Worm Breeder's Gazette 9(3): 113

These abstracts should not be cited in bibliographies. Material contained herein should be treated as personal communication and should be cited as such only with the consent of the author.

Computer Simulation of C. elegans Neurons

E. Niebur and P. Erdos

The morphology of nematode neurons is very simple, compared to those 
of higher animals. Together with the many details known about the 
nematode nerve circuitry 1, this makes it feasible to simulate in 
detail the voltage distribution in these neurons. The modelling of 
subcircuits of several neurons is also possible. We have chosen to 
simulate the neural circuitry controlling the somatic body musculature,
i.e. the neurons that generate the typical wave-like locomotion of 
Caenorhabditis  Recent experiments2 on 
the corresponding motoneurons in Ascaris have shown that the 
transmembrane conductivities are nearly voltage independent. Assuming 
that the neuronal activities of Ascaris and C. 
lar, this permits us to use the following 
partial differential equation for the transmembrane voltage Vi(x,t) at 
the position x of nerve process i at time t: 
{Figure 1}
Here ER is the resting potential and tau and lambda are the 
characteristic time and length constants of the cell membrane, 
respectively. They are determined from the electrical properties of 
the membrane3, which have been measured experimentally4 for Ascaris, 
but have to be estimated for C. ing the nerve 
process in compartments, the partial differential equation of each 
nerve process is transformed into a system of as many coupled ordinary 
differential equations as there are compartments. These equations are 
supplemented by boundary conditions, for instance dVi/dx=O at both 
ends of the process (i.e. no current leaves the ends of the process). 
Furthermore, it is assumed that all processes, except one, are at 
resting potential at t=0, the remaining one being excited. 
The coupling of nerve processes by synapses corresponds 
mathematically to the coupling of the corresponding differential 
equations. Electrical synapses (gap junctions) are modelled by ohmic 
resistors. At a chemical synapse, an enhanced presynaptic voltage 
causes transmitter release into the synaptic cleft. This opens ionic 
channels in the postsynaptic membrane, i.e. Iowers the resistivity 
across the membrane. Our model for a chemical synapse consists of a 
transmembrane resistivity, whose value depends on the presynaptic 
voltage, in series with a voltage source. The potential of this 
voltage source, representing the electrochemical potentials involved, 
is above the resting potential for an excitatory synapse and below (or 
equal to) the resting potential for an inhibitory synapse. 
One aim of the simulation is to explain the propagation of muscular 
waves along the body during the wave-like motion. It is known, that 
motoneurons in Ascaris are (almost) electrically passive2, i.e. 
their transmembrane conductivities are (nearly) independent of the 
transmembrane voltage. If we assume the same for the interneurons of 
the ventral cord of C. xclude the probably 
simplest model proposed for the muscular waves5. According to this 
model, first an 
excitation of an interneuron of the ventral cord is produced in the 
head (tail) for forward (backward) movement. Then this excitation 
travels along the ventral cord, stimulating en 
neurons. Our calculation shows, that the 
speed of the travelling excitation is by orders of magnitude higher 
than the observed speed of muscular waves. Hence the travelling wave 
cannot directly be responsible for the propagation of the muscular 
For a more detailed report, see the proceedings of the Conference on 
Computer Simulation in Brain Science, held in Copenhagen, Denmark, 20-
22 august 1986.