c302: a multiscale framework for modelling the nervous system of Caenorhabditis elegans

Abstract

The OpenWorm project has the ambitious goal of producing a highly detailed in silico model of the nematode Caenorhabditis elegans A crucial part of this work will be a model of the nervous system encompassing all known cell types and connections. The appropriate level of biophysical detail required in the neuronal model to reproduce observed high-level behaviours in the worm has yet to be determined. For this reason, we have developed a framework, c302, that allows different instances of neuronal networks to be generated incorporating varying levels of anatomical and physiological detail, which can be investigated and refined independently or linked to other tools developed in the OpenWorm modelling toolchain.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Keywords: C. elegans; computational neuroscience; open source; simulation; standardization.

Figure 1.

c302 overview. The increasing levels of biophysical detail that can be used for models generated by the framework are shown (A–D on y-axis), along with examples of subnetworks of the worm's neuromuscular system which are to be created (x-axis). Each of the 16 boxes represents a generated instance of cells (small circles for somas with black dendrites/axons where present) connected by chemical (orange) or electrical (red) synapses. The neurons can be represented by LIF- (blue) or conductance-based (dark orange) models, as can the muscle cells (light/dark green). Specific instances of the network can be generated by Python scripts, which save the model structure as NeuroML. This can in turn be automatically converted to supported formats, including NEURON to simulate the electrical activity of the model.

Figure 2.

c302–generated models visualized on Open Source Brain (OSB) website. (a) Screenshot of network of 20 neurons present in the pharynx of C. elegans. Spherical somas and dendrites/axons of the cells can be seen on top (each cell has different colour). Window on bottom shows interactive connectivity matrix, with bars on left/top of main matrix showing colour corresponding to pre/postsynaptic cells respectively (cells are defined on right of matrix). Each block in the matrix is coloured by the weight of the chemical connections based on number of known connections from the connectome (black: no connection; purple: one connection/0.01 nS; red: 13 connections, 0.13 nS). (b) Network with four pairs of synaptically connected cells (left; neurons in purple, pink and red, muscle in green; cells have same 3D locations as used for corresponding somas in c). Membrane potential plots from simulation executed via OSB Web interface are shown on right. In all cases the presynaptic neuron receives two pulses of input (top plot) and the response of neurons connected via excitatory chemical synapse (orange), inhibitory chemical synapse (purple) and gap junction (green) are shown in middle plot. Bottom plot shows response of muscle cell connected via excitatory synapse. (c) Screenshot of OSB project page for c302 showing network containing all neurons and muscles. Neurons are coloured according to type (red: interneurons; pink: sensory; purple: motor neurons) and the four quadrants of muscles (green) are located away from the body for clarity. Window on right shows connections in network in a 2D force-directed graph (colours of circles for cells correspond to those in 3D view). Cells with stronger connections are located closer together. The 20 cells of the pharynx are clearly separated on the right owing to lower numbers of connections from these to other cells in the rest of the network. Green muscle cells are also clearly visible on the periphery. Not all cells are listed on right, but hovering over individual circles in the Web browser will show the name of the cell.

Figure 3.

Simulation of neuronal and muscle activity of C. elegans during forward crawling. (a) Symbolic representation of the neural circuit composed of AVB interneurons, B-type and D-type motor neurons for generation of the forward crawling activity. Gap junction connections represented by black lines, excitatory chemical synapses by black arrows, inhibitory synapses by red connections. On the left, a high-level view of connectivity between classes of neurons and the dorsal (DM) and ventral (VM) muscle groups is shown. On the right, connections between the individual neurons within each of the DB, DD, VB and VD classes are illustrated (the dots indicate the same connections as between cells 1 and 2 are present between 2 and 3, and so on). (b) Hypothetical central pattern generator modulatory inputs to DB1 and VB1 motor neurons. (c) Motor neuron activity during 5 s of real-time simulation of the forward locomotion neural circuit. (d) Activity of the body-wall muscles (variations in [Ca²⁺]) during the forward locomotion simulation.

Figure 4.

Activity of forward locomotion network in c302 simulated and visualized on OSB. 3D image on top left shows the 39 neurons that are modelled as single compartments following the line of the worm body, along with the four muscle quadrants (as shown in figure 3c). Window on right shows the membrane potential of all cells as a heatmap. Cells are arranged in alphabetical order from top to bottom and a subset of the cell names are shown on the left of heatmap, with a scale on the right. Window on the bottom left shows a selection of membrane potential traces of muscles, and the current time of the simulation replay is also displayed. The scale on the heatmap is also used for the colouring for the 3D cells, which changes with time as the saved simulation results are replayed. The approximately synchronous activation of the two dorsal muscle quadrants, and out-of-phase activity of the ventral quadrants, can be seen in this 3D view.