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First published online January 18, 2008
Journal of Experimental Biology 211, 341-353 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.012682

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Performance trade-offs in the flight initiation of Drosophila

Gwyneth Card^* and Michael Dickinson

Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA

View larger version (13K): [in this window] [in a new window]   Fig. 1. Definition of kinematic frames of reference. The fixed lab frame (xf, yf, zf) is a right-handed coordinate system with the positive zf-axis pointing down towards the ground. A second frame of reference (xb, yb, zb) has its origin at the fly's center of mass with the xb-axis oriented along the long body axis towards the animal's head, the yb-axis oriented parallel to the fly's right wing, and the zb-axis positioned perpendicular to the xb- and yb-axes and directed towards the ventral surface of the animal. Right-wing down rotation about the xb-axis is positive roll, nose-up rotation around the yb-axis is positive pitch, and a turn to the fly's right around the zb-axis is positive yaw. For each video frame, a unit quaternion q specifies the rotation from body-centered coordinates to the fixed lab coordinates necessary to achieve the attitude of the fly in that frame.

View larger version (78K): [in this window] [in a new window]   Fig. 2. Video sequences for (A) voluntary and (B) escape take-offs. Only one of the three camera views is shown. Times noted are ms from lift-off, the first frame in which both the fly's mesothoracic legs are no longer touching the substrate. For complete video sequences, see supplementary material Movies 1 and 2.

View larger version (24K): [in this window] [in a new window]   Fig. 3. Timelines of leg and wing events during (A) voluntary (N=16) and (B) escape (N=27) take-offs. Each timeline represents the flight initiation sequence for an individual fly, and the timelines are aligned such that lift-off occurs at 0 ms. Black lines correspond to the duration of wing-opening for left (L; upper black line) and right (R; lower black line) wings. The line starts at the time of first wing movement, and ends when the wing is in its fully raised position. In some cases, the wing had not reached its fully raised position when the wings began stroking, leading to wing bending on the upstroke. Wing bending is represented by a thinner black line, which ends at the time when the wing was successfully unfurled. The grey and white bands represent the periods of upstroke and downstroke, respectively. These bands end when the fly left the field of view of the cameras. The red line shows the period of mesothoracic leg extension. It starts when the legs first begin to move and ends when the legs stop extending, usually at the point of lift-off, shown by the thin vertical red line.

View larger version (10K): [in this window] [in a new window]   Fig. 4. Latency of escape take-offs. Timelines of the subset of escape responses for which latency was measured are plotted in relation to the angular size of the falling black disk stimulus in the fly's visual field. Timeline notation is as in Fig. 2 (N=17).

View larger version (58K): [in this window] [in a new window]   Fig. 5. Wing bending during the first upstroke. The images show a comparison of wing shape during the first upstroke after take-off (A) and the second upstroke (B) of an example escape take-off. Two camera views are shown for each stroke (top and side views). The images show the fly's wing position 7 frames (1.2 ms) after the start of the respective upstrokes. The red arrows point to a flexure point along the left wing. The wing bends nearly 90° at this point during the first upstroke, but only minimal bend is evident during the second, more `normal' upstroke (see also supplementary material Movie 3). The right wing also appears to bend in a similar fashion.

View larger version (53K): [in this window] [in a new window]   Fig. 6. Example body kinematics for an (A) voluntary and (B) escape take-off. Lollipop diagrams show the 3D position of the fly during take-off. Lines represent the long axis of the fly, and the open circle represents the position of the fly's head. Positions are plotted every 2.5 ms. The center of mass (COM; Ai, Bi) was defined as the point along the long body axis of the fly 45% of the distance from the head to the tip of the abdomen. We defined the starting COM location of the animal to be the origin. Horizontal position of the COM is the Euclidian distance traveled in the horizontal (x-y) plane (parallel to the ground) from the starting position. Angular values (Aii, Bii) are expressed in a body-centered frame of reference. Roll, pitch and yaw position are the cumulative rotations around the xb, yb, and zb body axes, respectively (see Fig. 1 for axes definitions). The fly's starting position was determined by solving for the roll, pitch and yaw angles associated with the rotation required to move the body-centered frame from alignment with the lab frame to alignment with the fly's starting position.

View larger version (50K): [in this window] [in a new window]   Fig. 7. Average time courses for (A) translational and (B) rotational kinematic variables. Blue lines are mean values for voluntary take-offs and red lines are mean values for escape responses. Shaded area around the mean shows the standard error. Time courses are aligned so that lift-off occurred at 0 ms. The yaw angular position was adjusted to start at 0°. Roll and pitch starting positions for each fly were defined as in Fig. 5. Roll and yaw values for position, velocity and acceleration have been adjusted as if all first rolling and yawing motions were to the fly's right. The dark grey region represents the median time of leg extension for escape take-offs, and the light and dark grey regions together indicate the median time of leg extension for voluntary take-offs. Individual flies did not remain in the field of view of our cameras for uniform amounts of time (see Figs 2 and 6). The inset in the lower right hand corner of B shows the number of flies averaged at each point in time. See also supplementary material Fig. S2 for alternate conventions describing take-off rotations.

View larger version (20K): [in this window] [in a new window]   Fig. 8. Speed vs steadiness. (A) Time courses of center of mass (COM) speed shown for individual flies. Time courses are aligned so that lift-off occurred at 0 ms, and individual time courses end when the fly left the field of view of our cameras. The bar plot at the right indicates the COM speed (mean ± s.e.m.) for all flies over the first 2 ms of flight (grey region). (B) Time courses for steadiness (S) shown for individual flies. Steadiness was calculated from angular speed as described in the text, with large S-values corresponding to low angular speeds. Bar plots show steadiness (mean ± s.e.m.) over the first 2 ms of flight as in A. Voluntary (Vol.) trials are shown in blue, escape (Esc.) trials in red. Mean COM speed and steadiness are significantly different between voluntary and escape conditions, P0.001, ANOVA.

View larger version (50K): [in this window] [in a new window]   Fig. 9. Kinematics of escape responses for clipped-wing flies. (A) Video sequence of an example clipped-wing fly escape response to a falling disk stimulus. (B) Lollipop diagram of an example clipped-wing escape response showing the 3D position of the fly every 2.5 ms. (C,D) Average time courses (solid line, mean; shaded area, ± s.e.m.) for translational and rotational kinematic variables during clipped-wing take-off (as in Fig. 5). N=8 before the arrow on the time axis, and N=7 afterwards.

View larger version (13K): [in this window] [in a new window]   Fig. 10. Distributions of kinematic variables under different wing-raising conditions: voluntary take-off (Vol., N=16), escape take-offs with both wings raised before leg-extension (**Esc., N=5), escape take-offs with only one wing fully raised or wings only partially raised before leg-extension (*Esc., N=5), remaining escape take-offs in which wings move only minimally before leg-extension (Esc., N=17), and escape take-offs by flies with wings removed (Clip, N=8). Box plots are of values averaged over the first 2 ms of flight for (A) center of mass (COM) speed, (B) angular speed, (C) rotational kinetic energy, calculated from the angular speed and assuming the fly to be an ellipsoid body, and (D) the sum of potential (PE) and kinetic energy (KE). Kinetic energy is the sum of rotational kinetic energy (C) and translational kinetic energy (see text for derivation). Statistically significant differences were determined using Mann–Whitney pairwise comparisons with Bonferroni correction for multiple comparisons. Comparisons for which P0.05 are marked by different lower case letters.

View larger version (29K): [in this window] [in a new window]   Fig. 11. Model for achieving take-off performance. (A) We hypothesize that a minimum of four independent pathways are required to coordinate take-off behavior: one coordinating wing opening on either side of the body and two coordinating different types of leg extension. In our model, take-off performance is determined by both the latency between activation of wing and leg pathways and the choice of leg pathway. In our diagram 1 represents the delay due to sensory and/or central processing before one or both wing pathways are activated, and 2 represents the delay before activation of one of the leg pathways. The difference between these two delay times is the observed wing–leg interval, . We propose that which leg pathway is activated for a given take-off determines the speed of that take-off. Alt., alternate. (B) The latency between wing and leg pathway activation determines take-off steadiness. This model is supported by our data: the graph shows the time between first wing motion and first leg motion plotted against the resulting take-off steadiness S for each fly observed (N=43). Upward-pointing triangles represent voluntary take-offs, while upside-down triangles mark escape responses. The fill color of the upside-down triangles (escapes) indicates the conditions of the wings during take-off, as defined in Fig. 10: black, **Esc. (N=5); white, *Esc. (N=5); gray, Esc. (N=17). The green line is a best-fit linear regression to the data. The line has a positive slope, indicating a direct correlation between and steadiness. (C) Summary of how coordination of the hypothesized pathways leads to the observed differences in take-off performance.

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