort (force in) and the load (force out) must move their distances in the same time: distance advantage is the same as speed advantage.] Force advantage and distance advantage have a reciprocal relationship: a lever with a good force advantage will have a poor distance advantage; a lever with a poor force advantage will have a good distance advantage. [The latter is the case with the insect wing: muscles pulling (indirectly) close to the fulcrum: wing tips moving through a maximal distance as one wants in flying.] Muscles typically have to work with a poor force advantage.

3 classes of lever: classified on the basis of sequencing 3 items force in, force out and fulcrum (axis) FIRST EFFORT FULCRUM LOAD SECOND FULCRUM LOAD EFFORT THIRD FULCRUM EFFORT LOAD In order to place the load (force out) you need to decide the location of the centroid of a structure, its centre of gravity: this is the point of balance. Need to understand the idea of mechanical advantage: force advantage, distance advantage, speed advantage. These are ratios (unitless). Force advantage: force out divided by force in; Distance advantage: distance out divided by distance in; Speed advantage: speed out divided by speed in. A first class lever with a third-class lever, the two involving an antagonistic pair of muscles: this is one of the commonest arrangements in animal muscle systems. (For first class levers force advantage is usually >1, distance/speed advantage can be very good (wing of a fly for example) Second class levers: force advantage is always >1, speed advantage is always <1 Third class levers: force advantage is always <1, distance advantage >1

The wings of insects are first class levers The force in (EFFORT) is exerted by the longitudinal and tergosternal muscles acting indirectly via changes in shape of the thorax. Consider the wing as a very long lever. pivoted on the second axillary sclerite which sits atop a prominence on the thorax side, the pleural wing process. The PWP and the 2nd axillary represent the fulcrum. The force arm is a very short projection toward the body from the fulcrum. It goes through a small distance up and down when the thoracic movements push on it. The load lies far out on the wing and goes through a relatively large distance up and down. The force in and the force out lie on opposite sides of the fulcrum (hence FIRST CLASS LEVER) and though the muscles work at a considerable force disadvantage they have a very large distance advantage – this being the same thing as a speed advantage. Short movements of the tiny force arm at a slow speed displace the load arm through long movements at a much higher speed: just what you need for flying.

Examples of first class levers in animal movements already encountered in the course.

Scallop as a 2nd class lever The load is assumed to be acting through the centre of gravity of the bivalve; the force out lifts this load.

Class 3 lever both up and down

Tergum, sternum, pleuron Insects are segmented animals and the thorax is a locomotory tagma. Contrast the segments of the abdomen with those of the thorax. The thorax is ‘fixed’ to create a firm base against which muscles can pull, for walking and for flying. The pterothorax is the mesothorax + metathorax: two segments specialized for bearing the wings and for flight. Muscles involved in flight in insects (with exceptions) insert on the exoskeleton of the thoracic box and move the wings by distorting box shape. LONGITUDINALS DOWNSTROKE; TERGOSTERNALS UPSTROKE Attitude of the wings (pronation, supination) is achieved by the elastic interplay of the veins and membranes with the air flow. The wings don’t just go up and down and maintain elevation they must scull through the fluid (air) like a fish fin.

Locust flight {Source: R. E Locust flight {Source: R.E. Snodgrass The thoracic mechanism of a grasshopper, and its antecedents. Smithsonian Miscellaneous Collections 82, pp. 111. } [This reference is given just for completeness; it is not something you should try to obtain and read, but it is the source of much of the information here and in the lab.] Locusts are strong fliers. The flight-powering muscles of the locust are indirect: meaning they don’t insert on the wings. They have their effect upon the wings by distorting the pterothorax and by tergal tipping of the second axillary. (The pterothorax is the flight tagma (just segments 2 & 3, not the prothorax.) There are two antagonistic muscle sets: longitudinals (downstroke), and tergosternals (upstroke). contraction of the longitudinals wings go down contraction of the tergosternals wings go up

Sct2 is the scutum of the second segment of the thorax; scutum is the name given to a part of the tergum, as is Scl2 which is scutellum. Muscle 81, e.g., is a longitudinal flight muscle pulling between phragma 1 and 2, 112 is the same pulling between phragma 2 and 3. These increase the arching of the terga creating forces at the wing bases (PWP & 2nd axillary sclerite). Phragma: apodemes that allow for insertion of the longitudinal flight muscles. The longitudinals are situated high up in the pterothorax. Partially obscured behind them, arrayed against the pleuron, are the many tergosternals (83,84,89 etc.), running between the sterna (S2,S3) and the terga (Sct2,Sct3). The axes of the tergosternals all lean headward (the insect’s anterior is to the left). Notice how the upper end of the tergosternals insert on the terga where their contraction can reduce the convexity of this region. Reducing tergal convexity is associated with elevation of the wings.

More diagramatic views: Snodgrass drew the phragmata (Aph anterior phragma, Pph posterior phragma) of Fig. 129 purposely distorted, so as to show their interconnecting longitudinal muscles both ahead and behind: notice the critical placing of the second axillary, 2Ax, atop the pleural wing process, WP.

The wing is a double-layered outfolding of cuticle The wing is a double-layered outfolding of cuticle. At the wing base are 4 axillary sclerites and 2 median plates (m, m’) linking the basal/proximal ends of the veins (costa, subcosta, radius, median) to the margins of the tergum. The tergum is to the left (not shown). The third axillary serves in flexing the wing over the back when the insect is not flying. It is the anal field that becomes involved in stridulation in crickets and katydids.

subalare2 basilares2 2nd axillary PWP2 Seen here in dissection, the heavily sclerotized pleural wing process with the second axillary that contacts it above. See also the first basilare, 1Ba2, involved in wing pronation and upstroke and primitively a leg muscle now co-opted for flight.

Seen from below the wing, some of the same veins (Sc) and axillary sclerites appear, the 2nd axillary 2Ax, is crucial; it is concave and sits atop the wing process – providing the fulcrum of wing up and down movement.

Power: rate of doing work and ‘springs’ Forces can be exerted at different rates, quickly or slowly. When we say that a muscle’s effect is more powerful, we mean it is working more quickly. Work is Force X distance (force [mass X acceleration] is exerted over a distance to do work). Power is the rate at which work is done: done slowly it is low power, done quickly it is high power. A flea needs a powerful jump to get higher. Its muscles alone cannot achieve the necessary power in ‘real time’ – so muscle is aided by cuticular storage of energy. Forces can be stored to be released at a later time. And when, at that later time they are released, they can come back into action far more quickly than would have been the case if this movement emanated from the muscle that originally stored them. Elasticity of cuticle can be used to aid locomotion by increasing power and efficiency.

Explanation of how the prealar arm stores elastic energy: basilare muscle pulls on basilare sclerite which pulls on the ligament, stretching the prealar arm resilin. The two resilin springs, prealar arm of phragma 1 and hinge at top of PWP [red], store energy by tension during the upstroke, energy derived from the flight muscles. Beside the phragma that lies at the front of the pterothorax there is a prealar arm that is almost pure resilin. Cuticle modified to be highly elastic. The prealar arm is connected via a ligament to the basilare sclerite.

Shape change in the tergum (reduced convexity centrally, with outward and downward movement at the tergal margins) is brought about by the tergosternals. So over a very short-distance a downward force acts on the near end of the 2nd axillary (red arrow); this rotates the proximal end of the 2nd axillary around the pleural wing process (PWP) and raises the wing that is linked to the axillary. Elastic energy from the upstroke is stored in the wing hinge resilin (as well as the prealar arm [not shown]).

During the downstroke energy returns from the wing hinge and prealar arm contributing to the rebound of the wing. The longitiudinals, antagonists of the tergosternals are now changing the shape of the tergum back to more convex and the force acting on the proximal 2nd axillary is upward (red arrow).

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.

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 8/1000th of a second. 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 of 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.

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. 2011. Biomechanics of jumping in the flea. J Sutton G.P., Burrows M. 2011. Biomechanics of jumping in the flea. J. of exp. Biol 214: 836-847. 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).