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The correlation between wing kinematics and steering muscle activity in the blowfly Calliphora vicina

Claire N. Balint^* and Michael H. Dickinson

Department of Integrative Biology, University of California, Berkeley, CA 94720, USA

View larger version (22K): [in a new window]   Fig. 1. Schematic cartoon showing the method of data collection (not drawn to scale). (A) Tethered flies were suspended beneath a piezoelectric crystal in front of a wind tunnel with their left side facing the high-speed video camera. A brass rod was suspended with its base between the fly’s head and the wind tunnel and its upper end between an LED and a position sensor. Four to five pairs of electrode wires were implanted into the left side of the fly’s thorax. (B) Sample simultaneous data traces from five EMG channels, the piezoelectric crystal and framemarks from the high-speed video camera, shown with the kinematic wing elevation angles () digitized and calculated from the concurrent video frames. The phase of each muscle spike was quantified relative to the piezoelectric oscillations as described in the text (see arrows and broken vertical lines).

View larger version (15K): [in a new window]   Fig. 2. Coordinate system for measuring wing kinematics. The polar coordinate angles, deviation () and elevation (), of the wing in each frame were measured relative to the rotated body axis as described in the text.

View larger version (50K): [in a new window]   Fig. 3. Simultaneous steering muscle EMG recordings and kinematic measurements. (A) Diagram of the anatomy of the direct steering muscles recorded in this study. Two additional muscles attached at common sclerites are shown and marked by parentheses. (B) Sample EMG recording during one sequence of visually induced oscillatory turning. Each spike occurrence is reproduced as a raster of dots below each EMG trace. Each spike has been color-coded and is shown overlain on an expanded time base at the right. (C) Total set of wingbeat trajectories filmed simultaneously with EMG recordings in B separated into downstrokes (above) and upstrokes (below). The cross marks the wing base, which served as the origin. The dashed line indicates a wing elevation of –0.2 rad. Downstroke deviation was defined as the wing deviation at the point of intersection of the downstroke trajectory with the dashed line. Stroke amplitude was defined as the maximum anterior wing elevation in each cycle, marked by gray circles. (D) Downstroke deviation and maximum forward amplitude of each cycle plotted as a function of time. Plots in D and B share the same time scale. The gray box in the deviation plot in D indicates the section shown in more detail in Fig. 6.

View larger version (25K): [in a new window]   Fig. 4. Observed spike phases. (A) Composite phase histogram of all muscle spikes, shown relative to the wingbeat cycle. A single histogram is repeated twice to emphasize the cyclic nature of the firing pattern. Spike counts for muscles b2, b1, III1 and I1 came from 21 sequences recorded from nine individuals. Spike counts for III2–III4 came from 15 sequences recorded from five individuals. (B) Sample plot of phase () variation seen in a single sequence over time. The top trace represents the position of the pendulum during the sequence.

View larger version (24K): [in a new window]   Fig. 5. Downstroke deviation and maximum forward amplitude plots from one flight sequence for a fly without implanted electrodes. The pattern of deviation and amplitude modulations in this fly was very similar to that in Fig. 3D. The kinematics of flies with and without electrodes were qualitatively indistinguishable within the range of differences seen among individuals.

View larger version (17K): [in a new window]   Fig. 6. Cycle-by-cycle deviation change. (A) A portion of the downstroke deviations in Fig. 3D seen on a finer time scale, with a raster of muscle spikes (below). Each circle represents the downstroke deviation in a single wingbeat cycle. Circles representing cycles during which a b2 and a b1 spike occurred are black, circles representing cycles during which only a b1 spike occurred are gray, and circles representing cycles during which neither a b2 nor a b1 spike occurred are white. One example of an increase in downstroke deviation, d, from one cycle to the next is outlined in blue, and one example of a decrease in d from one cycle to the next is outlined in red. d,n is the value of the deviation in stroke n and d,n–1 is the deviation in stroke n–1. (B) Each of the downstroke deviation values in A plotted as a function of the value in the previous cycle. The diagonal line indicates d,n=d,n–1. Points above this line represent an increase in d from the previous to the current cycle, and points below this line represent a decrease. The corresponding cycle-to-cycle increase in d outlined in A is indicated here in blue. The corresponding decrease in d outlined in A is indicated here in red.

View larger version (24K): [in a new window]   Fig. 7. Spike-type-dependent regressions of deviation change. (A) Each downstroke deviation measured in three sequences (1105 cycles) of oscillatory turning in a single individual plotted as a function of the downstroke deviation in the previous wingbeat cycle. The color code for circles is as in Fig. 6. The red line is a Model I regression through all black points, the green line is the regression through all gray points and the blue line is the regression through all white points. The diagonal black line indicates d,n=d,n–1. d,n is the value of the deviation in stroke n and d,n–1 is the deviation in stroke n–1. (B) Data points in A re-plotted to show the change in downstroke deviation from one cycle to the next as a function of the starting deviation. The red line is a second-order Model I regression through the black points, and the green line is a second-order Model I regression through the gray points. The blue line is a first-order regression through all white points. (C) Spike-type-dependent regressions as in A shown for eight individuals.

View larger version (21K): [in a new window]   Fig. 8. Downstroke deviation in relation to shifts in firing phase. In all panels, the gray diagonal line represents n=n–1. d,n is the value of the deviation in stroke n and d,n–1 is the deviation in stroke n–1. Firing phase is denoted by color according to the color bar on the right, with blues representing the earliest phases and reds the latest. Black points indicate the occurrence of two spikes within one wingbeat cycle. (A) In the graph on the left, the black circles from Fig. 7A are re-plotted, with each point color-coded according to the firing phase of b2. In the graph on the right, the gray circles from Fig. 7A are replotted, with each point color-coded according to the firing phase of b1. (B) Composite graphs of downstroke deviations in seven sequences from seven individuals. Deviations from cycles in which a b2 and a b1 spike occurred are shown on the left, deviations from cycles in which only a b1 spike occurred are shown on the right, and all points are color-coded according to the firing phase of b2 or b1 as in A. (C) The b1-dependent deviations from B. Regressions through points representing deviation changes following spikes occurring during the first (0–30 %), second (30–60 %) or last third (60–90 %) of the wingbeat cycle produce three nearly parallel lines.

View larger version (32K): [in a new window]   Fig. 9. Patterns of maximum forward amplitude modulations. (A) Maximum forward amplitude (max) modulations during one sequence of visually induced oscillatory turning. Spiking in III2–III4 increased and decreased in frequency following a bursting pattern. For simplicity, III2–III4 was defined as ‘ON’ when spikes occurred at or above wingbeat frequency. The blue points represent the amplitudes measured while III2–III4 fired maximally, and the red points represent the amplitudes measured while III2–III4 did not fire or fired submaximally. Raster plots of the concomitant spike occurrences in b1, III2–III4 and I1 are shown at the bottom. (B) Forward amplitude modulations in the same individual during a flight sequence with no moving visual stimulus. III2–III4 fired at maximal frequency through the entire sequence. All points are colored green to represent constant III2–III4 activity. Raster plots of b1 and III2–III4 are shown as in A. (C) Forward amplitudes from the sequences in A and B plotted as a function of downstroke deviation. The blue and red points represent the blue and red points in A, and the green points represent all points in B. The red points are re-plotted on the right, with black points indicating cycles during which a I1 spike occurred. (D) Relationship between downstroke deviation (d) and forward amplitude in three additional individuals. As in C, blue points represent the two kinematic parameters measured while III2–III4 fired maximally, red points represent parameters measured while III2–III4 fired submaximally, and green points represent parameters measured during a continuous sequence of maximal III2–III4 activity. On the right, the red points are re-plotted, as in C.

View larger version (15K): [in a new window]   Fig. 10. Diagram of the relationship between downstroke deviation and forward amplitude when III2–III4 is active (blue) and when III2–III4 is not active (red). (A) Difference in forward amplitude under these two conditions given the same deviation value. A representative downstroke trajectory corresponding to each point is shown above. (B) Difference in downstroke deviation given the same amplitude value. A representative downstroke trajectory corresponding to each point is shown on the left.