Type-II phase resetting curve is optimal for stochastic synchrony

The phase-resetting curve (PRC) describes the response of a neural oscillator to small perturbations in membrane potential. Its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized. However, the inputs to real neurons may often be more accurately described as barrages of synaptic noise. Effective connectivity between cells may thus arise in the form of correlations between the noisy input streams. We use constrained optimization and perturbation methods to prove that the PRC shape determines susceptibility to synchrony among otherwise uncoupled noise-driven neural oscillators. PRCs can be placed into two general categories: type-I PRCs are non-negative, while type-II PRCs have a large negative region. Here we show that oscillators with type-II PRCs receiving common noisy input synchronize more readily than those with type-I PRCs.