Distance and force production during jumping in wild-type and mutant Drosophila melanogaster
Department of Biology, University of York, York, YO10 5YW, UK
Author for correspondence (e-mail:
cje2{at}york.ac.uk)
Accepted 13 July 2003
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Summary |
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We describe a sensitive strain gauge setup, which measures the forces produced by tethered flies through their mesothoracic legs. The peak force produced by the main jumping muscle of female flies from a wild-type (Canton-S) strain is 101±4.4 µN [and this is indistinguishable from a second wild-type (Texas) strain]. The force takes 8.2 ms to reach its peak. The peak force is not affected significantly by altering the leg angle (femurtibia joint angle) in the range of 75120°, but the peak force declines as the leg is extended further.
Measurements of jumping ability (distance jumped) showed that female Drosophila (with their wings removed) of two wild-type strains, Canton-S and Texas, produced jumps of 28.6±0.7 and 30.2±1.0 mm (mean ± S.E.M.). For a female wild-type Drosophila, a jump of 30 mm corresponds to a kinetic energy of 200 nJ on take-off (allowing 20% of the energy to overcome air resistance). We develop equations of motion for a linear forcetime model of take-off and calculate that the time to take-off is 5.0 ms and the peak force should be 274 µN (137 µN leg1).
We predicted, from the role of octopamine in enhancing muscle tension in several locust muscles, that if stored elastic energy plays no part in force development, then genetic manipulation of the octopaminergic system would directly affect force production and jumping in Drosophila. Using two mutants deficient in the octopaminergic system, TbhnM18 (M18) and TyrRhono (hono), we found significantly reduced jumping distances (20.7±0.7 and 20.7±0.4 mm, respectively) and force production (52% and 55%, respectively) compared with wild type.
From the reduced distance and force production in M18, a mutant deficient in octopamine synthesis, and in hono, a tyramine/octopamine receptor mutant, we conclude that in Drosophila, as in locusts, octopamine modulates escape jumping. We conclude that the fly does not need to store large quantities of elastic energy in order to make its jump because (1) the measured and calculated forces agree to within 40% and (2) the reduction in distances jumped by the mutants correlates well with their reduction in measured peak force.
Key words: Drosophila, jumping, tyramine, octopamine, tergal depressor of trochanter, tergotrochanteral muscle, M18, hono, biomechanics
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Introduction |
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However, the fruit fly Drosophila melanogaster, with a mass of 1 mg and a body size between that of locusts and fleas, is not noted for its jumping performance. In Drosophila, jumping is normally the prelude to flight and serves merely for the fly to clear the substrate and initiate contractions of the indirect flight muscles; so, the distance jumped is more modest. From this, we hypothesise that Drosophila do not need to store large quantities of elastic energy in order to jump.
In Drosophila, the jump is produced by extension of the
mesothoracic legs, as a result of contraction of the tergal depressor of
trochanter muscle (TDT; M66 of Miller,
1950), also known as the tergotrochanteral muscle
(Bacon and Strausfeld, 1986
).
This substantial, triangular, pennate muscle runs between the dorsal surface
of the thorax and the proximal end of the trochanter, and its contraction
extends the femur because the trochanter and femur are fused
(Trimarchi and Schneiderman,
1993
). A second muscle, the tibia-levator muscle (TLM), extends
the femurtibia joint during take-off
(Trimarchi and Schneiderman,
1993
), prolonging the time for which force is applied to the
substrate. The TDT is activated by the descending giant fibre from the brain
through a mixed electricalchemical synapse
(Blagburn et al., 1999
). Many
workers have exploited the restrained preparation developed by Tanouye and
Wyman (1980
), in which the
giant fibre is stimulated visually or electrically by electrodes implanted in
the eyes or neck, so the physiology of the giant fibreTDT system is
well known. Among these are Trimarchi and Schneiderman
(1995a
), who showed that
excitatory junction potential (EJP) in the TDT is activated with constant
latency and amplitude.
In locusts, the contraction of the metathoracic slow extensor tibia muscle
(SETi) is modulated both pre- and post-synaptically by octopamine. The overall
effect of octopamine is to make the twitch of the isolated muscle stronger,
increasing the peak force and narrowing the tension transient
(Evans and O'Shea, 1977).
During the locust jump, the octopaminergic midline neuron, DUM5A (originally
called DUMETI) is activated (Duch et al.,
1999
), so that octopamine is delivered in time for the contraction
to be enhanced. Nonetheless, in locusts, the extension of the leg is not
derived directly from muscle contraction but occurs when Heitler's catch is
suddenly relaxed to permit rapid release of stored elastic energy
(Heitler, 1974
). If, in flies,
muscle contraction during jumping is directly coupled to leg extension, we
predict that interference in the octopaminergic system would be expected to
reduce distance jumped as well as force production.
Among mutants known in Drosophila to affect the octopaminergic
system are TbhnM18 (M18;
Monastirioti et al., 1996) and
TyrRhono (hono;
Kutsukake et al., 2000
). The
M18 mutation is in the gene encoding tyramine ß hydroxylase,
which converts tyramine to octopamine. It is a hypomorph with <0.2% of the
normal level of octopamine but with elevated (x10) levels of tyramine
(Monastirioti et al., 1996
).
The hono mutation is in the gene for the tyr/oct receptor (also known
as the tyramine receptor). This receptor binds tyramine 33 times better than
octopamine in cos-7 cells (Saudou et al.,
1990
). However, when expressed in Xenopus oocytes, this
receptor couples to different second messenger pathways depending on whether
tyramine or octopamine was applied (Robb
et al., 1994
).
The main aim of the work presented here was to investigate whether
Drosophila store energy elastically for jumping. We have tested this
by measuring both the distance jumped and the forces produced by the jump
muscle (TDT). The distance jumped by unrestrained flies from which the wings
had been removed provides a behavioural estimate of the energy used in
jumping, which we have used to calculate the force exerted during take-off.
The forces produced by the TDT were obtained by an extension of the
physiological preparation of Trimarchi and Schneiderman
(1995a). Our calculations show
good agreement between behavioural and physiological estimates of force in the
wild-type flies, from which we conclude that Drosophila do not store
energy elastically for jumping. We predict that in the absence of stored
elastic energy, defects of the octopaminergic system would lead to direct
effects on force production and jumping.
We therefore compared our wild-type data with the distances jumped and forces produced in two Drosophila mutants of the octopaminergic system: TbhnM18 (M18) and TyrRhono (hono). Both mutants jump less well than the wild type and generate less force. Our data are consistent with the hypothesis that elastic energy storage is not a major factor in fly jumping.
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Materials and methods |
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Jumping behaviour
Newly hatched flies were isolated and left for two days. They were then
lightly anaesthetised using carbon dioxide and their wings removed. The flies
were weighed in batches of 58, and their mean masses calculated. After
a recovery period of 30 min, each fly was placed on lined paper. Flies were
stimulated to jump by moving a fine paintbrush towards them from the rear. The
flies were not touched but jumped in response to the visual and air movement
stimuli. The distances of the first 58 full jumps were recorded; we
ignored the pushups or small tumbling responses
(Kaplan and Trout, 1974) that
were sometimes elicited by these stimuli.
Mutants were always tested at the same times as wild-type controls: either CS or TX of the same gender. Comparisons between fly strains were assessed using t-tests, and significance was P<0.05. Unless otherwise stated, results are means ± S.E.M.
Muscle force determination
Two-day-old flies were lightly anaesthetised with carbon dioxide and the
dorsal surface of the thorax was attached to a fine tungsten needle using
rubber solution. All legs, except the right mesothoracic leg, were glued
either to the tungsten needle or to the fly's abdomen. The flies were then
allowed to recover for 30 min.
The tip of a glass capillary, drawn to a point, was mounted perpendicularly using shellac on a sensitive strain gauge, AE801 [MEMSCAP (formerly Capto AS), Skoppum, Norway]. The output was connected in a Wheatstone bridge circuit, dc amplified and recorded on a Gould recording oscilloscope (Model 1604) or PC using a National Instruments (Austin, TX, USA) PCI-6052E analogdigital card and DasyLab software (Bedford, NH, USA), sampling at 100 kHz.
The tungsten needle holding the fly and the strain gauge were mounted on micromanipulators arranged so that the tibia was parallel to the glass needle on the strain gauge. Cellulose nitrate glue was used to stick the tibia of the mesothoracic leg to the glass needle, leaving the femurtibia joint free of any glue (Fig. 1).
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Finally, the fly was impaled with two sharpened tungsten needles in the neck (or less often, in the eyes). These were connected to a stimulator, which generated variable amplitude pulses of 25, 50 or 100 µs, separated by 5001500 ms. When stimulated above threshold, the giant fibre was activated, causing the TDT muscle to contract. The force produced by the muscle was transmitted to the femur and thence to the tibia. As the tibia was stuck to the glass needle, the strain gauge was activated.
The output of the strain gauge was calibrated by pressing on it with glass capillaries, drawn to different lengths. The deflection of glass capillary was recorded under a travelling microscope, along with the voltage from the dc amplifier. The force needed to deflect the capillary was determined by hanging short coils of copper wire, of known mass, on their tips and recording the deflection of the glass.
The spring constant of the strain gauge is 2 kN m1 (Capto data sheet); for the peak force we measured, 300 µN, the deflection will be 150 nm, so that the measurements are effectively isometric.
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Results |
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We found no evidence for any differences in jumping ability between males
and females, even though females are significantly heavier than males (CS
, 1.13±0.03 mg;
, 0.81±0.03 mg).
For flies from both the mutant lines we tested, the distance jumped is
reduced compared with the wild type; female M18 and hono
mutants jumped 20.7±0.7 and 20.7±0.4 mm, respectively. This is
two-thirds of the distance jumped by the wild-type flies,
(Fig. 2B) and is statistically
significant (t-test: CS vs M18, t12d.f.=7.8,
P<0.001; CS vs hono, t10d.f.=8.15,
P<0.001). For the mutants, there is no difference in distances
jumped between male and female flies, even though the females are again
heavier (hono , 1.14±0.03 mg;
, 0.85±0.04
mg; M18
, 1.10±0.03 mg;
, 0.81±0.04
mg).
Force measurement
Representative forcetime traces for the forces generated by the TDT
muscle by female wild-type, M18 and hono flies are shown in
Fig. 3, where sub- and
supra-threshold stimuli were applied to the stimulating electrodes. The
stimulusresponse latency is 2.3±0.2 ms (N=8 CS flies),
probably mostly due to the neural conduction delay between the head and the
neuromuscular junction. The force occurs in an all-or-nothing fashion. It does
not seem to habituate quickly when repetitive 0.110 Hz stimuli are
applied. In the typical response, the force rises rapidly, reaches
88±2% of its maximum after 5 ms and peaks after 8.2±0.5 ms. It
declines more slowly, reaching 50% of peak force by 14.5±0.6 ms, and
becomes indistinguishable from the baseline by 25.0±1.4 ms.
|
When the position of the micromanipulator holding the strain gauge was adjusted so that the peak force was maximised for each individual, it became clear that mutant flies produced less peak force than the wild type (Fig. 3). This is confirmed by the summarised data (Fig. 4), where the means for M18 and hono are 52% and 55%, respectively, of the CS wild type. These reductions are both significant at the 0.1% level (female CS vs M18, t15d.f.=5.6; CS vs hono, t16d.f.=5.6). We have found no significant differences in the latency, time to maximum force development or half-width of the force transient when the M18 and hono mutants are compared with wild-type flies. No significant difference was found between the CS and TX wild types in any parameter.
|
The leg angle is critical for force production; as the TDT muscle
contracts, the leg straightens and the angle of the femurtibial joint
increases towards 180° (see Fig.
1). Over the range of 75120°, the averaged peak force
is constant at 101±4.4 µN (Fig.
5). As the leg is straightened by adjusting the micromanipulators,
the isometric force declines, until zero force is produced at
160°.
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Analysis
We have determined the distance jumped by unrestrained flies from which the
wings had been removed. From this distance, we now calculate the work done
during take-off and use this to estimate the minimum force required to propel
the fly. This force will then be compared with our direct TDT
measurements.
Our analysis of biomechanics of jumping follows the outline in the recent
review by Alexander (2003).
Neglecting air resistance, the distance (d) jumped by a fly is
determined solely by its velocity on take-off (v) and the angle of
take-off (
):
![]() | (1) |
At =45°, sin(2
) is the maximum, 1, and so the distance
jumped for a given velocity is also a maximum. At 45°:
![]() | (2) |
![]() | (3) |
In small insects, air resistance is an important energy loss, so that the
actual KE at take-off is larger than equation 3 predicts. In order to
estimate the actual KE at take-off, we note that Bennet-Clark and
Alder (1979) projected
Drosophila (from which the wings had been removed) vertically upwards
in air and in vacuo. For flies projected upwards 100 mm, 20% of the
energy was lost to air resistance. If we assume that the same loss occurs in
our experiments, the KE at take-off, allowing for air resistance
(KEair), will be 1.25 times as much. This would require
the take-off velocity to be increased by
1.25 (=1.1):
![]() | (4) |
![]() | (5) |
For female flies travelling a distance of 30 mm, allowing for air-resistance, with a mass of 1.1 mg and taking gravity as 10 m s2, the take-off velocity is 0.61 m s1 and the KE is 206 nJ. For the mutant flies, travelling only 20 mm, take-off velocity is 0.50 m s1 and the KE is 137 nJ.
For a fly jumping off the ground, accelerating from rest, force can only be
applied while the leg is touching the ground. On the assumption of a constant
force (CF) being applied, the KE is the product of the
extension of the leg (s) and the force (F), so that:
![]() | (6) |
![]() | (7) |
![]() | (8) |
The combined length of the femur tibia and tarsus is 1.36 mm
(Miller, 1950). Assuming that,
from rest to take-off, the mesothoracic legs extend by 1 mm, the force
required to take off is 206 mN and each leg would have to contribute
103
mN. The duration of the force will be 3.3 ms. If the flies extend their legs
less than 1 mm before they leave the ground, the force will be higher and
take-off time will be reduced. Mutant flies will need two-thirds of the force
(135 µN) and will take off in 4.0 ms.
However, our force measurements show that the force produced by the TDT is
not constant. Over the 5 ms that it takes for the fly to leave the ground
(Trimarchi and Schneiderman,
1995b), the TDT force increases, approximately linearly with time.
After 5 ms, the force starts to fall below the linear relationship
(Fig. 3), but by then the fly
will have left the ground. Appendix 1 derives the equations of motion for a
linear relationship between force and time. Equations A6 and A7 give the force
and time at the take-off point as 274 mN at 5.0 ms for the wild-type fly (137
mN per leg) and 183 mN at 6.1 ms for the mutants.
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Discussion |
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The take-off time can be calculated from the KE: on the basis of
our constant force (CF) model, take-off occurs after 3.3 ms, implying
a power of 60 µW. Our force data show, however, that the muscle force rises
with time, and on the more realistic linear forcetime (LFT) model, the
duration to take-off is calculated to be 5.0 ms and the mean power reduced to
40 µW. High-speed photography of Drosophila taking off shows that
there is 4.9±1.6 ms between the start of the jump and the legs losing
contact with the ground (Trimarchi and
Schneiderman, 1995b). This agrees very well with our LFT estimate
of 5.0 ms derived from the KE and from the length of the mesothoracic
femur and tibia.
We estimate that the TDT is 900 µm long and, at its insertion on
the dorsal cuticle, is
300 µm wide and 150 µm thick. Treating this
as a pyramid, its volume will be 13x106 µm3 and
its mass will be 13 µg. The two TDT muscles would then be just over 2% of
the mass of the fly. The power output, 40 µW, corresponds to a specific
power output of 1.5 W g1 during the period of take-off.
Taken over the full time to contract and relax (25 ms), the specific power
output of the TDT is lower, but still an impressive 300 mW
g1. This is much higher than the continuous power output of
Drosophila flight muscle, 80 mW g1, measured by
respirometry (Lehmann and Dickinson,
1997
) and is higher than the power output calculated from work
loops of the flight muscle of the beetle Cotinus (200 mW
g1; Josephson et al.,
2000
). The Drosophila TDT power output is also larger
than the specific power output of locust muscle during jumping, which averages
200 mW g1 but peaks at 450 mW g1 during
the contraction (Bennet-Clark,
1975
). All of this indicates that jumping is energetically
demanding.
The force exerted by the leg of female wild-type flies in the present study was measured to peak at 101 µN at 8.2 ms. This force was with the leg held at an angle of 90°, i.e. with the femur horizontal and the tibia vertical. The peak force produced was not significantly affected by adjustments of the leg angle over a range of 75120°, but as the leg was extended further the force dropped as its mechanical advantage declined. As the mean mass of female flies is 1.1 mg, their weight will be 11 µN. Thus, the peak force exerted by the two legs corresponds approximately to the weight of 20 flies, and the net force is upwards.
If there is no need for a substantial energy storage mechanism, the
measured force (101 µN) should agree with the force estimated from the
distance data. We calculated above that the KE was in the range of
180260 nJ and that the value of 200 nJ corresponded well with data from
high-speed video. On the assumption of a CF, this KE gives a
force of 100 µN for each leg, with a take-off time of 3.3 ms. If force
increases linearly with time (LFT model), this KE gives a peak force
of 137 µN leg1 and take-off in 5.0 ms. In both models,
force is proportional to KE and so the range of KE
corresponds to force in the region of 90180 µN. The measured force
peaks at 100 µN, at the lower end of the range. While the agreement here is
good, we need to consider four factors affecting the measured force. (1) The
fly produces a force that acts downwards and forwards, while we measured the
downwards component only. If we had measured in the direction of take-off,
optimally 45°, the force would be larger by a factor of 2 (=1.414),
increasing the force by 40 µN. (2) The fly takes off in 4.9 ms and the
force at 5 ms was 88% of the peak, i.e. a reduction of
10 µN. (3) As
the fly extends its leg, the mechanical advantage decreases so that, as the
leg angle reaches 150°, the force has been reduced by 25 µN. (4) Our
measurements were done isometrically, and this is likely to produce a maximal
estimate of muscle force, as during jumping the muscle contracts and so will
produce less force as its thin filaments slide together
(Gordon et al., 1966
). Since
the TDT inserts on the trochanter at the thoracic end
(Miller, 1950
;
Trimarchi and Schneiderman,
1993
; Peckham et al.,
1990
), it is unlikely to contract more than 5%. Assuming that the
TDT, like other muscles, starts at the optimal filament position, a 5% change
will not substantially change the sarcomeric thickthin filament overlap
and therefore the force will remain similar to that measured at the isometric
level. On balance, these factors indicate that the measured force has a scope
of 60140 µN, which agrees well with the range (90180 µN)
estimated from jumping. We therefore conclude that no substantial energy
storage is needed to account for the distance jumped by
Drosophila.
This conclusion is supported by analysis of the M18 and hono mutant flies, where the measured force is reduced to 52 and 55%, respectively. Our calculations show that distance travelled in a jump is proportional to the force produced (equations 7 or A4), so we expect that the mutant flies should travel 52 and 55% of the wild-type distance. This is consistent with the measured jump distance reductions to 66% for both mutants. If an elastic storage mechanism dominated the jump, we would not have expected the force to be proportionately reduced in these mutations of the aminergic systems.
The M18 flies synthesise no octopamine but accumulate excess
tyramine, so our observations suggest that Drosophila, like locusts
(Evans and O'Shea, 1977),
enhance their muscle contraction through the action of octopamine at the leg
nervemuscle synapse. The proportional reduction in jump distance (and
hence predicted force) with measured force suggests that, unlike locusts,
flies do not uncouple the contraction of the muscle from leg extension through
elastic energy storage. The amine could be delivered as a hormone in the blood
or locally from terminals of an unpaired medial neuron. Octopamine
immunoreactive fibres have been shown on the TDT of another dipteran, the
blowfly Calliphora (Schlurmann
and Hausen, 2003
), and on prothoracic muscles of
Drosophila (Rivlin et al.,
2004
), but the innervation of the TDT muscle in
Drosophila is not completely known. Exogenous octopamine also
increases the size of the EJP at the dorsal internal oblique muscles in the
Drosophila larval body wall by 15%, while tyramine produced a 15%
reduction (Kutsukake et al.,
2000
; Nagaya et al.,
2002
). If tyramine, rather than octopamine, were an excitatory
modulator, we would not expect the M18 flies to jump less far or
generate less force, as they have higher levels of tyramine than the wild
types.
Although hono gene expression has previously only been found in
the adult central nervous system (Arakawa
et al., 1990; Saudou et al.,
1990
; Hannan and Hall,
1996
; Kutsukake et al.,
2000
), our data indicate a role for hono in the adult
peripheral nervous system, specifically at the TDT neuromuscular junction. An
explanation for our observations of reductions in jumping distance and force
in hono is that octopamine action at the neuromuscular junction is
blocked. Thus, the M18 mutant fails to jump as far as the wild type
because of the lack of octopamine, while the hono mutant does so
because it cannot respond to octopamine. However, a problem with this
explanation is the proposal (Kutsukake et
al., 2000
) that hono is a mutation in a pure tyramine
receptor. Two lines of evidence support this. First, the receptor is much more
sensitive to tyramine than to octopamine
(Saudou et al., 1990
). Second,
in hono, the larval neuromuscular junction is modulated by tyramine
but not octopamine (Nagaya et al.,
2002
). Our data favour the proposal that the hono
mutation is in a dual tyr/oct receptor, possibly coupling to different systems
(Robb et al., 1994
;
Reale et al., 1997
). If
octopamine is acting at a separate receptor to hono, the reductions
in force and jump distance are hard to understand because the octopaminergic
pathways should be the same as the wild type.
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Appendix 1. Equations of motion for force increasing linearly with time |
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![]() | (A1) |
![]() | (A2) |
![]() | (A3) |
![]() | (A4) |
![]() | (A5) |
![]() | (A6) |
![]() | (A7) |
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Acknowledgments |
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Footnotes |
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References |
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