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.

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 the 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 wave. 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.