A Statistical Physics approach to dendritic computation

Neurons are biological examples of excitable media. In computational
neuroscience, the electric activity of neurons traditionally is modeled
by coupled nonlinear differential equations, representing the dynamics
of the membrane potential and variables related to the ionic
conductances present in the system. A recent trend consists of the
extension of this modeling strategy, detailing the neuronal dendritic
trees through a compartmental approach. This detailed modeling aims at
examining the possibility that these extensive tree-shaped neuronal
regions play important functions, that is, they may be the stage for a
complex “dendritic computation”. We propose a cellular automaton model
of an active dendritic tree whose dynamics of signal transmission is
simple, but whose topology is more faithfully reproduced by means of a
Cayley tree with a large number of compartments. We study how the
geometry of such an extended excitable system is able to perform
computations on incoming stimuli. By both numerical and analytical
means, we show that the model implements essential dendritic
computations, such as signal compression (with dynamic ranges of
more than 50 dB) and spike backpropagation. We also compare different
tree like topologies for possible artificial stimulus detector
applications. Finally, we discuss properties of other complex networks
present in central nervous system.