Neuronal Networks: A Discrete Model - Mathematical Concepts and Methods in Modern Biology - page 179

fires synchronously and different clusters are desynchronized from one another. By
dynamic clustering we mean that there are distinct episodes in which some subpop-
ulation of cells fire synchronously; however, membership within this subpopulation
may change over time. That is, two neurons may fire together during one episode but
not during a subsequent episode. Of course, more complicated population rhythms
are also possible. Neurons within the network may be totally desynchronized from
each other, or activity may propagate through the network in a wave-like manner.
6.2.3 Olfaction
These types of population rhythms have been implicated in many brain processes and
it is critically important to understand how they depend on parameters corresponding
to the intrinsic properties of cells, synaptic connections, and the underlying network
architecture. Our example is concernedwith olfaction; that is, the sense of smell. In the
insect and mammalian olfactory systems, any odor will activate a subset of receptor
cells, which then project this sensory information to a neural network in the antennal
lobe (AL) of insects or olfactory bulb (OB) of mammals in the brain. Processing
in this network transforms the sensory input to give rise to dynamic spatiotemporal
firing patterns. These patterns typically exhibit dynamic clustering. Any given neuron
might synchronize with different neurons at different stages, or episodes, and this
sequential activation of different groups of neurons gives rise to a transient series of
output patterns that through time converges to a stable activity pattern.
The role of these activity patterns in odor perception remains controversial. Dis-
tinct odors will stimulate different neurons, thereby generating different spatiotem-
poral firing patterns. It has been suggested that these firing patterns help the animal to
discriminate between similar odors. That is, it may be difficult initially for an insect's
brain to distinguish between similar odors, because similar odors stimulate similar
subsets of neurons within the insect's AL. However, because of dynamic clustering,
the subsets of neurons that fire during subsequent episodes change, so that the neural
representations of the odors—that is, the subsets of neurons that fire during a spe-
cific episode—become more distinct. This makes it easier for the insect's brain to
distinguish between the neural representations of the two odors.
Mechanisms underlying these firing patterns are poorly understood. One reason
for this is that many biological properties of the AL and OB are still not known; these
include intrinsic properties of neurons, as well as details of the underlying network
architecture. Many of these details are extremely difficult to determine experimentally
and computational modeling, along with mathematical analysis of these models, can
potentially be very useful in generating and testing hypotheses concerning mecha-
nisms underlying the observed patterns. In particular, a critical role for theoreticians
is to classify those networks that exhibit population rhythms consistent with known
biology and determine how activity patterns may change with network parameters.
This presents numerous very challenging problems for mathematicians. Any bio-
logical system is very complicated and it is not at all clear what details should be
included in the model so that the model both accounts for the key biological processes,