Demos from my Connectomics MCP

Great question! The fruit fly's path integration circuit is a beautiful example of neural computation. Let me query the hemibrain connectome for the key cell types involved in the path integration circuit. The core players are:

1. EPG neurons — the head direction "compass" cells forming the ring attractor in the ellipsoid body
2. PEN neurons — angular velocity integrators that shift the compass bump
3. PFN neurons — carry velocity signals for path integration
4. hDelta neurons — fan-shaped body interneurons that perform the vector computation

Let me pull all of these in parallel.

I have the EPG neurons - 46 of them spanning positions L1-L8 and R1-R8 in
the protocerebral bridge, corresponding to the 16 glomeruli that map to the
ring attractor. Now let me pull connectivity for representative neurons from
each key type.

Key finding: PEN neurons receive their strongest input from GLNO
(Gall/Nodulus) neurons, which carry angular velocity signals. Let me analyze
the PEN connectivity and find PFNd/hDeltaB neuron IDs from the existing data.

## Path Integration Circuit in the Fruit Fly Central Complex

Based on connectivity data from the hemibrain connectome, here's how the fly's path integration circuit works, organized by its three functional modules:

### Module 1: Head Direction Ring Attractor (Ellipsoid Body)

EPG neurons (46 neurons) are the compass cells. They tile 16 glomeruli of the protocerebral bridge (L1-L8, R1-R8), which map onto the ellipsoid body ring. A single bump of activity encodes the fly's current heading.

The ring attractor is maintained by three interacting cell types:
1. EPG → Delta7 (~550 per target cell): Strongest EPG output; Delta7 provides global inhibition across the ring to keep exactly one bump.
2. EPG ↔ EPG (~215 cell): Recurrent excitation stabilizes the bump.
3. ER  → EPG (~330-370/cell): Visual landmark input (ER4m, ER4d, ER2_c) anchors the bump to the world.

### Module 2: Angular Velocity Updates the Compass

PEN_a (PEN1) (20 neurons) and PEN_b (PEN2) (22 neurons) shift the bump when the fly turns:
1. GLNO → PEN_a (~318/cell): Angular velocity signal from the noduli — this is the rotation input!
2. PEN_a → EPG (~722/cell): Massive drive; PEN connects with a 1-column offset in the protocerebral bridge, so activity shifts the EPG bump left or right.
3. EPG → PEN_a (~299/cell): Feedback: the compass tells PEN where the bump currently is.

PEN_a and PEN_b shift the bump in opposite directions. When the fly turns right, one type is activated more, pushing the bump clockwise; turning left activates the other, pushing counterclockwise. The GLNO neurons from the noduli provide the angular velocity magnitude.

### Module 3: Translational Velocity → Position Integration (Fan-shaped Body)

This is the actual path integration — converting "how fast am I going in what direction" into "where am I":
1. LNO2 → PFNd (~162/cell): Translational velocity signal from the noduli (distinct from the angular velocity GLNO signal!).
2. Delta7/EPG → PFNd (~233 + 55/cell): Head direction information
3. PFNd → hDeltaB (~340/cell): PFNd combines heading × velocity; hDeltaB is the dominant recipient.
4. hDeltaB → PFR_aPFR_b/FR1 (~400/394/314 per cell): Output to steering neurons.

PFNd acts as a multiplier: it receives both heading (from EPG/Delta7) and speed (from LNO2), producing a velocity vector in an allocentric (world-centered) reference frame.

hDeltaB (19 neurons) is the integrator: it accumulates these velocity vectors over time in the fan-shaped body columns. Its overwhelmingly dominant input is PFNd (806 synapses from 18 PFNd neurons), making it essentially a dedicated readout of the heading-weighted velocity signal.

### Key Insight: Two Coupled Rings

The circuit uses two distinct ring-like representations:

1. Ellipsoid body ring (EPG + PEN + Delta7): a classical 1-D ring attractor encoding head direction. Angular velocity from GLNO rotates the bump. Visual landmarks from ER neurons anchor it.

2. Fan-shaped body columns (PFNd → hDeltaB): a columnar array encoding an integrated position vector. Each PFNd neuron carries velocity weighted by its preferred heading, and hDeltaB accumulates this over time.

The bridge between them is PFNd, which reads the compass (EPG/Delta7) and the speedometer (LNO2) to produce heading-weighted velocity — exactly the signal you need to integrate for path integration.

Would you like me to go deeper into any part of this circuit — for example, examining the column-by-column offset structure of PEN→EPG connections, or looking at how the output PFL neurons compare the goal vector with current heading?

## Results: Orientation Tuning of BC-Inhibited Pyramidal Neurons

### The short answer: functionally diverse, not clustered — but with subtle differences from controls.

### Orientation Preference
- Both BC targets and neighborhood controls show a strong cardinal bias peaking at ~90° (vertical/horizontal orientations), which is typical of mouse V1.
- The distributions are broadly similar, but BC targets (n=2,562) have a slightly tighter concentration around 72–108° (KS test p = 7×10⁻⁵). The circular variance confirms this: 0.69 for BC targets vs. 0.76 for controls — the BC targets are slightly less diverse in their orientation preferences.

### Selectivity Indices
| Metric | BCs         | Control     | Signif.   |
|--------|-------------|-------------|-----------|
| gOSI   | 0.23 ± 0.13 | 0.22 ± 0.13 | p = 0.005 |
| OSI    | 0.42 ± 0.20 | 0.40 ± 0.20 |           |
| DSI    | 0.23 ± 0.16 | 0.24 ± 0.17 |           |

BC-targeted pyramidal neurons are marginally more orientation-selective (higher gOSI/OSI) and slightly less direction-selective (lower DSI) than their neighbors (control, n=2,505, Mann-Whitney U-test). The effects are statistically significant given the large sample sizes but modest in magnitude (~5% relative difference).

### Per-Basket-Cell Diversity
The bottom-right panel shows that every individual basket cell targets a diverse pool of orientations (circular variance 0.65–0.80 across all 5 BCs) — none of them selectively inhibits a single orientation column.

### Interpretation
This is consistent with the known physiology of PV+ basket cells in mouse V1: they provide broad, non-selective perisomatic inhibition (the "blanket of inhibition" model). Each BC contacts thousands of local pyramidals spanning the full range of orientation preferences. The slight enrichment in orientation selectivity among BC targets may reflect that basket cells preferentially contact neurons with stronger sensory drive — which would make them better targets for gain control — but the effect is subtle. These BCs are not carving out orientation-specific subnetworks; they are performing divisive normalization across the local population.

## Martinotti Cell Pathway: Key Findings

### MC vs BC: Strikingly similar — but with a critical structural difference

The MC and BC pathways are functionally indistinguishable (KS tests: pref_ori p=0.88, gOSI p=0.99, DSI p=0.43). Both populations show:
- Circular mean orientation ~82°, broad cardinal bias
- Mean gOSI ~0.23, mean DSI ~0.22–0.23
- High circular variance (0.68–0.69) — diverse, not clustered

### The massive overlap is the real story

2,293 out of 3,226 MC-targeted L2/3 neurons (71%) are also targeted by the BCs. These two inhibitory pathways converge onto a largely shared pyramidal population, Shared (MC+BC). Breaking the targets into exclusive vs shared groups reveals a gradient:

| Group   | n     | gOSI  | CirVar | DSI   |
|---------|-------|-------|--------|-------|
| Shared  | 1,630 | 0.235 | 0.660  | 0.224 |
| BC-only | 932   | 0.226 | 0.754  | 0.237 |
| MC-only | 610   | 0.216 | 0.725  | 0.216 |
| Control | 1,970 | 0.219 | 0.743  | 0.247 |

The shared targets — neurons receiving convergent MC and BC inhibition — are the most orientation-selective (highest gOSI) and the most coherently tuned (lowest circular variance, CirVar). MC-only and BC-only targets look more like the general population.

### Interpretation

Both the Martinotti and basket cell arms of this disinhibitory circuit target a largely overlapping, functionally diverse pool of L2/3 pyramidals — but the neurons that sit at the intersection of both inhibitory streams are slightly but consistently more tuned. This is consistent with a model where the most visually driven neurons in the local population receive the strongest inhibitory regulation from both dendritic (MC) and perisomatic (BC) compartments. The ITC disinhibitor, by releasing both brakes simultaneously, would preferentially boost these well-tuned neurons — a form of feature-selective gain modulation emerging from a structurally non-selective circuit.

## The control

The control is a random sample of L2/3 pyramidal neurons from the same spatial neighborhood that are not targeted by any of the 5 BCs or 5 MCs in this analysis. "Same spatial neighborhood" is defined as neurons whose soma positions fall within ±2 standard deviations of the BC/MC target population's centroid in the x and z dimensions (the tangential cortical axes), without filtering on y (depth axis, which would conflate laminar identity with spatial proximity).

This controls for:
- Laminar identity (all are 23P)
- Retinotopic position (same cortical patch, so similar visual field coverage)
- Imaging coverage bias (same region is likely covered by the same 2-photon sessions)

## Does the Shared group need a separate control?

Yes, arguably it does, and the current analysis has a confound. The issue is:

Neurons targeted by more interneurons are, by definition, more synaptically connected. A neuron that receives convergent BC+MC input likely has a larger dendritic arbor, more total synapses, or sits in a denser part of the neuropil. These are neurons that are more "visible" to the connectome — and being more connected could correlate with being more visually driven (higher firing rates → more orientation selectivity) for purely structural reasons, not because of any specific circuit logic.

A proper control for the Shared group would be L2/3 pyramidals that are:
1. In the same spatial neighborhood
2. Matched in total inhibitory synapse count (or total postsynaptic count) — i.e., they receive a comparable amount of inhibition, just not from these specific MCs and BCs
3. Not targeted by any of the 10 interneurons in this analysis

Without that, the gOSI difference in the Shared group (0.235 vs 0.219 in control) could simply reflect a connectivity-selectivity correlation: neurons with more synaptic partners tend to be more orientation-selective because they're larger, healthier, or better-proofread neurons in the EM volume.

After matching controls on neuron volume (a proxy for total connectivity/arbor size), the picture changes substantially from the original analysis:

### Orientation Selectivity (gOSI): No longer significant

The gOSI differences we saw earlier do not survive volume matching. The Shared group's elevated selectivity (which looked interesting before) shrinks to a non-significant trend (p = 0.10, d = +0.08). This suggests the original effect was at least partly driven by the connectivity-selectivity confound we anticipated.

### Direction Selectivity (DSI): Robust and real

The one signal that does survive is in direction selectivity — all three target groups show lower DSI than their volume-matched controls (Shared: p = 1.3×10⁻⁴, MC-only: p = 4.2×10⁻³, BC-only: p = 8.8×10⁻³). These interneurons preferentially target pyramidal neurons that are less direction-selective than their neighbors of the same size.

### Orientation preference (CirVar): Only the Shared group shows tighter tuning

The tighter clustering of preferred orientation survives in the Shared group (CirVar 0.660 vs 0.764, KS p = 3.2×10⁻⁴) but not in MC-only (p = 0.80) or BC-only (p = 0.58). This means the orientation coherence is specific to the neurons receiving convergent MC+BC inhibition — not a generic property of being targeted by any one interneuron.

### Bottom line

The volume-matched controls reveal that:
1. The gOSI enrichment was largely a connectivity confound — more-connected neurons tend to be more orientation-selective, and that explained most of the effect.
2. The DSI depression is real — these interneurons preferentially target orientation-tuned but not direction-tuned pyramidals, regardless of neuron size.
3. The orientation coherence in the Shared group is the one genuinely circuit-specific signal — neurons at the intersection of dendritic (MC) and perisomatic (BC) inhibition share more similar orientation preferences than you'd expect by chance, even after controlling for volume.