Table 1.
Quantification of PV ganglion cell parameters.
BS, black spot; WS, white spot; NatS, natural scene/movie. Note, a one degree visual angle corresponds to ~31 μm on the mouse retina [48]. Blue rows are OFF layers, rose are ON layers and the green coloured row (PV3) is a border area between ON and OFF strata in the IPL. PV0 are bistratified cells.
Fig 1.
Validation of the QMI approach.
Reconstruction of a model neuron RFV: the spatio-temporal filter of the model cell (original filter) and the extracted RFV in response to natural stimuli (QMI filter, shown below each original filter). Each stimulus vector (x) consists of T frames of the size 101x101 pixels, total number of stimulus frames was 3175. The nonlinearity used was half squaring (positive filter responses squared, negative set to zero). The synthetic cell response was determined by averaging the number of spikes per frame for 25 repetitions of the image sequence. The average of the total number of spikes for the complete stimuli is denoted 〈spikes〉. A, Gabor filter (σx = 60μm, γ = 1.3, λ = 94μm, θ = π/6), T = 1, 〈spikes〉 = 268, stand. dev. = 20, Q = 0.79. Gabor filter: . B, vertical edge filter (T = 1, length 100μm, peak-to-peak separation 45μm, 〈spikes〉 = 427, Q = 0.78). C, horizontal edge (T = 1, 〈spikes〉 = 733, Q = 0.77). D, arbitrary angle (θ = 30°, T = 1, 〈spikes〉 = 635, Q = 0.81). E, Filter created by subtraction of two time-varying 2D Gaussians functions (σx = σy = 60 μm, separation 37.5 μm, T = 3, 〈spikes〉 = 644). F, Center-OFF filter (150μm diameter, T = 6, 〈spikes〉 = 304). G, Average number of spikes vs. projection of input vectors onto RFV, case (f). H, “Aperture cell” filter, detecting a moving edge (θ = 30°, T = 3, 〈spikes〉 = 209). I, Moving bar filter (T = 2, length 100μm, 〈spikes〉 = 372)–we added one more frame in the recovered filter to show that the QMI correctly returns an “empty” frame. J, Projection (Q) of the recovered filter vector on the original filter (Gabor filter case (a)) vs. average number of spikes per frame. Plotted are the average values for Q and error bars (n = 7 repeats). The same natural scene stimulus of 3175 frames used in each case. Insets show typical recovered filters for a selection of points (the average total number of spikes is: 2, 10, 75, 468 and 6496).
Fig 2.
Validation of using MI to estimate the Receptive Field Radius and the Cell Memory.
Left column, MI contained within an increasing radius. The decrease in MI indicates overfitting (see Results). The vertical red arrow indicates the identified radius before the onset of the overfitting artifacts (RMI). Middle column, the original filter with a circle of the radius RMI. Right, MI vs. number of frames that the RFV contains. The relevant receptive field history (or the Cell Memory) was estimated as for the radius and marked with a red arrow. (a) Gabor filter, same as in Fig 1(a), average number of spikes 650. (b) Gabor filter: σx = 38 μm, γ = 1.3, λ = 94 μm, θ = −π/7, 〈spikes〉 = 642. (c) Same filter as in Fig 1(f).
Fig 3.
QMI compared with STA technique.
The original and recovered filters using the QMI, STA and wSTA techniques. Reconstruction in the case of: natural stimulus (101x101 pixel frames) (a) filter from Fig 1(d), (b) filter from Fig 1(e), and white noise with (c) uniform and (d) Gaussian distributions, 16x16 pixel frame resolution input. (e) Direct comparison in accuracy between QMI and STA using the RFV projection measure (Q) vs. number of frames (and spikes) in the stimuli. Insets show the recovered filters for a selection of points. It is known that if the input signals are not white then the STA is a broadened version of the original filter; STA panels in (a) and (b). The attempt to remove correlations by multiplying the STA recovered filter by the inverse of the a priory covariance matrix (wSTA) doesn’t help much because the natural scene input is non-Gaussian, as discussed in detail in [25].
Fig 4.
Response of the eight PV-retina cell types (PV0-PV7) to three natural scene movies (labelled catMov1, catMov2 and catMov3).
For each cell type a different colour is used and three individual recordings are shown in a line. Each point represents a spike and red vertical lines represent the start (at 3 s) and the end of the movies. Before and after the stimuli the retinas were exposed to uniform gray illumination. The stimulus movies were centred around each individual cell being recorded from, i.e. every single recorded cell had approximately identical input. Additional raster plots are shown in S4 and S5 Figs.
Fig 5.
Receptive Field Vectors and estimates of the RFV radius and cell’s memory for: (A) PV0 and (B) PV1 cell types (results for representative cells shown).
a) Single RFV that maximally separate spiking from non-spiking inputs. Brighter responses represent higher (illumination) values; color bar shown below (colourmap is Matlab parula, range is [–1,1]. Two circles (diameters 350μm and 100μm), assist in the estimation of the size of the structures. Right, average number of spikes generated vs. projections of the input vectors onto the RFV. b) 3D plots of the RFVs and standard error, estimated as described in Methods. PV0: azimuth = 10°, elevation = 80°, PV1: azimuth = -45°, elevation = 10° (frames: 0, -1, -2) and elevation = -10° (frames: -3 and -4). Standard error plots: same azimuth, elevation = 90°, note different colourmap (Matlab jet, range is [0,1]). c) MI contained within an increasing radius across the entire RFV. The decrease in the MI indicates overfitting (see text for explanation). The vertical red line represents the identified radius before the onset of the overfitting artifacts (RMI). d) MI vs. number of frames that the RFV contains. The relevant receptive field history (or the Cell Memory) was estimated as in c) and marked with a red arrow.
Fig 6.
RFVs for: (A) PV2 and (B) PV4 cell classes.
a) 2D RFVs and average number of spikes vs. projections of the input vectors, b) 3D RFVs with 2D error plots c) receptive field radius and d) cell’s memory estimates. Azimuth = 45°, elevation = 10° (Frame 0, -1, -2 for PV2, and -3, -4, -5 for PV4), and -10° for the rest of the frames.
Fig 7.
RFVs for: (A) PV5 and (B) PV6 cell classes.
a) 2D and b) 3D RFVs with error bars and average number of spikes vs. projections of the input vectors, c) receptive field radius and d) cell’s memory estimates for cell types PV4 and PV5. Azimuth = 45°, elevation = –10° (Frame 0, -1, -2), and 10° for the rest of the frames.
Fig 8.
RFV, receptive field radius and cell’s memory estimates for cell type PV7.
Outer circle diameter is 250μm, the inner circle diameter 75μm. Panel a), bottom shows interpretation of the biological meaning of the discerned RFV. 3D RFV: azimuth = 37°, elevation = 20°, error: elevation: 80°. Average standard error: 0.18.