Computing temporal sequences associated with dynamic patterns on the C. elegans connectome

Abstract

Understanding how the structural connectivity of a network constrains the dynamics it is able to support is a very active and open area of research. We simulated the plausible dynamics resulting from the known C. elegans connectome using a recent model and theoretical analysis that computes the dynamics of neurobiological networks by focusing on how local interactions among connected neurons give rise to the global dynamics in an emergent way, independent of the biophysical or molecular details of the cells themselves. We studied the dynamics which resulted from stimulating a chemosensory neuron (ASEL) in a known feeding circuit, both in isolation and embedded in the full connectome. We show that contralateral motor neuron activations in ventral (VB) and dorsal (DB) classes of motor neurons emerged from the simulations, which are qualitatively similar to rhythmic motor neuron firing pattern associated with locomotion of the worm. One interpretation of these results is that there is an inherent - and we propose - purposeful structural wiring to the C. elegans connectome that has evolved to serve specific behavioral functions. To study network signaling pathways responsible for the dynamics we developed an analytic framework that constructs Temporal Sequences (TSeq), time-ordered walks of signals on graphs. We found that only 5% of TSeq are preserved between the isolated feeding network relative to its embedded counterpart. The remaining 95% of signaling pathways computed in the isolated network are not present in the embedded network. This suggests a cautionary note for computational studies of isolated neurobiological circuits and networks.

Understanding the Human Brain using Brain Organoids and a Structure-Function Theory

“…Below we give an example of how easily the 'wrong' geometry and connectivity in a network can kill dynamic activity, but do so in a simulation of a biological neural network [5]. We also discuss results that suggest that in the worm C. elegans at least, the wiring of the organism's connectome seems to have evolved to intentionally support sustained recurrent activity [8]. But such a basic theoretical hypothesis about the operation of the brain, grounded in fundamental ideas about its physical structure and dynamics, cannot be directly tested in humans.…”

“…The exact number of synapses varies significantly during the course of a person's lifetime and brain region being considered. For example, pyramidal neurons in the cortex have been estimated to have about 32,000 synapses (4), interneruons, which are the computational workhorses of the brain, between 2,200 and 16,000 (5), neurons in the rat visual cortex have about 11,000 per neuron (6), and neurons in other parts of the cortex in humans have roughly 7,200 synapses (7,8).…”

“…Basket cells seem to have optimized their morphology to achieve an almost theoretical ideal of the refraction ratio (Figure 3). We have also analyzed the signaling dynamics of the C. elegans connectome to infer a purposeful connectivity design to how the nervous system of the worm has evolved to be wired [8]. We simulated the dynamics of the C. elegans connectome using the competitive-refractory dynamics model that took advantage of the known spatial (geometric) connectivity of the worm.…”