Paper: The fly connectome reveals a path to the effectome

Title: The fly connectome reveals a path to the effectome
Link: https://doi.org/10.1038/s41586-024-07982-0

My takeaways:¹

• The first key idea is to use optogenetic stimulation coupled with bayesian priors based on the connectome to tease out causal relation between neurons (the effectome).
  A nice mathematical definition of the effectome from the paper (which I quite like) is the Jacobian, the partial derivates of voltage of a neuron w.r.t the voltage of every neuron. This is distinctly different from the connectome, effectively pooling the causal effect of voltage changes on one neuron onto another
  However, I got quite confused about the linear simplifications used through most of the paper. There connectome and effectome where used interchangeably.
  Overall, this is a good theoretical idea but I did not get a firm grasp on how to apply it properly so as to perform experiments in a principled fashion. It might be described in the supplementary information, which I am yet to read thoroughly (todo).
• The second key idea is using the connectome to pull out eigencircuits. Assuming a linear first order system (check key assumption below), the weight matrix transforms current neural activity to activity on the next time step. Eigencircuits are eigenvectors of the matrix, where activity just scales by eigenvalue.
  The idea is used to identify several eigenvectors, a couple of which are simulated. The simulations served the purpose of being first-order proof-of-concept simulations. These can be fleshed out better, something I should go back and look into for later (todo).
  Overall, I really like this idea and should try it out on the connectome.

Results:

• (Figure 1) In the presence of confounding variables (Z), causal link between X and Y is not captured when $L_t$ is not present (that is by direct observation), especially when ${ϵ}_t$ is correlated between neurons. Adding $W_{l,x}{L}_t$ allows the effectome to be estimated even in the presence of correlated input.
• (Figure 2) When simulating the entire brain with different plausible effectomes (with IID noise and stimulation), a simple IV based linear estimator will converge slowly than a IV-Bayes estimator with the fly connectome as a prior. Particularly, IV-Bayes will estimate weights (especially zero weights) with low residual error.
  • Needs individual control over all neurons to identify the effectome.
  • Sparse control of a subset of neurons allows identification of the effectome across multiple flies.
  • For continuous voltage, firing rate models, IV-bayes converges to the Jacobian of the model (which is essentially the voltage change per neuron for activations of other neurons). The argument made in the discussion is that this true effectome, which makes sense as it captures the causal effect of one neuron on all others. The linear simulation is the special case, I felt it made things a lot more confusing as it muddled connectome weights from effectome (which are different in the continuous case).
  • IV-Bayes estimates the effectome in cases of correct prior (connectome close to effectome), incorrect prior and naive bayes. The convergence of all three depends on the constant added to the prior variance (maybe except naive bayes?).
  • IV-Bayes also converges to the first-order effectome matrix in a higher-order auto-regressive model.
• (Figure 3) Eigendecomposition of the effectome showed that the fly neural dynamics is high dimensional and the top eigenvectors are sparse with non-overlapping groups of neurons in the first 10 eigenvectors.
  • The weight matrix is broken down into eigenvalues and eigenvectors. $W=Q\Lambda Q^{-1}$ $Q$ is the eigenvector and $\Lambda$ is the corresponding eigen value.
  • Eigenvalues decayed slowly. This indicated the dimensionality of the weight matrix is quite high (a lot of independent vectors). If the dimensionality was low, many of the eigenvalues should have been expected to be zero.
  • Eigenvalues span the whole complex space. All of them are less than 1 (as expected for stable dynamics). Some are positive indicating steady decay. Some have an imaginary value, indicating oscillation. And some have -ve, indicating a change in sign every timestep. They interpret this as rotational dynamics, which is a bit weird.
  • Correlation of eigenvectors (guessing dot product) is low for the first few values and then increases as the rank increases to 1000. This indicated that the initial few orthogonal vectors had non-overlapping groups of neurons, and as the rank increased neurons were part of multiple independent eigenvectors.
    Note that despite the correlation between eigenvectors, these are still eigenvectors - all this means that the same neuron is part of different independent circuits.
  • The first 10 are more or less independent from each other (low correlation) and as the rank increases the correlation go up. The number of neurons needed to account for 75% power of the loadings is still less than 10% of the total neuron number.
  • Example anatomical eigenvectors provided:
    • visual eigenvectors from the left and the right lobular plate neuron
    • olfactory eigenvectors from the mushroom body neurons, projection neurons and he lateral horn neurons.
    • eigenvectors linked to motor and navigational circuits.
  • Supplementary figures
    • top eigenvectors/eigencircuits were sparse and generally early eigencircuits were robust to noise.
    • anatomically localized eigencircuits were a minority (~10% of the top 100 eigencircuits).
• (Figure 4) Picking two of the several eigencircuits, they show either recent result or hypothesized result, validating the use of this method to generate testable hypothesis of circuits.
  • opponent motion across fly eyes
  • ring neuron WTA circuit

Key Assumption: For the causal results, the fly brain dynamics is assumed to be first-order vector auto-regressive model. That is, the activity of neurons in $t$ only dependent on $t-1$). $r_t=W{r}_{t-1}+W_{l,x}{L}_t+{ϵ}_t$The effectome goes out as $W$ with the laser stimulation as $W_{l,x}$ as the laser stimulation, $L_t$ as the time of stimulation and ${ϵ}_t$ represents noise and can be correlated between neurons.

My drawings:

Footnotes

1. Disclaimer: this is my understanding. Please correct me if I have misunderstood something. ↩