The iGIF model captures and explains complex forms of adaptation.

<p><b>(A)</b> Average effective membrane filters computed with iGIF model parameters extracted from 6 Pyr neurons by increasing <i>μ</i><sub>I</sub> from 0.05 nA (blue) to 0.5 nA (red, see colorbars in panel <i>D</i>). The passive membrane filter <i>κ</i><sub>m</sub>(<i>t</i>) (dashed black) is shown for comparison. Inset: average effective conductance as a function of <i>μ</i><sub>I</sub>. The gray area indicates one standard deviation across neurons and the dashed black line indicates the passive leak conductance <i>g</i><sub>L</sub>. <b>(B)</b> Same results as in panel <i>A</i>, but for the average integration filter . Inset: average coupling strength as a function of the mean input <i>μ</i><sub>I</sub>. Conventions are as in panel <i>A</i>. <b>(C)</b> The effective membrane timescale (red) and the effective timescale of integration (blue) predicted by the iGIF model with parameters extracted from six neurons match the experimental data (black; copied from <a href="" target="_blank">Fig 2D</a>). Colored lines and gray areas indicate the mean and one standard deviation across neurons. The effective timescales of integration (red) predicted by the iGIF model were obtained by fitting a single-exponential function to . <b>(D)</b> The iGIF model explains the adaptive changes in the spike-history filter <i>h</i><sub>GLM</sub>(<i>t</i>) (see <a href="" target="_blank">Fig 2C</a>). Left: average spike-history filter <i>h</i><sub>GLM</sub>(<i>t</i>) obtained by fitting a GLM to artificial data generated by simulating the iGIF model response to fluctuating currents of increasing <i>μ</i><sub>I</sub> (see colorbar). Right: average theoretical filters computed using iGIF model parameters extracted from 6 Pyr neurons. Because of the approximations involved in the analytical derivation of , the strength of the GLM spike-history filters are underestimated during the firsts ms (see <a href="" target="_blank">Materials and Methods</a>). <b>(E)-(F)</b> Switching experiment performed in a iGIF model (with parameters extracted from a typical cell) to study the temporal evolution of single neuron adaptation induced by a sudden change in <i>μ</i><sub>I</sub>. <b>(E)</b> Top: fluctuating current (gray) generated by periodically switching <i>μ</i><sub>I</sub> (dark gray) between 0.1 nA and 0.27 nA, with cycle period <i>T</i><sub>cycle</sub> = 10 s (only one cycle is shown). Middle: effective timescale of integration as a function of time. Bottom: output firing rate. While spike-frequency adaptation occurs on both fast and slow timescales, changes in triggered by a switch in <i>μ</i><sub>I</sub> are almost instantaneous. Horizontal black lines indicate (from top to bottom): 0 nA, 0 ms and 0 Hz. <b>(F)</b> Comparison between effective integration filters estimated at different moments in time during the switching experiment (see arrows in panel <i>E</i>). The filters estimated at steady-state (late low, late high; defined as the last 150 ms before the stimulus switch) closely resemble the ones estimated right after the stimulus switch (early low, early high; first 150 ms after the stimulus switch), indicating that adaptive changes in are almost instantaneous. The passive membrane filter <i>κ</i><sub>m</sub>(<i>t</i>) (dashed black) is shown for comparison. In all panels, input currents were generated according to <a href="" target="_blank">Eq 8</a> with <i>σ</i><sub>I</sub> = 100 pA and <i>τ</i><sub>I</sub> = 3 ms.</p>