Guided Graph Spectral Embedding: Application to the C. elegans Connectome

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based on wavelets and Slepians-that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion and its linear approximation, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode's neural network in terms of functionality and importance of cells. Compared to Laplacian embedding, the guided approach, focused on a certain class of cells (sensory, inter- and motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low or high order processing functions.Comment: 43 pages, 7 figures, submitted to Network Neuroscienc

Evolution and Analysis of Embodied Spiking Neural Networks Reveals Task-Specific Clusters of Effective Networks

Elucidating principles that underlie computation in neural networks is currently a major research topic of interest in neuroscience. Transfer Entropy (TE) is increasingly used as a tool to bridge the gap between network structure, function, and behavior in fMRI studies. Computational models allow us to bridge the gap even further by directly associating individual neuron activity with behavior. However, most computational models that have analyzed embodied behaviors have employed non-spiking neurons. On the other hand, computational models that employ spiking neural networks tend to be restricted to disembodied tasks. We show for the first time the artificial evolution and TE-analysis of embodied spiking neural networks to perform a cognitively-interesting behavior. Specifically, we evolved an agent controlled by an Izhikevich neural network to perform a visual categorization task. The smallest networks capable of performing the task were found by repeating evolutionary runs with different network sizes. Informational analysis of the best solution revealed task-specific TE-network clusters, suggesting that within-task homogeneity and across-task heterogeneity were key to behavioral success. Moreover, analysis of the ensemble of solutions revealed that task-specificity of TE-network clusters correlated with fitness. This provides an empirically testable hypothesis that links network structure to behavior.Comment: Camera ready version of accepted for GECCO'1

Information flow through a model of the C. elegans klinotaxis circuit

Understanding how information about external stimuli is transformed into behavior is one of the central goals of neuroscience. Here we characterize the information flow through a complete sensorimotor circuit: from stimulus, to sensory neurons, to interneurons, to motor neurons, to muscles, to motion. Specifically, we apply a recently developed framework for quantifying information flow to a previously published ensemble of models of salt klinotaxis in the nematode worm C. elegans. The models are grounded in the neuroanatomy and currently known neurophysiology of the worm. The unknown model parameters were optimized to reproduce the worm's behavior. Information flow analysis reveals several key principles underlying how the models operate: (1) Interneuron class AIY is responsible for integrating information about positive and negative changes in concentration, and exhibits a strong left/right information asymmetry. (2) Gap junctions play a crucial role in the transfer of information responsible for the information symmetry observed in interneuron class AIZ. (3) Neck motor neuron class SMB implements an information gating mechanism that underlies the circuit's state-dependent response. (4) The neck carries non-uniform distribution about changes in concentration. Thus, not all directions of movement are equally informative. Each of these findings corresponds to an experimental prediction that could be tested in the worm to greatly refine our understanding of the neural circuit underlying klinotaxis. Information flow analysis also allows us to explore how information flow relates to underlying electrophysiology. Despite large variations in the neural parameters of individual circuits, the overall information flow architecture circuit is remarkably consistent across the ensemble, suggesting that information flow analysis captures general principles of operation for the klinotaxis circuit