Fig. 5. Modulating the scale of network activity.
a, Direct and indirect pathways. S adjusts the magnitude of total input to PFL2 and PFL3 cells. b, Nonlinear activation function. c, Top, model PFL2 bump amplitude and (ΣPFL3R − ΣPFL3L) versus directional error. Bottom, rotational velocity produced by the direct or indirect pathway alone. With both pathways, results are similar to the indirect pathway alone. d, Model: directional error over time. As S increases, the network brings head direction towards the goal (red line). If the indirect pathway is omitted, high S produces overshooting. e, Data: example path during four jumps of the virtual environment, separated by 60 s. The fly corrects for the first jump, but not the rest. The probability of correction typically did not change over time. f, Change in PFL2 membrane potential (ΔVm) before and after each 180° jump, comparing corrected jumps with high ρ (n = 31 of 276 jumps) or uncorrected jumps with low ρ (n = 27 of 276 jumps). Variance in ΔVm is higher for corrected versus uncorrected jumps (P = 0.01363, Brown–Forsythe test). See also Extended Data Fig. 7. g, Same but for PFL3 (n = 60 of 348 corrected, 17 of 348 uncorrected, P = 0.02776). h, Absolute ΔVm and rotational speed during corrected jumps. Mean ± s.e.m., n = 157 of 701 (90°) and n = 91 of 624 (180°), pooling data from PFL2 and PFL3 cells. i, Path of two flies in a virtual environment over 10 min, one with high consistency of head direction (high ρ) and the other with low ρ. j, Spatial profile of PFL2 activity, divided into four bins based on head direction, relative to the directions associated with the highest and lowest PFL2 bump amplitude (darkest and lightest traces, respectively). Data (top) are from the two paths in i. Model results (bottom) are generated by setting S = 0.8 or S = 0.2, producing high or low ρ, respectively, as shown in d. k, Data (top): for each 10 min trial we computed ρ and also analysed the spatial profile of PFL2 activity as in j, taking the difference between the maximum and minimum bump amplitudes. Across trials (symbols), bump amplitude modulation is correlated with ρ (Pearson’s r = 0.37096, P = 1.7 × 10−4, n = 33 flies). Model (bottom): same analysis on model output. Here we obtained a range of model outcomes by varying S and using different random seeds. Scale bars, 5 cm (e,i), 1 s (f). In k, Max., maximum; min., minimum.