Interspike interval correlations in neuron models with adaptation and correlated noise
Fig 1
Linear response of a neuron models spike timing.
The membrane potential of a tonically firing neuron with deterministic ISI T* is subject to an arbitrary perturbation u(ti + τ) (left panel, red line). Here ti is the time of a reference spike and τ ∈ [0, T*] is the relative time since the last spike, resembling a phase. How strongly this perturbation advances or delays the “phase” τ will in general depend on the “phase” itself at which the perturbation is applied. This sensitivity is quantified by the phase-response curve Z(τ) shown in blue in the middle panel. The term Z(τ)u(ti + τ) can thus be thought of a perturbation of the phase (middle panel, red line). In linear response these phase perturbations can be integrated to yield the cumulative phase shift or spike time derivation δTi+1 = ti+1 − (ti + T*) (right panel, red arrow). Note that separating the perturbation from the deterministic dynamics of the neuron model, i.e. finding u(ti + τ) is part of the problem that we address in this paper and solve in detail in the Methods section.