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First published online August 8, 2003

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Load compensation in targeted limb movements of an insect

Tom Matheson^1,* and Volker Dürr²

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

View larger version (29K): [in a new window]   Fig. 1. Location of digitised points and experimental setup. (A) Tactile stimulation of the wing at one of two stimulus sites (open triangles, means ± 1 S.D.) elicited scratching movements that began with the tarsus of the ipsilateral hind leg standing on a rod that defined the start position (filled square, means ± 1 S.D., N=462 trials in 3 animals). In `loaded trials', a mass of 142 mg was added to the ipsilateral leg at one of three locations (a–c, open circles). In `control trials' the leg was left unloaded. The coordinate frame of reference used in all of the analyses was centred on the metathoracic coxa, with the horizontal x-axis passing through the mesothoracic coxa. (B) To track movements of the body and limb, eight points (filled circles) were digitised manually in all video frames. Stimulus location and start position of the tarsus were digitised in the first frame. (C) In the simplest representation of a movement, we reconstructed the trajectories of the points representing the proximal and distal ends of the femur, the distal end of the tarsus, and the tip of the wing. For clarity the tarsus is represented as a grey line segment. This example shows a movement made in response to a stimulus at the anterior target (open triangle) in the unloaded condition. The distal end of the femur described an arc dorsal to the body (femur–tibia joint positions), while the distal end of the tibia and tarsus moved towards the target and then in three repeated loops (tarsal positions). In this case the wing did not move (end of wing), and the coxa rotated only a little (coxa–trochanter positions).

View larger version (29K): [in a new window]   Fig. 2. Loading had little effect on the overall pattern of leg movement. Two example scratches are shown for each experimental situation (solid and broken lines respectively). (Ai–Di) Movements made in response to stimuli at the posterior target site (solid and open triangles are the targets corresponding to the scratches shown using solid and broken lines, respectively). The start positions are indicated by solid and open squares. (Aii–Dii) Movements made in response to stimuli at the anterior target. (Ai,ii) Unloaded condition; (Bi,ii) 142 mg load on the proximal femur (open circle); (Ci,ii) 142 mg load on the distal femur (open circle); (Di,ii) 142 mg load on the distal tibia (open circle).

View larger version (19K): [in a new window]   Fig. 3. Loading had no systematic effect on the initial direction of movement of the tarsus measured over the first 200 ms for scratches aimed at either the anterior (A) or posterior target (B). Median movement directions are represented by thick coloured vectors originating at the starting point of movement (black, unloaded; red, 142 mg load on the proximal femur; green, 142 mg load on the distal femur; blue, 142 mg load on the distal tibia). The correspondingly coloured long curved lines indicate the interquartile ranges of movement direction. The median velocity of movement over the first 200 ms is indicated by the length of each thick vector, and the interquartile range of velocity is indicated by the thin error bars (see Fig. 6 for additional analysis of movement velocity). Values of N are as follows. Anterior site, unloaded, 111; load on the proximal femur, 36; load on the distal femur, 33; load on the distal tibia, 40. Posterior site, N=121, 31, 34, 47 respectively.

View larger version (17K): [in a new window]   Fig. 4. Loading had no effect on the number of loops made by the leg for either the anterior stimulus site (A, N=220 trials pooled across three animals) or the posterior site (B, N=233 trials pooled across three animals). Bars show the relative frequency of occurrence of scratches with either 1, 2, 3 or more cyclic loops under each load condition. See text for details. Open bar, 0 loops; Light grey bar, 1 loop; mid-grey bar, 2 loops; black bar, 3 loops.

View larger version (25K): [in a new window]   Fig. 5. The part of the leg that is aimed most accurately at the stimulus site does not change with load. The leg of the locust (bottom) was subdivided into units (white lines), and the closest distance by which each unit approached the target (e.g. open triangle) was assessed for all scratches. (Ai–Di) Mean closest distances for each unit of the leg (cf. leg outlines below Ai,ii) for movements made in response to stimuli at the posterior target site; (Aii–Dii) corresponding data for movements to the anterior site. Black bars correspond to units on the femur and tarsus, grey bars to units on the tibia. The solid white and black lines indicate the range. (Ai,ii) Unloaded condition; (Bi,ii) 142 mg load on the proximal femur; (Ci,ii) 142 mg load on the distal femur; (Di,ii) 142 mg load on the distal tibia. The asterisks in A mark the part of the leg that was most reliably aimed, and which was used in the following analyses. Number of trials as in Fig. 6.

View larger version (20K): [in a new window]   Fig. 6. Loading had no effect on the initial velocity of movement. (A) Over the first 200 ms of movement, the median velocity was between 8.7 and 10.3 cm s–1 for all movements to the anterior stimulus site (horizontal lines in open boxes) and between 10.2 and 11.1 cm s–1 for movements to the posterior site (horizontal lines in grey boxes), irrespective of load condition. The variances were large so the interquartile ranges overlapped almost completely (boxes). The whiskers indicate the range containing 90% of values. (B) Movement velocity during the cyclic part of each scratch (`Loop velocity') was similarly unaffected by load on the proximal femur (8.7–9.6 cm s–1), but was faster when the leg was loaded on the distal femur or tibia, at least for movements to the posterior stimulus site (12.9–13.3 cm s–1; medians fall outside the interquartile range for unloaded movements). Numbers indicate the number of trials at each site and load condition.

View larger version (18K): [in a new window]   Fig. 7. Loading the leg with a mass of 142 mg had no effect on the mean closest point of approach of the tibia to either stimulus site (open triangles). Closest points of approach were determined for each trajectory. Small black square, unloaded condition; red circle, load on the proximal femur; green triangle, load on the distal femur; blue triangle, load on the distal tibia. The large black square indicates the mean starting position. The mean closest points of approach for movements aimed at the posterior stimulus site were, on average, anterior to the target. Those for movements aimed at the anterior stimulus site were, on average, posterior to the target. All values are the mean ± 1 S.D. of data pooled from three animals. Number of trials as in Fig. 6.

View larger version (36K): [in a new window]   Fig. 8. Load had no effect on the area crossed by the distal end of the tibia for scratches aimed at either the posterior stimulus site (Ai–Di, open triangles) or the anterior stimulus site (Aii–Dii, open triangles). Shading indicates the likelihood of a particular position within the leg's workspace to be scratched. The greyscale represents probability density between 0 (white) and 0.004 (black) at 1 mm spatial resolution (see bar at bottom). White circle, the centre of density; white square, the maximum. (Ai,ii) unloaded condition; (Bi,ii) 142 mg load on the proximal femur; (Ci,ii) 142 mg load on the distal femur; (Di,ii) 142 mg load on the distal tibia. Number of trials as in Fig. 6.

View larger version (21K): [in a new window]   Fig. 9. Iso-probability contours, derived from the probability distributions in Fig. 8, emphasise the remarkable similarity of scratching movements made under different loading conditions (black, unloaded; red, 142 mg load on the proximal femur; green, 142 mg load on the distal femur; blue, 142 mg load on the distal tibia). The insets show normal distributions to indicate the region of the distribution enclosed by the corresponding iso-probability line for 10, 20, 50, 75 and 90% levels. Black triangles mark the target sites; black squares mark the start postures, and coloured circles mark the corresponding centres of probability density. Number of trials as in Fig. 6.