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Beyond the connectome hairball:
Rational visualizations and analysis of the C. elegans connectome as a network graph using hive plots

Pedro Tabacof1, Tim Busbice1 and Stephen D. Larson1*
  • 1 OpenWorm.org, United States

The C. elegans connectome (White et al., 1986) is currently the most detailed connectome data set at the neuronal circuit level that is publicly available. Represented as a network graph, it consists of edges that distinguish between gap junctions and chemical synapses, weighted by synapse count, with nodes that represent neurons whose identities are unambiguous and well known.

Within the OpenWorm project (Palyanov et al., 2012), we have previously transformed this data set into NeuroML as the foundation for a computational simulation framework for C. elegans (Busbice et al., 2012). In the course of analyzing this data set, we have applied the hive plot methodology for visualizing complex networks (Krzywinski et al., 2012). Hive plots provide a rational and transparent visualization method for making complex networks by laying out nodes on radially oriented linear axes with a coordinate system based on nodes’ structural properties. While previous articles have explored the structure of the C. elegans connectome graph quantitatively (Chatterjee & Sinha, 2008; Sohn et al., 2011), to the best of our knowledge this is the first application of the hive plot visualization technique to any connectome data set.

We have created multiple hive plots based on the C. elegans complex graph to depict various aspects of its underlying structure via the JHive tool (http://hiveplot.net). Simple hive plots of the sensory, inter-, and motor neurons on different axes reveals strikingly dense connections for the top four interneurons compared to the rest. Hive plots show that the connections mediated by gap junctions that run between sensory neurons and interneurons are less dense than the connections between interneurons and motor neurons. This asymmetry is not present in the network of chemical synapses. Additionally, hive plots reveal that edges with high degree (10 synapses or greater) are present between motor neurons but not between sensory neurons (Fig 1). These findings have been verified with independent analysis of the connectome with the NetworkX complex network graph library (http://networkx.github.io/documentation/latest/overview.html).

We have found exploration of the C. elegans connectome using hive plots to lead to the discovery of interesting qualitative structure that was previously not obvious, enabling this structure to be further pursued quantitatively using complex network mathematics.

Figure 1. Hive plot of C. elegans connectome. Nodes on axis marked a3 are sensory neurons, nodes on a1 are interneurons and nodes on a2 are motor neurons. Only edges with connection weight greater than 10 are rendered (thin orange), and include connection weights greater than 15 (medium-thick cyan) and greater than 20 (thick green). Axes are duplicated to display edges between nodes on the same axis. This example shows the absence of connections between sensory neurons (between the a3 axes) and the presence of many high degree connections between motor neurons (between the a2 axes).

Figure 1
Image

Acknowledgements

Supported, in part, by the Neurolinx Research Institute (http://neurolinx.org)

References

Busbice, T., Gleeson, P., , Khayrulin, S., Cantarelli, M., Dibert, A., Idili, G., Palyanov, A., Larson., S. The NeuroML C. elegans Connectome, Neuroinformatics 2012 Abstract Book, September 11, 2012. http://g.ua/WNuf

Chatterjee, N., & Sinha, S. (2008). Understanding the mind of a worm: hierarchical network structure underlying nervous system function in C. elegans. Progress in brain research, 168(07), 145–53. doi:10.1016/S0079-6123(07)68012-1

Krzywinski, M., Birol, I., Jones, S. J. M., & Marra, M. a. (2012). Hive plots--rational approach to visualizing networks. Briefings in bioinformatics, 13(5), 627–44. doi:10.1093/bib/bbr069

Palyanov, A., Khayrulin, S., Larson, S. D., & Dibert, A. (2012). Towards a virtual C . elegans : A framework for simulation and visualization of the neuromuscular system in a 3D physical environment. In Silico Biology, 11, 137–147. doi:10.3233/ISB-2012-0445

Sohn, Y., Choi, M.-K., Ahn, Y.-Y., Lee, J., & Jeong, J. (2011). Topological cluster analysis reveals the systemic organization of the Caenorhabditis elegans connectome. PLoS computational biology, 7(5), e1001139. doi:10.1371/journal.pcbi.1001139

White, J. G., Southgate, E., Thomson, J. N., & Brenner, S. (1986). The Structure of the Nervous System of the Nematode Caenorhabditis elegans. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences (1934-1990), 314(1165), 1–340. doi:10.1098/rstb.1986.0056

Keywords: connectome, hive plot, networks, graph analysis, visualization, C. elegans, openworm

Conference: Neuroinformatics 2013, Stockholm, Sweden, 27 Aug - 29 Aug, 2013.

Presentation Type: Oral presentation

Topic: General neuroinformatics

Citation: Tabacof P, Busbice T and Larson SD (2013). Beyond the connectome hairball:
Rational visualizations and analysis of the C. elegans connectome as a network graph using hive plots. Front. Neuroinform. Conference Abstract: Neuroinformatics 2013. doi: 10.3389/conf.fninf.2013.09.00032

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Received: 30 Apr 2013; Published Online: 11 Jul 2013.

* Correspondence: Mr. Stephen D Larson, OpenWorm.org, San Diego, United States, stephen.larson@gmail.com