C. Elegans

C. Elegans is a free-living nematode (roundworm). It is being used extensively as a model organism in the field of neuronal research and development.

The Network of C. Elegans
The network of C. Elegans consists of a total of 298 neurons, divided into:
 * 71 sensory neurons
 * 86 interneurons
 * 92 motor neurons
 * 49 combinations of sensory/inter/motor neurons.

The connections between the neurons can be either electrical (gap junctions) or chemical. The former ones are undirected with a small delay and the latter ones are directed and divided into inhibitory and excitatory. The rate of E/I is 3:1. Because of the difference in the topology, we first decided to split the network into two subsets and observe whether they follow some kind of power law.

Gap Junctions
In total, 271 neurons use gap junctions, creating 1084 connections. To visualize the degree distribution, we use CCDF (Complementary Cumulative Distribution Function) which offers the advantage of low noise in the tail of the distribution. Our findings of a power law fit in the tail of the distribution agree with Varshney, Lav R, et al., where we compute a power law exponent of 3.08, suggesting that the gap junction network is scale-free.

Chemical Synapses
The chemical network consists of 279 neurons and 2279 directed connections. Working similarly to the gap junctions, we compute the CCDFs of the indegrees and outdegrees of the directed network. The distribution tails also suggest a scale-free network, with $$\alpha$$=2.94 and 4.2 for the indegree and outdegree respectively.

Full Network
Having considered the gap junction network and the chemical network, we look at the combined network, connecting the two networks together, thus treating the gap junctions as double-sided directed connections. The CCDFs of the full network follow a power law consistent with the network being scale-free in the sense of Barabasi and Albert.

Our Goal
The existence of power laws and scale-free networks lead us to the next step of searching for criticality using the distribution of neural avalanches.