Type-specific dendritic integration in mouse retinal ganglion cells

Neural computation relies on the integration of synaptic inputs across a neuron’s dendritic arbour. However, it is far from understood how different cell types tune this process to establish cell-type specific computations. Here, using two-photon imaging of dendritic Ca2+ signals, electrical recordings of somatic voltage and biophysical modelling, we demonstrate that four morphologically distinct types of mouse retinal ganglion cells with overlapping excitatory synaptic input (transient Off alpha, transient Off mini, sustained Off, and F-mini Off) exhibit type-specific dendritic integration profiles: in contrast to the other types, dendrites of transient Off alpha cells were spatially independent, with little receptive field overlap. The temporal correlation of dendritic signals varied also extensively, with the highest and lowest correlation in transient Off mini and transient Off alpha cells, respectively. We show that differences between cell types can likely be explained by differences in backpropagation efficiency, arising from the specific combinations of dendritic morphology and ion channel densities.


Receptive field (RF) estimation for simultaneous recorded electrical and Ca 2+ imaging data
For binary spike data, RF ( ) is characterized by a linear-nonlinear-Poisson (LNP) model, where is the spatio-temporal RF (STRF), is the binary dense noise stimulus, ( ) is the spike count in a time bin of size Δ at time , and is a nonlinear function that ensures the spike rate is nonnegative, which is fixed to be a soft-rectification function. RF outputs were summed and passed through to determine the conditional intensity ( ), which is then passed into a conditionally Poisson process to generate spike train: Since there is no ready-to-use evidence optimization method for LNP model, here we parameterized the STRF with a cubic regression spline basis 1, 2 to ensure smoothness. The number of basis functions used is chosen by cross-validation. Then, the model parameters ( , weights on the basis functions for STRF) are fitted by maximizing the log-likelihood: For both voltage and Ca 2+ data, RF is characterized by a Linear-Gaussian model, as same as the one used for dendritic RFs in the main text. However, for a fair comparison with the spike RF, we fit STRF with the same spline basis by minimizing the mean-squared error cost function with L1 regularization: where is either a voltage or a Ca 2+ trace, and is the regularization weight determined by crossvalidation.

Correlation between firing rates and calcium signal increment
Firing rates is calculated by binning its binary spikes according to the light stimuli trigger time, with a bin size of Δ=200 ms. Ca 2+ signals were also resampled to the trigger time, then the signal increment is calculated by passing the gradient of corresponding Ca 2+ signal to a rectified linear unit function (ReLU).
The correlation between firing rates and Ca 2+ signal increment is then quantified by the Pearson correlation coefficient ( ).

Receptive field size vs. dendritic distance
To model the dependence of receptive field (RF) size as a function of dendritic distance, we used a Gaussian Generalized Additive Model (GAM) with factor cell type, a smooth term for each type as a function of dendritic distance and random factor cell id.
rf_size ~ type + s(soma_dist, by = type, k = 50) + s(exp_date, bs = "re") We set the basis dimension k=50 to allow for sufficiently "wiggly" smooth terms. Inspection of the model fit indicated that this was high enough (using gam.check). The resulting model was fit using n=1,324 data points and yielded the following results: Thus, the smooth terms for the tOff alpha RGC and the mini alpha RGC are highly significant, indicating non-random variation of receptive field size with dendritic distance.
Overall, the model explained 54.6% of the deviance.
Analysis of the pairwise differences between cell types indicated that the RF size of tOff alpha RGC dendrites close to the soma (< 50 to 75 µm) was significantly larger than that of other RGC types.

Receptive field offset vs. dendritic distance
To model the dependence of RF offset as a function of dendritic distance, we used a Gaussian GAM with factor cell type, a smooth term for each type as a function of dendritic distance and random factor cell id.
offset ~ type + s(soma_dist, by = type, k = 50) + s(exp_date, bs = "re") We set the basis dimension k=50 to allow for sufficiently "wiggly" smooth terms. Inspection of the model fit indicated that this was high enough (using gam.check). The resulting model was fit using n=1,324 data points and yielded the following results: Overall, the model explained 63.2% of the deviance.

Receptive field overlap vs. dendritic distance and dendritic angle
To model the dependence of RF overlap as a function of dendritic distance and dendritic angle, we used a t-distributed GAM with 5 degrees of freedom. In this case, we found that allowing for tdistributed residuals improved the quality of the model (AIC: -61,825 vs. -59,202).
We included a factor cell type, a bivariate smooth term as a function distance and angle, unique for each type, and a random effect term for cell id.
The resulting model was fit on n=54,194 data points and yielded the following results: Overall, the model explained 72.8% of the deviance.

Correlations vs. dendritic distance and dendritic angle
To model the dependence of temporal correlation as a function of stimulus (local or global), dendritic distance and dendritic angle, we used a Gaussian GAM with factor cell type, stimulus, and a bivariate smooth term as a function distance and angle, unique for each combination of type and stimulus, and a random effect term for cell id.
The resulting model was fit on n= 33,796 data points and yielded the following results: Overall, the model explained 62.8% of the deviance.

Correlation between Ca 2+ signal increase and the number of spikes evoked by current injection
We used linear regression to analyse the relationship between Ca 2+ signal increase and the number of spikes evoked by current injection across four groups: proximal and distal dendrites of tOff alpha and mini alpha.

dendriticCalcium_area ~ SomaticSpikes * group
The resulting model was fit on n=276 data points and exploratory ANOVA yielded the following results: Thus the number of evoked spikes had a group specific impact on Ca 2+ signal increase.

Analysis of Variance
We computed the slope of the increase as a function of the number of evoked action potentials using lstrends for each group: This shows that the slopes between all compared groups were significantly different (p<0.05) except the one between proximal and distal dendrites of tOff alpha. Supplementary Fig. 1 Region of interest (ROI) selection. a, Exemplary scan field (top left) and automatically generated ROI mask (bottom left) from the region labelled by black rectangle on the reconstructed RGC morphology (right). b, Smoothed and normalized RF maps before (left) and after (right) up-sampling for the labelled ROIs indicated in (a). Coloured curves on up-sampled RF maps (right) show RF contours with three different thresholds used for the RF quality test (Methods). Only ROIs that passed the test (a single contour with Ii < 0.1 , > 1.8 • 1,000 µm 2 , at a contour threshold of 0.60; see also Methods) were used for further analysis. Red rectangles around the upsampled RF maps (right) indicate that RFs did not pass and were discarded. c, Histograms of recorded ROIs for tOff alpha (n=17\1,452\851 cells\total ROIs\ROIs that passed the RF quality test), tOff mini (n=5\387\295), sOff (n=4\208\154) and F-mini Off RGCs (n=5\265\126). Fig. 2 RFs estimated by simultaneous recordings of somatic voltage and somatic/proximal dendritic Ca 2+ signals. For binary spike data, RF was characterized by a linearnonlinear-Poisson (LNP) model; for both voltage and Ca 2+ data, RF was characterized by a Linear-Gaussian model (see Supplementary Methods). a, Exemplary somatic voltage and Ca 2+ traces in response to dense noise and the corresponding binary spike train normalized to the standard deviation (SD) of the baseline. b, RF maps estimated from somatic Ca 2+ , voltage and spike rates at different times (δ, [s]) before an event (small maps) and the up-sampled and smoothed singular value decomposition (SVD) maps with the RF contour. c, RF contours derived from somatic Ca 2+ , voltage and spike rates in response to dense noise for n=4 cells. d, Up-sampled and smoothed RF maps with the corresponding RF contours for the soma and proximal dendrites from simultaneous somatic voltage recording and Ca 2+ imaging from the proximal dendrites. e, RF contours from (d) and the proximal ROIs overlaid with the partially reconstructed cell morphology. Supplementary Fig. 3 Relationship between spike rates and Ca 2+ signal increments. a, Example for simultaneously recorded dendritic Ca 2+ (proximal, 44 µm from soma) and somatic voltage signals from a tOff alpha cell to dense noise stimulation. Below the voltage trace, the extracted spike pattern and traces for normalized Ca 2+ gradient (green) and normalized spike rates (black) are shown (values on the right from the overlaid traces indicate correlation between Ca 2+ gradient and spike rates). b, Normalized Ca 2+ gradient as a function of normalized spike rates. c, Like (a) but for a tOff mini cell (Ca 2+ from proximal location, 26 µm from soma). d, Like (b) but for the tOff mini cell. e, Correlation between normalized Ca 2+ gradient and normalized spike rates for n=2 tOff alpha and n=3 tOff mini cells (each star indicates one recording, colours indicate different cells; correlation range between 0.55 and 0.82). Fig. 4 Morphologies of all recorded retinal ganglion cells (RGCs). a-d, Reconstructed morphologies clustered into RGC types using the algorithm published by Bae et al. (ref 3 ): tOff alpha in (a), tOff mini in (b), sOff in (c) and F-mini Off in (d).

Supplementary Fig. 5
Quantification of RF offset angle. a, Illustration of the acute (top) and obtuse (below) angle measured between the lines from a ROI's centre to the dendritic arbour centre and a ROI's centre to its RF centre. Arrow points from the ROI´s centre to its RF contour centre. Red cross indicates the dendritic arbour centre. b, Color-coded RF offset angles as a function of dendritic distance to soma and distance from ROI to RF centre (RF offset). c, Distribution of acute (black) and obtuse (red) RF offset angles as function of dendritic distance from ROI to soma.