Growth strategy determines network performance

The interplay between structure and function is crucial in determining some emerging properties of many natural systems. Here we use an adaptive neural network model inspired in observations of synaptic pruning that couples activity and topological dynamics and reproduces experimental temporal profiles of synaptic density, including an initial transient period of relatively high synaptic connectivity. Using a simplified framework, we prove that the existence of this transient is critical in providing ordered stationary states that have the property of being able to store stable memories. In fact, there is a discontinuous phase transition between the ordered memory phase and a disordered one as a function of the initial transient synaptic density. We also show that intermediate synaptic density values are optimal in order to obtain these stable memory states with a minimum energy consumption, and that ultimately it is the transient heterogeneity in the network what determines the stationary state. Our results here could explain why the pruning curves observed in actual brain areas present their characteristic temporal profiles and, eventually, anomalies such as autism and schizophrenia associated, respectively, with a deficit or an excess of pruning.