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Interspike intervals within retinal spike bursts combinatorially encode multiple stimulus features
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. 
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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).
doi: https://doi.org/10.1371/journal.pcbi.1007726.g008