Polarity-specific high-level information propagation in neural networks

Abstract

Analyzing the connectome of a nervous system provides valuable information about the functions of its subsystems. Although much has been learned about the architectures of neural networks in various organisms by applying analytical tools developed for general networks, two distinct and functionally important properties of neural networks are often overlooked. First, neural networks are endowed with polarity at the circuit level: Information enters a neural network at input neurons, propagates through interneurons, and leaves via output neurons. Second, many functions of nervous systems are implemented by signal propagation through high-level pathways involving multiple and often recurrent connections rather than by the shortest paths between nodes. In the present study, we analyzed two neural networks: the somatic nervous system of Caenorhabditis elegans (C. elegans) and the partial central complex network of Drosophila, in light of these properties. Specifically, we quantified high-level propagation in the vertical and horizontal directions: the former characterizes how signals propagate from specific input nodes to specific output nodes and the latter characterizes how a signal from a specific input node is shared by all output nodes. We found that the two neural networks are characterized by very efficient vertical and horizontal propagation. In comparison, classic small-world networks show a trade-off between vertical and horizontal propagation; increasing the rewiring probability improves the efficiency of horizontal propagation but worsens the efficiency of vertical propagation. Our result provides insights into how the complex functions of natural neural networks may arise from a design that allows them to efficiently transform and combine input signals.

The Topographical Mapping in Drosophila Central Complex Network and Its Signal Routing

“…We hypothesize that although the global structural properties examined in the foregoing analysis may not be altered by the presence of atypical neurons, they are still likely to change certain network properties which can be revealed by analyzing information propagation in the network. To this end, we examined the connection matrices at high propagation levels (Lin et al, 2014) (see Section Methods). We discovered that while the connection matrices of the observed and model networks are very similar at the low propagation levels (levels 0 and 1), the difference between the two networks dramatically increases at the high levels (level 2 and above) (Figures 3A,B).…”

“…Large path numbers at the high levels have been shown to be the result of feedback (recurrent) connections (Lin et al, 2014). Given that the input neuron class EIP receives strong feedback from the output neuron classes PEN and PEI in EB (Figure 1B), we conjectured that the increase of the path numbers in the observed network mainly results from the atypical neuron-dependent strengthening of the feedback circuits between EB and PB.…”

“…In the novel analyses we investigated the connection matrices at the different propagation levels (Lin et al, 2014). The analysis has been shown to reveal different efficiency in signal propagation between various networks of similar small-world properties.…”

“…The analysis has been shown to reveal different efficiency in signal propagation between various networks of similar small-world properties. It also identified the functional modules associated with reflexive behaviors and complex/social behaviors of C. elegans (Lin et al, 2014). The propagation level is defined as the number of intermediate neurons making up a path between the given input (source) and output (destination) nodes.…”

“…The advantage of analyzing the connection matrix M l at high levels is that it reveals neuron pairs that are connected by strongly recurrent pathways, because m ( i, j ) l increases rapidly when neurons i and j are connected through strongly recurrent circuits (Lin et al, 2014). Theoretical studies have suggested that recurrent neural networks are associated with a variety of complex functions, including working memory, perceptual decision, oscillation, and etc (Wang, 1999, 2002; Brunel, 2000; Laje and Buonomano, 2013).…”