Spontaneous up-down transitions in stochastic leaky integrate-and-fire networks

Experimental observations have uncovered sub-populations of neurons switching between “up” (high activity) and “down” (low activity) states in numerous cortical areas. Firing rate models of up-down transitions often characterize this activity as noise-driven dynamics switching between bistable attractors. However, a comprehensive understanding of what drives these transitions in networks of spiking neurons is missing. In this work, we use a stochastic field theory formalization to derive a “quasi-potential” characterizing the bistable attractors in networks of stochastic leaky integrate-and-fire (sLIF) neurons. We find that homogeneous and excitatory-inhibitory (EI) networks sLIF neurons can exhibit bistability between high and low activity states as a function of synaptic coupling and input current. A finite-sized population of neurons can spontaneously transition between the two states due to intrinsic fluctuations that can be predicted by a quasi-potential, and verified in simulations. The quasi-potential qualitatively predicts the behavior of the transition rates as a function of network parameters and system size. Our formalism also applies to EI-networks, where we find in simulations that transitions occur more frequently than in homogeneous networks even if the EI mean-field (MF) dynamics are constrained to map exactly onto the homogeneous network MF dynamics. This difference is due to a two-dimensional manifold that connects the bistable states.