Spontaneous retinal wave activity shaping the visual system is a complex neurodevelopmental phenomenon. Retinal ganglion cells are the hubs through which activity diverges throughout the visual system. We consider how these divergent hubs emerge, using an adaptively rewiring neural network model. Adaptive rewiring models show in a principled way how brains could achieve their complex topologies. Modular small-world structures with rich-club effects and circuits of convergent-divergent units emerge as networks evolve, driven by their own spontaneous activity. Arbitrary nodes of an initially random model network were designated as retinal ganglion cells. They were intermittently exposed to the retinal waveform, as the network evolved through adaptive rewiring. A significant proportion of these nodes developed into divergent hubs within the characteristic complex network architecture. The proportion depends parametrically on the wave incidence rate. Higher rates increase the likelihood of hub formation, while increasing the potential of ganglion cell death. In addition, direct neighbors of designated ganglion cells differentiate like amacrine cells. The divergence observed in ganglion cells resulted in enhanced convergence downstream, suggesting that retinal waves control the formation of convergence in the lateral geniculate nuclei. We conclude that retinal waves stochastically control the distribution of converging and diverging activity in evolving complex networks. Author Summary Retinal waves consist of spontaneous neural activity that propagates across the retina during neural development. We simulate the intermittent spread of retinal waveforms originating from a designated node in an adaptively rewiring neural network model. Adaptive rewiring models simulate, in a highly abstracted manner, how brains may achieve their complex topologies during development. This way, we aim to uncover basic principles of neural maturation in the visual system. Namely, we seek to shed light onto how retinal waves might be responsible for the differentiation of immature neurons into specific cell types (e.g., retinal ganglion cells, amacrine cells) and how these waves shape the connectivity structure in the visual system.

Author Summary Dynamic synchronization in coupled oscillators has been studied extensively. Previously, it has been shown how these dynamics can adaptively rewire a random network structure into a complex, brain-like one. For biological and artificial networks to benefit from this dynamic self-organization, these networks must have input and memory facilities. Both functions involve breaking the symmetry of uniform network oscillators and network connectivity strength. We show that adaptive rewiring is generally robust against such perturbations. Notably, we show—via novel methods of comparing network structures—that local symmetry-breaking perturbations can develop discernible anatomical and functional connectivity structures at the global level. Our research qualifies adaptive rewiring as a potential tool for optimizing connectivity in biological and artificial neural networks. Abstract Structural plasticity of the brain can be represented in a highly simplified form as adaptive rewiring, the relay of connections according to the spontaneous dynamic synchronization in network activity. Adaptive rewiring, over time, leads from initial random networks to brain-like complex networks, that is, networks with modular small-world structures and a rich-club effect. Adaptive rewiring has only been studied, however, in networks of identical oscillators with uniform or random coupling strengths. To implement information-processing functions (e.g., stimulus selection or memory storage), it is necessary to consider symmetry-breaking perturbations of oscillator amplitudes and coupling strengths. We studied whether nonuniformities in amplitude or connection strength could operate in tandem with adaptive rewiring. Throughout network evolution, either amplitude or connection strength of a subset of oscillators was kept different from the rest. In these extreme conditions, subsets might become isolated from the rest of the network or otherwise interfere with the development of network complexity. However, whereas these subsets form distinctive structural and functional communities, they generally maintain connectivity with the rest of the network and allow the development of network complexity. Pathological development was observed only in a small proportion of the models. These results suggest that adaptive rewiring can robustly operate alongside information processing in biological and artificial neural networks.