Synaptic and intrinsic determinants of the phase resetting curve for weak coupling

A phase resetting curve (PRC) keeps track of the extent to which a perturbation at a given phase advances or delays the next spike, and can be used to predict phase locking in networks of oscillators. The PRC can be estimated by convolving the waveform of the perturbation with the infinitesimal PRC (iPRC) under the assumption of weak coupling. The iPRC is often defined with respect to an infinitesimal current as z_i(ϕ), where ϕ is phase, but can also be defined with respect to an infinitesimal conductance change as z_g(ϕ). In this paper, we first show that the two approaches are equivalent. Coupling waveforms corresponding to synapses with different time courses sample z_g(ϕ) in predictably different ways. We show that for oscillators with Type I excitability, an anomalous region in z_g(ϕ) with opposite sign to that seen otherwise is often observed during an action potential. If the duration of the synaptic perturbation is such that it effectively samples this region, PRCs with both advances and delays can be observed despite Type I excitability. We also show that changing the duration of a perturbation so that it preferentially samples regions of stable or unstable slopes in z_g(ϕ) can stabilize or destabilize synchrony in a network with the corresponding dynamics.