Searching for collective behavior in a small brain

Abstract

In large neuronal networks, it is believed that functions emerge through the collective behavior of many interconnected neurons. Recently, the development of experimental techniques that allow simultaneous recording of calcium concentration from a large fraction of all neurons in Caenorhabditis elegans - a nematode with 302 neurons - creates the opportunity to ask if such emergence is universal, reaching down to even the smallest brains. Here, we measure the activity of 50+ neurons in C. elegans, and analyze the data by building the maximum entropy model that matches the mean activity and pairwise correlations among these neurons. To capture the graded nature of the cells' responses, we assign each cell multiple states. These models, which are equivalent to a family of Potts glasses, successfully predict higher statistical structure in the network. In addition, these models exhibit signatures of collective behavior: the state of single cells can be predicted from the state of the rest of the network; the network, despite being sparse in a way similar to the structural connectome, distributes its response globally when locally perturbed; the distribution over network states has multiple local maxima, as in models for memory; and the parameters that describe the real network are close to a critical surface in this family of models.

arXiv comment14 pages, 12 figures

References in corpus (12)

• Weak pairwise correlations imply strongly correlated network states in a neural population
• Identification of direct residue contacts in protein-protein interaction by message passing
• Statistical mechanics for natural flocks of birds
• Are biological systems poised at criticality?
• Colloquium: Criticality and dynamical scaling in living systems
• Whole-brain calcium imaging with cellular resolution in freely behaving C. elegans
• Maximum entropy models for antibody diversity
• Searching for collective behavior in a network of real neurons
• Collective behavior of place and non-place neurons in the hippocampal network
• Automatically tracking neurons in a moving and deforming brain
• Temporal processing and context dependency in C. elegans mechanosensation
• Transitions between spatial attractors in place-cell networks

Cited by in corpus (8)

• Adaptive, locally-linear models of complex dynamics
• The broad edge of synchronisation: Griffiths effects and collective phenomena in brain networks
• Inferring couplings in networks across order-disorder phase transitions
• Inference of stochastic time series with missing data
• Discovering sparse control strategies in C. elegans
• Capturing the Continuous Complexity of Behavior in C. elegans
• The growing topology of the C. elegans connectome
• Functional Renormalization Group Approach for Signal Detection