The behavioural transition from straight to curve walking: kinetics of leg movement parameters and the initiation of turning
Abteilung für Biologische Kybernetik und Theoretische Biologie, Fakultät für Biologie, Universität Bielefeld, Postfach 10 01 33501 Bielefeld, Germany
* Author for correspondence (e-mail: volker.duerr{at}uni-bielefeld.de)
Accepted 12 April 2005
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Summary |
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Kinematics of stick insect walking vary considerably among trials and within trials. As a consequence, the behavioural states of straight walking and curve walking are described by the distributions of 13 kinematic parameters per leg and of orientation angles of head and antennae. The transitions between the behavioural states are then characterised by the fraction of the variance within states by which these distributions differ, and by the rate of change of the corresponding time courses. The antennal optomotor response leads that of the locomotor system. Visually elicited turning is shown to be initiated by stance direction changes of both front legs. The transition from straight to curve walking in stick insects follows different time courses for different legs, with time constants of kinematic parameters ranging from 1.7 s to more than 3 s. Therefore, turning is a behavioural transition that involves a characteristic orchestration of events rather than synchronous parallel actions with a single time constant.
Key words: curve walking, turning, behavioural transition, stick insect, Carausius morosus
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Introduction |
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A prominent example of a well-studied change in locomotor context is curve
walking in arthropods, where kinematic changes, gaits in particular, are
documented in insects (Zolotov et al.,
1975; Franklin et al.,
1981
; Jander,
1985
; Strauss and Heisenberg,
1990
; Zollikofer,
1994
; Jindrich and Full,
1999
), arachnids (Land,
1972
) and crustaceans (Cruse
and Silva Saavedra, 1996
; Domenici et al.,
1998
,
1999
;
Copp and Jamon, 2001
). Although
two of these studies have identified the contribution of individual legs to
yaw torque (Domenici et al.,
1999
) or a lateral component in ground reaction force
(Jindrich and Full, 1999
),
they do not reveal how a particular event in one leg, e.g. the strong outward
push of a front leg, relates to the action sequence of the remaining legs. In
other studies where fast turning reactions could be related to triggering
sensory events, the subsequent series of actions have either not been analysed
in terms of leg kinematics (Camhi and
Johnson, 1999
; Hedwig and
Poulet, 2004
) or not as a temporal sequence
(Nye and Ritzmann, 1992
).
In the stick insect Carausius morosus, leg kinematics
(Cruse and Bartling, 1995) and
gait (Graham, 1972
) in
straight walking have been well studied. During curve walking, associated
changes of leg movements can be related to the curvature of the walked path
(Jander, 1982
), yielding a
rather complete description of stepping pattern for any given steady state of
the motor system (where `state' refers to the set turning tendency).
Nevertheless, it remains unclear how the animal actually begins to turn, i.e.
how the transition from one of these patterns to another takes place. This
behavioural transition, however, is most interesting because steady state
curves are not very likely to occur in a real life situation. Rather, it is
plausible to assume that any turn performed by a stick insect is a transient
change in walking direction, much as in cockroach wall-following
(Camhi and Johnson, 1999
) or
cricket phonotaxis (Hedwig and Poulet,
2004
). The objective of this study was to analyse the temporal
sequence of leg movements during a transition in walking direction, in order
to decide whether the underlying mechanisms act at the same rate in all legs
or should be grouped into primary actions that initiate turning and secondary
actions that support turning.
A model simulation of the stick insect walking system implemented turning
tendency by a course control module that reduced/increased retraction
amplitude in legs at the inner/outer side of the curvature
(Cruse et al., 1998). Curve
walking performance of this controller was quantified for different path
curvatures and walking speeds (Kindermann,
2002
). It does well for shallow curves but increasingly deviates
from observations on real stick insects on tighter curves, suggesting that the
implemented mechanism is different in real stick insects. At least two
alternative mechanisms are conceivable. Firstly, altering the target
touch-down location of the swing movements (leg protraction through the air)
of front legs could cause a change in direction of front leg stance movements
(leg retraction during ground contact) which, due to a targeting mechanism in
middle and rear legs (Cruse,
1979
), affects stance direction of the trailing legs. Secondly, a
change of stance direction rather than, or additional to, retraction amplitude
could act to rotate the resulting ground reaction force vectors to generate a
yaw torque. This would be similar to what has been found in cockroaches
(Jindrich and Full, 1999
). The
present study can distinguish between these alternatives.
The experiment was designed as a three-part measurement with two steady
state intervals of equal duration, an initial straight walk state and a
terminal curve walk state, separated by a transition interval. The analysis
was carried out in two steps. First, the kinematic parameters that
significantly changed between the two steady states were identified and their
relative magnitude was calculated. In a second step, the time course of each
parameter having a statistically significant change between steady states was
determined by finding the time constant that best described the kinetics of
the observed change. It is shown that the behavioural transition from straight
to curve walking is initiated by a primary change in stance direction in both
front legs, followed by a number of secondary changes in all other legs.
Preliminary results have been published in abstract form
(Dürr and Authmann,
2002).
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Materials and methods |
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Drum rotation and data acquisition was controlled by a PC computer. Direction of visual motion was randomised, but data of counter-clockwise trials were reversed during the analysis to allow pooling of trials. All trials were thus standardised to clockwise stimulus motion and, therefore, clockwise turning reactions. Accordingly, with respect to the curved path, left legs are always outer legs, right legs are always inner legs.
To prohibit sideward and forward translation of the body relative to the
set-up without constraining body height, animals were tethered to a 9 cm rod
made of balsa wood that was hinged on a horizontal rotation axis. A metal
screw at the opposite end of the rod counter-balanced the weight of the lever
arm such that the animals only had to carry their own body weight. The surface
of the ball was covered by evenly spaced patches of retro-reflective foil
(Scotchlite 8850, 3M, Neuss, Germany). As the walking insect caused rotation
of the ball, all three degrees of freedom of rotation were monitored by an
optical tracking system (custom-made by Dr Hansjürgen Dahmen, Department
of Cognitive Neuroscience, University of Tübingen, Germany). Two motion
sensors, located at the equator of the sphere (Sx and Sy in
Fig. 1A), flashed brief
infrared light pulses at the surface of the sphere and recorded the shift of
the reflected image by means of a CMOS chip
(Arreguit et al., 1996).
Sampling rate of the tracker sensors was 832 Hz and angular resolution was
approximately 0.15°. Upon receiving a synchronisation trigger pulse from
the video system (see below), the computer recorded the summed sensor readings
and sent a reset signal. Sensor readings were then converted into measures of
intended yaw rotation, and forward and sideward translation of the animal (R,
Tx and Ty, respectively, in Fig.
1A). Arrows in Fig.
1A indicate the direction of positive sign of the
measurements.
Video analysis of leg movements
Walking animals were filmed by a CCD camera (Fricke GmbH, CCD-7250,
Lübbecke, Germany; 1 ms shutter speed) located 1.4 m above the sphere.
Video films were time-stamped (Magnasonic VTG 200, Spitzer-Mileger, Basel,
Switzerland) and recorded on video tape (Panasonic NV-F70). Spatial and
temporal resolution were 0.2 mm and 0.04 s,respectively. For synchronisation
with the tracker measurements, LEDs on the stimulus set-up indicated the start
and end of data recording. Also, the synchronisation pulse of the video signal
was electronically extracted and converted into a TTL trigger pulse at a
frequency of 50 Hz.
After the experiments, selected video sequences were captured as AVI files on a PC computer (MiroVideo 30plus, Pinnacle Systems GmbH, Braunschweig, Germany) and analysed manually on a frame-to-frame basis, using a custom-written program. Only those video frames in which a stanceswing transition or swingstance transition occurred were analysed, i.e. the first and last frame of each stance movement, immediately after a leg touched down or was lifted off the ground. The position of the tibiatarsus joint was recorded at these instances of transition, equivalent to the Anterior and Posterior Extreme Positions of the step cycle (AEP and PEP, respectively). The coordinates of the tarsus location were then converted into metric measures and transformed into relative coordinates with respect to the coxa of the respective leg. Data sequences of each leg always began with the first AEP and ended with the last transition point (either AEP or PEP) after stop of stimulus motion.
Data analysis
A simple sign test (Hayes,
1988, p. 139) was
applied to determine the directional bias of spontaneous turning without
stimulus motion. For the kinematic analysis, 13 parameters were determined for
each leg and step cycle. These were direction, length, duration and duty cycle
of both stance and swing movements, the x- and y-coordinates
of the AEP and PEP, and the step period. The experimental period of 21.5 s was
divided into 42 time bins. In each bin, data points were pooled from all
trials in which either a stance or swing movement began in that bin. Means and
standard deviations (S.D.) of all parameters and legs were
determined, and a MannWhitney test on statistical difference of the
median between the pre-stimulus period and the late stimulus period was
calculated (Statistics Package for the Social Sciences 10, SPSS Inc.). Tests
where P
0.001 was reached were considered significant, which
seemed appropriate given the large sample sizes of 337439 steps for the
straight walking period and 134295 steps for the late curve walking
period. Typically, this level was reached if the ratio
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Results |
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After a transition period, the turning tendency of the insect generally assumed a constant level, resulting in a curve walk with steady path curvature (Fig. 1C). The change in walking direction was accompanied by obvious kinematic changes in all legs. Also, head orientation and the beating field of both antennae shifted toward the turning direction (see below).
Continuity of walking behaviour and strength of the optomotor response, as indicated by the curvature of the walked path, varied both between and within individual animals. To ensure that parameters were only pooled from qualitatively similar trials, the following two criteria were applied to select a representative and homogenous sample of walking sequences: firstly, forward translation had to be steady throughout the entire measurement; secondly, the diameter of the walked path had to be less than 10 cm. According to these criteria, 33 out of 318 walking sequences from eight animals were selected for further analysis. The steadiness criterion caused us to discard many trials in which the animals transiently stopped walking. This was particularly frequent during the pre-stimulus period, i.e. in a stationary environment. The curvature criterion selected for persistently strong turning responses.
A representative single trial is shown in Fig. 1B, illustrating the three movement components and the walked path. The corresponding tarsus trajectories and stepping pattern are shown in Fig. 2. Prior to stimulus motion, the movement of the animal consisted of steady forward and moderate sideward translation (Fig. 1Biii,iv). A weak bias rotation, as measured in this trial, was also commonly observed. In response to the step of stimulus motion (Fig. 1Bi), the rotation angle reversed sign and increased with constant slope (Fig. 1Bii), indicating steady turning of the animal. During turning, sideward translation remained stable, whereas forward velocity decreased. Reconstruction of the walked path from the movement components reveals a moderately leftward curved trail that enters a nearly perfect circular trail shortly after stimulus onset (Fig. 1C, vertical line indicates stimulus onset).
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Apart from the spatial changes of leg movements illustrated in
Fig. 2A, temporal coordination
between legs also changed during curve walking. This is shown by the sequence
of stance phases from the same trial in
Fig. 2B. The stepping pattern
during the straight walk period (black) is almost a tripod gait, where stance
and swing movements (bars and gaps, respectively) of ipsilateral front and
hind legs coincide with those of the contralateral middle leg. After start of
stimulus motion (grey) the stepping pattern becomes rather asymmetrical, with
markedly prolonged stance durations in the inner middle and hind leg. As the
current study is concerned with the temporal order of kinematic changes during
turning, only the parameters step period, stance and swing phase duration and
duty cycle of individual legs are considered here. Leg coordination, i.e.
coupling between limbs, is treated separately in the accompanying paper
(Dürr, 2005).
Kinetics of overall turning behaviour
As Figs 1 and
2 illustrate the variability of
step parameters within a single trial, it is trivial to observe that there is
variability between trials, and also between animals. Variability is of
central importance to the analyses explained below, not only because it
determines whether a given change in magnitude is statistically significant,
but also because it is an indicator of consistency among trials that allows
ranking of effects irrespective of their unit. For example, consistency of the
change in stance direction can be directly compared to the consistency of the
change in duty cycle, while their magnitudes cannot be related.
Assuming that there is only a single neural mechanism to elicit visually induced curve walking, this mechanism will directly affect some kinematic parameters (primary parameters), whereas others will be affected by subsequent indirect, mechanical or neural interactions (secondary parameters). Due to the direct action, visually induced changes of primary parameters are likely to be confounded relatively little by trial-to-trial variability in experimental history, current body posture, neural noise, etc. In contrast, indirect changes of the secondary parameters are likely to be affected more. As the onset of visual stimulus motion causes a change in locomotor context, primary parameters should therefore change more consistently than secondary parameters. This assumption has two implications for the present analysis: (1) primary kinematic parameters that are most important for the initiation of turning, should change most strongly with respect to their variability during the behavioural states before and after the transition; (2) the time course of transition between two behavioural states should be less prone to disturbances or noise and, thus, more reliably detectable in primary than in secondary parameters.
Following these considerations, Fig.
3 describes the behavioural transition from straight to curve
walking by the fraction of variability by which each locomotion component
changes, and by its rate of change. As the behavioural transition was induced
by visual input, the onset of stimulus motion could serve as a reference time
for the start of transition. Also, because locomotion was steady before and
after the transition period, the steady state magnitude of each locomotion
component was measured as the average value in the straight walk and curve
walk interval, respectively. The average angular velocity of rotation was
close to zero during straight walking (1°). During turning, it
increased by 34.1° with a time constant of 2.4 s. The steady state
magnitude changed by 114% of its variability (=1.14) and the time
course yielded a statistically significant curve fit (
2=0.8,
r2=0.986). Translation components changed considerably
less with respect to their steady state variability, resulting in
=0.33
and
=0.18 for sideward and forward speed, respectively. This
corresponded to a sideward acceleration by 3.6 mm s1 per 7.5
s and forward deceleration by 2.8 mm s1 per 7.5 s. As the
latter difference was not statistically significant, the average turning
response to the visual motion stimulus consisted of a large increase in
angular velocity, accompanied by a weak increase in sideward velocity.
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Changes of step frequency, stride length and stance direction
Previous studies on curve walking have often been motivated by alternative
hypotheses stating that curve walking requires an asymmetry in either step
frequencies or step lengths or both on the outside and inside of the curve.
Figs 5 and
6 show that, indeed, both step
frequency and step length changed, but these changes were not simply due to
unilateral increases or decreases in magnitude. Rather, each leg underwent a
typical change during the transition to curve walking.
Fig. 5 shows the average step
frequencies among trials for all six legs. Wilcoxon's matched-pair test was
applied to compare step frequencies of the straight walk interval with those
of the subsequent curve walk interval on a trial-by-trial basis. This test is
insensitive to differences in walking speed among trials, as it only considers
sign and size of frequency changes rather than the difference of the sample
median. The result reveals that step frequency significantly increased for all
outer legs and inner front legs. Note that this significant increase in step
frequency was not paralleled by an increase in forward walking speed (see
Fig. 3). Interestingly, the
apparent reduction of step frequency by the inner hind leg was too variable to
be statistically significant. During curve walking, step frequencies
significantly differed between contralateral neighbours such that each outer
leg stepped at a higher rate than its inner neighbour (P0.002).
During straight walking, there was no difference between contralateral
neighbours (P>0.3).
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What changes the most?
The exact magnitude of all kinematic parameters that undergo a
statistically significant change are listed in
Table 1. As has been argued
above, parameters that are important for the initiation of turning need not
necessarily change their magnitude by a large percentage, but are likely to
change reliably, i.e. by a significant fraction of their standard deviation in
the previous behavioural state. This fraction is expressed by the value
, which is related to the t-test statistic. Since the number
of observations will increase the chance of any statistical test to yield a
significant result, it is useful to choose a threshold value of
, that
coincides well with a given significance level. In this study,
<0.25
coincided well with P<0.001 of a MannWhitney test or, in
the case of angular measures, a circular statistics test for common median
(Fisher, 1993
). Out of 54
parameters with
0.25 or P<0.001, two reached the
significance level with
<0.25, and three were not significant
despite
>0.25, leaving 49 that satisfied both criteria
(Table 1). As
is a
dimensionless ratio, it is suitable for ranking and comparing magnitude
changes of all parameters, irrespective of their unit.
Four of the five strongest changes occurred in the inner front leg,
affecting step direction and AEP coordinates. Further strong changes occurred
in the outer front leg and inner middle leg, also concerning step direction
and coordinates of extreme points. Generally, step direction, step length and
extreme point coordinates revealed larger values than measures of
duration or duty cycle. Timing of lift-off or touch-down is more variable and,
thus, less likely to be directly affected by a descending turning command than
are positional and directional parameters.
What changes the fastest?
Given that the turning response of the whole animal occurred with a time
constant of 2.4 s (Fig. 3), it
was clear that the primary kinematic parameters, i.e. those that initiate
turning, must have changed equally fast or faster than that. Following the
same approach as described in relation to
Fig. 3, exponential curve fits
were calculated to reveal the temporal sequence of all parameters that change
significantly as the animal enters a curve. For illustration of the fitting
process and results obtained, Fig.
7 shows the time course of the average stance direction for each
leg, and the curve fit obtained for the kinetics of the transition. Reliable
curve fits were obtained for three out of the five legs that show a
significant change in stance direction. These were the two front legs and the
inner middle leg. Of these three, the rise time constants of both front legs
were both 1.7 s, indicating that they reliably change stance direction some
0.7 s before the effect of this change can be picked up in the behaviour of
the whole animal. The time constant of the stance direction of the inner
middle leg is considerably slower (3.3 s), indicating that it is not a primary
parameter for the initiation of turning, albeit experiencing one of the
strongest changes during the transition. Time courses of the outer middle and
hind leg did not allow a significant curve fit (2>27.5
and/or r2<0.36). No fit was calculated for the inner
hind leg, because the steady state values were not significantly
different.
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The orchestration of the retrieved primary parameters is illustrated in Fig. 8, where the time constants of the time courses are plotted in the order of their magnitude, indicating the sequence of events in which a given parameter completed 67% of the context-dependent change. Eight parameters have shorter time constants than yaw rotation (see Fig. 3), indicating that they lead the change in overall turning behaviour of the animal. These are stance directions of the two front legs, PEP of the inner front leg, swing direction of the front legs and the outer middle leg, and swing length and AEP of the outer front leg. All other parameters lag behind the turning of the animal and are, thus, secondary. Furthermore, because stance parameters of front legs change consistently faster than the corresponding swing parameters, we conclude that the front legs initiate a turn by altering their stance direction rather than by altering their swing direction.
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Discussion |
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Methodological considerations
Various methodological aspects affect curve walking behaviour in
arthropods, for instance the behavioural situation, which can be characterised
by the experimental method of eliciting a turn. Previous studies have analysed
turning during optomotor responses to visual large-field motion (e.g.
Zolotov et al., 1975;
Jander, 1985
;
Cruse and Silva Saavedra,
1996
), visual tracking of small objects
(Land, 1972
), spontaneous
turns (Jindrich and Full,
1999
) or particular behaviours such as mating
(Franklin et al., 1981
) or
defence behaviour (Copp and Jamon,
2001
). Moreover, the locomotor state (static vs dynamic
locomotion) and movement constraints (tethered vs free walking,
natural vs un-natural inertia) varied among these studies. Three of
these aspects need to be discussed in relation to the presented results: (1)
effect of tethering, (2) increased inertia and (3) sustained visual
stimulation.
Tethering
The tethering method of this study ensured natural height control by the
animal, because load was normal and the body height range was virtually
un-restricted. Theoretically, the placement of the animal on the sphere could
have biased the ratio of forward and sideward translation, for instance
causing a pronounced sideward component. However, as turning directions were
randomised during the experiments, such a translation bias should have
averaged out among trials, resulting in increased variance only. Thus, the
significant increase in stimulus-induced sideward translation
(Fig. 3) cannot be due to
tethering. Rather, sideward translation is a component of turning.
Inertia
Because the moment of inertia of the sphere was markedly larger than that
of the stick insect body (by a factor of 139), angular acceleration and
deceleration required the insects to produce considerably more force than when
walking on a plane surface. However, comparison with Jander's results on stick
insects that walked on an actively counter-rotating sphere
(Jander, 1982), particularly
stance length and direction (Fig.
6) show no sign of differences attributable to load. Given the
experimental situation of the present study, angular acceleration of the
sphere was very low during the steady states, but strong at the onset of
turning. Therefore, any significant impact of increased inertia should have
shown up immediately after stimulus onset, possibly resulting in an increased
variance of the movement components. There was no indication of such effects.
Inertia will have affected stance movements more than swing movements. As
stance direction showed a faster rate of change compared to swing direction
(Fig. 8) in spite of increased
force requirement, the observed differences between stance and swing movements
must be expected to be the same or even larger under normal walking
conditions. Hence, the claims made by this study are not affected by increased
inertia.
Prolonged stimulation
The experimental situation ensured that locomotion was steady over a period
of many steps. Qualitatively, the locomotor pattern remained the same,
quantitatively it remained within a characteristic distribution. Following a
period of steady forward walking, sustained visual motion stimulation caused
the locomotor system to assume another steady state after a transition period.
Of course, prolonged stimulation causes a rather un-natural situation.
However, the two steady locomotor states merely served as a reference to
define the bounds of the behavioural transition, which is a prerequisite to
determine the rate of change. In other words, the final behavioural state may
well be un-natural, nevertheless it can be exploited as a key to determine the
sequence of events that occurs during natural short-term course
corrections.
Experimental parameters such as stimulus velocity are known to cause
quantitative changes in path curvature and associated kinematic parameters
(e.g. Jander, 1982), and to
give rise to qualitatively different turning behaviours
(Zolotov et al., 1975
).
Therefore, stimulus conditions were held constant in the present study, and
trials were pooled only if the walked path was qualitatively similar (see
Fig. 1C). The existence of a
descending visual input to motor networks and the reliable strong turning
response it mediates suggest that visually elicited turning does play an
important role in insect walking. Of course, it is possible that visually
induced turning differs from other behavioural situations, e.g. spontaneous
turning. Yet, the finding that kinetics of movement parameters differ strongly
between legs shows that the functions of the six legs during turning also
differ strongly. Moreover, it suggests that descending input causes a stronger
drive on the front legs than on the other legs.
A final methodological consideration concerns the difficulty to measure the
effect of a continuous descending drive on discrete variables of leg movement,
i.e. kinematic parameters of alternating and mutually exclusive swing and
stance modes. This problem was solved by fitting a continuous function to
discrete sample distributions of each parameter. Theoretically, important
effects could have been missed by this approach, provided they were small
and/or rather variable, in spite of their importance. Since the transition
bounds RS and RC, as well as the
-value, depend on both the average change and on variability, small
effects cannot reach a large coefficient of determination
r2 and might have gone undetected (even if
2 was very small). However, the existence of fast, strong and
consistent effects, particularly on front leg movement, which can explain a
strong yaw moment, can hardly be accounted for by any potentially undetected
effect in another leg.
What changes during turning?
Many previous studies on curve walking claimed that there were two
principal alternatives for negotiating a curve: by changing either step
frequency or stride length. This view is based on the assumption that the
movements of each leg are caused by a protractionretraction oscillator
with adjustable frequency and amplitude. It implicitly relies on a unilateral
change of one of these variables, e.g. by an increase on one side and decrease
on the other. There are three reasons why this view is too simple to
understand turning behaviour: Firstly, rhythmic patterns are not particularly
stable, compromising the importance of an oscillator. Secondly, the forces on
the ground that ultimately determine the movement of the body axis, are not a
simple function of stride length or stance duration, but vary considerably
between legs (Cruse, 1976;
Jindrich and Full, 1999
;
Domenici et al., 1999
).
Thirdly, rotation of the body axis requires differing ground force directions
among legs. Since stance direction has a strong effect on the ground force
direction, it may be most efficient for an animal to alter stance direction
rather than stride length or duration. This is in line with the present
results, showing that each leg undergoes a specific change of step frequency,
stride length, and stance direction (Figs
5,
6;
Table 1). Incontrast to insects
that tend to maintain a tripod coordination during turning (fly:
Strauss and Heisenberg, 1990
;
ant: Zollikofer, 1994
), stick
insects change their gait during curve walking
(Fig. 2B). While stepping
becomes seemingly more regular among outer legs, it becomes less regular among
inner legs (Dürr, 2005
).
In particular, the inner hind leg appears to be taken out of the normal leg
coordination, executing only infrequent, short swing movements and prolonged
stance movements with very complex trajectories. Jander
(1985
) showed that the
stepping behaviour of the inner hind leg in a turning stick insect is tightly
linked to the location of the centre of gravity within the stability polygon
spanned by the legs on ground. As the centre of gravity of a stick insect is
located posterior to the hind leg coxae, Jander suggested that the inner hind
leg lifts off the ground so rarely because it seldom is sufficiently
unloaded.
Strongest changes were observed in both front legs, the inner middle leg
and the outer hind leg (Table
1). This is similar to the cockroach, where the inner front legs
show strong kinematic changes in tactile-mediated turning behaviour
(Ridgel et al., 2002) and the
inner middle legs strongly affect wind-elicited turns at the beginning of
escape reactions (Nye and Ritzmann,
1992
). Based on model calculations, Jindrich and Full
(1999
) concluded that the
front legs of the cockroach would be most effective to cause turning, although
all legs could theoretically rotate the body axis. For the stick insect,
Tables 1 and
2 show that the set of
kinematic parameters that exhibit the fastest change corresponds well to the
set of parameters with the most consistent change, i.e. largest
-value.
Thus, front leg movement appears to be the primary target of the descending
visual information that triggers turning. The observed fast and strong change
in stance direction requires coordinated action of all leg joints, rather than
a simple modulation of retraction amplitude and speed.
Primary vs secondary parameters
Optomotor responses generally resemble low-pass filtered versions of the
stimulus function (reviewed in
Hengstenberg, 1993). For
instance, activation of fly steering muscles in response to descending
information about large-field visual motion is low-pass filtered compared to
the properties of the visual interneurons of the optic lobe
(Egelhaaf, 1989
). As the
stimulus function in the present study was a step onset of visual motion, an
associative exponential function was assumed to model continuous descending
visual input to the motor networks of the thoracic ganglia. The discrete
nature of the stepping rhythm was dissolved by calculation of sample
distributions of each kinematic parameter over a sequence of 42 brief time
bins. Accordingly, the curve fit should be interpreted as the drive of
descending inputs on a given kinematic parameter. If it was a stance
parameter, a point on the time course would show the most likely magnitude of
this parameter for a stance movement elicited at that time.
Behavioural relevance of a given parameter is assessed by determining the consistency of the change observed, which necessitates relating the magnitude of the change to the natural bandwidth during stable behavioural states. Statistical significance by itself is not a very useful indicator of behavioural relevance, as it strongly depends on the sample size, and sample size is not of behavioural relevance in our case. In other words, while the large sample size allows statistical discrimination of context dependency for many parameters (see Table 1), functional importance to the animal may vary strongly, for instance when considering whether a change is active or passive. Due to lack of information about neural activation patterns, we cannot discriminate here between active and passive changes. However, based on differences in the time course, we can discriminate between primary and secondary parameters. It is clear that the fastest changes, which lead the yaw rotation of the whole animal, must be due to an active effort of the animal, as there is nothing else to cause them. The slower time courses of secondary parameters, those that lag behind yaw rotation of the whole animal, could have at least three different causes. Firstly, they could be caused by passive effects, e.g. due to mechanical constraints imposed by other, active effects. Secondly, they could be due to active movements of the animal that are less consistent at the beginning of the transition, resulting in a slow change of the mean. Thirdly, they could be due to active movements that lag behind the actions underlying the primary parameters. Accordingly, the orchestration of kinematic events shown in Fig. 8 begins with a sequence of active events, followed by both active and passive secondary events interspersed.
Intuitively, one might think that all legs in stance should change stance direction with the same time constant, and that both front legs, which typically step alternately, should have different time constants. On a single trial basis this intuitive view is true. However, time constants were determined for a pool of responses, and stance direction changes in a front leg need not always coincide with the same set of corresponding changes in other legs. Since fit functions and corresponding time constants reflect the most consistent time course, stance direction in other legs may well change more slowly than in front legs, despite occasional fast reactions. Similarly, front legs need not step synchronously to achieve the same average time course in stance direction.
Interestingly, the antennal movement pattern undergoes a faster change than
any leg, as revealed by time constants between 1.5 and 2.0 s for antennal
angle relative to the head or body (Fig.
4). These time constants were not included in
Fig. 8 as antennae do not
physically contribute to yaw rotation. Nevertheless, these fast reactions
suggest that an antennal orienting response leads the response of the
locomotor system. This is in line with the results of Dürr et al.
(2001) who suggested that
stick insects use their antennae for active tactile searching of the locomotor
action range.
Swing or stance? Implications for modelling studies on turning behaviour
Since we analysed a set of sample distributions rather than single
behavioural chains, the results presented here may not apply to every single
trial. Rather, they capture the most likely scenario. If there were different
strategies involved, the result would have been dominated by the strategy that
is elicited most reliably among trials, i.e. by the set of kinematic changes
that are most robust within the sample. For example, stick insects may be able
to initiate a turn by targeting swing movements to another AEP, just as they
can retarget ongoing swing movements following antennal contact
(Dürr and Krause, 2001),
but if they had done this consistently, the distribution of swing direction
would have shifted earlier than that of stance direction and, as a
consequence, the current analysis would have detected a shorter time constant
for swing direction than for stance direction. This was not the case. Rather,
time constants of stance direction were approximately 0.5 s shorter than those
of swing direction. Accordingly, turning was initiated most consistently by a
bilateral change in front leg stance direction, followed by corresponding
changes in swing direction. Together with the complex sequence of events,
revealing different time courses in each leg, the importance of the front leg
stance contradicts all current models of curve walking. Cruse et al.
(1998
) suggested that curve
walking is caused by a differential change in angular velocity of the
thoraxcoxa joint in outer and inner legs. According to their model, a
positive displacement feedback mechanism then accounts for adjustments in the
femurtibia joint, while the coxatrochanter joint is controlled
separately by a negative feedback mechanism that adjusts clearance over
ground. Curve walking performance in this model is fairly good, but a
quantitative description of its stance trajectories
(Kindermann, 2002
) reveals
major differences to the data shown in Fig.
6. The most profound discrepancies concern mediad stance direction
of the outer hind leg and shortening of the inner hind leg's stance. Both of
these discrepancies might be removed by a model in which descending visual
input only affects stance direction in both front legs, leaving all other
changes to mechanical coupling and assistance reflexes as implemented by
Kindermann (2002
). For
example, infrequent short steps of the inner hind leg may be simply due to
rare unloading of this leg because of its closeness to the centre of gravity
(Jander, 1985
). It is possible
that the kinematic changes described above need to be accompanied by
corresponding changes in coupling strength of leg coordinating mechanisms.
Such context-dependent changes in coupling strength are described in the
accompanying paper (Dürr,
2005
). As yet, it is difficult to judge whether changes in
coupling strength by themselves would suffice to cause curve walking, e.g. by
causing un-equal step frequencies and stride lengths on both sides. Most
certainly, however, changes in coupling strength will act to support the
kinematic changes described, e.g. by uncoupling the inner hind leg and
enhancing coherence of outer stance movements along a single convex
trajectory. Due to the large number of interacting parameters, modelling
studies will have to unravel the relative contributions of local changes in
step kinematics on the one hand, and inter-leg coordination mechanisms on the
other.
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