Load compensation in targeted limb movements of an insect
1 Department of Zoology, University of Cambridge, Downing Street, Cambridge
CB2 3EJ, UK
2 Abteilung für Biokybernetik und Theoretische Biologie, Fakultät
für Biologie, Universität Bielefeld, Postfach 10 01 31, D-33501
Bielefeld, Germany
* Author for correspondence (e-mail: tm114{at}hermes.cam.ac.uk)
Accepted 12 June 2003
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Summary |
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We show that loading the femur or tibia with the equivalent of 8.5 times the mass of the tibia (corresponding to an increase of up to 11.6 times the rotational moment of inertia at the femurtibia joint) does not impair the animal's ability to make well-coordinated, aimed movements of that leg towards different targets. The kinematics of the movements are the same, and animals aim the same part of their distal tibia at the target, regardless of loading. The movements are carried out with equal accuracy and at the same initial velocity under all load conditions. Because loading of the leg does not change the behavioural performance, there is no indication of a change in aiming strategy. This implies high leg joint stiffness and/or the existence of high gain proprioceptive control loops. We have previously shown that in the unloaded condition, movements elicited by stimuli to different places on the wing are driven by a single underlying movement pattern that shifts depending on stimulus location along the wing surface. Our present data show that leg proprioceptive inputs are also integrated into the leg motor networks, rendering hind limb targeting robust against large changes in moment of inertia.
Key words: reaching, load compensation, scratching, locust, Schistocerca gregaria, coordination, insect, motor control, sensory feedback
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Introduction |
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In walking stick insects the protraction (swing phase) movements of the
rear legs are targeted at the position on the ground where the foot of the
next anterior leg already has a foothold. Perturbations of the position of the
anterior foot lead to adjustments of the touch-down position of the posterior
leg (Cruse, 1979), and when the
swing movement is resisted by an external force the targeting also remains
accurate (Dean, 1984
). When the
swing movement of a rear leg is assisted by an external force, the velocity is
increased only slightly. Taken together, Dean's data show that position is
controlled for the endpoint of swing, but that velocity is controlled during
the movement itself (reviewed in Dean and
Cruse, 1986
). Nevertheless, in walking, the control of any given
leg is influenced by the actions of the others. For example, when the animal
drags a load the velocity of swing movements is increased, presumably to
permit a relatively longer stance phase
(Foth and Graham, 1983
). Such
interactions between limbs can be excluded in the present study because (1)
the load is added directly to the leg that is observed, (2) the leg moves to a
target location that is independent of the postures of the other legs and (3)
the aimed movement is carried out while the other legs remain still.
To test whether loading affects the performance of a targeted leg movement
we analysed scratching movements made by a hind leg of a locust in response to
tactile stimuli on the ipsilateral wing (see Matheson,
1997,
1998
;
Dürr and Matheson, 2003
).
We have previously shown that in unloaded conditions the pattern of leg
movements used by locusts to move the distal end of their tibia towards
different targets forms a continuum that is modified (shifted) by changes in
target location on the wing surface. The location of the target signalled by
wing exteroceptors is monitored throughout the movement so that re-targeting
can occur to track a moving object
(Matheson, 1998
), but it is
not known whether proprioceptive signals from the moving leg are similarly
used to maintain accuracy.
To examine the effects of loading different leg joints, we loaded either a basal or a distal position on the femur or a distal location on the tibia. Loading the leg so that the rotational moment of inertia was increased by up to 11.6-fold had no detectable effect on any of the measured kinematic variables. We conclude that both position and velocity are controlled in this targeted movement, and that proprioceptive signals from receptors on the leg must be integrated throughout the movement with exteroceptive signals from the wing that signal target location.
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Materials and methods |
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Animals and stimulation protocol
Experiments were carried out on adult female desert locusts
Schistocerca gregaria Forskål. They were tethered by a loop of
fine wire that passed around their pronotum without obstructing movements of
any of the legs and were suspended above a light (4.5 g) foam ball on which
they stood or walked. The eyes were covered with solvent-free typists'
correction fluid, and the tarsus of a hind leg was placed on a horizontal rod
located at a fixed position (Fig.
1A) that corresponded to the anterior position used in Dürr
and Matheson (2003). To elicit
scratching movements of the hind leg, the ipsilateral forewing was touched
gently with a fine paintbrush. Stimuli were applied to one of two different
locations in pseudo-random order. These locations correspond to positions 2
(anterior) and 5 (posterior) used in Dürr and Matheson
(2003
). The exact location of
the stimulus and the resulting movements were measured from videotape as
described below. A small metal bead of mass 142 mg was fixed using sticky wax
(Lactona Surgident, Philadelphia, USA) to the hind leg at one of three
different locations (ac in Fig.
1A) to provide a load (the hind leg mass was approximately 138
mg). The added mass was chosen so that it approximately matched the leg mass.
By adding this mass to different sites on the leg, the moment of inertia of a
single joint was altered in a range from 1% to 1160% of the normal value. Each
set of scratches elicited under loaded conditions was interspersed with a set
of control scratches elicited under unloaded conditions. There was no evidence
of a temporal change in scratching behaviour (i.e. learning) throughout the
course of the experiments, which lasted for 630 h in total. Each animal
was tested for periods of up to 90 min at a time separated by intervals of at
least 90 min to avoid fatigue. Experiments were carried out at
2224°C.
|
Video acquisition and analysis
Animals were videotaped from the side using a calibrated CCD camera with a
spatial resolution of 0.1 mm pixel1, allowing manual
digitising accuracy of 0.5 mm, as determined from the standard deviation of
all digitised points in repeated analyses of three sequences. The images were
recorded on video tape, captured on a personal computer and deinterlaced to
yield AVI files with a frame size of 768x576 pixels at a frame rate of
50 s1. A custom-written program (Borland Delphi) was used to
access the AVI files and digitise the coordinates of up to 12 points per frame
(Fig. 1B). The coordinates of
the digitised points were output as a text file that was read into a second
custom-written program for a variety of analyses (see below). The stimulus
location and the position of the tarsus rod were digitised in the first frame
of each trial. A further eight points were digitised in all frames to record
movements of the stimulated wing and the ipsilateral hind leg. These were: (1)
the front leg coxa, (2) the base of the wing on its midline, (3) the distal
end of the wing on its midline, (4) the hind leg coxa, (5) the hind leg
trochanter, (6) the distal end of the hind leg femur, (7) the distal end of
the hind leg tibia and (8) the distal end of the second segment of the hind
leg tarsus (Fig. 1A,B).
Sequences were analysed from the first frame of tarsal movement until one of
the following four events occurred: (1) the tarsus touched the ground, (2) the
tarsus hit the stimulus brush, (3) the leg completed three complete cycles of
movement or (4) the tarsus stopped moving for 120 ms.
Analysis
453 loaded or unloaded (control) scratches were analysed in three animals,
all of which expressed qualitatively the same behaviour. Two components of
each response were distinguished: a short (200 ms) initial component, in which
the trajectory of the tarsus was relatively straight, and a second cyclic
component, in which the tarsus moved in repeated loops near the target (see
e.g. Fig. 2). The average
velocities of the initial and cyclic components were calculated separately.
The cyclic component was further quantified by means of probability
distributions, which described the likelihood that a particular part of the
leg moved across any given point in the leg's work space (for derivation, see
Dürr and Matheson,
2003).
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Results |
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The effect of load on limb trajectory
Locusts made aimed scratching movements of a hind leg (e.g.
Fig. 1C) in response to tactile
stimuli at one of two target sites on the dorsal surface of the ipsilateral
forewing (the outermost surface when the wings are folded into the normal
resting posture, Fig. 1A). The
leg always started from the same position, which was defined by a small rod on
which was placed the animal's tarsus (Fig.
1A).
Stimulation of the distal (posterior) site elicited movements in which the
tarsus was lifted and moved posteriorly towards the target before making a
variable number of cyclical movements in the vicinity of the target
(Fig. 2Ai). Stimulation of the
proximal (anterior) site elicited movements in which the tarsus was lifted and
moved approximately vertically towards the target before again making cyclic
movements largely dorsal to the animal
(Fig. 2Aii). Only the first
three cycles were analysed. For a detailed analysis of unloaded scratching
movements and their natural variability, see Matheson
(1997,
1998
) and Dürr and
Matheson (2003
).
Addition of a 142 mg load to the proximal femur, distal femur or distal tibia had no effect on the general form of scratching movements for either target site (compare Fig. 2Ai,ii with Bi,ii, Ci,ii and Di,ii). Slight variations in the movements illustrated in Fig. 2 fall well within the variance seen in unloaded scratches, as we go on to demonstrate in the following sections.
To examine the movements in more detail we analysed separately the initial
200 ms of movement that formed the outgoing trajectory and the remaining part
of the movement during which the tarsus followed a cyclical path. The use of
200 ms as a cut-off criterion is justified quantitatively in Dürr and
Matheson (2003). It is the
mean duration of the outgoing trajectory. When the leg was unloaded the median
direction of movement in the first 200 ms was 112° for scratches elicited
by stimulation of the anterior site (black vector in
Fig. 3A), and 134° for
scratches elicited by stimulation of the posterior site (black vector in
Fig. 3B). Loading the leg had
no significant effect on initial movement direction (coloured vectors and
curved lines in Fig. 3A,B: Dunnett's two sided t-test for each treatment versus
control, 453 scratches from three animals pooled; all values of
P>0.05). Each animal was also analysed separately. For movements
to the anterior site, loading the distal femur caused a significant increase
in the angle of movement for one animal (Dunnett's t-test,
P=0.005, N=28 unloaded, nine loaded scratches), but a
decrease in the second (P=0.047, N=36, 15), and had no
effect in the third (P=0.089, N=57, 10). For movements to
the posterior site loading the distal femur caused a significant reduction in
the angle of initial movement in one animal (P=0.005, N=43,
12). No other load condition caused any significant difference in initial
movement direction in any animal (all values of P>0.05).
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What part of the leg is aimed?
When the leg is unloaded the part of the leg that is most reliably aimed at
the stimulus, irrespective of stimulus location, is the distal end of the
tibia (Dürr and Matheson,
2003). To test whether locusts change this aiming strategy when
the limb is loaded we determined the point on the leg that came closest to the
target under each loading condition. For unloaded movements made in response
to stimulation of the posterior target site, the distal end of the tibia and
the base of the tarsus were, on average, aimed most accurately
(Fig. 5Ai). The minimum values
of closest distance (i.e. highest accuracy) reached 0 mm only for the distal
end of the tibia and tarsus, indicating that the proximal tibia and femur
could not reach the target (white line in
Fig. 5Ai). For movements made
in response to stimulation of the anterior target the distal end of the tibia
was aimed most accurately (Fig.
5Aii). The morphology of the hind leg means that when a locust
rotates the femur forward to move its tarsus near the anterior target (but not
the posterior one), a point on the femur may also cross the target (see e.g.
Figs 1,
2Cii). This results in a local
minimum in the measures of closest distance for the femur in
Fig. 5Aii. It is important to
note that the femoral minimum is the inevitable result of forward rotation of
the femur that is required to bring the distal tibia and tarsus close to the
target. The tibia crossed the stimulus site repeatedly during the cyclic part
of grooming, whereas the femur was typically rotated forwards so that it
passed the target only once and was then held anterior to the target
throughout the response (see Fig.
1C). This indicates that, although the femur can pass over
proximal targets, it is not specifically aimed at them.
|
Loading the leg had no effect on the aimed point for any of the three load
sites or either of the targets (Fig.
5Bi,iiDi,ii). The absolute measures of accuracy for each
point along the leg were similar to the corresponding values for unloaded
movements (compare Fig.
5Bi,iiDi,ii with corresponding
Fig. 5Ai,ii), and the overall
pattern of accuracy was the same in all cases. For unloaded scratching
movements we have shown previously that a point 4 mm from the distal end of
the tibia is the most consistently aimed part of the leg
(Dürr and Matheson, 2003,
asterisk in their fig. 2).
Because load has no effect on movement strategy, we used the same point for
all further analyses in the present paper (asterisks in
Fig. 5Ai,ii).
The effect of load on limb velocity
There was a weak but significant positive correlation between the initial
velocity (over the first 200 ms) and the velocity during the cyclical part of
the movement in all three animals analysed separately and in the pooled data
(Pearson correlation coefficient r=0.285, P<0.001,
N=414; note that not all responses included a cyclical component).
The median velocity of movement of the distal end of the tibia during the
first 200 ms was unaffected by load for either the anterior stimulus (open
bars in Fig. 6A) or the
posterior stimulus (grey bars in Fig.
6A). This was also the case for each animal analysed separately
(data not shown).
The velocity of movement in the cyclical part of the response was unaffected by load on the proximal femur for scratches aimed at either stimulus site (Fig. 6B). In contrast, loading the distal femur or tibia caused an increase in the median velocities for movements made in response to the posterior stimulus (two extreme right grey bars in Fig. 6B; 43% and 48% increases, respectively).
Load does not affect the cyclic component of scratching
Two measures were used to investigate the effect of loading on the cyclical
part of the movement. First, the point of closest approach to the target was
determined to obtain a measure of performance accuracy. Second, the average
`movement distribution' was calculated to describe the region of the leg's
workspace covered during the responses.
For unloaded movements to the posterior target, the mean point of closest approach was 5.0±2.7 mm (mean ± S.D.) anterior to the target (Fig. 7). For unloaded movements to the anterior target, the point of closest approach was 1.9±2.5 mm posterior to the target. Loading the leg had no effect on the point of closest approach in any experimental situation.
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To assess the part of the leg's workspace that is most likely to be
scratched, we calculated the likelihood that the distal part of the tibia
crossed each point in space between two subsequent video frames, given a
particular stimulus:load condition. This was done by counting the number of
times the distal tibia crossed a given location in the leg's workspace during
a single trial, and standardising the resulting distribution to a volume of 1.
Averaging these two-dimensional distributions resulted in distributions of the
average likelihood of observing a movement across any point in the workspace.
Fig. 8 illustrates this as grey
level maps in body coordinates (for details of the calculation, see
Dürr and Matheson,
2003).
|
In the unloaded condition, the cyclical parts of scratching movements aimed towards the posterior target (Fig. 8Ai)differed from those aimed at the anterior target (Fig. 8Aii). The probability distribution for posterior scratches was centred anterior to the target site, extending both ventrally and dorsally above and below the wing (Fig. 8Ai). The centre of each distribution was characterised by the `centre of gravity' (white circles in Fig. 8) and by the `most likely point' (white squares in Fig. 8). For unloaded movements aimed at the posterior target, both measures lay approximately 8 mm anterior to the target near the ventral (leading) edge of the wing. The probability distribution for anterior scratches peaked approximately 7 mm posterior and dorsal to the corresponding target (Fig. 8Aii). The centre of gravity was a further 4 mm posterior and dorsal, reflecting the `tail' of the distribution.
Bayes' theorem (see e.g. Quinn and
Keough, 2002) was used to test whether the probability
distributions resulting from movements to different targets or made under
different load conditions could be distinguished from each other. This was
done by estimating the minimum number of video frames in a scratching sequence
that was required to determine statistically which experimental condition had
given rise to the observed behaviour. For any given load condition, the
probability distributions for movements made in response to stimulation of the
anterior target site (Fig.
8AiiDii) could be distinguished easily from those made in
response to stimulation of the posterior target
(Fig. 8AiDi; see
Table 2).
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Loading the leg had no significant effect on the probability distributions
for movements made to the posterior target
(Table 3, Fig. 8BiDi). For
movements aimed at the anterior target, loading the leg increased slightly the
density of the tail of the distribution, reflecting the terminal downward
movement of the trajectory as the tarsus returned to the ground. Accordingly
the centre of gravity (but not the most likely point) shifted ventrally
(Fig. 8BiiDii). Despite
this subtle change, the distributions for movements to the anterior target
were also statistically indistinguishable
(Table 3). Observation of more
than 450 video frames (which is approximately equivalent to the duration of 10
scratches), would have been required to reliably detect the different loading
conditions. In addition to these analyses of the pooled data from three
animals, we examined each animal separately. None of the load conditions had
any significant effect on the probability distributions in any of the animals
(all P>0.15), with the single exception that loading the distal
femur caused a marginally significant shift in one of the animals
(P0.04).
|
The marked similarity of the probability distributions obtained under different load conditions becomes even more apparent when examining the pattern of iso-density contours that delimit different proportions of the total volume (Fig. 9). Contours that contained only the top 10% of volume (i.e. delimited the peaks of the distributions) overlapped each other almost completely, especially for anterior scratches (Fig. 9, top row). Contours for successively greater proportions of the total volume (25, 50, 75 and 90%) revealed an approximately symmetrical pattern of expansion for posterior scratches, irrespective of load condition (Fig. 9, left column). For anterior scratches the 50% contours revealed the posteriorventral tail of the distributions, which was more pronounced for loaded trials (e.g. Fig. 9, 50%, right). The 90% contour revealed a slight anterior dorsal shift and a less pronounced tail when the proximal femur was loaded (Fig. 9, 90%, right; red line).
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Discussion |
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Equilibrium point control and joint stiffness
To move the tarsus along a particular trajectory to a target requires
computation of motor commands that will act to rotate the individual leg
joints against their specific internal and external loads. This requires that
the motor signals are represented in a coordinate system that encodes the
magnitude of joint rotations, torques or muscle actions i.e. it must
be an intrinsic coordinate system, as opposed to the extrinsic system used by
sensory receptors to encode the spatial location of the tarsus and target. In
theory, an equilibrium point mechanism could permit the planning and execution
of the trajectory of a coordinated reaching movement, even for a redundant
manipulator like the locust leg (Feldman
and Levin, 1995). Such a control mechanism requires high joint
stiffness, however, particularly if the trajectory is to remain similar after
changing the moments of inertia. Passive rotations of the locust
femurtibia joint that are observed during ongoing leg movements
(Berkowitz and Laurent, 1996
)
indicate that stiffness of this joint is low in the absence of external load.
During scratching the femurtibia joint can extend with considerable
force in the absence of extensor motor activity, at least in part as a result
of energy transfer from the movements of more proximal joints
(Berkowitz and Laurent, 1996
).
In other words, the stiffness of the unloaded femurtibia joint is
insufficient to stabilise the joint against the tibia's intrinsic moment of
inertia. Only if proprioceptive information was to adapt joint stiffness to
the additional load could joint stiffness explain the load compensation that
we describe.
Joint stiffness is affected by three active mechanisms: cocontraction of
antagonist muscles, neuromuscular inhibition and neuromodulation. The timing
of activity of common inhibitory neurones during active movements must
contribute to the low leg joint stiffness by downregulating tonic contraction
forces of antagonist muscles at each joint
(Wolf, 1990). Insect leg
muscles are controlled not only by their excitatory and inhibitory motor
neurones, but also by the activity of specific neuromodulatory neurones
[`dorsal unpaired median' (DUM) neurones; reviewed in
Burrows, 1996
]. These leg DUM
neurones can affect muscle tonus and force production
(Hoyle, 1978
) so, if their
activity is modified as a result of loading, they might also contribute to
load compensation. Nevertheless, none of these mechanisms could participate in
load compensation in the absence of proprioceptive feedback, so we rule out
the possibility that a pure equilibrium point control mechanism underlies the
load compensation we observed.
Our conclusion concurs with Dean's claim
(Dean, 1992) that if stick
insects use an equilibrium point mechanism to control targeted stepping
movements, then they must also use proprioceptive signals. Indeed, most
current versions of the equilibrium point hypothesis accept that joint
interaction torques are not automatically compensated for by joint stiffness,
but that internal models of the limb's properties must be calibrated by
sensory feedback (e.g. Hollerbach and
Flash, 1982
; Shadmehr and
Mussa-Ivaldi, 1994
; Ghez and
Sainberg, 1995
). Human arm stiffness is too low to permit pure
equilibrium point control (Gomi and Kawato,
1996
,
1997
), and subjects who lack
proprioception due to large-fibre neuropathy show marked errors in limb
trajectory (Gordon et al.,
1995
). In spinal frogs, where loading of a hind leg has little or
no effect on targeting accuracy (Schotland
and Rymer, 1993
), proprioception has similarly marked influences
on initial trajectory direction, path straightness, knee joint velocity and
overall accuracy (Kargo and Giszter,
2000
).
Proprioceptive feedback in insect leg motor control
Proprioceptive feedback is clearly essential for the generation of normal
motor patterns in most rhythmic motor systems (reviewed in
Pearson and Ramirez, 1997). In
insects the angle, velocity and acceleration of each leg joint are monitored
by internal chordotonal organs (Hofmann et
al., 1985
; Matheson and Field,
1990
; reviewed in Field and
Matheson, 1998
), the receptors of which have powerful reflex
effects on motor neurones of the same joint
(Field and Burrows, 1982
) and
of other joints of the same leg (Hess and
Büschges, 1999
). In the locust, information about hind leg
joint angles excites particular spiking local interneurones that are also
excited by exteroceptive inputs that signal a touch on the wings
(Matheson, 2002
). These
interneurones are likely to be key elements in the generation of aimed leg
movements and in compensation against load perturbations.
Increased load affects muscle forces that are monitored by multipolar
tension receptors, which also have intra- and interjoint effects
(Theophilidis and Burns, 1979;
Matheson and Field, 1995
).
Load-induced strain in the exoskeleton is sensed by campaniform sensilla
(Spinola and Chapman, 1975
),
which are generally located near joints
(Pringle, 1938
). Those on the
coxal and trochanteral segments near the base of the leg are key elements in
load-compensating reactions during walking, when the leg is in contact with
the ground (e.g. Zill et al.,
1999
; Noah et al.,
2001
). These campaniform sensilla are generally inactive when the
leg is off the ground (as during scratching). Nevertheless, loading the leg as
we did is likely to have caused activation of these receptors, when muscles
were acting against increased rotational inertias to accelerate and decelerate
each leg segment throughout the scratch. Whether the resultant feedback
pathways alone (e.g. Newland and Emptage,
1996
) could provide the complete control of movement velocity and
accuracy that we see is unknown. Signals from campaniform sensilla converge
onto leg motor neurones along with position-dependent signals from other leg
sense organs (Schmitz and Stein,
2000
), and the leg motor neurone output is modulated by non-linear
interactions between the two modalities.
Proprioceptive mechanisms underlying load compensation
In humans, loading a limb results in complex EMG responses, the gain of
which depends on the simultaneous angular motion of other limb joints
(Lacquaniti and Soechting,
1986). This implies that the spinal cord integrates proprioceptive
inputs from several muscles. Some neurones in the motor cortex are sensitive
to loading at either the shoulder or the elbow, or respond to loads at both
locations (Cabel et al., 2001
).
In insects, sensory influences on leg movements have been demonstrated in a
wide range of experiments (for reviews, see
Burrows, 1996
;
Cruse et al., 1984
;
Bässler and Büschges,
1998
), and there is widespread convergence of proprioceptive
information from different leg segments onto leg motor neurones. This holds
for joint position- and movement-sensitive chordotonal organs (Hess and
Büschges, 1997
,
1999
), load-sensitive
campaniform sensilla (Zill et al.,
1981
), and muscle tension receptors
(Matheson and Field, 1995
). In
a walking stick insect, the protraction movement of a posterior leg is aimed
at the position where the next most anterior leg already has a foothold
(Cruse, 1979
). Loading the
posterior leg has little effect on either the accuracy or velocity of its
movement (Dean, 1984
). In
walking, however, the control system driving these movements is constrained by
the need to coordinate the posterior leg with the weight-bearing legs so as to
maintain a stable gait. Our data show complete compensation for loading during
a limb-targeting behaviour in which the aimed limb is not subject to such
coordinating influences. The control of movement velocity is therefore not a
consequence of the requirement for interleg coordination, but instead appears
to be a general feature of insect leg movements across species and in
different behaviours. In compensating for increased leg loading, locusts did
not trade-off accuracy for velocity, nor did they switch to an alternative
movement strategy. Because trajectories do not change when the leg is loaded,
and targeting is strongly dependent on the exteroceptive cue of a tactile
stimulus (Dürr and Matheson,
2003
), we conclude that load compensation in locusts must be due
to a high-gain position control loop.
Our previous work shows that in locusts, unloaded scratching movements
elicited by stimuli to different places on the wing form a fine-grained
continuum (Dürr and Matheson,
2003), suggesting that a single underlying motor pattern is
modulated in a continuous way by a somatosensory representation of the wing
surface. The present results show that locusts, like vertebrates, also
integrate leg proprioceptive information into an internal body model that is
used to control aimed limb movements.
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Acknowledgments |
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