Response functions of neurons in an ensemble.

(a) Cortical ensemble of networks. The spike input received by a neuron can be partitioned into functional (solid black arrows) and background (dashed dark blue arrows) input. The background can be partitioned into an excitatory and an inhibitory subset (dashed light blue arrows). In the following panels, we consider one such neuron under five different illustrative background regimes, each of which is assigned a specific color. (b) Steady-state free membrane potential distributions. Shaded areas: numerical simulation; solid lines: analytical approximation using Eqs 1 and 2. Purple, orange, green: same σ_u, different μ_u; blue, orange, red: same μ_u, different σ_u. (c) Corresponding neuronal response functions. Crosses: numerical simulation; solid lines: logistic fit with Eq 3. (d) Slope parameter β and (e) offset I₀ of response functions under various background regimes defined by their respective pairs of excitatory and inhibitory input rates (ν_exc, ν_inh). Dashed isolines indicate configurations of constant slope (cf. Eq 4) or offset, with specific values given as colorbar ticks. Note the approximate linearity of the contour lines.