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First published online June 6, 2005
Journal of Experimental Biology 208, 2237-2252 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01637

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The behavioural transition from straight to curve walking: kinetics of leg movement parameters and the initiation of turning

Volker Dürr^* and Wiebke Ebeling

Abteilung für Biologische Kybernetik und Theoretische Biologie, Fakultät für Biologie, Universität Bielefeld, Postfach 10 01 33501 Bielefeld, Germany

View larger version (20K): [in a new window]   Fig. 1. Experimental design and automated tracking of the walked path. (A) Schematic drawing of the experimental set-up (not drawn to scale). A stick insect was tethered above a sphere on which it stood or walked. Stationary walking caused rotation of the sphere. Two optic sensors (Sx and Sy) detected all three degrees of freedom of rotation of the sphere, each of which could be attributed to one of three components of walking direction: turning, i.e. yaw rotation around the vertical axis (R), forward translation (Tx) and sideward translation (Ty). Arrows indicate the sign of the measurements taken. A large-field visual motion stimulus (M) elicited an optomotor turning response, causing the animal to walk on a curved path. The stimulus pattern was a vertical grating. (B) Each trial lasted 22.5 s and was divided into three periods of equal duration. A pre-stimulus period without stimulus motion was followed by two periods with constant stimulus motion. Diagrams show representative measurements of R, Tx and Ty in response to a step of stimulus velocity. Movement components were used to reconstruct the walked path (C), visualising the overall walking behaviour (same trial as in B). Each symbol indicates the location and orientation of the body axis. Filled circles label the head. Symbols are plotted every 200 ms. Vertical bar indicates stimulus onset. Grid width, 10 cm.

View larger version (20K): [in a new window]   Fig. 2. Stance trajectories and gait pattern change during turning. (A) Stance trajectories of the tibia–tarsus joint on the surface of the sphere, drawn relative to the tethered body. Trajectories are largely parallel to the body axis during straight walking (Ai; before stimulus motion) but of different length and orientation during curve walking (Aii; during stimulus motion). Same trial as in Fig. 1. Each line shows a stance trajectory in body-centred coordinates, with the animal facing to the right. Circles labelled T1, T2 and T3 mark the location of the coxae of the first, second and third thorax segment, respectively. Horizontal dotted reference lines are drawn parallel to the body long axis. Left and right legs are outside and inside the curvature, respectively. For clarity, stance trajectories of middle legs are shown in grey. Numbered arrows on the lower panel indicate selected start- or endpoints of the first and second trajectories after onset of visual motion. (B) The stepping pattern of the same trial as in A. Horizontal line segments depict stance phases of a given leg. O1, O2 to O3 denote outer front, middle and hind legs, respectively (left legs). I1 to I3 denote corresponding inner legs (right legs). Steps that started during the stimulus period are shown in grey.

View larger version (31K): [in a new window]   Fig. 3. Kinetics of rotation and translation components during turning. (A) In response to the onset of a visual motion stimulus, i.e. a step in the temporal frequency (TF), stick insects change their locomotor behaviour from a steady straight walk to a steady curve walk. (B–D) The three degrees of freedom of horizontal locomotion were analysed separately and illustrated by their average rate of change per 0.54 s (14 time bins per 7.5 s) among 33 trials from eight animals (square symbols). (B) Angular velocity of yaw rotation (R), (C) speed of sideward translation (Ty) and (D) speed of forward translation (Tx). Values are means ± S.D., indicating the variability among trials. Arrows in the insert show the sign convention. In response to the visual motion stimulus, angular velocity increases with a time constant of 2.4 s. The speed of sideward translation also increases significantly with a time constant of 2.7 s. Forward speed does not change significantly. Steady state velocities during straight and curve walking are indicated by horizontal solid lines in the first and third measurement interval. Exponential curve fits link significantly different steady states.

View larger version (71K): [in a new window]   Fig. 4. Antennal beating field and head orientation shift during curve walking. (A) A representative sequence of head and antennal movements during curve walking. Vertical grid lines mark the three experimental periods (straight, transition, curve). Orientation angles of the head (H) and outer (O) and inner (I) antenna relative to the body axis (see insert for a schematic top view) alternate rhythmically during straight walking. The mean orientation and amplitude of oscillations change after the start of visual motion (line marked with arrowheads). (B) Distribution of antennal orientation angles relative to the body axis over time. Greyscale codes the probability (darker, more probable) of the left (top range) or right (bottom range) antenna to point into a given sector (width 5°). Solid lines indicate mean angles during straight and curve walking, connected by best-fit exponential time course. During straight walking, both antennae are most likely to point at ±33°. After stimulus onset, antennal beating fields shift into turning direction. The shift is faster than for body yaw rotation. (C) As B, but for head angle relative to body axis. Head orientation shifts into turning direction, but slower than antennal beating field. (D) As B, but for antennal angle relative to head. The outer antenna moves closer to the midline but does not cross it. The beating field of the inner antenna shifts into turning direction with a shorter time constant than that of the head.

View larger version (40K): [in a new window]   Fig. 5. Step frequency (f) changes during curve walking, but not in a unilateral way. Average step frequencies of each leg during straight walking (white bars, first 7.5 s interval) and curve walking (grey hatched bars, third 7.5 s interval). Values are means ± S.D. of 33 trials from eight animals. Outer front, middle and hind legs (O1 to O3, respectively) significantly increase their step frequency during curve walking. So does the inner front leg (I1). Inner middle and hind legs (I2 and I3) show no statistically significant change. Wilcoxon test for matched pairs with H0: fstraight=fcurve; N=33; ***P0.001; **P0.01. All contralateral leg pairs step at the same frequency during straight walking (P>0.3), but at different frequencies during curve walking (P0.002)

View larger version (15K): [in a new window]   Fig. 6. Stance direction, stance length, and location of extreme positions change differently for each leg. (A) Average stance trajectories during the straight walk interval were nearly parallel to the body long axis (33 trials from 8 animals). Mean positions of touch-down (triangles) and lift-off (inverted triangles) of each leg are drawn in a body-centred coordinate system with the front of the animal facing to the right. T1–T3 label the location of coxae of the three thorax segments. Arrows mark the average stance direction, pointing in the direction of movement. Values are means ± S.D. of the average positional x- and y-components. (B) During curve walking, stance directions of front and middle legs rotate outward with respect to the curve (towards the top of the panel), and stance direction of the outer hind leg rotates inward. Symbols and black arrows as in A. For comparison, grey arrows duplicate the straight walk condition. Stance length significantly increases for all outer legs and decreases for all inner legs. Front legs undergo the strongest changes during turning, the outer middle leg shows the least difference. Movements of the inner hind leg are the most variable.

View larger version (42K): [in a new window]   Fig. 7. Kinetics of stance direction is fastest in front legs. The time course of stance direction during turning differs between legs. (O1–O3) Time courses of outer front, middle, and hind leg, respectively, as the animal turns to the right. (I1–I3) Time courses of inner legs (see insert on lower right). Values are means ± S.D. of 33 trials in eight animals, every 0.54 s (14 bins per 7.5 s interval). Bold solid lines show the time course of the exponential fitting function that explains most of the variance. Differences between the steady state stance directions (RC–RS) and time constants of the time course () are indicated in the top left corner of each diagram. Values in grey are not statistically significant. Stance direction changes strongest and fastest in front legs. The equally strong change in the inner middle leg is, on average, much slower. Since the change RC–RS in the inner hind leg is not significant, no curve fit was calculated for this data set.

View larger version (23K): [in a new window]   Fig. 8. Orchestration of kinematic changes during turning. As an illustration of the temporal sequence of the kinematic changes, time constants of all reliable curve fits (2 value n.s. at P>0.5, and r2>0.36) are drawn in their temporal order from left to right. Time constants of parameters of the same leg are arranged in individual rows: O1–O3 and I1–I3 label outer and inner front, middle and hind legs, respectively. =0 denotes stimulus onset. Filled squares in the centre of the graph mark the time constants of the locomotion parameters, i.e. angular velocity of rotation (R) and speed of sideward translation (Ty). Circles mark time constants of stance phase (filled) and swing phase parameters (open). The identity of a stance phase parameter is indicated above the symbol, that of a swing phase parameter is indicated below (AEP, Anterior Extreme Position; L, length; PEP, Posterior Extreme Position; .x and .y, components of position vectors; , direction). The grey bar separates primary parameters that lead the overall locomotor change from those that lag behind (secondary). The leading parameters, i.e. stance direction of both front legs and shifts in PEP of the inner front leg and AEP of outer front leg, initiate turning.