Emergent Orientation Selectivity from Random Networks in Mouse Visual Cortex

Abstract

The connectivity principles underlying the emergence of orientation selectivity in primary visual cortex (V1) of mammals lacking an orientation map (such as rodents and lagomorphs) are poorly understood. We present a computational model in which random connectivity gives rise to orientation selectivity that matches experimental observations. The model predicts that mouse V1 neurons should exhibit intricate receptive fields in the two-dimensional frequency domain, causing a shift in orientation preferences with spatial frequency. We find evidence for these features in mouse V1 using calcium imaging and intracellular whole-cell recordings.

Keywords: balance of excitation and inhibition; conductance-based modeling; orientation selectivity; recurrent neuronal networks; visual cortex.

Figure 1.. Receptive Fields, Random Connectivity, Spatial Frequency (SF) Tuning, and Orientation Tuning

(A) Hubel and Wiesel connectivity in which ON (red) and OFF (blue) thalamo-cortical afferents, with spatial receptive fields indicated by each circle, converge onto a neuron in primary visual cortex. The summation of these afferent receptive fields generates a Gabor-like receptive field in visual cortex (inset). (B) Orientation preference does not change with SF for such receptive fields. Tuning curves of the temporal modulation of the response for low (red), medium (green), and high (blue) spatial frequencies are plotted. In frequency space, these receptive fields maintain a peak response at a consistent angle that points toward the origin at the midpoint of the graph (inset). (C) Random connectivity from the lateral geniculate nucleus (LGN) in which ON and OFF thalamo-cortical neurons with similar spatial receptive fields converge on cortical neurons also generates orientation selectivity in the temporal modulation of the response. The linear summation of LGN ON and OFF neuron receptive fields shows oriented profiles (inset). Scale bar indicates 35 degrees. (D) Orientation preference shifts for random connectivity as SF changes. Orientation tuning curves are plotted as in (B). In frequency space, these receptive fields tilt in a manner that does not project back to the origin.

Figure 2.. Orientation Selectivity Emerges in the Mouse V1 Model

(A)Examples of tuning curves (peak firing rate) of three excitatory V1 neurons in the model. SF of the drifting grating is 0.03 cyc/deg. OSIs from left to right are as follows: 0.62, 0.23, and 0.15. Error bars represent the SEM. (B)Distribution of OSI (peak response) over all the neurons (neurons in the central part of the network; see STAR Methods; n = 5,041). Mean OSI = 0.24 (mean OSIs of the F0 and F1 components of the response are 0.29 and 0.19). (C)Examples of tuning curves of excitatory neurons in networks with different average number of thalamic inputs per neuron. From left to right: OSI = 0.47, 0.48,and 0.49. (D)Population average OSIs versus average number of thalamic inputs. Red: Peak spike response. Black: F1 component of the spike response. Blue: F1 component of the thalamic excitatory input.

Figure 3.. The Contribution of the Offset of ON and OFF Subregions of the Thalamic Excitation to Its Orientation Preference

The ON and OFF subfields of the thalamic inputs were estimated by presenting spots at different locations to the model network as in Lien and Scanziani (2013) (see STAR Methods). (A) Top panels: ON (red) and OFF (green) subfields of the thalamic excitation for four example neurons. Dark spots: Center of mass of the subfields. The solid line indicates the axis of the offset of the two centers of mass. Receptive fields based on the summed ON and OFF thalamic inputs are shown on the right. The scale bar on the right applies to all receptive fields. Bottom panels: Tuning curves of the thalamic excitation for these neurons. The SF of the drifting grating is 0.03 cyc/deg. Vertical dashed line indicates the orientation of the offset axis (0 corresponds to an horizontal axis). Offset amplitude and orientation and preference of the thalamic excitation are as follows: E14493, 11.4°, 166.1°, 160.3°; E14847, 4.7°, 18.2°, 31.1°; E14664, 3.9°, 111.4°, 80.7°; E15022, 2.8°, 20.6°, 88.0°. (B) Offset distribution across neurons (n = 361;neurons are at the center of the network, see STAR Methods). Mean offset: 4.1°. (C) Orientation preference of the thalamic input conductance (drifting grating with 0.03 cyc/deg) versus orientation from the offset axis (perpendicular to the offset axis) for all neurons with an offset larger than 4 (n = 170). The CC is 0.24.

Figure 4.. SF and Orientation Selectivity in the Model and Mouse V1

(A) Example orientation tuning curves based onspike rate are plotted for neurons in the spiking network model (left), electrophysiology (middle), and based on fluorescence changes from calcium imaging experiments (right). Orientation tuning curves are plotted for different spatial frequencies, from 0.01 to 0.04 cyc/deg, indicated by line thickness. If the error bars are not visible, they are smaller than the symbol size. Error bars represent SEM. (B) Top row: The relationship between preferred orientation in the model. Left: 0.04 cyc/deg and 0.01 cyc/deg. Middle: 0.04 cyc/deg and 0.02 cyc/deg. Right: 0.04 cyc/deg and 0.03 cyc/deg. Bottom row: The same for the calcium and electrophysiological records (green and blue symbols, respectively). The bootstrapped vector average is used as the estimate of the preferred orientation. For calcium and spiking data, statistically significant shifts in orientation preference are indicated by filled circles. Number of cells in the imaging data for comparison of 0.01 and 0.04 cyc/deg is 90, for comparison of 0.02 and 0.04 cyc/deg is 228, and for comparison of 0.03 and 0.04 cyc/deg is 288. Number of cells in the electrophysiological data for comparison of 0.01 and 0.04 cyc/deg is 19, for comparison of 0.02 and 0.04 cyc/deg is 19, and for comparison of 0.03 and 0.04 cyc/deg is 17. (C)Histograms of the difference in orientation preference between 0.04 cyc/deg and 0.01 (left), 0.02 (middle), and 0.03 (right) cyc/deg. Filled bars for electrophysiology and calcium imaging data indicate statistically significant changes in orientation preference.

Figure 5.. Comparison between Model and Experimental Results

Graph indicates the observed CC between preferred orientations of single neurons at two spatial frequencies. The pairs of spatial frequencies being compared are indicated on the x axis. Green: Calcium imaging. Blue: Electrophysiology. Purple: Model with circular thalamic receptive fields (same as in Figure 4). Red: Model with elongated thalamic receptive fields (see Results and Figure S9). Error bars are bootstrapped 95% confidence intervals on the CC. For calcium: CC for 0.01–0.04 cyc/deg = 0.08, for 0.02–0.04 cyc/ deg = 0.33, and for 0.03–0.04 cyc/deg = 0.53. Electrophysiological data: CC for 0.01–0.04 cyc/deg = 0.03, for 0.02–0.04 cyc/deg = 0.28, and for 0.03–0.04 cyc/deg = 0.67.

Figure 6.. Neuron Receptive Fields in the Frequency Domain Are Intricate

(A) Mean membrane potential responses to Hartley stimuli (see STAR Methods) are plotted for combinations of horizontal and vertical spatial frequencies (top row). Circles indicate stimulus combinations corresponding to oriented gratings at fixed spatial frequencies. The red and black dots indicate the peak response at those spatial frequencies. Each panel corresponds to a different example cell. Orientation tuning curves for drifting gratings at 0.014 cyc/deg (red) and 0.044 cyc/deg (black) are shown for these four neurons (bottom row). Error bars represent SEM. (B)Example frequency receptive fields for four neurons in the model. Orientation tuning curves at 0.01 cyc/deg (red) and 0.04 cyc/deg (black) are shown for these neurons (bottom row) based on responses to drifting gratings.