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.