Table 1.
Detailed description of datasets.
Figure 1.
Orientation tuning of spike latencies.
(A) Raster plot for of a sample cell in the data (taken from dataset 1 in Table 1). For each orientation, 100 randomly chosen trials (out of 400) are shown. For clarity, only the first 120 ms after stimulus onset are shown. Stimulus duration was 400 ms. (B) Cumulative distribution functions of first, second and third spike latencies (n denotes the spike number) for the same neuron. Each row corresponds to a different stimulus orientation and the gray levels represent the probability of the spike occurring before the time indicated on the abscissa. (C) Tuning curves of first, second and third spike latencies, computed as level curves of the corresponding cumulative distributions at 0.5. Cosine fits are shown as solid lines and are also shown as dashed lines in (A). (Error bars were calculated according to the method described in Materials and Methods, but are often smaller than the marker size). (D) Rate tuning curve for the same cell over the entire stimulus duration (black circles) and a fitted von-Mises function (solid line). (Error bars were calculated using the standard error of the mean, but are smaller than the marker size).
Figure 2.
Additional examples of spike latency tuning.
Each column, (A)–(C), corresponds to data from a different unit. First row: Raster plot for each of the 8 orientations. For each orientation, 100 randomly chosen trials are shown for 120 ms after stimulus onset. Second row: PSTH (Post Stimulus Time Histogram) for the same time window. Third row: Tuning curve of first spike latency. Cosine fit is shown as a solid line. Fourth row: Rate tuning curve (black circles) and a fitted von-Mises function (solid line). The cell in (A) is taken from dataset 1 in Table 1, in which stimulus duration was 400 ms and the number of trials was 400. The cells in (B) and (C) are taken from dataset 5 in Table 1, in which stimulus duration was 300 ms and the number of trials was 300. These are the same 3 cells as in Figure 5.
Figure 3.
Population statistics of latency tuning.
The tuning curves were fitted using a cosine function, , where θ is the stimulus orientation and φ is the latency preferred orientation. (A) Dependence of the mean DC component, A, on spike number (averaged over the population). (B) Dependence of the modulation amplitude, B, on spike number (averaged over the population). Error bars in (A) and (B) represent ±onestandard error of the mean. (C) A scatter plot of A vs. B for first spike latency (each point represents one unit; correlation coefficient 0.85). The cells that are marked in red are onset detectors (see text and Figure 4). The statistical analyses in panels (A)–(C) were performed using dataset 3 in Table 1 (159 cells). Similar results were obtained for the other 4 datasets. The correlation coefficients between A and B were, in decreasing order: 0.88, 0.84, 0.76 and 0.66 (D) Histogram of the difference between the first spike latency-based preferred orientation and the conventional rate-based preferred orientation. In order to avoid artifacts from poorly tuned cells, the histogram shows only cells for which the modulation, B, of the first spike latency tuning curve was larger than 15 ms (∼50% of the cells from datasets 1 to 5 in Table 1).
Figure 4.
(A) Mean spontaneous firing rate vs. the modulation amplitude, B, of the first spike latency tuning curves. Each point corresponds to a single neuron. All neurons in this figure were taken from the same dataset (dataset 3 in Table 1). Neurons were categorized as onset detectors if the modulation was smaller than 15 ms and the spontaneous rate was below 5 spks/sec (shaded box in the lower left corner, 25 cells). (B) ‘ROC’ curve of the onset detection mechanism for a time window of 20 ms. The inset shows the false alarm rate as a function of detection threshold in standard deviations. (C) Mean onset time as a function of detection threshold. The gray band represents ±1 standard deviation. The black circles in (B) and (C) mark the detection threshold of 4 standard deviations above baseline, which we use throughout the paper. (D) Distribution of onset times. The number of spikes was required to be 4 standard deviations above the mean number of spikes in a 20 ms window during spontaneous firing.
Figure 5.
Orientation discrimination using single cell spike latencies and firing rates.
(A) Neurometric curves for a single cell using the first spike latency (red), second spike latency (green), third spike latency (blue) and the firing rate (black). These curves represent the probability of correct discrimination in a 2AFC paradigm where one stimulus is at the cell's preferred orientation, PO, and the other at PO±Δθ. (Error bars represent the standard error of the mean, but are often smaller than the marker size). (B) Neurometric curves for 90° discrimination as a function of decision time. The black curve represents probability of correct discrimination based on firing rate for different time windows starting at stimulus onset (the curve starts at 60 ms because deviation from spontaneous activity starts at about this time). (The gray band represents ± standard error of the mean). The horizontal line represents the asymptotic performance using firing rate from the full response (black circle at 90° in A). The filled circles represent decisions using first, second and third spike latencies with the same color code as in (A) (error bars are smaller than the marker size). Each circle is plotted at the corresponding mean decision time. This cell was taken from dataset 1 in Table 1. (C)–(F) The same as (A) and (B) for two other cells from dataset 5 in Table 1. (The 3 cells in this figure are the same cells as in Figure 2).
Figure 6.
Statistics of orientation discrimination using single cell spike latencies and firing rates.
(A)–(B) Pc (probability of correct discrimination) using first spike latency vs. Pc using the spike count of the entire response. Each point corresponds to a single cell. The identity line is shown for comparison (solid black line). (A) Comparison of performance at a fine resolution discrimination task, Δθ = 22.5°. (B) Comparison of performance at a coarse resolution discrimination task, Δθ = 90°. (C) Proportion of cells above a given performance level. The dashed curves correspond to a 22.5° discrimination task and the solid curves to a 90° discrimination task. Different curves correspond to first spike latency (red), second spike latency (green), third spike latency (blue) and firing rate from the entire response (black). (D) Comparison of latency and rate performance at a given decision time. The abscissa is the difference between Pc using the n'th spike latency and Pc of the conventional rate code readout, where the rate is estimated from the spike count in the time window from stimulus onset to the mean decision time using the n'th spike latency. These differences correspond to the vertical distances between the circles and the solid black curve in the right panels of Figure 5. The curves show the proportion of cells above a given difference. The color code is the same as in (C). The data for all panels are from the tuned cells (B>15 ms) in datasets 1, 2, 4 and 5 in Table 1 (244 cells).
Figure 7.
Orientation discrimination using the n-tWTA readout in populations of neurons.
(A–C) Probability of correct discrimination (Pc) as a function of population size (N) for two populations that differ in preferred orientation by 45° (A), 67.5° (B) and 80° (C). Different curves correspond to different values of n (see legend). (D–F) Probability of correct discrimination using the optimal value of n for each N (for the above pairs of populations). The inset shows the optimal n for each N. (G–I) Mean decision times relative to the onset signal for the neurometric curves in the top panels. (Decision times larger than 200 ms are not shown. Error bars represent ± standard error of the mean). The black circles mark the decision times when n = N; i.e., when the number of spikes used for the decision is equal to the group size. Note that the data for the left two columns are from dataset 5 in Table 1 whereas the data for the right column are from dataset 3. These datasets had different levels of spontaneous and evoked firing, which are responsible for the differences in the optimal n and in the decision times.
Figure 8.
Effect of onset time on orientation discrimination using the first spike latency.
To investigate the effect of onset time, we measured the spike times relative to an artificial reference signal. The curves show the probability of correct discrimination (Pc) as a function of onset time for two populations that differ in preferred orientation by 90°. Each curve corresponds to a different population size, N (see legend). The black vertical line and the gray band represent the mean onset time ±1 standard deviation using the onset detection mechanism.
Figure 9.
Discrimination among multiple alternatives using the n-tWTA in populations of neurons.
(A) The tuned neurons in one of the datasets (dataset 3 in Table 1) were divided according to their preferred orientations into M groups of equal orientation width, Δθ = 180°/M. To illustrate this division, each point on the circle represents a neuron (the angle is twice the preferred orientation). The left plot illustrates division into M = 4 groups of width Δθ = 45° and the right plot illustrates division into M = 9 groups of width Δθ = 20°. Each group is labeled by the orientation of its center. The lengths of the blue bars are proportional to the number of neurons in each group. (B) Probability of correct discrimination of the n-tWTA as a function of group width. The different curves correspond to n = 1,2,3,4,5 and 20. (C–D) Distribution of errors for group width of Δθ = 1° for n = 1 (C) and n = 2 (D).
Figure 10.
Neuronal architectures for implementing the tWTA readout for a two-alternative task.
The figure describes in a qualitative manner neuronal architectures that can implement the tWTA readout in the context of a two-alternative task. The inputs from population A and population B represent the two alternatives. Both architectures rely on reciprocal inhibition for implementing a ‘race to threshold’ competition but they differ in the implementation of the gating mechanism (see Discussion for details). (A) Implementation of the gating mechanism using NMDA synapses. (B) Implementation of the gating mechanism using disinhibition.