Generative network modeling reveals quantitative definitions of bilateral symmetry exhibited by a whole insect brain connectome
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eLife assessment
This important work demonstrates a significant asymmetry between the connectivity statistics of the left and right hemispheres of the Drosophila larva brain. The evidence supporting the conclusions is compelling and represents a first step toward the development of statistical tests for comparing pairs of connectomes more generally. This work will therefore be of interest to the broad neuroscience community.
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Abstract
Comparing connectomes can help explain how neural connectivity is related to genetics, disease, development, learning, and behavior. However, making statistical inferences about the significance and nature of differences between two networks is an open problem, and such analysis has not been extensively applied to nanoscale connectomes. Here, we investigate this problem via a case study on the bilateral symmetry of a larval Drosophila brain connectome. We translate notions of ‘bilateral symmetry’ to generative models of the network structure of the left and right hemispheres, allowing us to test and refine our understanding of symmetry. We find significant differences in connection probabilities both across the entire left and right networks and between specific cell types. By rescaling connection probabilities or removing certain edges based on weight, we also present adjusted definitions of bilateral symmetry exhibited by this connectome. This work shows how statistical inferences from networks can inform the study of connectomes, facilitating future comparisons of neural structures.
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eLife assessment
This important work demonstrates a significant asymmetry between the connectivity statistics of the left and right hemispheres of the Drosophila larva brain. The evidence supporting the conclusions is compelling and represents a first step toward the development of statistical tests for comparing pairs of connectomes more generally. This work will therefore be of interest to the broad neuroscience community.
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Reviewer #1 (Public Review):
Pedigo et al, apply statistical modeling to a complete brain nanoscale network - a synaptic connectome of an insect brain: the Drosophila larva. They use a series of approaches to explore the symmetry of the right and left hemispheres. First, they compare network densities and find significant differences between the two hemispheres, with the right hemisphere having a higher density. They further grouped neurons by cell type to determine whether the differences were distributed across the entire brain or to specific connections and find the differences involving neurons in the learning and memory center, the mushroom body. Finally, they explored different definitions of an edge by using different thresholds either based on synaptic counts or proportions of synaptic inputs to a downstream neuron and found …
Reviewer #1 (Public Review):
Pedigo et al, apply statistical modeling to a complete brain nanoscale network - a synaptic connectome of an insect brain: the Drosophila larva. They use a series of approaches to explore the symmetry of the right and left hemispheres. First, they compare network densities and find significant differences between the two hemispheres, with the right hemisphere having a higher density. They further grouped neurons by cell type to determine whether the differences were distributed across the entire brain or to specific connections and find the differences involving neurons in the learning and memory center, the mushroom body. Finally, they explored different definitions of an edge by using different thresholds either based on synaptic counts or proportions of synaptic inputs to a downstream neuron and found that when using the proportion of synaptic inputs, removing fewer edges (compared to when using synaptic count) was necessary to achieve left and right symmetry. The presentation of the methodology and writing is very clear and effective and is accessible to scientists from various backgrounds: both biologists and theoreticians. The methodology and approach used in this paper on the assessment of the degree of bilateral symmetry will serve as a basis for comparing networks and connectomes in general by providing a clear framework for statistical network modeling. This work is particularly timely as an increasing number of synaptic connectomes is being generated giving opportunities for various connectome comparisons. It will be of interest to neuroscientists in order to address various biological questions: to evaluate the degree of inter-individual variability/stereotypy of connectivity in the brain and how it relates to behavioral variability/stereotypy, to characterize changes in network connectivity due to different diseases, etc.
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Reviewer #2 (Public Review):
The authors develop statistical tests for assessing whether two hemispheres of the Drosophila larval brain are bilaterally symmetric, and more generally to develop a framework for comparisons of connectomes. The study is organized in order of increasing complexity of the statistical test, beginning with a simple test of whether or not the two sides of the brain have equal connection density. A more sophisticated approach is applied to a model in which neurons are partitioned into groups defined by preexisting known cell types on the left and right hemispheres and densities are allowed to vary between groups (a stochastic block model). A correction is included for an overall difference in density between hemispheres. Finally, analyses are applied to assess which cell types contribute to differences in the …
Reviewer #2 (Public Review):
The authors develop statistical tests for assessing whether two hemispheres of the Drosophila larval brain are bilaterally symmetric, and more generally to develop a framework for comparisons of connectomes. The study is organized in order of increasing complexity of the statistical test, beginning with a simple test of whether or not the two sides of the brain have equal connection density. A more sophisticated approach is applied to a model in which neurons are partitioned into groups defined by preexisting known cell types on the left and right hemispheres and densities are allowed to vary between groups (a stochastic block model). A correction is included for an overall difference in density between hemispheres. Finally, analyses are applied to assess which cell types contribute to differences in the larval connectome. This identifies Kenyon cells as particularly distinct - a density-corrected stochastic block model with Kenyon cells removed results in no significant bilateral asymmetry. Results are also compared across different choices for thresholding of connection weights.
This manuscript tackles an interesting and timely problem. The analyses are largely straightforward applications of standard hypothesis tests for binomially distributed random variables. However, the observation that a density correction is needed to account for the two hemispheres' connection probabilities, and that a stochastic block model is sufficient to describe these probabilities, with the exception of the Kenyon cells, is interesting and makes more precise the notion of bilateral symmetry, at least at the level of connection probabilities, than previous approaches.
There are still several questions that remain about the generality of the results. The first concerns assumptions about the generative model for the graph. As the authors acknowledge, an Erdos-Renyi random network is a strong simplifying assumption. In particular, independent edge weights may be a restrictive model of connectome data given the broad degree distribution, spatial dependencies, and other features that characterize biological connectivity. A second question concerns the issue of statistical power. After partitioning neurons into groups, the most significant difference in connection probabilities comes from Kenyon cells, with the smallest p-value in the density-corrected comparison coming from KC-to-KC connections (Fig. 4B). However, KCs represent a large group of neurons, and the KC-to-KC connection probability is among the highest in the larval brain (Fig. 3B), raising the question of whether the observation of a significant difference specifically for these neurons is simply due to increased power. Third, connection density is only one of the many graph features that may be relevant for evaluating connectome similarity.
In total, although the analyses are straightforward, the study represents a first step toward the evaluation of connectome similarity and should spur further work in this important direction.
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