Passive forces in the fly leg are much stronger than gravitational force.

A1.Experimental set-up. UAS-GtACR1; VGlut-Gal4 flies expressing light-activated anionic channels (GtACR1) under the control of VGlut promoter are rotated. Motor neurons in these flies are inactivated when stimulated with green light. One leg is kept intact, and a weight (blue square) is attached. A2. When a weight (blue arrow) is added, the additional gravitational force is sufficient to elicit a measureable change in leg posture upon inactivation of the motor neurons. B. The two camera views are used to reconstruct the 3D configuration of the leg. The cross placed on the fly’s back (blue cross) is used to align the leg with respect to the body. C. Multiple trials for each body orientation is shown. Body was rotated through five angles from -30 to +30. Each body orientation is shown in different color. Same color scheme will signify body orientation in Figures 1-3. For each orientation, the leg configuration is similar. The leg configuration changes with changes in body angle because the gravitational torque is different.

An angular spring describes the passive torques at each joint.

A.Schematic that describes our analytical framework. As gravity (black arrow) pulls a limb segment away from its rest position (dotted red), passive forces increase linearly until torques due the passive forces balance torques due to gravity (at black dotted line). B. Definition of each of the four degrees of freedom (R=Right, A=Anterior, I=Inferior). C. Equilibrium angle is plotted as a function of body angle and changes with body rotation. Each marker is a separate measurement (n >6). As in Figure 1C, marker color denotes body orientation. D. The gravitational torque around the levation-depression axis was calculated. The torque changes linearly with the joint angle as shown by the large correlation between the levation-depression angle and the passive torque generated to counter gravitation forces.

Passive torques at each of the four joints within a leg are well-described by a linear spring A.

Definition of each of the four degrees of freedom (R=Right, A=Anterior, I=Inferior). Same as Figure 2A. B. Torque-angle relationships for the joints in the mesothoracic leg showing a linear relationship for each degree of freedom. Number of trials between 9-12. C. The passive force spring constant (κ) and equilibrium joint angles for four degrees of freedom for each leg. The red line is the median; the blue lines mark the inter-quartile range. The median values can also be found in Table 1.

Median stiffness for each of the measured joints in mN/º

Ellipsoid radii for each body (μm)

OpenSim model shows that the passive forces are ∼100-fold weaker than the forces required to support the fly.

A. Schematic of the fly in the OpenSim model showing the fly in all three views (Scale bar = 0.5mm). B. Three timepoints of the simulation showing that the fly falls within 20 millisecond. C. Final equilibrium positions of the body at 4 different stiffnesses. D. Height of the CoM as a function of joint stiffness. The x-axis is scaled so that measured stiffness is 1.

Passive forces alone are not stong enough to support the weight of a fly.

A. A schematic of the walking chamber used to collect data about falling experiments. Because we have four views of the fly, the fly’s head could be located in multiple views to extract its position in all three dimensions. B. An example of a falling trial. Light on at t=0. Three frames showing the position of the fly at different times is shown. C. Flies stand at different heights in different trials. Few trials from one fly are plotted - the starting height varies from 0.4 mm to 0.1 mm in this fly. D. Time it takes to initiate a fall depends on the height of the fly. There is a significant correlation between height and time for fall initiation (r2=0.35). E. Apart from the time to initiate a fall, the rate of falling is much slower than that anticipated from immediate dissipation of the active forces (dotted line). F. The distribution of the slopes of the fall. Note that the rate of falling if the active forces dissipated immediately would be 37 mm/s.

The dynamics of the fly’s fall suggest that active forces decay with a timeconstant of ∼100 ms and is consistent with the time-course of motor neuron inactivation.

A. Schematic of the set-up used to evaluate motor neuron inactivation. A DMD projector was used to either shine light on the motor neuron cell body (T), stimulate a non-target area (N), or provide full-field stimulation (F). B. Sample trace from a single-neuron showing that stimulating just the cell-body (left 5 trials) causes similar inhibition as the full field stimulation (right 5 trials). Stimulating regions not including the cell body (middle 5 traces) causes only a small depolarization. C. Time course of hyperpolarization in different motor neurons. D. OpenSim simulations show that an exponential decay with a time constant 100 ms best fits the dynamics of the fall. An exponential decay of 200 ms and 300 ms produces falls that are considerably slower.

Reconstruction errors resulting from the camera calibration are small.

A.To test the accuracy of calibration coefficients obtained from the DLT camera calibration, we used inverse DLT to obtain pixel coordinates from the 3D-reconstructed XYZ leg joint positions and overlaid these points on the corresponding frames. The reconstructed leg segments lie on top of the actual leg.

B.Error distribution across each axis for DLT camera calibrations used for 3D reconstruction of leg kinematics. Error values were obtained by 100 iterations of random subsampling of control points into two sets: The training set for calculating calibration coefficients and the testing set for evaluating prediction accuracy.

C.The error distribution for each camera calibration is well-captured by a normal distribution.

D.We sampled from the Gaussian distribution in C to create 1000 simulated legs. This figure shows 4 randomly selected simulations. The first panel shows the original data, while the other four show randomly selected iterations. The variation in results due to DLT error propagation is small.

E.Final stiffness distributions for levation-depression from all 1000 iterations of DLT error propagation simulations show that variation in results due to DLT error is small.

Larger weight and silencing octopaminergic neurons does not affect spring constant measurements.

A. Standard deviations (SDs) of joint angle values across experimental conditions: x20 etc. refers to the mass of the additional weight. x20, x50, x100 means 20,50,100 times the mass of the leg, respectively. Three masses were used. Tdc2 refers to the case when both glutamatergic and octopaminergic neurons are silenced. Tdc2 experiments were performed with x50 weight. Joint angle SD values per trial for each experimental condition. Probability density functions for trial joint angle SDs by experimental condition. Higher weight reduces the standard deviation. There is no further decrease in SD when both glutamatergic and octopaminergic neurons are silenced.

B.Stiffness values obtained from experiments with higher weights and when octopaminergic neurons are inactivated. The values lie within the interquartile range observed with the smaller weights.

Octopaminergic neuromodulation is silenced optogenetically along with motor neurons using the genetic construct Tdc2-Gal4;UAS-GtACR1(lll) x VGlut(OK371)-Gal4(ll). For all other flies, only motor neurons are optogenetically silenced via the construct VGlut(OK371)-Gal4(ll) x UAS-GtACR1(lll).

Variation in torque can be explained by the coupled actions of multiple degrees of freedom, as well as other internal forces.

A.Examples showing that the angle at one degree of freedom is correlated with residuals (torque that is not explained by changes at the original angle) in other degrees of freedom suggesting that torque variation at one degree of freedom (DOF) may depend on other DOFs. As an explicit example of this analysis, for the leftmost panel in A, we first fit the retraction-protraction torque to the changes in retraction-protraction angle as shown in Figures 2-3. Residuals are calculated as the difference between the actual torque and linear fit and are plotted here against the value of the levation-depression angle on the same torque. A significant correlation is found in >60% of cases implying a coupling between the different angles. Importantly, these correlations are likely to be second-order effects.

B.Using multiple DOF angles to predict levation-depression (LD) torque results in a higher R-squared value than when using only the LD angle. We did not perform this analysis systematically. However, in the 6 flies (just to test the idea), we performed the analysis on we found that there was a much higher correlation when other degrees of freedom were used. Extension-flexion degrees of freedom seem to have a particularly large effect. Levation-depression for two of the flies are shown.