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Jan 31, 2013

Jan 31, 2013. Jump of the locust Distortion energy storage during isometric contraction Buckling when kicking errs Power amplification. Clarification from last lecture. Comments re term test to be given in lecture Thurs. Feb. 7.

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Jan 31, 2013

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  1. Jan 31, 2013 Jump of the locust Distortion energy storage during isometric contraction Buckling when kicking errs Power amplification

  2. Clarification from last lecture

  3. Comments re term test to be given in lecture Thurs. Feb. 7 • Questions on the test are drawn from the first 8 lectures and the first three labs. The lecture material of Tuesday Feb 5 is not. • The test will involve some choice. Choose carefully. • In preparing remember to read the lab preambles. • Use my time investment in lecture as a guide to the more important topics. • Labelled diagrams to put a structure into its anatomical context are important in almost every answer. • Better answers: its not a question of whether you mention all relevant facts, but how you present them: how well you explain. Marking tries to reward the better answers.

  4. Orthoptera Species File Locusta migratoria in a prejump crouch. Heitler W.J. 1974. The locust jump. J. comp. Physiol. 89: 93-104 from Wikkipedia

  5. Heitler W.J. 1974. The locust jump. Journal of comparative Physiology 89: 93-104.Its well-written and clear; read it in detail to understand the paradox(see below). • He starts with behaviour: what the structure does: the mechanics of the jump in increasing detail. There is passing reference to the adaptive context. • “The locust jumps to escape from danger, to launch itself for flight, or simply to achieve a more rapid form of locomotion than walking. Prior to a jump the locust assumes a crouched position, with the metathoracic tibiae flexed, and it may maintain this for some seconds until it either jumps or relaxes. The jump is achieved through a rapid extension of both the metathoracic tibiae... [through a femorotibial joint “excursion of about 150 degrees”].

  6. Paradox • Both muscles work with a poor mechanical advantage due to constraints of body shape and a good speed, distance advantage – good to have speed and distance when trying to jump. • “Myograms show that there is co-activation of the extensor and flexor muscles during the pre-jump crouch... • “Complete extension of the tibia takes some 20 ms... to develop peak power ...in the jump the extensor muscle must first build up tension isometrically. [Isometric muscle contraction: the two antagonists simultaneously contract but there is no movement at the joint; isometric means muscles generate force without changing length.] • [Isometric contraction of antagonists can store energy as distortion/elasticity.] • “The extensor muscle is massive and occupies the greater part of the femoral volume. Its fibres are short [pinnately arranged fibres, like a feather], and occur in chevron blocks; an arrangement which enables the muscle to develop a very large force at its tendon [apodeme]. The flexor muscle, by contrast, is composed of long thin parallel fibres, and is of comparatively small cross-sectional area. This weak muscle must hold the tibia flexed against the full force of the powerful extensor muscle.” • How is this achieved during isometric contraction? The answer: special adaptations of leverage at the joint and a flexor apodeme lock. What is adaptive about chevron blocks? Reminds one of amphioxus.

  7. Anatomy of locust metathoracic leg femorotibial joint • Flexion and extension: during a jump or kick the joint angle goes from 0 to 150 º • Diconcylic joint: condyles [= pivot pegs] are part of femur, the sockets part of tibia. • Extensor of tibia, flexor of tibia are antagonists. The femorotibial (dicondylic) joint is axis about which the tibia pivots relative to the femur. • Below the two antagonists are modelled as levers. The extensor works as a 1st class lever; the flexor is 3rd class. • Notice that the lever arm has a distinctive shape (see below). • The angles of ‘force in’ change as the tibia moves from completely flexed to maximally extended (see below). • Pocket and lump = flexor apodeme lock.

  8. Geometry/anatomy of the joint see Heitler’s Fig. 1 • a Fully flexed joint, lock engaged: bifurcate pocket of apodeme of flexor sits astride the lump. Note apodeme of extensor and two accessory muscles. • b Lock is disengaged and joint extended midway; flexor apodeme is now readily visible and rides pulley-like on top of the lump. • c The two condyles of the dicondylic joint seen dorsally along with the lump.

  9. Last lecture’s models of levers didn’t address moments of force. For example the distance (and angle) at which an apodeme pulls on an insect’s mandible varies between species. Perhaps the adductor inserts 2 mm from the axis, perhaps 1 mm. This will affect the moment of force. As well the direction (angle) of the force exerted by the muscle on lever can change as the joint moves and the shape of the lever arm can vary. 2 Newtons imaginary value

  10. Moments of force • A moment is defined as the perpendicular distance from a point to a line or surface • A moment of force about an axis is the force magnitude X the moment, i.e., the product of force magnitude and the perpendicular distance to the axis (units Newton metres). • [Newtons are units of force: 1 Newton is the force required to accelerate a mass of 1 km at 1 m/s/s (~.2lb); units of a moment of force are Newton metres.] • To keep the two leg muscles in isometric contraction the moment of force of the weaker muscle must be made equal to the moment of force of the stronger.

  11. We need to think about moments of force in analysing the movements at the joint. Here is a diagram based upon Heitler’s Fig. 2 c. “The thick blue and purple lines “represent a mechanical analogue of the joint structure”.

  12. Go back to the paradox: how is it that during isometric contraction the smaller, weaker muscle is able to match the effort of the larger? The force advantage of the flexor muscle is different at different angles of flexion of the femorotibial joint. Part of the answer to the above question is that when the angle of flexion is less than 5 degrees (top) the mechanical advantage of the flexor muscle is superior to that of the extensor.

  13. With the joint angle at 5º (top), the apodeme of the flexor makes an angle with the effort arm of the lever of almost 90º; this is because it rides up over the 'lump'. The lump functions as a pulley: (a pulley can change force direction from down to up); it changes the ‘force-in’ direction of the flexor apodeme making it nearly 90 º; by contrast the stronger extensor, exerting more force, has a force-in direction at a very poor angle of 6 º. So the moments of force for the two antagonists can be equal.

  14. But the grasshopper gets extra force into its leap by simultaneous contraction of these antagonists. It prepares to jump by contracting both muscles simultaneously and isometrically (no movement at the joint). This distorts the exoskeleton in the neighbourhood of the joint and so stores elastic energy that will later be released during the jump and so contribute to the forces the leg exerts against the ground. The pocket is pulled over the lump during the early stages of the flexion and so the distortion can be retained even if the antagonists relax.

  15. The effort arm (the distance between the point of insertion of the apodeme on the tibia and the axis of rotation) is quite short for the extensor; much longer for the flexor. So the moments of force can be balanced at 5º. To keep the two leg muscles in isometric contraction the moment of force of the weaker muscle has been made equal to the moment of force of the stronger

  16. Flexor apodeme lock • “Once the tibia is fully flexed a lock is engaged [and the dynamic tension between the two muscles can be ramped up more dramatically than just by leverage] which can hold the tibia in this positiion against the developing extensor tension. Just proximal to its insertion onto the tibia the strap-like flexor tendon effectively bifurcates into strands which insert on either side of the tibia, leaving a strengthened pocket of connective tissue in the middle. At any angle of extension greater than about 5 degrees the flexor tendon rides on top of the femoral lump, which thus acts as the classical described pulley (e.g. Snodgrass, 1935) (Fig. 1b). As the tibia approaches the fully flexed position however, the two arms of the tendon slide down on either side of the lump, fitting into grooves at its base, while the lump fits snugly into the connective tissue pocket in the middle (Fig. 1a). In this position the tibia is now locked against the femur, and considerable extensor tension can be developed without the tibia moving.” • How is it unlocked? Extensor keeps increasing and flexor decreases just a little.

  17. Burrows M., Sutton G.P. 2012. Locusts use a composite of resilin and hard cuticle as an energy store for jumping and kicking. J. exp. Biol. 215: 3501-3512. • Power amplification (Patek 2011) involves storing muscle energy as cuticle distortion. • Power is rate of doing work. • Energy stored relatively slowly, at a low rate [low power] is released over a very short time perior [high power]. Very useful in creating powerful jumps. • Burrows & Sutton have explained where the energy of isometric contraction is stored. It goes into paired semilunar processes of the femur, located at the sides of its distal extremity, lateral to where the condyles protrude into the sockets of the tibia. Cuticle is a composite material consisting of arrangements of highly crystalline chitin nanofibres embedded in a matrix of protein, polyphyenols and water, with small amounts of lipid (*Vincent 2004). semilunar process *Vincent J.F.V. & Wegst U.G.K. 2004. Design and mechanical properties of insect cuticle. Arthropod Structure & Development 33: 187-199.

  18. contin. from Burrows & Sutton 2012 Resilin: an elastomeric protein; rubbery; low Young’s modulus. • “The inside surface of a semi-lunar process consists of a layer of resilin, particularly thick along an inwardly pointing ridge and tightly bonded to the external, black cuticle.” • There is (shown by imaging [movie]) distortion/bending in all three dimensions during the isometric contraction. • “Externally visible resilin was compressed and wrinkled as a semi-lunar process was bent. It then sprung back to restore the semi-lunar process to its original shape. • “It is suggested that composite storage devices that combine the elastic properties of resilin with the stiffness of hard cuticle allow energy to be stored by bending hard cuticle over only a small distance and without fracturing. In this way all the stored energy is returned and the natural shape of the femur is restored rapidly so that a jump or kick can be repeated.” from Wikki: A recombinant form of the resilin protein of the fly Drosophila melanogaster, pro-resilin, was synthesized in 2005 by expressing a part of the fly gene in the bacteriumEscherichia coli. It is expected to have many applications in the athletic footwear, medical, microelectronics and other industries.

  19. Bayley T.G., Sutton G.P., Burrows M. 2012. A buckling region in locust hindlegs contains resilin and absorbs energy when jumping or kicking goes wrong. J. exp. Biol. 215: 1151-1161.See also: JEB highlight by Kathryn Knight in same issue: Buckling zone protects locust legs • Energy of a kick that misses its target (or a foot that slips on the substrate) is dissipated by a specialized proximal region of the tibia. There is resilin in this region, revealed as a band that fluoresces blue under UV illumination (with appropriate filters to confirm identity). There are also special campaniform sensilla (proprioceptors, mechanoreceptors) that monitor the buckling. “The features of the buckling region show that it can act as a shock absorber as proposed previously [by Heitler] when jumping and kicking movements go wrong.”

  20. Next lecture: Patek S.N., Dudek D.M., Rosario M.V. 2011. From bouncy legs to poisoned arrows: elastic movements in invertebrates. [in detail] • Fundamental principles underlying elastic mechanisms • Power amplification: engine, amplifier, tool [muscle, bow, arrow of an archer] • Froghopper jumping • Mantis shrimp raptorial strike • Jellyfish stinging • Cicada singing • Roach running • Scallop swimming

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