Learning dynamic representations of the functional connectome in neurobiological networks

TL;DR

Dynamic functional connectomes in neurobiological networks are time-varying and state-dependent, not captured by static connectivity. The authors propose an unsupervised pipeline that computes time-varying instantaneous affinities $a_{ij}^{(t)}$ from calcium traces and decomposes a time x worm x pairwise-affinity tensor with non-negative tensor factorization to extract affinity patterns $f_a$, temporal loadings $f_t$, and worm loadings $f_w$, followed by nested weighted SBM to reveal dynamic neuronal communities, demonstrated in C. elegans with validation. The approach identifies biologically meaningful motifs, including salt-sensing and attractant-associated modules, and a targeted AWB silencing experiment supports predictive power. The framework is generalizable to other species and domains (e.g., fMRI and social networks) where time-varying interaction motifs govern behavior.

Abstract

The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors at different times. We introduce an unsupervised approach to learn the dynamic affinities between neurons in live, behaving animals, and to reveal which communities form among neurons at different times. The inference occurs in two major steps. First, pairwise non-linear affinities between neuronal traces from brain-wide calcium activity are organized by non-negative tensor factorization (NTF). Each factor specifies which groups of neurons are most likely interacting for an inferred interval in time, and for which animals. Finally, a generative model that allows for weighted community detection is applied to the functional motifs produced by NTF to reveal a dynamic functional connectome. Since time codes the different experimental variables (e.g., application of chemical stimuli), this provides an atlas of neural motifs active during separate stages of an experiment (e.g., stimulus application or spontaneous behaviors). Results from our analysis are experimentally validated, confirming that our method is able to robustly predict causal interactions between neurons to generate behavior. Code is available at https://github.com/dyballa/dynamic-connectomes.

Figures (8)

• Figure 1: From static to dynamic connectomes. (a) Different modes of neural communication are represented by substantially different connectomes. Shown here are chemical synapses (Syn), gap junctions (GJ), monoamines (MA), and neuropeptide (NP) connectomes for the nematode worm C. elegans (image adapted from bentley2016multilayer). How these relate to behavior has been problematic, however. The immediate neighborhoods for neuron AWB are shown (b) from Syn and (c) from GJ; which governs AWB communication and when? (d, top) The dataset consists of activity traces from each neuron in C. elegans across time; dashed lines illustrate stimulus presentation of e.g. a repulsive chemical that is directly sensed by the worm. Note how the traces differ across time and across worms. (d, bottom) Different modules, or communities of neurons, become active at different time periods, revealing how neurons interact dynamically to encode behavior. Our goal is to infer these communities comprising the dynamic functional connectome.
• Figure 2: Computation of dynamic differential affinity. (a, top) Activity traces of two neurons, AWCL and ASER, across time. Note that they share marked periods of similar trends in activity. (a, middle) Smoothed derivatives of the top traces. Note how the derivatives agree during periods in which both traces vary together. (a, bottom) Affinity trace across time computed between AWCL and ASER (see section \ref{['section:affinities']} and Appendix \ref{['appendix:bumps']} for details). Note how the "bumps" coincide with regions of potential interest. (b) Similar plots for a different neuron pair. Again, our non-linear affinity measure has low value except for periods when both neurons increase or decrease their activities, i.e., are more likely to be interacting.
• Figure 3: The procedure for inferring dynamic functional connectomes in three stages. (a) Stage 1: Building affinities. Neurons in behaving worms are imaged to yield a matrix of activity (in time) for each neuron for each worm. The differential affinity computation compares traces to yield a tensor of affinities (in time) for each neuron pair for each worm. (b) Stage 2: Non-negative tensor factorization yields components that reveal affinity patterns found for certain worms (bar plot) over different time intervals (temporal curve). For example, component 2 indicates that neuron pairs with high affinity in worms 4 and 6 are active early in the experiment, and the last factor applies mainly to worm 2. (c) Stage 3: From affinities to a functional connectome. The affinity factor from a selected tensor component is rearranged as an affinity matrix, from which an equivalent weighted graph is implicitly built. A community detection algorithm then reveals groupings of neurons behaving similarly over the indicated time interval.
• Figure 4: Tensor components for a real worm during an experiment in which repellent and attractive stimuli were applied. The application of these stimuli is important, since it provides correspondence between the time axes. (a) One tensor component that selects out the interval during which repulsive NaCl (salt) was applied. All worms reacted, but worms 5, 6, and 7 showed higher responses for certain pairs of neurons (from the affinity factor, shown as an unsorted matrix). The weighted graph visualized with a traditional force-directed embedding is difficult to interpret, but the nested community structure revealed by the NWSBM algorithm (b) provides a clear view of the neuronal modules involved in salt perception. (c) A different tensor component that selects several time intervals when stimuli were applied, but is especially involved with the attractant 2,3-pentanedione. Most worms are again implicated, but the community of neurons (d) is qualitatively different.
• Figure 5: A transient community for salt sensing. (a) We here highlight one community from the dendrogram shown in Fig. \ref{['fig:factors']}a (cf. inset below). By reverting back to the original activity traces, we can confirm that the individual neuronal responses agree with a functional circuit organization, and that the affinity measure is meaningful. (b) The temporal factor of the corresponding tensor component shows that this particular circuit is most prominently involved in a response to NaCl (salt), plus minor but non-negligible responses to the other two stimuli (2-butanone and 2,3-pentanedione). (c) Individual activity traces for the most strongly connected neurons within the community, highlighted in proportion to the instantaneous temporal loadings. Note that the traces are most similar precisely during the NaCl interval for several worms; traces are plotted from the three worms with highest loadings in the corresponding worm factor (see Fig. \ref{['fig:factors']}a). (d) Note the complexity of the traces outside this interval. In particular, even though in worm 7 all the selected neurons were correlated throughout the experiment, this was not true for other worms, which explains the NaCl specificity in the temporal factor. Notice that, because the affinities are computed from absolute derivatives, neurons will be strongly connected even when their traces have opposite signs.