Inhibitory Actions Unified by Network Integration

Abstract

Cortical function is regulated by a strikingly diverse array of local-circuit inhibitory neurons. We evaluated how optogenetically activating somatostatin- and parvalbumin-positive interneurons subtractively or divisively suppressed auditory cortical cells' responses to tones. In both awake and anesthetized animals, we found that activating either family of interneurons produced mixtures of divisive and subtractive effects and that simultaneously recorded neurons were often suppressed in qualitatively different ways. A simple network model shows that threshold nonlinearities can interact with network activity to transform subtractive inhibition of neurons into divisive inhibition of networks, or vice versa. Varying threshold and the strength of suppression of a model neuron could determine whether the effect of inhibition appeared divisive, subtractive, or both. We conclude that the characteristics of response inhibition specific to a single interneuron type can be "masked" by the network configuration and cellular properties of the network in which they are embedded.

Figure 1. Optogenetic Activation of Sst+ and Pvalb+ Interneurons in A1

(A) Left: schematic of prominent connections from Sst+ interneurons (blue) onto the dendrites of a pyramidal neuron (gray). Right: immunofluores-cent labeling of Pvalb (red) did not co-localize with ChR2 (green) when Cre-dependent ChR2 was expressed in Sst-Cre mice (“Ai32/Sst”). Scale bar: 50 µm. (B) Blue light illumination of the cortical surface (top, cyan) of anesthetized Ai32/Sst mice increased the activity of some units (middle/blue: rasters, PSTH, and spike waveform for an example light-activated unit), while suppressing activity of others (bottom/ black: rasters, PSTH, andwaveform for anexample light-suppressed unit). Scale bar: 2 ms. (C) Distribution of light effects on tone-evoked firing rate in anesthetized Ai32/Sst mice. Dark blue bars: units for which light significantly reduced activity (n = 76 of 145 units), light blue bars: units for which light significantly increased activity (n = 3 of 145 units), gray bars: units for which light did not significantly change activity (n = 66 of 145 units), as determined by a rank-sum test between control and light-activation trials, α = 0.05. (D and E) Raster of tone-evoked firing for a representative unit without (D) and with (E) light (cyan bar). Black and cyan lines: periods of tone and light stimuli. Yellow region: times during which firing rate was significantly elevated above baseline (rank-sum test, α = 0.001 following multiple comparisons correction). (F) Aggregate PSTHs of spikes across all tones on trials without light (black) versus with light (blue). Dashed line: baseline firing rate. Yellow region: time range during which firing rate was significantly elevated above baseline (rank-sum test, α = 0.001). Data are represented as mean ± SEM. (G) FTP of spike counts during the response region (yellow) on trials without light (black) versus with light (blue). Dashed line: baseline firing rate. Data are represented as mean ± SEM. (H) Left: schematic of prominent connections from Pvalb+ interneurons (red) onto perisomatic regions of a pyramidal neuron (gray). Right: immunofluorescent labeling of Pvalb (red) co-localized with ChR2 (green) when Cre-dependent ChR2 was expressed in Pvalb-Cre mice (“Ai32/Pvalb”). (I–N) Corresponding to (B)–(G): example waveforms, responses, and effect distributions from recordings in Ai32/Pvalb rather than Ai32/Sst mice.

Figure 2. Sst+ and Pvalb+ Interneuron Activation Cause Similar Linear Suppression of Tone-Evoked Firing in Anesthetized Mice

(A) Schematic: control (black), divisively suppressed (purple), and subtractively suppressed (green) responses as a function of stimulus frequency. (B) Schematic: divisively (purple) or subtractively (green) suppressed responses as a linear function of the unsuppressed response, for stimuli evoking firing rates above baseline in both conditions. (C) Cumulative distribution of r² values (i.e., quality of linear fit) in Ai32/Sst (blue) and Ai32/Pvalb (red) mice shows that a linear fit accounts for a high proportion of the total variance of suppression. Dashed line: median. Ai32/Sst: n = 76 units. Ai32/ Pvalb: n = 63 units. (D–I) Activating Sst+ (blue) or Pvalb+ (red) in-terneurons leads to various forms of suppression in individual units: units in (D) and (G) are divisively suppressed, with slopes < 1, y-intercepts ≥ 0; (E) and (H) are subtractively suppressed, with slopes ≥ 1, y-intercepts<0;(F)isboth divisively and subtractively suppressed; and (I) is neither divi-sively nor subtractively suppressed. The data in the response curves are represented as mean ± SEM. The data in the regression plots are represented as lines of best-fit with 95% confidence intervals. (J) Similar proportions of cells were divisively and subtractively suppressed by activation of Sst+ (blue) or Pvalb+ (red) interneurons (g-test p = 0.54). Error bars: 95% confidence intervals (Bernoulli distributions). Ai32/Sst: n = 76 units, Ai32/Pvalb: n = 63 units. (K) Distributions of best-fit slope coefficients (i.e., relative strength of divisive suppression) when activating Sst+ or Pvalb+ interneurons. Dark bars: units in which slope was significantly less than unity (n = 47 of 57 Ai32/Sst, n = 43 of 63 Ai32/Pvalb). Distributions were not significantly different (rank-sum p = 0.19 for all units, rank-sum p = 0.44 for units with significant slopes only). (L) Distributions of best-fit y-intercept coefficients (i.e., relative strength of subtractive suppression) when activating Sst+ or Pvalb+ interneurons. Dark bars: units in which intercept was significantly less than 0 (n = 24 of 76 Ai32/Sst, n = 24 of 63 Ai32/Pv). Distributions were not significantly different (rank-sum p = 0.61 for all units, p = 0.20 for units with significant intercepts only).

Figure 3. Sst+ and Pvalb+ Interneuron Activation Have Similar Effects on Response Bandwidths in Anesthetized Mice

(A–C) FTPs for three representative units (A, B,and C) recorded in anesthetized mice without (black) and with (blue) activation of Sst+ interneurons. Data are represented as mean ± SEM. Dashed lines: bandwidths at half-height. Inset: unit’s mean waveform ± SD. Scale bar: 2 ms. (D) Half-height bandwidths with versus without activation of Sst+ interneurons across the population of n = 76 units. Dark circles: units for which bandwidth change was significant (bootstrap test, n= 20 of 76 units). Light circles: units for which bandwidth change was not significant (n = 56 of 76 units). (E–H) Corresponding to (A)–(D): representative units and group data showing the effect of Pvalb+ neuron activation (red) on FTP bandwidth in n = 63 units in anesthetized mice (n = 14 of 63 units significant). (I) Box-and-whisker summary of the effects of Sst+ versus Pvalb+ interneuron activation on half-height bandwidths shows significant bandwidth reduction (sign-rank p < 0.001) that was not significantly different between groups (rank-sum p = 0.63).

Figure 4. Activating Sst+ or Pvalb+ Interneurons Can Suppress Simultaneously Recorded Neurons in Divergent Ways

Correlations of slope coefficients (A), y-intercepts (B), and differences in bandwidths (C) for pairs of neurons simultaneously recorded on the same probe. (A given unit may be represented more than once if it was recorded simultaneously with more than one other unit.) Ai32/Sst: blue, Ai32/ Pvalb: red.

Figure 5. Sst+ and Pvalb+ Interneuron Activation Cause Similar Linear Suppression of Tone-Evoked Firing in Awake Mice

(A) Blue light illumination of the cortical surface (top, cyan) of awake Ai32/Sst mice increased the activity of some units (middle/light blue: rasters, PSTH, and spike waveform for an example light-activated unit) while suppressing activity of others (bottom/black: rasters, PSTH, and waveform for an example light-suppressed unit). Scale bar: 2 ms. (B) Distribution of light effects on tone-evoked firing rate in awake Ai32/Sst mice. Dark blue bars: units for which light significantly reduced activity (n = 38 of 69 units), light blue bars: units for which light significantly increased activity (n = 17 of 69 units), gray bars: units for which light did not significantly change activity (n = 14 of 69 units), as determined by a permutation test between control and light-activation trials, α = 0.05. (C) Blue light illumination of the cortical surface (top, cyan) of awake Ai32/Pvalb mice increased the activity of some units (middle/pink: rasters, PSTH, and spike waveform for an example light-activated unit) while suppressing activity of others (bottom/black: rasters, PSTH, and waveform for an example light-suppressed unit). Scale bar: 2 ms. (D) Distribution of light effects on tone-evoked firing rate in awake Ai32/Pvalb mice. Dark pink bars: units for which light significantly reduced activity (n = 29 of 67 units), light pink bars: units for which light significantly increased activity (n = 16 of 67 units), gray bars: units for which light did not significantly change activity (n = 22 of 67 units), as determined by a permutation test between control and light-activation trials, α = 0.05. (E–J) Activating Sst+ (blue) or Pvalb+ (red) interneurons in awake mice leads to various forms of suppression in individual units: units in (E) and (H) are divisively suppressed, with slopes < 1, y-intercepts ≥ 0; (F) and (I) are subtractively suppressed, with slopes ≥ 1, y-intercepts < 0; (J) is both divisively and subtractively suppressed; and (G) is neither divisively or subtractively suppressed. The data in the response curves are represented as mean ±SEM. The data in the regression plots are represented as lines of best-fit with 95% confidence intervals. (K) Similar proportions of cells are divisively and subtractively suppressed by activation of Sst+ (blue) or Pvalb+ (red) interneurons. Error bars: 95% confidence intervals (Bernoulli distributions). (L) Distributions of best-fit slope coefficients (i.e., relative strength of divisive suppression) when activating Sst+ (blue) or Pvalb+ (pink) interneurons. Dark bars: units in which slope was significantly less than unity (n = 19 of 38 Ai32/Sst, n = 17 of 29 Ai32/Pvalb). Distributions are not significantly different (rank-sum p = 0.58 for all units; p = 0.46 for units with significant slopes). (M) Distributions of best-fit y-intercept coefficients (i.e., relative strength of subtractive suppression) when activating Sst+ or Pvalb+ interneurons. Dark bars: units in which intercept was significantly less than 0 (n = 21 of 38 Ai32/Sst, n = 14 of 29 Ai32/Pvalb). Distributions are not significantly different (rank-sum p = 0.472 for all units; for units with significant intercepts, p = 0.45).

Figure 6. Sst+ and Pvalb+ Interneuron Activation Have Similar Effects on Response Bandwidths in Awake Mice

(A–C) FTPs for three representative units (A, B, C) recorded in awake mice without (black) and with (light blue) activation of Sst+ interneurons. Data are represented as mean ± SEM. Dashed lines: bandwidths at half-height. Inset: unit’s mean waveform ± SD. Scale bar: 2 ms. (D) Half-height bandwidths with versus without activation of Sst+ interneurons across the population of n = 38 units. Dark circles: units for which bandwidth change was significant (bootstrapped signrank test, n = 21 of 38 units). Light circles: units for which bandwidth change was not significant (n = 17 of 38 units). (E–H) Corresponding to (A)–(D): representative units and group data showing the effect of Pvalb+ neuron activation (pink) on FTP bandwidth in n = 29 units (15 significant, 14 non-significant) in awake mice. (I) Box-and-whisker summary of the effects of Sst+ versus Pvalb+ interneuron activation on half-height bandwidths shows significant bandwidth reduction (sign-rank p < 0.0005) that was not significantly different between groups (rank-sum p = 0.84).

Figure 7. In Awake Mice, Activating Sst+ or Pvalb+ Interneurons Can Suppress Simultaneously Recorded Neurons in Divergent Ways

Correlations of slope coefficients (A), y-intercepts (B), and differences in bandwidths (C) for pairs of neurons simultaneously recorded on the same probe. (A given unit may berepresented more than once if it was recorded simultaneously with more than one other unit.) Ai32/Sst: cyan, Ai32/Pvalb: pink.

Figure 8. Linear Suppression Types May Be Obscured by Network Properties

(A) Neurons tuned to different frequencies (top) are connected to a downstream neuron (large purple neuron in the center) by a connectivity function that weakens with distance (shading). (B) The contributions of many tuned input neurons (colors) are summed by the downstream neuron, producing a center-peaked tuning curve (black). (C) Schematic similar to (A) in which input neurons are divisively suppressed (dashed versus color). (D) Left: sum (black) of individually suppressed inputs (color) is divisively suppressed compared to control (dashed). Center: decreases in contributions from each input (color) as a function of frequency. Right: input strength comparison for divisively suppressed inputs (black) versus control (dashed). (E) Divisive suppression (purple, left) can appear subtractive (right) when spiking threshold (dashed red) limits observable output. (F–I) Variations in suppression strength and threshold can cause divisive suppression of inputs to produce primarily divisive (F), subtractive (H), or mixed (G) suppression of the spiking output (overlaid in I). (J–P) Similar to (C)–(I) but for subtractive suppression. Note that because firing rates cannot be negative, subtractively suppressed inputs are not uniformly suppressed (H, center). As a result (H, right), the sum of subtractively suppressed inputs (thick black) differs from theoretical subtractive suppression (thin gray).