STABILIZATION OF COMPLEX INPUT OUTPUT FUNCTIONS IN NEURAL CLUSTERS FORMED BY SYNAPSE SELECTION

We numerically analyze the self-organization of formal neurons disposed in a two-dimensional layer, and receiving inputs from two sets of afferent axons A and B. The probability for a given afferent to innervate some neuron depends initially on both afferent and target neuron types, which may be excitatory or inhibitory. This early wiring diagram leads to relatively ill-defined functional groups within the neuronal assembly. There follows a period during which the system differentiates, under the presence of external inputs, into groups of neurons with stable input-output relationships. The mechanism proposed for this maturation is based on the management of a limited provision of retrograde trophic factor distributed from postsynaptic neurons to presynaptic terminals whenever a Hebb-like condition is satisfied. Those boutons which do not receive sufficient trophic support ultimately degenerate. The remaining circuitry is characterized by emergent "mexican-hat" type interactions, i.e., short-range excitation vs. longer-range inhibition, and exhibits well-defined functional properties. These final properties are found to depend both on the initial wiring diagram, and on the correlations between the afferent inputs. Thus, increasing the frequency of, e.g., simultaneous activation of A and B, leads to an increased size of those patches which display activity when A and B are active together. Patches can be observed which realize in a stable and reliable manner any of the 16 Boolean functions of the variables A and B. Usually, patches endowed with different functions may coexist in a given system.