The retina was stimulated with a black and white grating (see inset Figure
G). The grating constantly illuminated the retina, with the contrast borders aligned to the electrode rows of the multi-electrode array (MEA). Stimulation started by moving the grating up or down with one of 22 different, randomly chosen velocities. Stimulation paused when the contrast borders reached the neighbouring electrode rows (Figure
G). Movement direction changed after every second movement step. This ensured that the grating reversed in half of the stimuli.
Figure 1 Responses to different velocities. (A) Example raster plot showing the activity of the 32 recorded ganglion cells from experiment 2 during 2500ms of movement stimulation with various velocities (2 m/s, 5 m/s, 3 m/s, 2 m/s, 6 m/s). The responses show a (more ...)
Generally, the recorded ganglion cells showed precise spike timing with short latencies after movement onset when stimulated with the different velocities. This is depicted in the example shown in Figure
. The raster plots show that all units elicited only a few spikes within a small time window (Figures
A & D). In this example spontaneous activity was completely absent, and at movement offset no responses were observed. The population PSTH of all units illustrates the sharp response peaks for all velocities (Figures
B & E).
Comparison of stimulus reconstruction with latency, first inter-spike interval and rate
To see which response component conveys most information about the 22 velocities, we calculated latencies, the first inter spike interval (ISI) and the rate in a 100 ms time window after stimulus onset. In addition to the latencies calculated with respect to the known stimulus onset (absolute latencies) we also calculated the population responses to the various velocities and determined the latencies of the single ganglion cell responses with reference to these population response onsets. This will be termed relative latencies in the following.
The tuning curves of the whole population in Figures
A – D show the velocity dependence of the respective response component. For absolute latencies the shortest median values of 22 ms occurred at stimulus speeds around 5 and 6 m/s in both directions (Figure
A). This is comparable to the response latencies to light flashes of the same intensity with an average value of 21 ms (not shown). Latencies increased towards both higher and lower velocities. For the first ISI no velocity dependence of the median values could be observed (Figure
B). However, the response variability for all cells taken together differed between downward and upward movements. The 50% percentiles increased for the upward directions. The same was true for the spike rate (Figure
C). Response rate variability was smaller for downward movements compared to upward movements.
Figure 2 Comparison of absolute latency, first inter spike interval, rate and relative latency. (A) The tuning curve for absolute latencies of the whole population over all stimuli showed clear velocity dependence. The median of the fastest responses was 22ms (more ...)
Velocity estimation with the maximum a posteriori (MAP) estimator on basis of the respective response component is shown in Figures
E – H. Estimations using absolute latencies yielded nearly perfect stimulus reconstruction (Figure
E). Errors occurred mainly in mistaking the different velocities producing similar latencies, e.g. -20 m/s and -1 m/s or the same velocities for different directions, e.g. -20 and 20 m/s. This has an influence on the centre of mass for all estimations, which is mainly shifted to lower speeds both for downward and upward movements. The best estimation by a single trial was able to correctly reconstruct all velocities (Figure
I, red line).
In contrast to absolute latency, the overall estimations based on first ISI (Figures
F & J) or rate (Figures
G & K) were not able to reconstruct the stimulus velocity. The best trial yielded five correct velocity estimations out of 22 for the rate (red line in Figure
K), but none for the first ISI (Figure
J). In addition, the centres of mass showed clear direction dependence in case of the rate (Figure
G), yet within each direction velocity could not be discriminated. Weak signs of direction discrimination were also found for the first ISI, but the centres of mass were always in the region of estimated positive direction, independent of whether the stimulus direction was upwards or downwards (Figure
Absolute latencies versus relative latencies
These results show that velocity estimation with absolute latencies is superior to estimation with the first ISI or the spike rate. The brain, however, has no knowledge about stimulus onset – information that is contained in absolute latency determination.
Therefore, we compared velocity estimation based on the known stimulus (absolute latencies) and the population response (relative latencies).
Since the population response results from the addition of the single responses, the population response onset latencies consequently showed a similar behaviour as the average of the single ganglion cell response latencies (the population response onset latencies are shown for the single experiments in Figures
K –O). Consequently, the tuning curve of the relative latencies of all ganglion cells, calculated with respect to the population response onsets, were rather constant around 10 ms (Figure
D). Despite the fact that the tuning curve of the relative latencies of the whole population showed no velocity dependence, the accuracy of the overall velocity reconstruction was still acceptable (Figure
H). Compared to estimation with absolute latencies (Figure
E), however, the centres of mass were more deteriorated, especially at higher velocities. The best trial still yielded 18 correct estimations out of 22 (Figure
Figure 4 Comparison of different experiments. The 5 experiments showed differences in reconstruction quality based on absolute latencies (A to E). Experiments 1 - 3 (A - C) showed very good results while in experiments 4 and 5 (D+E) many errors (more ...)
Velocity tuning curve types for the different response components
The tuning curves of the whole population from Figures
A – D potentially mask ganglion cell subpopulations with differing tuning curves that might be important for stimulus reconstruction. Therefore, cluster analysis was applied to separate the single cells into distinct types of velocity tuning functions based on their individual tuning curves. The median values of the relevant response components for each velocity were used from each individual cell, respectively.
Three W-shaped tuning curve types could be discriminated for absolute latencies (Figure
A – C). They were symmetrical (Figure
A) or asymmetrical with shortest latencies for upward movement (Figure
B) or with shortest latencies for downward movement (Figure
Figure 3 Tuning curve types. Cluster analysis was applied to separate the single cells into distinct types of velocity tuning functions based on their individual tuning curves. The numbers (n) indicate how many cells belong to each cluster. (A – C) One (more ...)
Two tuning curves types were identified based on the first ISI (Figures
D & E). One had very short first ISI for all velocities (Figure
D) and the other type had short ISI for downward movement and long first ISI for upward movements (Figure
F), indicating directional tuning. The latter tuning curve type showed very high variability among cells for upward movement. Both types exhibited little variability among cells for downward movements.
Four tuning curves types were separated based on rate (Figures
F – I). Three of them showed a similar asymmetry in variability among cells: high variability for upward movements, very precise rates among cells for downward movements (Figures
H – I). Two of these tuning types (Figures
H & I) showed directional tuning and one had a flat tuning curve (Figure
G). The remaining tuning curve type is also flat, however, it exhibited similar variability among cells, both for upward and downward movements and a slightly lower average rate (Figure
Four tuning type clusters were identified for relative latencies (Figures
K - N). All of them showed directional tuning: one of them with longer relative latencies for upward movement (Figure
M), and three with longer latencies for downward movements (Figures
K, L & N). The latter three types were discriminated mainly based on the duration of the relative latencies: short latencies (Figure
N), intermediate latencies (Figure
K), and long latencies (Figure
These results show that subpopulations of ganglion cells with different tuning curves exist for the various response components. By comparison of Figure
these results also qualitatively explain the differences in stimulus reconstruction using the different response parameters. The good velocity tuning in all three tuning curve types for absolute latencies is in accordance with the good velocity reconstruction using this parameter (Figure
E). For rate the directional selective tuning curves of about half of the recorded cells are in accordance with the good reconstruction of movement direction (Figure
G), but since no velocity tuning exists in the tuning curves, velocity could not be reconstructed. In the case of the first ISI only 26 out of 109 cells showed directional tuning, with high variability for upward movements among cells. In the reconstruction this obviously led to some degree of direction reconstruction, as indicated by the centres of mass in Figure
F, however, with a shift in the reconstruction to upward movement. For the case of relative latencies the tuning curves are qualitatively in good agreement with the centres of mass for velocity reconstruction shown in Figure
H. It remains still unclear, however, how the remaining velocity reconstruction, indicated by the diagonal in Figure
H, is accomplished.
Comparison of individual experiments
The ability to reconstruct the different velocities on the basis of latencies differed between the individual experiments. Whereas three of the five experiments showed a very good reconstruction using latency as response parameter (Figures
A – C), two experiments performed significantly worse (Figures
D and E), independently whether reconstruction was based on absolute or relative latencies (Figures
D, E, I, J).
When using absolute latencies for estimation obviously some information about stimulus velocity was retained in experiments 4 and 5 (Figures
D and E). Most errors occurred in mistaking different velocities producing similar latencies or mistaking velocities for opposite directions. This information was gone when using relative latencies, where only estimation of the correct direction was possible in experiment 4 (Figure
I) and no correct estimation at all was possible in experiment 5 (Figure
J). The tuning curves of the population response onsets showed clear velocity dependence in all experiments (Figure
K - O), but the variability in experiments 4 and 5 was considerably higher. Since the population response onset is determined by the sum of the single cell responses this led us to the suggestion that precision of single cell responses might vary between experiments.
Precision of single cell latencies
The temporal difference between population response onset and the following spike of each individual cell, respectively, is the relevant parameter for the MAP estimation based on relative latencies. Therefore, global tuning curves from all cells (Figure
D), and average tuning curve types from subpopulations of cells as shown in Figure
K - N, potentially mask important information retained in single cell tuning curves. An example is shown in Figure
for one cell from experiment 1. The tuning curve for absolute latencies from this cell is symmetrical and belongs to the tuning type shown in Figure
A. However, the individual tuning curve shows considerable differences in the variability of the absolute latency between upward and downward velocities, not retained in the average tuning curve from Figure
A. A raster plot of the responses of this cell to all presentations of the stimuli with velocities of -6 m/s and +6 m/s illustrates this differing behaviour for upward and downward movement (Figure
C). This difference in variability is also visible for the tuning curve based on relative latencies (Figure
B), which belongs to the tuning curve type shown in Figure
M. In addition, this cell still exhibits shallow velocity tuning for upward movements, the region of the tuning curve with low variability.
Figure 5 Variability of response latency in single cells. The latency tuning curves of many cells showed differing response variability, depending on the direction of movement, as depicted in this example from unit 1 in experiment 1. (A) In this example, the typical (more ...)
This observation suggested that the estimation quality might correlate with the precision of the latencies of individual cells, which in turn might be different for upward and downward movements. With high precision latencies even a shallow velocity dependence will contribute to correct velocity reconstruction. Therefore, we determined the quartile ranges as a measure of precision for each velocity and for each cell separately and plotted these values against the number of correct estimations for each cell. This was done for absolute and relative latencies, and the results are shown in Figure
, separately for the different experiments 1 to 5. In the experiments 1 – 3, with good reconstruction, quartile ranges were in most cases below 10 ms. In addition, the number of correct estimations correlated with the quartile range. A smaller quartile range correlated with a higher number of correct estimations, a larger quartile range with a lower number of correct estimations. This was independent whether absolute or relative latencies were used or whether upward or downward movement was applied. The difference between absolute and relative latencies was, however, that even for similar quartile ranges the number of correct estimations was always smaller when based on relative latencies (see for instance Figure
; experiment 3). In contrast to experiments 1 to 3, quartile ranges were mostly above 10 ms in experiments 4 and 5. This correlated with low numbers of correct estimations.
Figure 6 Correlation of correct estimation with variability of response latency. The number of correct estimations was plotted against the variability of the response latency of each cell, quantified by the median of the latency quartile ranges. Data are separately (more ...)
When iteratively increasing the number of ganglion cells used for estimation, the calculated mean of the root mean square error (RMSE) for stimulus reconstruction with relative latencies decreased for all individual experiments (Figures
A-E). Experiment two (Figure
B) with the largest number of recorded cells (n
32) performed best with a mean RMSE of 4.72 m/s. In experiment 5 the mean RMSE stayed almost constant at a high level (Figure
E). When estimating the stimulus velocity with all 109 units of the combined experiments, the mean RMSE decreased to 0.028 m/s with a parallel decreasing standard deviation.
Figure 7 Reconstruction error for increasing number of ganglion cells. (A – E) The mean of the root mean square error (RMSE) for stimulus reconstruction with relative latencies was calculated for each experiment with random choice of increasing number (more ...)