Steady-state threshold curves.

<p>Threshold curves resulting from optimizing the threshold model to recordings in 16 cells. The dashed line is the diagonal and the shaded area represents the average ± standard deviation over all recording conditions in each cell.</p

Fitting procedure applied on an intracellular voltage trace.

<p><b>a</b>, Top: voltage trace (top, black) and predicted threshold (red). Bottom: steady-state threshold in the fitted model. <b>b</b>, vs. predicted threshold for the trace in (a). The identity line (red) sharply separates subthreshold fluctuations from spikes.</p

Fitting procedure applied on a multicompartmental model of a cortical neuron

<p><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003560#pcbi.1003560-Hu1" target="_blank">[<b>7</b>]</a><b>. </b><b>a</b>, Spike threshold measured at the soma vs. logarithm of the sodium inactivation variable h at the axonal initiation site. The dashed line shows the linear regression (slope 3.2 mV). <b>b</b>, The fitting procedure is run on the somatic voltage trace (blue), and the predicted threshold (red) is compared to the threshold calculated from the value of ionic channel variables (green; as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003560#pcbi.1003560-Platkiewicz2" target="_blank">[26]</a>). <b>c</b>, Predicted threshold resulting from the fitting procedure vs. measured threshold for all spikes. The dashed line is the identity. <b>d</b>, Steady-state threshold function of the optimized model (red) compared to the corresponding function calculated from the properties of sodium channel inactivation. <b>e</b>, Estimated time constant of threshold adaptation (red) vs. time constant of sodium inactivation. The estimation is correct in the spike initiation zone (−50 to −40 mV). <b>f</b>, Logarithm of the sodium inactivation variable h at the axonal initiation site plotted against predicted threshold for the entire simulation, excluding spikes.</p

<i>In vivo</i> intracellular recordings.

<p><b>a</b>, Intracellular recordings () in the owl's ICx, with binaural stimuli (L: left, R: right). Either ITD is varied at best IID (top) or IID is varied at best ITD (bottom). Owl picture source: <a href="http://openclipart.org/detail/17566/cartoon-owl-by-lemmling" target="_blank">http://openclipart.org/detail/17566/cartoon-owl-by-lemmling</a>. <b>b</b>, Two spikes from the traces in (a); red dots indicate the estimated spiking threshold. <b>c</b>, Trace from (a) shown in phase space: vs. . Spike threshold is detected when exceeds a fixed value (red dashed line). <b>d</b>, Distribution of subthreshold membrane potential (blue) and spike threshold (green). <b>e</b>, Spike threshold vs. average before spike. <b>f</b>, Spike threshold vs. depolarization slope before spike. <b>g</b>, Spike threshold vs. preceding interspike interval. Red lines are linear regressions.</p

Model fitting approach.

<p><b>a</b>, Steady-state threshold function, defined by 5 parameters. <b>b</b>, Illustration of the model fitness computation, Voltage trace (blue) and the corresponding dynamic threshold in the model (red). A spike is predicted when the curves cross, and a refractory period follows (grey). Prediction is considered correct when the actual and predicted spikes are within a fixed coincidence window (green). Left: incorrect predictions, right: correct prediction. Note that for the sake of illustration the coincidence window is drawn larger than what it is in reality. <b>c–f</b>, Top: output of the fitting procedure on neuron models with explicit dynamic threshold (green: actual dynamic threshold, red: model prediction), with four different steady-state threshold functions and threshold time constants (bottom). <b>g</b>, The fitting procedure was run for the same model shown in <b>f</b>, but with input currents varying in mean (20–200 pA) and standard deviation (50–400 pA). The shaded area shows the mean and standard deviation of the fitted steady-state threshold function: optimization results were not strongly dependent on the input current used for training. <b>h</b>, Same as <b>g</b>, but with ms and input current with short autocorrelation time constant (0.5 ms).</p

Fit quality vs. threshold time constant.

<p>To show that the optimized threshold time constant (about 260 µs on average) is accurate, we fitted the threshold model to the recordings while setting the time constant to a fixed value, i.e., the time constant is no longer a parameter to be optimized. The plots show the resulting gamma factor (in black, right ordinate) and explained variance (in red, left ordinate) as a function of threshold time constant for 9 cells. Moving the time constant away from its optimal value results in large increases in the fitting error.</p

Fitting results.

<p>The optimization results for all cells are shown for three parameters: high voltage slope (<b>a</b>), low voltage slope (<b>b</b>) and time constant (<b>c</b>). Blue bars correspond to mean ± standard deviation over all recordings categorized by average membrane potential, and red bars (when available) correspond to mean ± standard deviation over all recordings categorized by stimulus condition (e.g. varying ITD with fixed IID). <b>d</b>, Distribution of average distance within cells between steady-state threshold functions (grey) and between steady-state threshold functions and the diagonal (green). <b>e</b>, Distribution of false alarm rates when the models are tested against recordings with a different mean (blue) and with different sound stimulation (red) than used for fitting. <b>f</b>, Same as (d) for the explained variance of measured spike threshold.</p