Self-stabilization of neuronal networks. I. The compensation algorithm for synaptogenesis.

Between the extreme views concerning ontogenesis (genetic vs. environmental determination), we use a moderate approach: a somehow pre-established neuronal model network reacts to activity deviations (reflecting input to be compensated), and stabilizes itself during a complex feed-back process. Morphogenesis is based on an algorithm formalizing the compensation theory of synaptogenesis (Wolff and Wagner 1983). This algorithm is applied to randomly connected McCulloch-Pitts networks that are able to maintain oscillations of their activity patterns over time. The algorithm can lead to networks which are morphogenetically stable but preserve self-maintained oscillations in activity. This is in contrast to most of the current models of synaptogenesis and synaptic modification based on Hebbian rules of plasticity. Hebbian networks are morphogenetically unstable without additional assumptions. The effects of compensation on structural and functional properties of the networks are described. It is concluded that the compensation theory of synaptogenesis can account for the development of morphogenetically stable neuronal networks out of randomly connected networks via selective stabilization and elimination of synapses. The logic of the compensation algorithm is based on experimental results. The present paper shows that the compensation theory can not only predict the behavior of synaptic populations (Wagner and Wolff, in preparation), but it can also describe the behavior of neurons interconnected in a network, with the resulting additional system properties. The neuronal interactions--leading to equilibrium in certain cases--are a self-organizing process in the sense that all decisions are performed on the individual cell level without knowing the overall network situation or goal.