Generic modeling of chemotactic based self-wiring of neural networks.

The proper functioning of the nervous system depends critically on the intricate network of synaptic connections that are generated during the system development. During the network formation, the growth cones migrate through the embryonic environment to their targets using chemical communication. A major obstacle in the elucidation of fundamental principles underlying this self-wiring is the complexity of the system being analyzed. Hence much effort is devoted to in vitro experiments of simpler (two-dimensional) 2D model systems. In these experiments neurons are placed on Poly-L-Lysine (PLL) surfaces, so it is easier to monitor their self-wiring. We developed a model to reproduce the salient features of the 2D systems, inspired by the study of the growth of bacterial colonies and the aggregation of amoebae. We represent the neurons (each composed of cell's soma, neurites and growth cones) by active elements that capture the generic features of the real neurons. The model also incorporates stationary units representing the cells' soma and communicating walkers representing the growth cones. The stationary units send neurites one at a time, and respond to chemical signaling. The walkers migrate in response to chemotaxis substances emitted by the soma and communicate with each other and with the soma by means of chemotactic "feedback". The interplay between the chemo-repulsive and chemo-attractive responses is determined by the dynamics of the walker's internal energy which is controlled by the soma. These features enable the neurons to perform the complex task of self-wiring. We present numerical experiments of the model to demonstrate its ability to form fine structures in simple networks of few neurons. Our results raise two fundamental issues: (1) one needs to develop characterization methods (beyond number of connections per neuron) to distinguish the various possible networks; (2) what are the relations between the network organization and its computational properties and efficiency?