Schematic representation of the procedure used for GIF model parameter extraction.

<p>In <i>Step 1</i> (first row), the experimental spike train <i>S</i>_data(<i>t</i>) is extracted from the voltage trace <i>V</i>_data(<i>t</i>) using a standard threshold-crossing method (left, dashed line). Parameters related to absolute refractoriness are extracted from the average spike shape (middle). In <i>Step 2</i> (second row), given the injected current <i>I</i>_tr(<i>t</i>) and the recorded potential <i>V</i>_data, all the parameters <i>θ</i>_sub defining the dynamics of the subthreshold membrane potential (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004275#pcbi.1004275.e002" target="_blank">Eq 1</a>) are extracted by performing a least-square multilinear regression on the membrane potential derivative </p><p></p><p></p><p></p><p><mi>V</mi><mo>.</mo></p>data<p></p><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><p></p><p></p>. Since <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004275#pcbi.1004275.e002" target="_blank">Eq 1</a> does not describe the membrane potential dynamics during action potentials, all the data close to spikes are discarded. In <i>Step 3</i> (third row), the subthreshold parameters <i>θ</i>_sub are first used to compute the subthreshold voltage of the model <p></p><p></p><p></p><p><mi>V</mi><mo>^</mo></p>model<p></p><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><p></p><p></p>. The parameters <i>θ</i>_th defining the dynamics of the firing threshold (left, dashed line) are then extracted by maximizing the probability (i.e., the <i>log-likelihood</i>) that the experimental spike train <i>S</i>_data(<i>t</i>) was produced by the model, given the subthreshold dynamics <p></p><p></p><p></p><p><mi>V</mi><mo>^</mo></p>model<p></p><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><p></p><p></p>.<p>