worm-sim

A browser simulation of the nematode Caenorhabditis elegans, in which a model of the worm's nervous system, built from its published connectome, controls a physically simulated body.

C. elegans is one of the simplest multicellular animals and the first whose complete connectome (the map of every neuron and synapse) was reconstructed. Despite its small nervous system it shows a range of behaviours: it crawls by propagating a bending wave along its body, reverses and turns when touched, and moves toward food.

Usage

The simulation runs at heyseth.github.io/worm-sim. To run it locally, open index.html in a browser; no build step is required.

Food. Click or tap to place food. The food-sensing neurons ASEL and ASER are stimulated as the concentration at the worm's head rises or falls. Chemotaxis in the model is still rudimentary, so the worm does not yet seek food reliably.
Touch. When the worm's nose meets the edge of the window, the nose touch neurons are stimulated and the worm reverses. If its tail meets the edge while reversing, the tail touch neurons are stimulated and it moves forward again.
Hunger. The interneurons RIM and RIC receive a constant input, representing a worm that has been away from food, which raises the rate of spontaneous reversals.
Connectome panel. Each dot is a neuron, arranged in a spiral with the most highly connected neurons at the centre, and brightens with that neuron's activity. Hover over or tap a dot to see its name. The two rows of bars beneath show dorsal and ventral muscle activation from head to tail, so the bending wave can be seen travelling along the body.
Toolbar. The toolbar recentres the worm, clears food, toggles the connectome panel and links to this repository.

The worm's movement is produced entirely by the simulated nervous system; there is no scripted animation!

The Nervous System

Connectome

The wiring is the adult hermaphrodite connectome of Cook et al. (2019): 272 neurons with their chemical synapses, gap junctions and neuromuscular junctions. tools/build_connectome.py generates js/constants.js from the published tables.

The connectome specifies which cells are connected but not whether each chemical synapse is excitatory or inhibitory. Synaptic signs are taken from Fenyves et al. (2020), who predicted them from each neuron's neurotransmitter and the receptors expressed by its partner. Two further rules apply:

RIM's synapses onto AVB, RMD, SMD and the neck muscles are inhibitory, because RIM releases tyramine, which inhibits these cells through the tyramine-gated chloride channel LGC-55 (Pirri et al., 2009).
At neuromuscular junctions, acetylcholine is excitatory and GABA inhibitory.

Synapses whose sign could not be predicted are omitted.

Neuron model

Most C. elegans neurons do not fire action potentials, so each simulated neuron has a graded membrane potential and an output between 0 and 1. Chemical synapses transmit the presynaptic output scaled by the signed synaptic weight, and gap junctions pass current in proportion to the difference in potential between the coupled cells. Each neuron also adapts slowly to its own recent activity and receives a small random input representing synaptic and channel noise.

Modelling assumption

One element of the wiring is assumed rather than taken from data. The forward and backward command interneurons are active at different times in real worms (Kato et al., 2015), and circuit models commonly represent this as mutual inhibition (Roberts et al., 2016). The predicted synaptic signs do not contain such inhibition, so the model adds it: AVA and AVD inhibit AVB and PVC, and vice versa. All other connections come from the published data.

Locomotion

Body mechanics

The body is modelled as a chain of linked segments. At each time step, motor neuron output determines the activation of the dorsal and ventral muscles in each of 24 muscle rows from head to tail; because the worm crawls on its side, these are the two directions in which it bends on the agar surface.

At the worm's scale inertia is negligible, so the body is overdamped: each segment moves at a velocity set by the forces acting on it and by drag that is 30 times greater perpendicular to the body than along it, as for a worm crawling in a groove in agar. This anisotropic drag is what converts the bending wave into motion. A wave travelling from head to tail propels the worm forward at about 0.2 body lengths per second, and a wave travelling from tail to head propels it backward. Steering arises solely from asymmetric bending of the head.

Generating the bending wave

No bending wave is imposed on the muscles. The wave is generated by the motor neurons together with proprioception, the body's sensing of its own posture:

Forward locomotion. The head motor neurons SMD and RMD alternate between dorsal and ventral activation at about 0.6 Hz. Real worms maintain this head rhythm even when the rest of the body is paralysed (Fouad et al., 2018). Each B-type motor neuron (DB, VB) senses the curvature of the body immediately anterior to its muscles and activates to bend its own segment the same way, so each bend propagates from head to tail (Wen et al., 2012; Boyle, Berri & Cohen, 2012).
Backward locomotion. The same mechanism operates in reverse. The A-type motor neurons in the tail (DA, VA) set the rhythm (Gao et al., 2018), and the remaining A-type neurons follow the curvature immediately posterior to them, so the wave travels from tail to head.

Choosing a direction

The command interneurons determine which circuit is active: AVB and PVC drive forward locomotion, and AVA and AVD drive backward locomotion. The worm reverses whenever AVA is more active than AVB.

Touch-evoked reversals. A nose touch excites AVA and AVD through the connectome and shifts the balance toward reversal within a fraction of a second.
Spontaneous reversals. Noise in the network occasionally shifts the balance, producing spontaneous reversals about once or twice a minute. Each reversal ends as AVA adapts.
Omega turns. Long reversals are followed by an omega turn, a deep ventral bend of the head driven by RIV and SMDV, which reorients the worm (Gray, Hill & Bargmann, 2005).

Development

tools/measure.js runs the simulation without a browser and reports forward and backward speed, reversal rate and duration, head-swing frequency and touch responses, for comparing the model with measurements from real worms:

node tools/measure.js 120 open    # two minutes with no walls
node tools/measure.js 20 touch    # a nose touch after five seconds

To regenerate the connectome, download the two source tables listed at the top of tools/build_connectome.py and run:

python3 tools/build_connectome.py COOK.xlsx FENYVES.xlsx

References

Boyle, J. H., Berri, S. & Cohen, N. (2012). Gait modulation in C. elegans: an integrated neuromechanical model. Frontiers in Computational Neuroscience.
Cook, S. J. et al. (2019). Whole-animal connectomes of both Caenorhabditis elegans sexes. Nature.
Fenyves, B. G. et al. (2020). Synaptic polarity and sign-balance prediction using gene expression data in the Caenorhabditis elegans chemical synapse neuronal connectome network. PLoS Computational Biology.
Fouad, A. D. et al. (2018). Distributed rhythm generators underlie Caenorhabditis elegans forward locomotion. eLife.
Gao, S. et al. (2018). Excitatory motor neurons are local oscillators for backward locomotion. eLife.
Gray, J. M., Hill, J. J. & Bargmann, C. I. (2005). A circuit for navigation in Caenorhabditis elegans. PNAS.
Kato, S. et al. (2015). Global brain dynamics embed the motor command sequence of Caenorhabditis elegans. Cell.
Pirri, J. K. et al. (2009). A tyramine-gated chloride channel coordinates distinct motor programs of a Caenorhabditis elegans escape response. Neuron.
Roberts, W. M. et al. (2016). A stochastic neuronal model predicts random search behaviors at multiple spatial scales in C. elegans. eLife.
Wen, Q. et al. (2012). Proprioceptive coupling within motor neurons drives C. elegans forward locomotion. Neuron.

License

This project is licensed under the MIT License; see license.md for details.

Acknowledgments

Timothy Busbice, Gabriel Garrett, Geoffrey Churchill and the other contributors to the GoPiGo Connectome, on which the original version of this simulation was based.
Zach Rispoli, for the initial porting of the GoPiGo connectome to JavaScript.
OpenWorm's ConnectomeToolbox and the WormNeuroAtlas, which host the connectome and synaptic-sign tables used here.