The cellular density distribution and excitatory-inhibitory balance vary across layers in the mouse barrel cortex.

A) Schematic representation of the recorded area. B) Immunohistochemical staining using markers for inhibitory neurons (GABAergic, somatostatin-positive) and excitatory neurons (calretinin-, VIP-positive). C) Quantitative analysis of neuronal density in the barrel column. Cell bodies were quantified across layer 4 with cortical depth 440-629 µm and layer 2/3 with cortical depth 22-418 µm using immunochemical labeling and confocal microscopy. Red and yellow colors represent excitatory neuron density and light and dark blue represent inhibitory neuron density across layers 4 and layer 2/3 respectively. The final column demonstrates the relative ratio of excitatory to inhibitory neurons in each layer. Key findings include a variation in the number of excitatory and inhibitory neurons across cortical depth (418-629 µm) and a changing ratio of excitatory to inhibitory neurons as a function of cortical depth. A solid vertical line demonstrates the EI ratio in the classical balanced state. Figure adapted from Huang et al. (2022) (19) with permission.

Spiking neural network diagram and activity.

A) The network model consists of excitatory and inhibitory neurons that are randomly connected. We explored the effects on network dynamics and computation of the following variables: the number of inhibitory neurons Ninh (between 2500 and 1000), and consequently the EI ratio (between 4 and 10), the synaptic coupling strength Jei (between −0.75 mV and −0.5 mV), the inhibitory firing threshold θinh (between 18 mV and 20 mV). Further, we used a fixed number of excitatory neurons (Nexc = 10,000), external input (μ0 = 24 mV) and probability of connection (10%). B) Averaged firing rate of the neurons in the network across EI ratios, Jei, and θinh. Four circles (black, gray, red, and blue) demonstrate the network dynamics in four different states: black and grey: balanced excitation-inhibition dynamics (black circle: EI ratio = 4, Jei = −0.5 mV, θinh = 20 mV (14), grey circle: EI ratio = 5.71, Jei = −0.525 mV, θinh = 20 mV), red: excitation-dominated dynamics (EI ratio = 10, Jei= −0.5 mV, θinh = 20 mV), blue circle: inhibition-dominated dynamics (EI ratio = 4, Jei = −0.75 mV, θinh = 20 mV) C) Averaged firing rate of the neurons in the network across EI ratios, Jei, and θinh = 20 mV with the same four dots demonstrating four states mentioned in B. D) Corresponding raster plots of the four states in B. Red dots indicate excitatory spikes and blue dots inhibitory spikes.

The network activity across varying EI ratios, Jei and θinh explores a high-dimensional space when inhibition dominates. A) Two different temporally varying inputs, stimulus 1 and stimulus 2 were given to the network. B) top: Average coefficient of variation of inter-spike intervals (CVISI) averaged over the neurons in the network for the following parameters: the number of inhibitory neurons Ninh between 2500 and 1000, and consequently the EI ratio between 4 and 10, Jei between −0.75 mV and −0.5 mV, and θinh = 20 mV. Bottom: Same as top, but for θinh values between 18 mV and 20 mV. C) top: Normalized averaged synchrony between all neuron pairs in the network measured by cross-correlation for the same EI ratios, Jei, and θinh as in A. Bottom: Same as top, but for the θinh between 20 mV and 18 mV. D) top: Average participation ratio (PR) of the network for the same parameters: EI ratio, Jei, and θinh as in A. Bottom: Same as top, but for θinh between 18 mV and 20 mV.

Networks mimicking the properties of cortical layers 2/3 (B) and layer 4 (C) respectively, show a difference in response dimensionality. A) The participation ratio of the network at averaged neuron firing rates of 8 Hz, 4 Hz, and 2 Hz as a function of the EI ratio (the number of inhibitory neurons), and θinh. For all θinh and EI ratios, Jei were adjusted to maintain the average firing rate of the network at these three values. Vertical lines at EI ratios of 5.3 (Ninh= 1900) and 7.7 (Ninh = 1300) represent layers 2/3 and layer 4 of the barrel cortex with different θinh, firing rates, and Jei. We compared layer 2/3 with layer 4 at two different firing rates: Black dots: Layer 2/3 (EI ratio = 5.3, θinh = 20 mV, Jei = −0.575, firing rate = 4 Hz) and layer 4 (EI ratio = 7.7, θinh = 20 mV, Jei =-0.575 mV, firing rate = 8 Hz). Red dots: Layer 2/3 (EI ratio = 5.3, θinh = 20 mV, Jei = −0.7125, firing rate = 2 Hz) and layer 4 (EI ratio = 7.7, θinh = 20 mV, Jei = −0.675, firing rate = 4 Hz). B) Top: A raster plot of layer 2/3 neurons, matching the left black dot in panel A with EI ratio = 5.3, PR = 15.1, firing rate = 4 Hz, and θinh = 20 mV. Blue and red dots represent spike times of excitatory and inhibitory neurons, respectively. Bottom: A principal component analysis (PCA) quantifies the dimensionality of the neurons in this model of layer 2/3. C) Same as B, but for a model mimicking layer 4 with EI ratio = 7.7, PR = 7.6, firing rate = 8 Hz, and θinh = 20 mV, right black dot in panel A.

Correlation between response dimensionality and coding accuracy

A) Network dimensionality, measured as the the PR, as a function of the Ninh which determines EI ratio, Jei at an inhibitory threshold θinh = 19.5 mV, of the activity of the network responding to two temporal inputs. The black and red dots represent the parameter values corresponding to layer 4 and layer 2/3 of the barrel cortex. Black dots correspond to higher firing rates (layer 4: 8 Hz, EI ratio of 7.7, Jei = −0.55 mV; layer 2/3: 4 Hz, EI ratio of 5.3, Jei = −0.525 mV), while red dots represent lower firing rates (layer 4: 4 Hz, EI ratio of 7.7, Jei = −0.6125; layer 2/3: 2 Hz, EI ratio of 5.3, Jei = −0.55) B) Network encoding capacity, evaluated using an SVM classifier to decode two temporal input stimuli from network activity, as a function of the EI ratio and Jei at θinh = 19.5 mV. The black and red dots correspond to the same parameter values as in panel A. C) Synchrony of the neurons in the network in relation to the PR and network encoding capacity (Accuracy). The red line represents a linear fit between the accuracy and participation ratio (slope: 1.9, intercept: 48.74, which have a correlation of 0.85 and a p-value of p < 0.001). D) Regularity of network spike patterns (CVISI) in relation to the PR, firing rate (FR) and network encoding capacity (Accuracy).

Distribution of firing threshold in inhibitory and excitatory neurons of the mouse barrel cortex.

The dashed line indicates the threshold for differentiating between the two cell types, revealing that inhibitory neurons generally have lower firing thresholds than excitatory neurons (data from (31))

Classification of mouse primary visual cortex neurons based on waveform duration.

The dashed line represents the threshold for distinguishing excitatory from inhibitory cells (data from (32))

Firing rate of the network across varying the number of inhibitory neurons Ninh (between 2500 and 1000), and consequently the EI ratio (between 4 and 10), the synaptic coupling strength Jei (between −0.75 mV and −0.5 mV), the inhibitory firing threshold θinh = 20 mV. The figure displays three firing rates: a green line at 8 Hz, a brown line at 4 Hz, and a purple line at 2 Hz, which remain consistent across all EI ratios and Jei values due to a constant inhibitory drive.