Introduction to Connectomics

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Introduction to Connectomics

Module 7 · EN.585.781 Frontiers in Neuroengineering

Will Gray Roncal · Johns Hopkins University

Part A — The case for mapping
Part B — Three scales that are not the same thing
Part C — The field as it stands

Human cortex · H01
Object segmentation over electron microscopy

H01 release · Lichtman Lab / Harvard & Connectomics at Google
Image: CC BY 4.0 · Shapson-Coe et al. (2024) · doi:10.1126/science.adk4858
Lecture: CC BY-SA 4.0 · neurotrailblazers.org

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Where this module sits

Three modules, one argument: measure it, build it, use it

The through-line is the same in all three: a connectomics result is a measurement with a stated sampling, a stated error rate, and a stated non-claim. Everything else is illustration.

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The discovery pipeline

One path from question to claim. Every technique in these three modules sits on it.

   QUESTION        SPECIMEN         IMAGE           RECONSTRUCTION      GRAPH        CLAIM
      |               |               |                   |              |            |
  measurable      fixation        alignment          segmentation    node/edge      null
   endpoint       staining        ingest             proofreading    definition     model
   null model     sectioning      storage            synapses        inclusion      error band
   non-claim      imaging         serving            versioning      boundary       non-claim
      |               |               |                   |              |            |
  -- Module 7 --  -------- Module 8 --------   ----------- Module 9 -----------

Every stage adds a decision that changes the answer, and every stage has a characteristic failure. The three modules walk the pipeline once, in order.

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Learning objectives

By the end of Module 7 you will be able to:

7.1 — Explain the scope of connectomics across macro-, meso-, and nanoscale.

7.2 — Differentiate the three scales by resolution, volume, and the claims each can support.

7.3 — Classify a connectivity claim as supported by structure alone, supported by structure plus a declared assumption, or not supportable by structure.

7.4 — Communicate the current challenges and opportunities in connectomics to a technical audience without overclaiming.

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Roadmap

Three parts, roughly fifty minutes each

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Part A

The case for mapping

• The resolution argument, in numbers
• The cost argument, in numbers you can compute
• What structure can and cannot establish

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A connectome, defined

A map of the connections in a nervous system, at a stated resolution, from a stated sample

What it is. A graph whose nodes are neurons (or cell types, or compartments) and whose edges are measured connections, derived from imaging a physical specimen.

What it is not:

• Not a set of synaptic weights — synapse count is a proxy for strength, not a weight.
• Not a set of dynamics — it is one animal, at one moment, fixed.
• Not a runnable brain — the map constrains the space of possible dynamics; it does not simulate them.
• Not one thing — "connectome" names three different measurements at three scales that are routinely conflated. That conflation is Part B.

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Why map: the question types only structure can answer

The "why" of connectomics, stated as a list rather than an enthusiasm

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Vocabulary that will recur for three modules

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Three claims about the same circuit.

Which one does a wiring diagram support?

1. "Neuron X makes 42 synapses onto neuron Y."
2. "Neuron X strongly excites neuron Y."
3. "This circuit computes heading direction during navigation."

Hold your answer. We come back to this in eleven slides.

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The resolution argument

Connectomics exists because of a physical mismatch

Electron microscopy at 4 × 4 × 40 nm resolves every row. That is the entire reason the field tolerates the cost on the next slides.

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Overlap is not connection

The consequence is specific, not general

Light microscopy can tell you that two neurons' arbors occupy the same space. It cannot tell you they are connected, because at 250 nm two membranes 20 nm apart are one blur.

In dense cortical neuropil a 1 µm³ box contains on the order of a dozen distinct neurites. Below the diffraction limit they are indistinguishable.

A colleague proposes confocal imaging of sparsely labeled neurons to "map the connectome" of a cortical column. Strongest single objection?

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What EM buys, and what it does not

Resolving a synapse is not the same as knowing what it does

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Calling a synapse: the three criteria

What "we observed a synapse" actually means, operationally

An anatomical synapse is called on converging independent evidence, not on one cue:

1. A presynaptic vesicle cluster — a pool of ~40 nm vesicles gathered at the membrane, not scattered through the cytoplasm.
2. A synaptic cleft — a consistent ~20 nm gap with visible density in it, held parallel over the apposition.
3. A postsynaptic specialization — a thickened, electron-dense band on the receiving side (the postsynaptic density).

Gray type I vs type II. Asymmetric, prominent PSD, round vesicles → putatively excitatory. Symmetric, thin PSD, often flattened vesicles → putatively inhibitory. Note the word "putatively": this is the Bin B assumption from three slides ahead, and it is the single most common unstated assumption in the literature.

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The cost argument

Arithmetic you should be able to do in your head

Raw voxel count = volume ÷ voxel volume. Take 1 mm³ of cortex at 4 × 4 × 40 nm:

x: 1 mm / 4 nm   = 1,000,000 nm / 4 nm  = 250,000 voxels
y: 1 mm / 4 nm   =                        250,000 voxels
z: 1 mm / 40 nm  = 1,000,000 nm / 40 nm =  25,000 voxels

total = 250,000 x 250,000 x 25,000      = 1.56 x 10^15 voxels

At 8-bit grayscale: ~1.56 petabytes of raw image data for one cubic millimeter — before alignment, before segmentation, before meshes, before any derived product.

Published petascale volumes land here. H01 (human temporal cortex) and MICrONS (mouse visual cortex) are both roughly 1 mm³ and both are reported in the 1.4–2 PB range, depending on what is counted and how it is compressed.

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Now extrapolate, and notice where it breaks

NIH BRAIN CONNECTS (first awards 2023) exists because that 500× is an engineering program, not a microscope purchase.

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Check yourself

You are offered beam time for 0.05 mm³ of mouse hippocampus at isotropic 8 nm (FIB-SEM). How much data, and what changes?

voxel volume = 8 x 8 x 8 = 512 nm^3
0.05 mm^3    = 5 x 10^16 nm^3

5e16 / 512   = ~1 x 10^14 voxels
             = ~100 TB

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What structure can and cannot establish

Sort every claim you plan to make into one of three bins

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Bin A — structure alone is sufficient evidence

• "Neuron X makes 42 synapses onto neuron Y." Direct anatomical observation.

• "Cell type A targets the proximal dendrites of type B, while type C targets distal dendrites." Compartment targeting is measured, not inferred.

• "Reciprocal pairs occur 4× more often than expected under a degree-preserving null model." A structural statistic — against a stated null. Drop the null and it leaves Bin A.

• "This projection does not exist in this volume." A negative result — with a stated detection sensitivity. Drop the sensitivity and it is not a claim at all.

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Bin B — structure plus one declared assumption

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Bin C — structure cannot establish this

• "This circuit computes X during behavior Y." → requires physiology
• "This synapse is potentiated." → requires a functional or molecular measure
• "This wiring causes the animal's decision." → requires perturbation
• "Neuromodulatory state Z reconfigures this circuit." → volume transmission is largely invisible in a standard EM volume

This is not a counsel of despair. Bin C claims are answerable — with a second measurement. MICrONS exists precisely because someone decided to co-register two-photon physiology with the EM volume. The move is to add the measurement, not to soften the verb.

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Back to the cold open.

Claim 3 is true of the fly central complex. It took the connectome plus a decade of physiology. The connectome alone could not have established it — and did not.

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Worked example: repairing a research question

Version 0 — "We will use connectomics to understand how the cortex implements predictive coding."

Bin C, no measurable endpoint, no result could falsify it. Four moves to repair it:

1 — Find the structural signature. Predictive-coding architectures require asymmetry between feedforward and feedback pathways. Candidate signature: feedback axons from higher visual areas target a different dendritic compartment of L2/3 pyramidal cells than feedforward L4 inputs do.

2 — Define the measurement, with units. Per proofread L2/3 pyramidal cell, the fraction of input synapses by presynaptic source class, binned by path distance from soma (0–50, 50–150, 150–300, >300 µm) and by compartment (spine head, neck, shaft, soma, AIS).

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Worked example, continued

3 — State the null. Sources are distributed across compartments in proportion to available postsynaptic surface area.

4 — Write the non-claim. "These data constrain where feedback input arrives on the dendritic tree. They do not establish that these synapses carry prediction-error signals, and they do not establish sign."

Version 1 can be answered, can be wrong, and can be scoped in a grant.

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Sizing the claim to the reconstruction

A structural claim is only as good as the completeness behind it

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Part A checkpoint — four things to stop believing

"Higher resolution is always better." No. The rule is the coarsest scale whose reconstruction resolves your analysis unit.

"If two neurons touch, they probably connect." Contact predicts connectivity poorly, and non-uniformly by cell type.

"The connectome tells you the circuit's function." It constrains the space of possible dynamics. Function needs a second measurement.

"Segmentation errors just add noise." Merges bias results toward dense motifs — the direction of the interesting answer.

Break. When we come back: why "connectome" names three different measurements.

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Part B

Three scales that are not the same thing

• Acquisition, reconstruction, and analysis scale
• The modality chart and the tradeoff triangle
• Representations, and cross-scale linkage

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Three scales practitioners routinely conflate

Separating them prevents most downstream confusion

Acquisition scale — the voxel size and field of view your instrument produces. Set by physics and budget. Fixed once the data exists.

Reconstruction scale — the smallest object you can reliably segment. Always coarser than acquisition scale, sometimes much coarser. At 4 × 4 × 40 nm you acquire enough signal to see a 20 nm cleft, but you can reliably segment neurites down to roughly 50–100 nm — and reliability drops sharply for processes running steeply through z.

Analysis scale — the unit your conclusions are about: a synapse, a cell, a cell type, a layer, an area, a projection.

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The decision rule, applied

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The modality chart

Ranges are typical rather than record-setting. Learn the shape of this table, not the digits.

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The tradeoff triangle

Resolution, volume, throughput — you may choose two

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Different tools for different jobs

Two scales we will not cover — and why naming them still matters

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Mesoscale: projections without synapses

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Nanoscale: the volume EM family

The only scale that observes synapses directly

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Scale leakage

A claim measured at one scale, asserted at another, with the sampling silently dropped.

This is the single most useful idea in Part B, and it costs nothing to apply. Registration residuals (four slides on) are the quantitative version of the same discipline.

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Representations: what each one throws away

The same neuron exists in four representations, and conversions are lossy and one-way

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Which representation for which question

Transferable principle: choose the representation whose native operation is your endpoint metric; reject coarser candidates by naming the discarded quantity that disqualifies them; archive the next-richer one specifically to bound the bias.

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Cross-scale linkage: registration and its residuals

Where confident-looking errors are manufactured

1. Choose anchors. Vasculature is the best EM↔LM anchor in cortex: sparse, high-contrast in both modalities, distributed, biologically stable. Somata are second. Layer boundaries are weak — gradual and observer-dependent.

2. Fit the lowest-complexity transform that works. Rigid → affine → non-linear, in that order. A sufficiently flexible warp will align anything, including things that do not correspond.

3. Report residuals locally. A 3 µm mean over the whole volume can hide a 40 µm error in one corner. Report a residual map, or per-region distributions with the maximum.

4. Hold out anchors. Fit on a subset, measure on anchors the fit never saw. A model evaluated on its training points reports its flexibility, not its accuracy.

5. Propagate the uncertainty. 5 µm residual, somata 15 µm across and sometimes 10 µm apart → some assignments are wrong. Quantify how many; carry that number into the result.

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Check yourself, and one standing warning

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Part B checkpoint — the five-minute scale audit

Apply this to your own question before Part C

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Part C

The field as it stands

• What has actually been delivered, 1986 to 2025
• Where to get the data
• The open problems worth your attention

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Eight streams the field moves along

Progress is not one curve. Read any new paper by asking which stream it advances.

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Forty years in one table

Stream numbers refer to the previous slide. Bold marks the stream each milestone principally advanced. Compiled from the NeuroTrailblazers connectomics evidence map; DOIs on the references slide.

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C. elegans, and its useful negative lesson

302 neurons, complete since 1986 — and it did not immediately explain behavior

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Drosophila: from one brain to a community resource

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Mouse and human at 1 mm³

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Structure → function: three results that actually landed

The strongest form of connectomics result available today

1. Retinal direction selectivity (Briggman 2011; Kim 2014). Reconstruction showed that starburst amacrine cell inhibition onto direction-selective ganglion cells is organized by space–time wiring specificity — a structural asymmetry that predicts the computation. Structure gave the mechanism; physiology confirmed it.

2. The fly central complex as a ring attractor. The connectome showed a ring of heading-tuned cells with the recurrent and inhibitory architecture a ring attractor requires. The theory pre-existed; the wiring made it a specific, testable claim about identified cells.

3. Connectome-constrained models (Lappalainen et al. 2024). Fix a network model's connectivity to the measured fly visual connectome, fit only the remaining parameters, and the model predicts neural responses that were then tested.

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Comparative connectomics: the underrated frontier

Comparison controls for reconstruction biases that a single measurement cannot

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Where to get the data

Module 8 covers the storage formats and query APIs behind all of these, and Module 8's assignment is a reproducible query against one of them.

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Open problems worth your attention

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How fast is the field actually moving?

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Human tissue: provenance is an interpretive fact

Not a compliance footnote

Where human samples come from. Surgical resections — most often epilepsy surgery — and postmortem brain banking. Both carry consent frameworks, and both carry biology.

What this means for how you write. State the provenance in the results, not the supplement. "Human temporal cortex (surgical resection, epilepsy)" is the honest noun phrase. "Human cortex" is not.

And for how you read. When a comparative claim runs mouse-versus-human, ask whether the human sample's clinical history could produce the difference. Often it cannot be excluded — and saying so is part of doing this work credibly.

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How to read a connectomics paper

A checklist you can apply in ten minutes

1. What is the sample? Species, region, n, provenance, fixation. Is n = 1?
2. What resolution, and what was the reconstruction scale? Not the same number.
3. What fraction is proofread, and to what standard? "Proofread" is not binary.
4. How was the graph built? Synapse threshold, inclusion criteria, boundary handling. (Module 9 Part B.)
5. Which materialization version? If the paper does not say, its numbers are not reproducible. (Module 8 Part C.)
6. What is the null model? For any enrichment or preference claim.
7. What error rates are reported, and how do they propagate to the headline number?
8. Sort the abstract's central claim into Bin A, B, or C. Then check whether the results section supports that bin.

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Part C checkpoint — what a good answer sounds like

Every right-hand phrasing is *shorter on certainty and longer on information.* That trade is the whole professional skill.

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Discussion forum — this week

Post by Wednesday, respond to two classmates by Sunday

Prompt 1 — Bin sorting. Find one connectomics paper published in the last two years. Quote its central claim verbatim. Sort it into Bin A, B, or C, and say what evidence would be needed to move it one bin stronger. Be fair to the paper — quote the claim as written, not as you would summarize it.

Prompt 2 — Scale matching. Describe a brain question from your own area. Name the analysis scale, then the reconstruction scale it forces, then the modality. If the answer is not EM, say so — the decision rule rewards the coarsest scale that works.

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Module 7 assignment

Five short-answer questions plus a study brief. Due before Module 8.

Short answer (5 questions). Resolution arithmetic; the extrapolation table; a Bin A/B/C sort; a modality choice with justification; a registration-residual interpretation.

Study brief (the graded artifact). One page, on a question you care about:

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What to bring to Module 8

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References and sources

Landmark datasets. White et al. 1986 (C. elegans); Cook et al. 2019 (10.1038/s41586-019-1352-7); Witvliet et al. 2021 (developmental series); Briggman et al. 2011 (retina); Helmstaedter et al. 2013 (IPL); Kim et al. 2014 (10.1038/nature13240, EyeWire); Kasthuri et al. 2015 (saturated reconstruction); Hildebrand et al. 2017 (larval zebrafish); Zheng et al. 2018 (FAFB); Scheffer et al. 2020 (10.7554/eLife.57443, hemibrain); Shapson-Coe et al. (H01); Winding et al. 2023 (larval CNS); Dorkenwald et al. 2024 (FlyWire); MICrONS Consortium 2025 (10.1038/s41586-025-08790-w).

Methods and modalities. Denk & Horstmann 2004 (10.1371/journal.pbio.0020329, SBF-SEM); Knott et al. 2008 (10.1523/JNEUROSCI.3189-07.2008, FIB-SEM); Bock et al. 2011 (10.1038/nature09802, TEMCA); Eberle et al. 2015 (10.1111/jmi.12224, multibeam); Xu et al. 2017 (10.7554/eLife.25916, long-run FIB-SEM); Phelps et al. 2021 (10.1016/j.cell.2020.12.013, GridTape); Kievits et al. 2024 (10.1515/mim-2024-0005, FAST-EM); Tavakoli et al. 2025 (10.1038/s41586-025-08985-1, LICONN); SmartEM 2025 (10.1038/s41592-025-02929-3).

Analysis and modeling. Milo et al. 2002 (10.1126/science.298.5594.824, motifs); Bassett, Zurn & Gold 2018 (model taxonomy); Lappalainen et al. 2024 (10.1038/s41586-024-07939-3, connectome-constrained models); Abbott et al. 2020 (10.1016/j.cell.2020.08.010, "The Mind of a Mouse").

Course material. NeuroTrailblazers technical training Units 01, 02 and the connectomics evidence map. https://neurotrailblazers.org

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Use, adapt, and credit

These slides are openly licensed for community use

Cover image: H01 release, Lichtman Lab / Harvard & Connectomics at Google, CC BY 4.0. Shapson-Coe et al. (2024), doi:10.1126/science.adk4858. The image retains its own licence. Cited papers carry their own licences; citation is not reproduction.