Fig 1.
Retinal ganglion cells generate reproducible bursts.
Raster plot of a single salamander OFF ganglion cell. Short vertical lines represent single spikes and each row shows spikes that occurred during a single repeat of the stimulation. Spikes of different events are shown in different colors. The gray continuous line shows the normalized light intensity of the stimulus (the mean and SD are 0 and 1, respectively).
Fig 2.
The spike number within a burst encodes the amplitude of light intensity modulation.
(A) 1-, 2-, 3-, and 4-BTA indicate the average of stimulus sequences preceding isolated spikes and 2-, 3-, and 4-spike bursts, respectively. The average and standard error of the mean (SEM) were calculated across n = 41 cells. (B) Difference between 3-BTA and 1-BTA, averaged across n = 41 cells. The thin lines indicate the SEM calculated across the cells. (C) Analysis of s3−1, the stimulus projected onto 3-BTA−1-BTA. The dashed line indicates P(s3−1) averaged across n = 41 cells. The SEM calculated across for P(s3−1) cells is not shown because it was very small. The thick lines correspond to P(s3−1|1-spike), P(s3−1|2-spike), P(s3−1|3-spike), and P(s3−1|4-spike) averaged across n = 41 cells. The thin lines are the SEM calculated across the cells. (D) Similar to (C), calculated for s3−1,burst, which was normalized for values at all time points of isolated spikes and bursts.
Fig 3.
Intraburst ISIs of 2-spike bursts encode an oscillatory component of the visual input.
(A–G) Data from the cell shown in Fig 1. (A) Raster plot. The colored lines represent 2-spike bursts. The short gray lines are the remaining spikes. The gray continuous line shows the normalized light intensity of the stimulus (the mean and SD are 0 and 1, respectively). Event IDs are shown. (B and C) Intraburst ISIs of 2-spike bursts (B) and the average and SD of the spike number (C) of the four events shown in (A). (D) Relationship between 2-spike burst ISIs and the mean spike number. Each dot represents an event with at least one 2-spike burst. The horizontal and vertical axes represent the mean ISI of 2-spike bursts and the mean spike number, respectively. The correlation was −0.15 for this cell. (E) Stimulus sequences preceding 2-spike bursts with an intraburst ISI of < 6.0 ms (top) and > 16.0 ms (bottom) are aligned with respect to the first spike in the bursts. (F) The thick black line indicates the average of all stimulus sequences preceding 2-spike bursts (2-BTA). The thick colored lines indicate the average of the stimulus sequences preceding 2-spike bursts with different intraburst ISIs. The thin lines indicate the SEM values calculated across bursts. (G) The thick yellow and blue lines indicate the deviations from 2-BTA, i.e., the average of the stimulus sequence preceding 2-spike bursts with the longest and shortest 50% of intraburst ISIs, respectively, from which the 2-BTA was subtracted. The thin lines indicate SEM values calculated across bursts. (H) Population analysis. The thick lines indicate the deviation from 2-BTA represented by the thick lines in (G) averaged among 19 cells that generated at least 1500 2-spike bursts. The thin lines represent SEM values calculated among the cells. (I) Analysis of sD2,2-spike, the stimulus projected onto the deviation from the 2-BTA and collected at the time points of all 2-spike bursts and normalized to have a mean = 0 and a SD = 1. The dashed line shows P(sD2,2-spike) averaged across the 19 cells. The thick solid lines are the probability distribution of sD2,2-spike at 2-spike bursts with short, medium, and long ISIs, P(sD2,2-spike|0−10% ISI), P(sD2,2-spike|45−55% ISI), and P(sD2,2-spike|90−100% ISI), respectively, averaged across the 19 cells. The thin lines are the SEM calculated across the cells. (J) Similar to (I), calculated for s3−1,2-spike, the stimulus projected onto 3-BTA−1-BTA.
Fig 4.
Interspike interval (ISI) patterns of three-spike bursts.
Data from the cell shown in Fig 1. (A) Raster plot. The colored lines represent 3-spike bursts. The short gray lines are remaining spikes. The gray continuous line shows the normalized light intensity of the stimulus (the mean and SD are 0 and 1, respectively). (B) Distribution of ISI1 and ISI2. Each dot represents a 3-spike burst. The colored dots are bursts generated in seven different events, four of which are shown in (A) with the same color. The gray dots represent remaining bursts. (C) Variability of ISIs. Each dot represents an event. The horizontal and vertical axes are the average and SD of ISIs in an event, respectively. The gray lines show the linear fits. m1 and m2 are the intersects. (D and E) Coordinate transformation of intraburst ISIs. (D) v1 and v2 determined using Eq (1) provided in the text. Each dot represents a 3-spike burst. (E) u1 and u2 were determined by linear scaling of v1 and v2, as shown by Eq (2) provided in the text. The colors in the circle indicate the burst phases. ~1.5% of bursts are out of the range of the plot in (B), (D), and (E).
Fig 5.
3-Spike burst ISI patterns encode the phase and amplitude of oscillatory components.
(A–C) Analysis of the cell shown in Fig 1. (A) Stimulus sequences preceding 3-spike bursts with different burst phases. Bursts were divided into 12 groups according to the burst phase (bin size = 30°). Stimulus sequences preceding the bursts in each group were averaged and are shown in each row. (B) Average stimulus sequence preceding 3-spike bursts (3-BTA). (C) Deviation from 3-BTA calculated by subtracting the 3-BTA shown in (B) from the preceding sequences shown in (A). (D–F) Population analyses. (D) Same analysis as in (C), averaged among 19 cells that generated at least 1200 3-spike bursts. (E) Thick lines indicate data in (D) at the indicated burst phase. Thin lines indicate the SEM values calculated across the cells. Peaks around −100 ms are indicated. (F) Horizontal axis: , i.e., the distance of the point (u1,u2) from the origin in the u1–u2 plane in Fig 4E. Vertical axis: the root mean square of the oscillatory components between −200 and 25 ms. The error bars indicate SEM values for the 19 cells.
Fig 6.
ISI analysis of bursts elicited by natural scene stimulation.
(A) Responses of a single ganglion cell. (Right) Raster plots. The colored dots indicate 3-spike bursts. The gray dots represent remaining spikes. (Left) Image frames acquired at −60 ms relative to the average timing of the first spike in bursts. White ellipses show receptive field centers determined by reverse correlation and Gaussian fitting. Bar, 1 mm. (B–D) Analyses performed using light intensity at the receptive field center. (B) Analysis of 2-spike bursts of a single cell. The thick black line indicates the average of all stimulus sequences preceding 2-spike bursts (2-BTA). The thick colored lines indicate the average of stimulus sequences preceding 2-spike bursts with different intraburst ISIs. The thin lines indicate SEM values calculated across bursts. (C) Population analysis of the deviation from 2-BTA. For each cell, the deviation from 2-BTA was calculated by subtracting 2-BTA from the average stimulus sequence preceding 2-spike bursts with the longest and shortest 50% of intraburst ISIs. The thick lines indicate the deviation from 2-BTA averaged across the 13 cells that generated more than 800 2-spike bursts (yellow, longest ISIs; blue, shortest ISIs). The thin lines indicate the SEM values calculated across the cells. (D) Deviation from 3-BTA. For each cell, the deviation from 3-BTA was calculated by subtracting 3-BTA from the average stimulus sequence preceding 3-spike bursts with the burst phase within a specific range. The thick lines indicate the deviation from 3-BTA averaged across the 8 cells that generated more than 1000 3-spike bursts. The thin lines show SEM values calculated across the cells. The arrows indicate the first peak before the first spike in bursts.
Fig 7.
Linear reconstruction of the stimulus using 3-spike bursts patterns.
(A) Short vertical lines represent spikes in an example burst where ISI1 = 7 ms and ISI2 = 10 ms. The three thin black lines indicate STAs calculated for 3-spike bursts of the cell used in (Fig 5A–5C) and aligned on the three spikes. The STAs were summed to calculate the reconstructed stimulus (thick gray line). (B) Analysis similar to (Fig 5A) conducted for stimuli reconstructed as in (A) using the same bursts used in (Fig 5A). Color-coding is the same as in (Fig 5A). (C) Population analysis similar to (Fig 5E), conducted for the reconstructed stimuli.
Fig 8.
Identification of independent components that determine burst patterns.
(A) The average value of 2-spike burst ISIs and the average values of 3-spike bursts u1 and u2 were determined for each event. (B, C, E, and G) Data from the cell shown in Fig 1. (B) Dependence of 2-spike burst ISIs on 3-spike burst patterns. Each dot represents an event in which the cell generated both 2- and 3-spike bursts. The horizontal and vertical axes are the averages of u1 and u2 of 3-spike bursts in an event, respectively. The color indicates the average ISI of 2-spike bursts. The arrow shows the direction of the steepest gradient of 2-spike burst ISIs. (C) Trial-to-trial variations of u1 and u2 in each event. Each dot represents a 3-spike burst. and
represent the average u1 and u2 in each event. Dots with the same color are bursts in the same event. The yellow and green lines indicate the orientation of the principle components with the smaller and larger variances, respectively. The lengths represent the SD along the axes (compare with Fig 4E). (D) Population analyses for n = 41 cells. Each dot represents a cell. (Magenta) The direction of the steepest gradient of 2-spike burst ISIs, determined as in (B). (Yellow and green) Principle axes of the trial-to-trial variations of u1 and u2, determined as in (C). The yellow color shows the axis with the smaller variance. Straight and curved lines indicate the circular average and SD, respectively. (E) Distribution of u1 and u2. Each dot represents a 3-spike burst. Dots with the same color are bursts in the same event. The yellow and green lines are the principle axes shown in (C). θ represents the angle between the u1 axis and the principle axis with the smaller variance (yellow line). The approximately independent components w1 and w2 are shown (compare with Fig 4E). (F) Stimulus sequences encoded by the independent components w1 and w2. For each cell, the deviation from 3-BTA were calculated by subtracting 3-BTA from the average stimulus sequence preceding 3-spike bursts with the burst phase within the range centered by θ (for w1) and θ + 90° (for w2). The thick lines indicate the deviation from 3-BTA averaged across 19 cells that generated at least 1200 3-spike bursts (yellow: w1; green: w2). The thin lines show SEM values calculated across the cells. (G) The axes and circle in (E) are plotted on the ISI1–ISI2 plane. (H) The stimulus was projected onto the stimulus feature encoded by w1. sw1,3-spike was defined by collecting the values at the time points of all 3-spike bursts and normalizing them to have a mean = 0 and a SD = 1. The dashed line shows P(sw1,3-spike) averaged for the 19 cells. The thin lines indicate the SEM calculated across the cells. The colored thick lines are the probability distribution of sw1,3-spike at the time points of 3-spike bursts with a small, medium, and large w1, i.e., P(sw1,3-spike|w1<−2), P(sw1,3-spike|−0.5≤w1<0.5), and P(sw1,3-spike|2≤w1), respectively, averaged among the 19 cells. The thin lines show the SEM calculated across the cells. (I) Similar to (H), showing P(sw2,3-spike), P(sw2,3-spike|w1<−2), P(sw2,3-spike|−0.5≤w1<0.5), and P(sw2,3-spike|2≤w1). (J) Similar to (H), showing P(sw1,3-spike), P(sw1,3-spike|w2<−2), P(sw1,3-spike|−0.5≤w2<0.5), and P(sw1,3-spike|2≤w2). (K) Similar to (H), showing P(sw2,3-spike), P(sw2,3-spike|w2<−2), P(sw2,3-spike|−0.5≤w2<0.5), and P(sw2,3-spike|2≤w2). ~1.5% of bursts are out of the range of the plot in (C), (E), and (G).
Fig 9.
Schematic view of burst coding.
The dotted line indicates the sum of the oscillatory components 1 and 2, whose amplitude and phase are encoded by the 3-spike burst pattern.