Figure 1.
In vivo intracellular recordings.
a, 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: http://openclipart.org/detail/17566/cartoon-owl-by-lemmling. b, Two spikes from the traces in (a); red dots indicate the estimated spiking threshold. c, Trace from (a) shown in phase space:
vs.
. Spike threshold is detected when
exceeds a fixed value (red dashed line). d, Distribution of subthreshold membrane potential (blue) and spike threshold (green). e, Spike threshold vs. average
before spike. f, Spike threshold vs. depolarization slope before spike. g, Spike threshold vs. preceding interspike interval. Red lines are linear regressions.
Figure 2.
a, Steady-state threshold function, defined by 5 parameters. 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. c–f, 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). g, The fitting procedure was run for the same model shown in f, 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. h, Same as g, but with ms and input current with short autocorrelation time constant (0.5 ms).
Figure 3.
Fitting procedure applied on a multicompartmental model of a cortical neuron
[7]. a, 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, 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 [26]). c, Predicted threshold resulting from the fitting procedure vs. measured threshold for all spikes. The dashed line is the identity. d, Steady-state threshold function of the optimized model (red) compared to the corresponding function calculated from the properties of sodium channel inactivation. e, 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). f, Logarithm of the sodium inactivation variable h at the axonal initiation site plotted against predicted threshold for the entire simulation, excluding spikes.
Figure 4.
Fitting procedure applied on an intracellular voltage trace.
a, Top: voltage trace (top, black) and predicted threshold (red). Bottom: steady-state threshold in the fitted model. b, vs. predicted threshold for the trace in (a). The identity line (red) sharply separates subthreshold fluctuations from spikes.
Figure 5.
Steady-state threshold curves.
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.
Figure 6.
The optimization results for all cells are shown for three parameters: high voltage slope (a), low voltage slope
(b) and time constant
(c). 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). d, Distribution of average distance within cells between steady-state threshold functions (grey) and between steady-state threshold functions and the diagonal (green). e, 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. f, Same as (d) for the explained variance of measured spike threshold.
Figure 7.
Fit quality vs. threshold time constant.
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.
Figure 8.
a, Top: voltage trace (black) and the corresponding fitted threshold (red). Bottom: the effective signal (black) is the difference. A spike occurs when it crosses 0 mV (red). b, Distribution of
(top) and of the effective signal (bottom). c, Autocorrelogram of
(top) and of the effective signal (bottom), showing the half-height width (HHW). d, Top: postsynaptic potential (PSP, black) and its effect on the threshold (red). Bottom: effective PSP. e, Standard deviation of the effective signal vs. standard deviation of
(line: identity). f, HHW of the effective signal's autocorrelogram vs. HHW of
's autocorrelogram.