Connectocross: statistical characterizations and comparisons of nanoscale connectomes across taxa

Datasets

C. elegans male and hermaphrodite, full body

Notes

• has chemical and gap junction graphs
• has some single-cell transcriptomics
• has cell lineage

C. elegans timeseries, nerve ring

Notes

• time series of graphs (though from different animals)
• 2 animals at the last timepoint
• I have code to pull data

Drosophila larva brain

Notes:

• Have incomplete cell lineage
• I think Marta's lab has some single cell scRNAseq
• Have edge type split by axo, dendrite

Drosophila adult brain chunk (hemibrain)

Drosophila adult brain sparse (FAFB)

Platynereis larva full

MiCRONS

Bryan Jones Retina

Cionia intestinalis

Simple a priori models

a.k.a. look at the data, more or less

Simplest statistics

Things that we always want to know about a graph. Usually:

• Number of nodes
• Number of edges
• For a connectome, maybe number of actual synapses

Density (ER)

• compute the density (p) for each connectome, can simply plot each.

Left/right (SBM/DCSBM)

• Test different hypotheses about $\hat{B}$ (see statistical connectomics)
  • is it more densely connected within block than between? To what extent?
    • maybe can compare this for many of the connectomes. probably not all
  • core-periphery
  • etc.

Left/right + any known metadata (SBM/DCSBM)

• If any putative cell types are known, use those
• now we get a more refined SBM than the above, maybe interesting, maybe not?
  • cell type data may not be available for all of the above
• can do similar tests, results may or may not be different

General low rank (RDPG)

• Scree plots
• estimation of rank (ZG2)
• not sure that this will be interesting to compare across connectome or not. would have to normalize for the number of nodes somehow, i'd think.

Distribution of weights, degrees

• Can just look at distribution of edge weight for each, i guess where weight is number of synapses
• in/out degree distribution, marginals and joint, is easy enough to plot.
  • again, don't know whether it'll be meaningful to compare across connectome or not

More complicated a priori models

Homotypic affinity

• can test for whether cell pairs (or blocks?) are more likely than chance to connect (homotypic affinity)
• requires having cell pairs
  • probably only maggot and c. elegans

Testing left vs right, quantify correlation, spectral similarity, GM performance, etc.

Testing for gaia's directedness (or just quantifying to what extent it happens)

• degree of reciprocal feedback? had thought about something along the lines of testing for the difference between left and right latent positions. but maybe a simpler first statistic to compute is: P(edge from j to i | edge from i to j)

A posteriori models

Spectral clustering and estimating an SBM, DCSBM, DDSBM

• can try to incorporate homotypic affinity also... or correlation L/R
• figure 3 from maggot paper

Feedforward layout and proportion of feedforward edges

Models with biological metadata

Testing for Peter's rule via the contact graph

• is the adjacency a noisy version of the contact graph?
• how does rank change as we jitter xyz of synapses
• could we also just swap synapses in an epsilon ball and see how structure changes?

Spectral clustering that uses morphology

Configuration models that swap synapses within an epsilon ball

Can we cluster edges via connectivity + space?

• had talked about trying to cluster the line graph
• spectral embedding of the line graph looked bad when I tried it. Need to follow up.

Niche models that may not work for all data

Different hypotheses for a multilayer SBM-like model

• maggot data

Matching FAFB and hemibrain or either to maggot

• could be spectral, could be GM
• results maybe bad?
• could use morphology, could not

Spectral coarsening between maggot and adult