Activity-dependent Outgrowth of Neurons and Overshoot Phenomena in Developing Neural Networks

During the development of the nervous system, all kinds of structural elements such as neurons, neuritic extensions and synapses are initially overproduced (so-called overshoot phenomena). Neurite outgrowth has been found to be regulated by electrical activity of the neuron. High levels of activity, resulting in high intracellular calcium concentrations, cause neurites to retract whereas low levels of activity, and consequently low calcium concentrations, allow further outgrowth. In this article, we have studied the implications of such activity-dependent neurite outgrowth for network formation, using a distributed simulation model. The model consists of initially disconnected cells that organize themselves into a network under the influence of their intrinsic activity. A neuron is modelled as a neuritic field, the growth of which depends upon its own level of activity, and the neurons become connected when their fields overlap. It is demonstrated here that activity-dependent outgrowth in combination with a neuronal response function with some form of firing threshold—which gives rise to a hysteresis effect—is sufficient to cause an overshoot with respect to connectivity or number of synapses. As a consequence of such hysteresis, the network connectivity at which a phase transition occurs from the quiescent to the activated state must be higher than that for maintaining activity at a level where neuritic fields and connectivity remain constant. A developing network will therefore first increase its connectivity until it becomes activated, upon which the neurites begin to retract. Connectivity then decreases until the equilibrium value is reached, thus causing the growth curve to exhibit overshoot. The results are robust under various alternative formulations of the model, and show certain similarities with findings in developing cultures of dissociated nerve cells, namely a transient overproduction of synapses and the existence of a transition period in which increasing electrical activity is associated with retraction of neurites.