Cortical Phase Transitions as an Effect of Topology of Neural Network

Understanding the emerging of cortical dynamical state, its functional role, and its relationship with network topology, is one of the most interesting open questions in computational neuroscience. Spontaneous cortical dynamics often shows spontaneous fluctuations with UP/DOWN alternations and critical avalanches which resemble the critical fluctuations of a system posed near a non-equilibrium noise-induced phase transition. A model with structured connectivity and dynamical attractors has been shown to sustain two different dynamic states and a phase transition with critical behaviour is observed. We investigate here which are the features of the connectivity which permit the emergence of the phase transition and the large fluctuations near the critical line. We start from the original connectivity, that comes from the learning of the spatiotemporal patterns, and we shuffle the presynaptic units, leaving unchanged both the postsynaptic units and the value of the connections. The original structured network has a large clustering coefficient, since it has more directed connections which cooperate to activate a precise order of neurons, respect to randomized network. When we shuffle the connections we reduce the clustering coefficient and we destroy the spatiotemporal pattern attractors. We observe that the phase transition is gradually destroyed when we increase the ratio of shuffled connections, and already at a shuffling ratio of 70% both the phase transition and its critical features disappear.