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First published online November 30, 2007
Journal of Experimental Biology 210, 4319-4334 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.010389
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Turning behaviour depends on frictional damping in the fruit fly Drosophila

Thomas Hesselberg and Fritz-Olaf Lehmann*

Biofuture Research Group, Institute of Neurobiology, University of Ulm, Albert-Einstein-Allee 11, 89081 Ulm, Germany


Figure 1
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  		Fig. 1. Closed-loop feedback flight simulator. (A) The animals were placed in the centre of the simulator and modulated their wing stroke amplitudes in response to visual stimuli. An infra-red light cast shadows of the wings on a wing stroke analyser and an infra-red camera tracked the wings for calibration. Schematics not to scale. (B–D) Patterns displayed inside the simulator. (E) Output of a 1-D, 72-receptor-wide model of the fly's elementary motion detector (EMD) to rotation of a 24° spatial wavelength stripe pattern (M. Mronz and F.-O. Lehmann, manuscript submitted for publication). Dark grey areas indicate 100 (±125 deg. s–1) and light grey areas 50% (±390 deg. s–1) response threshold. L, left eye; R, right eye.

 

Figure 2
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  		Fig. 2. Alterations in the prediction of the numerical damping model to changes in morphometrics and kinematic parameters. Damping coefficient plotted as a function of (A) stroke amplitude (black line) and frequency (blue line), (B) active amplitude component {Phi}A (black line) and relative duration of the downstroke (blue line), (C) turning rate within a flight saccade (black line) and wing length (blue line), and (D) centre of pressure (black line) and mean drag coefficient (blue line).

 

Figure 3
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  		Fig. 3. Modelling damping coefficient in Drosophila. (A) During yaw turning, stroke amplitude changes due to an active component ({Phi}A) caused by the fly's steering muscles, and passive changes ({Phi}P) due to body rotation. Note the different contribution of passive components during the stroke cycle (downstroke, top; upstroke, bottom). (B) Turning rate of a fruit fly in response to the impulsive start of yaw torque. Data were modelled at different frictional damping coefficients, at a constant torque of 0.29 pNm, and 0.52 pNm s2 moment of inertia. Numbers in parentheses (1–8) correspond to damping coefficients 52, 156, 208, 260, 520, 1040, 2080 and 5200 pNm s, respectively. The shaded area indicates the maximum threshold range for visual motion detection (cf. Fig. 1E).

 

Figure 4
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  		Fig. 4. Difference in stroke amplitude (left-minus-right wing, blue) of Drosophila melanogaster while responding to the black stripe. Time traces show the fly's behaviour 10 s after switching on the stimulus bias. (A–F) Flight at the damping coefficients 52, 156, 260, 520, 1040 and 5200 pNm s, respectively. The outcome of the numerical model for compensation of the velocity bias (Eqn 9) is shown in red. The visual target (black stripe) oscillated with an amplitude of ±48° and 0.5 Hz. The shaded areas indicate fixation behaviour. Positive (negative) differences indicate clockwise (counter clockwise) rotation.

 

Figure 5
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  		Fig. 5. Angular velocity of the visual panorama while the animal tried to keep the black stripe in the frontal position of the compound eyes. Data correspond to the time traces shown in Fig. 4. (A–F) Flight at the damping coefficients 52, 156, 260, 520, 1040 and 5200 pNm s, respectively. Solid black lines indicate the threshold (±390 deg. s–1) for visual motion detection (50% response, Fig. 1E). See Fig. 4 for more details. Positive (negative) velocities indicate clockwise (counter clockwise) rotation.

 

Figure 6
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  		Fig. 6. Position of the black stripe inside the visual panorama during flight (Fig. 1B). Data correspond to the time traces shown in Figs 4 and 5. (A–F) Flight at the damping coefficients 52, 156, 260, 520, 1040 and 5200 pNm s, respectively. The grey area indicates the 90° frontal window used to score fixation behaviour.

 

Figure 7
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  		Fig. 7. Mean data of the tested flies responding to the black stripe displayed in the simulator at various frictional dampings. (A) Index of fixation (blue) and antifixation (red), calculated from the times the flies kept the stripe in the 90° frontal or caudal region of their the visual field, respectively. (B) Mean rotational velocity of the visual panorama during fixation (blue) and times without fixation behaviour (red). Grey area indicates threshold range of the visual system (cf. Materials and methods). (C) Relative probability of mean stripe position of the complete flight sequences plotted in pseudo-colour. Numbers in parentheses correspond to damping coefficients as listed in the legend to Fig. 3. Values are means ± s.e.m., N=24 flies.

 

Figure 8
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  		Fig. 8. Mean wing kinematics during object orientation behaviour plotted as a function of the simulated damping coefficient. (A) Stroke frequency, (B) sum of left and right stroke amplitude, (C) absolute difference between left and right wing stroke amplitude. Linear regressions fit to measured data is shown in red while the shaded area indicates the upper limits of the visual system that allows visual control of the stripe (Eqn 5; 50 and 100% threshold). Dotted line in C indicates where the regression line crosses with the x-axis. Values are means ± s.e.m., N=24 flies.

 

Figure 9
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  		Fig. 9. Response of Drosophila (blue) to a velocity bias on two random-dot backgrounds at different dampings. Amplitude response (left-minus-right) to a low- (A; pattern shown in Fig. 1C) and high-contrast panorama (B; pattern shown in Fig. 1D). (C) Mean values of panorama velocity and (D) mean relative amplitude difference, both plotted as a function of frictional damping coefficient. Data are mean values of entire flight sequences using low- (red) and high (blue) contrast pattern and during object orientation behaviour (black). Grey area indicates threshold range of the visual system (cf. Materials and methods). For more details, see legend to Fig. 4. Values are means ± s.e.m., N=24 (black), N=8 (red), and N=15 flies (blue).

 

Figure 10
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  		Fig. 10. Deviation of measured, absolute stroke amplitude between both wings from the numerical model, which predicts the wing motion required to compensate for the velocity bias. Object orientation and optomotor experiments using low (high) contrast patterns are plotted in black and red (blue), respectively. Mean minimum deviation at 520 pNm s damping coefficient amounted to approximately 6°, while the animals responded to the bias applied to the high-contrast background (blue). Values are means ± s.e.m., N=24 (black), N=8 (red) and N=15 flies (blue).

 

Figure 11
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  		Fig. 11. Numerical modelling of a flight saccadic in Drosophila. (A–D) Time courses of turning rate in response to torque without counter-torque (A,C) and with counter-torque (B,D). Data are plotted at low (red line, 0.52 pNm s) and high (grey line, 54 pNm s) damping coefficient. The torque profile in D was averaged from Fig. 3C in Fry et al. (Fry et al., 2003Go), reported for a freely flying fruit fly. Turning rate was calculated from Eqn 4 and moment of inertia was 0.52 pNm s2.

 

Figure 12
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  		Fig. 12. Numerical modelling of free flight saccades in Drosophila. (A–C) Profiles of turning rate (black line, left scale) found in three previous studies; (A) (Tammero and Dickinson, 2002bGo), (B) M. Mronz and F.-O. Lehmann (manuscript submitted for publication) and (C) (Fry et al., 2003Go). Turning angle (blue line, right scale) was calculated from turning velocity. Broken green line indicates reported turning angle. (D–F) The corresponding torque profiles were derived from Eqn 1 at 0.52 (red line) and 54 pNm s damping coefficient (grey line). Note the mismatch in the measured final turning angle and the angle calculated from the velocity profile in A.

 

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© The Company of Biologists Ltd 2007