Connectivity in real and evolved associative memories

Peer reviewe

Neural development features: Spatio-temporal development of the Caenorhabditis elegans neuronal network

The nematode Caenorhabditis elegans, with information on neural connectivity, three-dimensional position and cell linage provides a unique system for understanding the development of neural networks. Although C. elegans has been widely studied in the past, we present the first statistical study from a developmental perspective, with findings that raise interesting suggestions on the establishment of long-distance connections and network hubs. Here, we analyze the neuro-development for temporal and spatial features, using birth times of neurons and their three-dimensional positions. Comparisons of growth in C. elegans with random spatial network growth highlight two findings relevant to neural network development. First, most neurons which are linked by long-distance connections are born around the same time and early on, suggesting the possibility of early contact or interaction between connected neurons during development. Second, early-born neurons are more highly connected (tendency to form hubs) than later born neurons. This indicates that the longer time frame available to them might underlie high connectivity. Both outcomes are not observed for random connection formation. The study finds that around one-third of electrically coupled long-range connections are late forming, raising the question of what mechanisms are involved in ensuring their accuracy, particularly in light of the extremely invariant connectivity observed in C. elegans. In conclusion, the sequence of neural network development highlights the possibility of early contact or interaction in securing long-distance and high-degree connectivity

From Caenorhabditis elegans to the Human Connectome: A Specific Modular Organisation Increases Metabolic, Functional, and Developmental Efficiency

The connectome, or the entire connectivity of a neural system represented by network, ranges various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of C. elegans and the fibre tract network of human brains yielded through diffusion spectrum imaging (DSI). We compare them to their respective benchmark networks with varying modularities, which are generated by link swapping to have desired modularity values but otherwise maximally random. We find several network properties that are specific to the neural networks and cannot be fully explained by the modularity alone. First, the clustering coefficient and the characteristic path length of C. elegans and human connectomes are both higher than those of the benchmark networks with similar modularity. High clustering coefficient indicates efficient local information distribution and high characteristic path length suggests reduced global integration. Second, the total wiring length is smaller than for the alternative configurations with similar modularity. This is due to lower dispersion of connections, which means each neuron in C. elegans connectome or each region of interest (ROI) in human connectome reaches fewer ganglia or cortical areas, respectively. Third, both neural networks show lower algorithmic entropy compared to the alternative arrangements. This implies that fewer rules are needed to encode for the organisation of neural systems

The brainstem reticular formation is a small-world, not scale-free, network

Recently, it has been demonstrated that several complex systems may have simple graph-theoretic characterizations as so-called ‘small-world’ and ‘scale-free’ networks. These networks have also been applied to the gross neural connectivity between primate cortical areas and the nervous system of Caenorhabditis elegans. Here, we extend this work to a specific neural circuit of the vertebrate brain—the medial reticular formation (RF) of the brainstem—and, in doing so, we have made three key contributions. First, this work constitutes the first model (and quantitative review) of this important brain structure for over three decades. Second, we have developed the first graph-theoretic analysis of vertebrate brain connectivity at the neural network level. Third, we propose simple metrics to quantitatively assess the extent to which the networks studied are small-world or scale-free. We conclude that the medial RF is configured to create small-world (implying coherent rapid-processing capabilities), but not scale-free, type networks under assumptions which are amenable to quantitative measurement

Resolving structural variability in network models and the brain

Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar diagnostics presented in statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling---in addition to several summary statistics, including the mean clustering coefficient, shortest path length, and network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be embedded in anatomical brain regions tend to produce distributions that are similar to those extracted from the brain. We also find that network models hardcoded to display one network property do not in general also display a second, suggesting that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.Comment: 24 pages, 11 figures, 1 table, supplementary material