Biomedical Engineering Reference
In-Depth Information
likely to fire action potentials. Such activity-dependent cellular adaptation proc-
ess would shift the input/output function of the neurons and make them less re-
sponsive to inputs.
Finally, it must be stressed that no particular network structure or cellular
properties are thought to underlie the pattern of activity. As mentioned above,
spontaneous episodic activity is observed in developing networks with a great
variety of structure, and a similar type of activity is observed in dissociated cul-
tures of spinal neurons for which inhibitory transmission has been blocked (35).
In the chick embryo, lesion studies have shown that ventral networks of the spi-
nal cord can generate the activity despite transversal or horizontal sectioning
(47), and pharmacological studies have shown that episodic activity is still gen-
erated when individual neurotransmitters are blocked (7). In addition, there is no
evidence that cellular pacemaker properties underlie the rhythmic activity. It is
through their (excitatory) network interactions that the rhythm arises, i.e., the
rhythmic activity is an emergent property of the network and the dynamics of
the recurrent connections.
The main hypothesis is therefore that the spontaneous, episodic activity is
generated by a purely excitatory network. This activity depresses network excit-
ability and when excitability is too low the activity stops. In the silent period,
network excitability can recover until a new episode starts. In order to test this
hypothesis, we have built a very idealized model (schematized in Figure 2A)
based on all these observations. This differential-equations model can be ana-
lyzed qualitatively using phase-plane and dynamical-systems concepts, so we
can understand its dynamical behavior. It allowed us to explain some experi-
mental results and made some predictions, some of which are presented below.
3.
MODEL OF SPONTANEOUS ACTIVITY IN
THE EMBRYONIC CHICK SPINAL CORD
According to the experimental findings presented above, we model a purely
excitatory network whose detailed structure (connectivity pattern, heterogeneity
of cell types) is not known but does not seem to be important. We also assume
that the membrane properties of the neurons are not important either and all the
neurons are active or inactive together. We therefore use a "mean-field" repre-
sentation of the activity and depression variables, as used by Wilson and Cowan
(44). According to this formulation, the activity
a
(
t
) of the network is an average
of the neuronal firing rate over the population of neurons (see Figure 2A,B).
Individual spikes are not modeled (and assumed not to occur synchronously);
this firing rate is a temporally coarse-grained representation, that is, averaged
over a short period of time.
2
Thus,
a
can be related to the (pre)synaptic drive,
i.e., the amount of synaptic input exciting neurons in the network (29). The
model consists of three equations (36):
