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
•
•
•
•
•
•
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.
Orthoptera Species File
Locusta migratoria in a prejump crouch.
Heitler W.J. 1974. The locust
jump. J. comp. Physiol.
89: 93-104
from Wikkipedia
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”].
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 crosssectional 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.
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.
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.
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
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.
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”.
•
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.
•
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.
•
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.
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
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.
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).
*Vincent J.F.V. & Wegst U.G.K. 2004. Design and
mechanical properties of insect cuticle. Arthropod
Structure & Development 33: 187-199.
semilunar process
Resilin: an elastomeric
protein; rubbery; low Young’s
modulus.
•
•
•
•
contin. from Burrows & Sutton 2012
“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 bacterium Escherichia coli. It is expected
to have many applications in the athletic footwear, medical, microelectronics and other industries.
Photographs of the femoro-tibial joint of a right hind leg of an adult locust.
Burrows M , Sutton G P J Exp Biol 2012;215:3501-3512
©2012 by The Company of Biologists Ltd
Photographs of the distal femur of the right hind leg taken under white and UV epi-illumination,
and then combined.
Burrows M , Sutton G P J Exp Biol 2012;215:3501-3512
©2012 by The Company of Biologists Ltd
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: 11511161.
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.”
Selected images of a jump by a male locust.
Bayley T G et al. J Exp Biol 2012;215:1151-1161
©2012 by The Company of Biologists Ltd
Buckling of the right hind-tibia of a locust during a kick that missed its target.
Bayley T G et al. J Exp Biol 2012;215:1151-1161
©2012 by The Company of Biologists Ltd
The buckling region of the right hind-tibia viewed under white and UV illumination.
Bayley T G et al. J Exp Biol 2012;215:1151-1161
©2012 by The Company of Biologists Ltd
Scanning electron micrographs of the buckling region and adjacent sensory structures.
Bayley T G et al. J Exp Biol 2012;215:1151-1161
©2012 by The Company of Biologists Ltd
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