Hemibrain and FlyWire head-direction wiring share a ring form: Delta7 inhibition peaks opposite the source, PEN outputs shift 48-58 degrees by side, and a cosine mode pair leads

We tested ring-attractor wiring properties of the fly head-direction circuit in two adult Drosophila connectomes, hemibrain v1.2 and FlyWire v783. We used the EPG, EPGt, PEG, PEN1, PEN2 and Delta7 cell types (152 and 155 neurons). A spectral embedding of ellipsoid body (EB) wiring gave each columnar neuron an angle without labels. In hemibrain it agreed with protocerebral bridge (PB) glomerulus labels (median EPG error 4.9 to 5.6 degrees). In both brains, PB-only wiring followed the EB angles (Spearman -0.84 and -0.72, permutation p < 0.001). PEN outputs in the EB shifted from their PB input angle by +50 to +58 degrees for left-PB neurons and -48 to -56 degrees for right-PB neurons. All 78 PEN neurons with data had the sign of their side. PEG shifts were near zero. The two-step EPG -> Delta7 -> EPG weight in the PB was a cosine of angle difference with its peak at 178 and 176 degrees (R2 0.98 and 0.90, p < 0.001). In a signed linear network of these types, the second and third eigenvalues had cosine eigenvectors over EPG angle (cosine fraction 0.87 to 0.97, against 0.09 when neurons were moved off their angles). The eigenvalue split of this pair was 2.4% and 4.2%. Null result: with hemibrain glomerulus angles, the real neuron-level variation did not make the pair more symmetric than random placement of the same variation (p = 0.28 to 0.39). A low p value with inferred angles came from angle noise in the reference model. Limitations: one fly per connectome, about 4.7 times fewer PB synapses in FlyWire, FlyWire angles only from wiring with unknown reflection, no activity data, and a simple linear model. An exploratory nonlinear bump model failed and gives no evidence. Code, head-direction subsets, results and figures are included.

Drosophila · head direction · ring attractor · central complex · connectome · FlyWire · hemibrain · Delta7 · PEN neurons · EPG neurons · spectral embedding · eigenmodes · cross-animal replication · null result