Reciprocally connected pairs (RCPs) of neurons are the simplest structural motif in neuronal networks. More complex structural motifs are composed of three or more neurons. RCPs are formed by reciprocal synapses, and represent local microcircuits that can act as feedback loops. Evidence of the ubiquitous presence of RCPs in the central nervous system of different animals is well-established. Statistical analysis of connections between principal cortical cells has shown that RCPs are overrepresented in the somatosensory cortex, neocortex, and olfactory bulb. RCPs are also overrepresented in the neuronal network of the nematode Caenorhabditis elegans (C. elegans) [1].
In this work we analysed the statistics of reciprocal and undirectional chemical connections between pairs of neurons in the neuronal connectomes of the male and hermaphrodite C. elegans, using data recently published in [2]. First, our analysis shows that even if all unidirectional connections are removed, i.e. if approximately 63% of all connections are removed, approximately 83% of neurons with chemical synapses in the male (87%) in the hermaphrodite) remain in the strongly connected cluster, where they are reachable from each other through sequences of reciprocal connections. This result shows that reciprocal connections provide communication between most neurons with chemical synapses in the C. elegans. Second, average multiplicity was found to be larger among reciprocal connections than unidirectional connections, both among afferent and efferent connections. The probability that a connection has large multiplicity (over 10 synapses per connection) is larger among reciprocal connections. Third, it was found that most neurons with an above-average number of presynaptic neighbors have a number of afferent synapses which is on average larger than the average connectome multiplicity. Moreover, the larger the in-degree of a neuron the larger the multiplicity of the afferent connections to this neuron (Figure 1). The number of efferent connections, however, was found to be largely independent of the number of postsynaptic neurons. Fourth, the number of afferent synapses and the number of presynaptic neurons are strongly correlated, such that neurons with more presynaptic neighbors receive disproportionally more synapses.
Given the known functional roles of some RCPs, it is possible that enhanced multiplicity among RCPs is the result of their function. For example, RCPs have been implicated in memory formation. Since the formation of long-term memory results in an increase in the number of dendritic spines on neurons that are part of a memory engram, it is possible that a similar mechanism plays a role in the enhanced multiplicity of reciprocal connections in the C. elegans. The enhanced multiplicity may in part result from Hebbian structural plasticity. As neurons with a larger number of presynaptic neighbors are more likely to be activated, they are also more likely to experience prolonged periods of high activity, which in turn can induce the formation of more synapses. Conversely, the multiplicity of neurons with less presynaptic neighbors should decrease as the result of increased periods of low neuronal activity.
1. L. R Varshney et al, Structural properties of C. elegance neural network. PLoS comput. biol. 7:e1001066, 2011.
2. S.J. Cook et al, Whole-Animal Connectomes of Both Caenorhabditis Elegans Sexes. Nature, 571, 63–71, 2019.
