Sequence Detection at Different Resting Potentials

<p>(A) The temporal profile of the excitatory sequence and the area under the ROC curves for the IFB and IF models in the excitatory sequence detection task at different resting potentials with stimulus SNR = 1/2.</p> <p>(B) The temporal profile of the inhibitory sequence and the ROC areas for the IFB and IF models in the task involving the detection of the offset of inhibitory sequences at different resting potentials with stimulus SNR = 1/2.</p> <p>(C) The temporal profile of the biphasic sequence and the ROC areas for the IFB and IF models in the biphasic sequence detection task at different resting potentials with stimulus SNR = 1/2.</p> <p>(D) The ROC areas for the IFB and IF models in the biphasic sequence detection task at different overall firing rates with stimulus SNR = 1/2 and <i>V_T </i> = −60 mV. The mean firing rate of the models was varied by changing the gain of the filter relating stimulus intensity to membrane potential. </p

Detection of the Offset of Inhibitory Luminance Sequences

<p>(A) LGN responses to a noisy stimulus in which an inhibitory sequence randomly appeared were simulated. The stimulus was classified as <i>S</i>₀ (black) or <i>S</i>₁ (red) depending on whether or not each interval contained the excitatory transient of the sequence. A typical realization of the stimulus with SNR = 1/2 and sequence duration = 128 ms is shown (intensity averaged over all pixels in RF center). The black line indicates the actual stimulus and the gray line indicates the underlying sequence. </p> <p>(B) Voltage traces of the IFB and IF responses to the stimulus shown in (A) at two different resting potentials, <i>V_R </i> = −67 mV (top) and <i>V_R </i> = −50 mV (bottom), with <i>V_T </i> = −60 mV. The interval in the response that corresponds to condition <i>S</i>₁ is shaded (response was shifted for presentation to remove latency between stimulus and response). The spike threshold ( <i>V_Θ, </i> green), burst de-inactivation potential and threshold ( <i>V_T, </i> red), and resting potential ( <i>V_R, </i> blue) are shown. </p> <p>(C) The probability distributions of the firing rate of the IFB and IF models during the <i>S</i>₀ (black) and <i>S</i>₁ (red) stimulus conditions at <i>V_R </i> = −67 mV (top) and <i>V_R </i> = −50 mV (bottom). </p> <p>(D) ROC curves for the IFB and IF models at <i>V_R </i> = −67 mV (top) and <i>V_R </i> = −50 mV (bottom). The area under the ROC curve is indicated. </p

The Luminance Sequences That Trigger Burst Events

<p>(A) The BTAs calculated from simulated responses to a two-minute segment of natural scene movie at different resting potentials. The resting potential of the model and BP of the response corresponding to each BTA are indicated. Full spatiotemporal BTAs were calculated, and the plots show the intensity of the BTA averaged over all pixels in the RF center. Each BTA was scaled so that the integral of its absolute value was 1.</p> <p>(B) A plot of E/I ratio of the BTA versus resting potential for simulated responses to natural scene movies. E/I ratio was calculated as the ratio of the areas of the excitatory and inhibitory components of the BTA (see inset).</p> <p>(C) The BTAs calculated from the experimental responses of three LGN Y cells recorded at different times during a single experiment to natural scene movies (average of nine different two-minute segments). The BP of each response is indicated. Spatiotemporal BTAs were averaged and scaled as in (A).</p> <p>(D) A scatter plot of E/I ratio of the BTA versus BP for a sample of 27 LGN cells (11 X cells, 16 Y cells). E/I ratio was calculated as described in (B).</p> <p>(E) The normalized BTAs for three LGN Y cells. BTAs were normalized for the temporal correlations in the natural scene movies by spectral normalization (see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0040209#s4" target="_blank">Materials and Methods</a>). The non-normalized BTAs corresponding to each normalized BTAs are shown in gray (same BTAs as in (C)). </p> <p>(F) A scatter plot of E/I ratio of the normalized BTA versus BP for a sample of 27 LGN cells. E/I ratio was calculated as described in (B).</p

Detection of the Onset of Excitatory Luminance Sequences

<p>(A) LGN responses to a noisy stimulus in which an excitatory sequence randomly appeared were simulated with and without bursts using the IFB and IF models (see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0040209#s4" target="_blank">Materials and Methods</a>). The stimulus was classified as <i>S</i>₀ (black) or <i>S</i>₁ (red), depending on whether or not each interval contained the excitatory transient of the sequence. A typical realization of the stimulus with SNR = 1/2 is shown (intensity averaged over all pixels in RF center). The black line indicates the actual stimulus and the gray line indicates the underlying sequence. </p> <p>(B) Voltage traces of the IFB and IF responses to the stimulus shown in (A) at two different resting potentials, <i>V_R </i> = −67 mV (top) and <i>V_R </i> = −50 mV (bottom), with <i>V_T </i> = −60 mV. The interval in the response that corresponds to condition <i>S</i>₁ is shaded. (The response was shifted for presentation to remove latency between stimulus and response). The spike threshold ( <i>V_Θ, </i> green), burst de-inactivation potential and threshold ( <i>V_T, </i> red), and resting potential ( <i>V_R, </i> blue) are shown. </p> <p>(C) The probability distributions of the firing rate of the IFB and IF models during the <i>S</i>₀ (black) and <i>S</i>₁ (red) stimulus conditions at <i>V_R </i> = −67 mV (top) and <i>V_R </i> = −50 mV (bottom) with stimulus SNR = 1/2. Distributions were calculated using the response to a stimulus segment that contained 100 sequences. </p> <p>(D) ROC curves for the IFB and IF models at <i>V_R </i> = −67 mV (top) and <i>V_R </i> = −50 mV (bottom) calculated from the distributions in (C) using likelihood ratios as described in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0040209#s4" target="_blank">Materials and Methods</a>. The area under the ROC curve is indicated. </p

Quadratic efficiency is relatively invariant to tuning width.

<p><b>A</b>. When taking the mean (normalized) efficiency curve across the spectrum of reasonable spike count tuning widths (HWHH, degrees), the arragement of optimal efficiencies does not appear to be patterened in any particular way. <b>B</b>. When broken out into individual efficiency curves we see that for each tuning width a quadratic polynomial still remains the best fit for most tuning widths. At pathologically narrow tuning curves, we see that higher synchronization is indeed absolutely preferable. We also note that the sigmoid fit to mean data arises, in part, because the peak of the polynomials are distributed over a range and the mean of them produces a roughly constant function below 25 ms of timing jitter.</p

Synchrony does not affect the relationship between and mean and variance of output, but does affect discriminability.

<p><b>A</b>. Across all values of synchrony the mean and variance increase in roughly the same linear pattern; each dot is a stimulus orientation from 0 to 180. At high synchrony values relationship is ultimately violated as the spike count variance plateaus, when the timing variance is smaller than the integration window. Jitter values (in units of ms) are indicated next to the dots that represent the simulation results corresponding to those minimum jitter values. <b>B</b>. Each curve shows the spike probability distribution at the preferred orientation. Increasing synchrony shifts the spike count distributions away from the origin, giving more freedom to spread and making adjacent orientations more distinguishable (not shown).</p

Filling in population from recorded neuron receptive fields.

<p><b>A</b>. The original simultaneously recorded receptive fields of 5 neurons. <b>B,C</b>. The original receptive fields were duplicated and randomly shifted so that the resulting population (<b>C</b>) matched the previously measured distribution of RFCD values (<b>B</b>) Solid circles indicate RFCD measures from the population in <b>C</b>, while the dashed line indicates the expected distribution (see Methods). <b>D</b>. The spatial shift in each receptive field describes a particular distance perpendicular to the stimulus orientation that each receptive field shifts; using the spatial and temporal frequencies of the stimulus this can be translated into a timing shift. <b>E</b>. Once spike times are appropriately shifted for each neuron in the population, rastergrams reveal spiking alignment only for 90 and 270 degree stimulus orientations.</p

Tuned output of cortical model.

<p><b>A</b>. Example tuning curve (black line) at 6 ms of minimum jitter is fit very well by a Gaussian curve (gray dashed line). Standard deviation is illustrated at 10 degree increments, revealing sometimes significant variance in output spike count. In general this reflects the variability of the input spike counts. <b>B</b>. The integrate and fire cortical model outputs tuning curves that are well-described by a Gaussian model with an amplitude that decreases with increasing minimum jitter (dark red: 6 ms, dark blue: 40 ms). <b>C</b>. The tuning width varies over a small range across the entire range of minimum jitter values simulated.</p

Information efficiency peaks as synchrony increases.

<p><b>A</b>. Estimator standard deviation monotonically decreases as the minimum jitter of the input decreases. <b>B</b>. The absolute amount of information decreases approximately linearly with increasing minimum jitter. Error bars of ±1 S.D. are shown to illustrate deviations from linearity are not strictly due to random chance. <b>C</b>. When weighted by the total output spike count, information efficiency peaks at 15 ms of jitter and then decreases for inputs with smaller amounts of jitter.</p

Model and simulated output characteristics.

<p><b>A</b>. The model imposes simple control over input spike synchrony and uses a leaky integrate-and-fire construction to determine membrane potential and output spike times. <b>B</b>. The simulated cortical membrane potential has an amplitude that is strongly affected by the stimulus orientation, but also a mean value that changes with orientation due to reset characteristics. <b>C</b>. Orientations which are closer to the preferred orientation produce dramatically increased numbers of spikes.</p