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C ( t )
V 1
V 2
V 3
V 4
Ventral
muscle
Dorsal
muscle
V D
V V
Figure 2 Neural network model for the chemotaxis control circuit of C. elegans.
The state variable of each neuron (circle) is voltageV i . The model contains one chemosensory
neuron (V 1 , three interneurons (V 2 - V 4 ) and two motor neurons V D V V . The chemosensory
neuron receives input equal to the chemical concentration Ct at the tip of the nose, and the
motor neurons innervate dorsal (D) and ventral (V) neck muscles. Based on a similar diagram
from Feree and Lockery.
propose that one can look at a simplified linearization of the chemotaxis system
that can give some insights about this behavior, albeit as a first approximation.
The model building proceeds from the organismal level down. It starts from
a model of the nematode body, which captures the head and neck turning
movements (head-sweep), then seeks a neural implementation of the head-sweep
mechanism. Ferrée and Lockery argue that their neural model is based on the
worm's neurophysiology, but only - at this point - weakly on the neuroanatomy.
Citing Goodman et al., 1998, they suggest the neurons can be represented as
single electrical compartments. (Compartment models, like the simpler cable
theory models that backgrounded some of H and H's investigation, are one of
the traditional strategies used in neuroscience; see Bower & Beeman, 1995.)
An equation for the voltage V i of the ith neuron can be written using standard
compartment modeling as
dV i
C cell
dt =−
G cel i V i
E cel i
I ele i V
I chem
I sen i t
V
(1)
i
i
where C cell
is the whole-cell capacitance, G cell
is the effective ohmic conductance
i
i
V curve, and E cell
associated with the linear region of the I
is the resting
i
potential of an isolated neuron. Here I ele i V and I chem
V represent electrical
i
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