Dynamics of Temporal Integration in the Lateral Geniculate Nucleus

Comparison of ISI-efficacy (left column) and RH (right column) models. A, Relationship between retinal ISI and retinal efficacy for binary white noise (blue) and drifting grating data (red) for pair 208. B, Retinal filters learned by the RH model fit to binary white noise (blue) and drifting grating (red) data from pair 208. Shading indicates ±1 SE of the optimization (see Materials and Methods). The time base for GLM filters is always relative to the retinal spike about which a prediction (relayed or nonrelayed) is being made (i.e., the “target spike”). C, Normalized ISI-efficacy relation averaged across the population. Efficacies for each pair were normalized to the mean efficacy across all ISIs for that pair before averaging. Shading represents the 95% CI across pairs from 5000 bootstrap resamples (see Materials and Methods, Statistics). D, Same as B but showing the average filters across pairs. Filters fit to the data from each pair were scaled to have a unit norm before averaging. Shading represents the 95% CI across pairs. E, Normalized ISI-efficacy relations for all eight pairs from the awake dataset (thin gray lines) and the population average (thick gold line). Normalization was performed as in C. F, Retinal filters learned by RH models fit to data from each pair in the awake dataset (thin gray lines) and the population average (thick gold line). Filters were scaled to have unit norm (as in D) to aid visualization.

Summary of filters learned by the two-component, CH model. The left column shows the retinal filters, and the right column shows the LGN filters for example pairs and the population for each dataset. A, Retinal filters learned by the CH model for binary white noise (blue) and drifting grating (red) data from pair 208. B, Same as A but showing the LGN filters learned by the CH model. The time base for retinal and LGN filters is the same (0 is the time of the “target” retinal spike), but LGN filters operate on the prior activity of the LGN cell. C, Same as A but for the population. Filters fit to the data from each pair were scaled to have a unit norm before averaging. Shading represents 95% CI across pairs. D, Same as C but for LGN filters. E, Same as C but showing retinal filters learned from the awake dataset (thin gray lines show filters from each pair, the thick gold line shows the mean across pairs). F, Same as E but showing LGN filters.

Retinal (A, C) and LGN (B, D) filters from the CH model fit to data where noncardinal burst spikes were first removed. The first row (A, B) use the classic burst spike definition by Lu et al. (1992): a quiescent period ≥100 ms followed by two or spikes with ISIs ≤4 ms. The second row (C, D) use a more relaxed criteria: a quiescent period ≥50 ms followed by two or more spikes with ISIs ≤6 ms.

Qualitative comparison of model performance. A, Left, The predicted efficacies from each model were used to group retinal spikes into bins, and the observed efficacy for each group (median across pairs) is plotted against the corresponding bin label (error bars represent the MAD across pairs). Both predicted and observed efficacies from each pair were normalized by the mean efficacy of that pair before calculating the median and MAD. A, Right, The performance ( I_Bernoulli) of the GLMs relative to the ISI-efficacy model is shown as a function if ISI. Lines show the median performance difference across pairs; shading represents the MAD. B, C, Same as A but for the binary white noise (B) and awake (C) datasets.

Performance comparison of all models for binary white noise data. A, Upper, Comparison of ISI-efficacy and RH models. Each dot indicates the meanI_Bernoulli for a given pair and model; lines connect data belonging to the same pair across models (thus the slope of the lines depicts the change inI_Bernoulli). The height of the vertical, colored bars indicates the MAD ofI_Bernoulli across pairs for a given model, with the filled circle indicating the median value. A, Lower, Estimated paired median differenceI_Bernoulli between ISI-efficacy and RH models. The black dot indicates the observed paired median difference and the vertical black line indicates the 95% CI of the bootstrap distribution (5000 samples) shown in blue. B, Same as A but comparing ISI-efficacy and CH model performance. C, Same as A but comparing RH and CH model performance.

Performance comparison of all models for drifting grating data. All conventions exactly follow those from Figure 6. Correlates of model performance are shown in Extended Data Figure 7-1. Model performance for the awake dataset is shown in Extended Data Figure 7-2.

Comparison of RH models fit separately to subsets (quartiles) of the data grouped by LGN activity level. A, Average retinal filters from RH models fit to each quartile of the binary white noise dataset from low (Q1, green) to high (Q4, purple) based on the activity level of the LGN neuron within a 100-ms period directly preceding the target retinal spike att = 0. Shading represents 95% CI across N = 38 pairs. B, Upper, Comparison of model performance (I_Bernoulli) across all activity subsets. Each dot represents the model performance for a single pair (the spread along the x-axis is to aid visualization). B, Lower, Bootstrap estimation of median model performance for each subset. Black dots indicate the median across pairs and black vertical lines indicate the 95% CI of the bootstrap distribution (shown in color, 5000 samples). C, D, Same as A, B, but for the drifting gratings dataset (N = 33). Results from a control analysis wherein relay status was simulated via GLMs is shown in Extended Data Figure 8-1 (see main text for details). Results of changing the spike quartile classification window are shown in Extended Data Figure 8-2.