# Distinct dendritic integration strategies control dynamics of inhibition in the neocortex

Annunziato Morabito, Yann Zerlaut, Dhanasak Dhanasobhon, Emmanuelle Berthaux, Cibele Martins Pinho, Alexandra Tzilivaki, Gael Moneron, Laurence Cathala, Panayiota Poirazi, Alberto Bacci, et al.

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► To cite this version:

Annunziato Morabito, Yann Zerlaut, Dhanasak Dhanasobhon, Emmanuelle Berthaux, Cibele Martins Pinho, et al. Distinct dendritic integration strategies control dynamics of inhibition in the neocortex. Neuron, 2025, 113 (18), pp.2962-2978. 10.1016/j.neuron.2025.05.029. hal-05407924

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# Neuron

## Distinct dendritic integration strategies control dynamics of inhibition in the neocortex

### Graphical abstract

<figure><img src="image_3.png" /></figure>

### Authors

Annunziato Morabito, Yann Zerlaut, Dhanasak Dhanasobhon, ..., David A. DiGregorio, Joana Lourenço, Nelson Rebola

### Correspondence

annunziato_morabito@hms.harvard.edu (A.M.), yann.zerlaut@icm-institute.org (Y.Z.), alberto.bacci@icm-institute.org (A.B.), david.digregorio@cuanschutz.edu (D.A. D.), joana.lourenco@icm-institute.org (J.L.), nelson.rebola@icm-institute.org (N.R.)

### In brief

Morabito et al. observed that different neocortical interneuron (IN) populations display distinct dendritic properties by varying synaptic receptor composition and input location. These IN-specific dendritic properties enhance synaptic efficiency but are tailored to different temporal processing modes. In the visual cortex, this mechanism supports the distinct dynamics of PV- and SST-INs.

### Highlights

* Cortical PV and SST interneurons (INs) show distinct dendritic integration properties

* SST-INs display NMDAR-dependent supralinearity, while PV-INs integrate sublinearly

* Different integration modes are linked to distinct strategies for synapse distribution

* Cell-specific dendritic properties enable distinct temporal dynamics in PV and SST-INs

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## Article

# Distinct dendritic integration strategies control dynamics of inhibition in the neocortex

Annunziato Morabito,<fnref n="1" />,<fnref n="7" />,<fnref n="10" />,* Yann Zerlaut,<fnref n="1" />,<fnref n="10" />,* Dhanasak Dhanasobhon,<fnref n="1" /> Emmanuelle Berthaux,<fnref n="1" /> Cibele Martins Pinho,<fnref n="1" />

Alexandra Tzilivaki,<fnref n="2" />,<fnref n="3" />,<fnref n="4" /> Gael Moneron,<fnref n="5" />,<fnref n="9" /> Laurence Cathala,<fnref n="1" />,<fnref n="8" /> Panayiota Poirazi,<fnref n="6" /> Alberto Bacci,<fnref n="1" />,<fnref n="11" />,*

David A. DiGregorio,<fnref n="5" />,<fnref n="8" />,<fnref n="11" />,* Joana Lourenço,<fnref n="1" />,<fnref n="11" />,* and Nelson Rebola<fnref n="1" />,<fnref n="11" />,<fnref n="12" />,*

## SUMMARY

Dendrites critically influence single-neuron computations, but their role in neocortical GABAergic interneurons (INs) remains poorly understood. We found that the two major cortical IN subtypes—somatostatin (SST)- and parvalbumin (PV)-expressing cells—use distinct strategies for distributing and integrating excitatory synaptic inputs along their dendrites. SST-INs exhibit NMDAR-dependent supralinear integration and a uniform distribution of synapses, whereas PV-INs show sublinear integration with a higher density of synapses on proximal dendrites with low NMDAR expression. Compartmental modeling revealed that, while both strategies enhance synaptic efficacy, passive integration and proximally biased inputs enable precise tracking of fast-changing signals in PV-INs, whereas NMDARs in SST-INs promote broader temporal integration, supporting sustained activity tuned to slower input variations. Consistent with these predictions, *in vivo* measurements showed differentially shaped dynamic visual responses in PV- and SST-INs. Therefore, the heterogeneity of dendritic mechanisms strongly influences the spatiotemporal dynamics of IN-specific inhibition in cortical circuits.

## INTRODUCTION

In the neocortex, fast synaptic inhibition is fundamental for regulating cortical function by shaping network dynamics. Cortical inhibition originates from a rich diversity of interneurons (INs) that differently control the activity of large populations of pyramidal neurons (PNs).<fnref n="1" />⁻<fnref n="4" /> Among these, parvalbumin (PV)- and somatostatin (SST)-expressing INs are the two major subtypes. PV-INs target the perisomatic region of PNs, while SST-INs primarily innervate dendritic compartments. These subtypes also differ in their temporal dynamics: PV-INs are fast-spiking and regulate PN activity with millisecond precision,<fnref n="5" />⁻<fnref n="8" /> whereas SST-INs fire more slowly and modulate dendritic activity over longer timescales.<fnref n="9" />⁻¹⁵ These complementary temporal profiles are crucial for cortical network operations, influencing oscillatory

activity and enabling learning through dendritic inhibition and synaptic plasticity gating.<fnref n="5" />⁻<fnref n="11" />

Previous studies suggest that PV- and SST-INs represent distinct recurrent inhibitory circuits that capture different temporal features of ongoing network activity to route inhibition to distinct locations along PN compartments.<fnref n="12" />,¹³ PV-INs rapidly track the onset of spike series, providing fast perisomatic inhibition to PNs, while SST-INs provide dendritic inhibition in proportion to spike rate.<fnref n="12" /> Traditionally, functional differences between PV- and SST-INs have been attributed to their connectivity, intrinsic biophysical properties, and synaptic release dynamics.<fnref n="12" />,¹⁴⁻¹⁷ However, since INs primarily receive synaptic inputs through their dendrites, it remains unresolved whether dendritic integration also contributes to these subtype-specific inhibitory functions.

<footnote n="1">¹Sorbonne Université, Institut du Cerveau, Paris Brain Institute, ICM, Inserm, CNRS, APHP, Hôpital de la Pitié Salpêtrière, Paris, France</footnote>

<footnote n="2">²Charité – Universitätsmedizin Berlin, Freie Universität zu Berlin, Humboldt-Universität zu Berlin, and Berlin Institute of Health, Neuroscience Research Center, 10117 Berlin, Germany</footnote>

<footnote n="3">³Einstein Center for Neurosciences, Chariteplatz 1, 10117 Berlin, Germany</footnote>

<footnote n="4">⁴NeuroCure Cluster of Excellence, Chariteplatz 1, 10117 Berlin, Germany</footnote>

<footnote n="5">⁵Institut Pasteur, CNRS UMR3571, Synapse and Circuit Dynamics Unit, 75015 Paris, France</footnote>

<footnote n="6">⁶Institute of Molecular Biology and Biotechnology (IMBB), Foundation for Research and Technology Hellas (FORTH), 70013 Heraklion, Greece</footnote>

<footnote n="7">⁷Present address: Department of Neurobiology, Harvard Medical School, Boston, MA, USA</footnote>

<footnote n="8">⁸Present address: Department of Physiology and Biophysics, University of Colorado Anschutz Medical Campus, Aurora, CO 80045</footnote>

<footnote n="9">⁹Present address: Institut Pasteur, Université Paris Cité, CNRS UMR 3571, Signaling and Dynamic of Receptors Unit, F-75015 Paris, France</footnote>

<footnote n="10">¹⁰These authors contributed equally</footnote>

<footnote n="11">¹¹Senior author</footnote>

<footnote n="12">¹²Lead contact</footnote>

<footnote>*Correspondence: annunziato_morabito@hms.harvard.edu (A.M.), yann.zerlaut@icm-institute.org (Y.Z.), alberto.bacci@icm-institute.org (A.B.), david.digregorio@cuanschutz.edu (D.A.D.), joana.lourenco@icm-institute.org (J.L.), nelson.rebola@icm-institute.org (N.R.)
https://doi.org/10.1016/j.neuron.2025.05.029</footnote>
Dendritic integration plays a critical role in neuronal function by modulating how neurons process and respond to synaptic inputs.¹⁸,¹⁹ Rather than merely relaying signals to the soma, dendrites are capable of performing simple computations through a combination of linear and nonlinear mechanisms, thus enhancing the computational capacity of individual neurons.¹⁹⁻²² Nonlinear mechanisms, such as NMDA receptor activation (NMDAR) and local dendritic spikes support key functions of PNs including coincidence detection, synaptic plasticity, and input specificity.¹⁸,²⁰,²³⁻²⁶ In contrast, the role of dendritic processing in shaping the activity of diverse GABAergic INs is less understood.

Evidence from the cerebellum and hippocampus indicates that IN dendrites can also support nonlinear integration (for a review see Hu et al.¹⁴ and others¹⁹,²⁷,²⁸). For example, the thin dendrites of cerebellar PV-INs showed passive, sublinear responses,²²,²⁹ whereas the thin hippocampal PV-IN dendrites exhibit both sublinear and supralinear synaptic integration.²⁸,³⁰⁻³³ SST-INs dendritic integration has been less-well studied, though some data suggest they possess distinct voltage-gated channel distributions along their dendrites when compared with PV-INs.³⁴

Here, we report that the timing of inhibition generated by PV- and SST-INs is largely determined by two distinct dendritic integration configurations: SST-INs exhibit uniform synapse distribution and NMDAR-dependent supralinear integration, while PV-INs have proximally enriched synapses and passive, sublinear integration. Computational modeling revealed that both configurations enhance synaptic efficacy in thin dendrites but support opposing temporal dynamics. PV-INs, with low NMDAR expression and proximal inputs, are optimized for fast, linear summation of synaptic potentials. In contrast, the presence of NMDARs and short-term facilitation of neurotransmitter release in SST-INs support temporal integration of synaptic potentials and delayed spiking, followed by long-lasting evoked activity. Thus, PV-INs support temporally precise coding of sensory onset, while SST-INs are tuned to slow input variations. *In vivo* electrophysiological and two-photon Ca²⁺ imaging experiments confirmed our numerical predictions as PV- and SST-INs responded with markedly different dynamics to visual stimulations. These findings demonstrate that specialized dendritic integration mechanisms play a central role in shaping the IN-specific inhibitory dynamics in cortical circuits.

## RESULTS

### PV- and SST-INs possess distinct dendritic integration properties

To investigate synaptic integration in dendrites of neocortical INs, we performed *ex vivo* whole-cell current-clamp recordings from PV- and SST-INs in layer 2/3 (L2/3) of the adult mouse primary somatosensory cortex and used two-photon glutamate uncaging to mimic synapse activation²²,³⁵ (Figures 1A–1D). We monitored somatic voltage responses to both single-synapse activation and multiple quasi-synchronous input sequences. To assess deviations from linear synaptic integration, we compared the arithmetic sum (representing linear prediction) of individual photolysis-evoked excitatory postsynaptic potentials

(pEPSPs) with actual responses evoked by quasi-simultaneous (0.12 ms inter-pulse interval) activation of all locations (Figures 1A and 1C). We found an overall sublinear integration mode in PV-IN dendrites (Figures 1A and 1B) and an overall supralinear integration in SST-INs (Figures 1C and 1D). A similar difference was observed for varying time intervals between active inputs (Figures S1A–S1F) and was also evident in PV- and SST-INs recorded in the primary visual cortex (Figures S1G–S1I). This suggests that the differences in dendritic integration between the two IN populations are likely present across different primary cortical areas. The supralinear integration observed in SST-INs was also not significantly different from the values obtained in PNs (Figures 1D and 1E).

In PNs, integration of glutamatergic synaptic inputs along individual dendritic branches was shown to be strongly dependent on the presence of synaptic NMDARs.²⁵,³⁶,³⁷ We explored whether variations in dendritic integration were associated with differences in the relative contribution of N-methyl-D-aspartate (NMDA) and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors (AMPAR) at excitatory synapses onto PV- and SST-INs. Using voltage-clamp recordings and extracellular stimulations, we observed that SST-INs exhibited a higher NMDA-to-AMPA ratio when compared with PV-INs in agreement with previous reports¹⁷,³⁸ (Figures 1F and 1G). This difference was confirmed by paired recordings from unitary synaptic connections between individual L2/3 PNs and PV- or SST-INs (Figures S2A and S2B). Furthermore, by examining NMDAR-dependent miniature excitatory postsynaptic currents (EPSCs) at –30 mV (isolated using the NMDAR blocker D-AP5, 50 µM), we found that the marked NMDA/AMPA differences between PV- and SST-INs were predominantly due to a much weaker NMDAR-mediated component in PV-INs (Figures S2C and S2D). To test whether supralinear dendritic integration in SST-INs was due to pronounced expression of NMDARs, we measured the subthreshold input-output function of L2/3 SST-INs in the presence of a pharmacological blockade (MK-801 and D-AP5) or upon genetic removal of NMDARs selectively from SST-INs (SST::GluN1-KO, see STAR Methods). In both conditions, supralinear integration was abolished, and integration of quasi-synchronous inputs resulted in compound EPSPs smaller than the arithmetic linear sum (Figures 1H).

Sublinear integration observed in PV-INs is compatible with a decrease in driving force due to large local dendritic depolarizations as observed in cerebellar stellate²² and Golgi cells,²⁹ as well as in hippocampal and L5 prefrontal cortex PV-INs, where both supralinear and sublinear branches coexist.³²,³³ To investigate whether such an effect could explain neocortical PV-IN integration, we analyzed a reduced theoretical model implementing cable theory in a simplified morphology³⁹ (Figure 1I). Model parameters were constrained to match our electrophysiological and morphological measurements in PV-INs (see STAR Methods). This simple passive dendritic model recapitulated sublinear integration (Figure 1J, top) and predicted that input-output curves are highly sensitive to the spatial location of stimulated excitatory synapses, with sublinear integration being especially pronounced at distal sites (Figure 1J, bottom).

To test this prediction experimentally, we performed synaptic integration recordings at proximal and distal locations, separately,
<figure><img src="image_5.png" /><figcaption>**Figure 1.** PV- and SST-INs display different dendritic integration properties</figcaption></figure>

(A) (Left) Two-photon laser scanning microscopy (2PLSM) image (maximum-intensity projection, MIP) of a PV-IN patch-loaded with Alexa-594 (20 µM). The inset shows a selected dendrite and uncaging sites for 10 synapses. (Right) Example of dendritic pEPSPs evoked by increasing stimulated synapse number (from sites in A, activated at 0.12 ms intervals), comparing recorded responses to the linear sum of individual inputs. The input-output curve plots recorded somatic EPSP amplitudes against expected linear sum.

(B) Summary plot of input-output curves for dendrites of PV-INs. Gray lines represent individual experiments and red dots population average for the different numbers of coactive synapses listed in (A).

(C and D) Same as (A) and (B), but for SST-INs.

(E) Same as (A) and (B), but for pyramidal neurons (PNs).

(F) Schematic of experimental setup used to stimulate and record glutamatergic EPSCs in PV- and SST-INs in L2/3 of S1.

(G) Representative traces (left) and summary plot (right) of EPSCs recorded at -70 and +40 mV in PV- (n = 14) and SST-INs (n = 8; *p* < 0.0001, Mann-Whitney).

(H) Percentage of non-linearity obtained in PNs (green, n = 25), SST-INs (orange, n = 25), PV-INs (red, n = 17), SST-INs in the presence of NMDA blockers (light green, n = 14), and SST-INs from GluN1-KO mice (violet, n = 7).

(I) Properties of the simplified PV-IN model. (Left) Morphology with soma and symmetrically branching dendrites. (Right) Input and transfer resistance profiles relative to soma distance.

(J) Input-output curves for model in I. (Top inset) Depolarization values from quasi-synchronous synapse activation (1-6 synapses) at various dendritic sites; dashed vs. solid lines reflects predicted vs. recorded responses. (Bottom) Relationship between expected (sum) and observed (real) peak EPSP values at different dendritic locations (color-coded), normalized to single event EPSP values.

(K) Subthreshold input-output relationship of pEPSPs in proximal (<40 µm from soma) and distal (100 µm from soma) dendrites using quantal adjusted pEPSP amplitude. Dashed line indicates slope of 1.

(L) Summary plot of non-linearity (%) obtained from experiments described in (K).

Data are average ± SEM, *p* < 0.05, \*p < 0.01, \*\*p < 0.001, and \*\*\*p < 0.001, Kruskal-Wallis test with Dunn's correction.

See also Figures S1–S4.

in PV-INs (Figure 1K, <40 and >100 µm from the soma, respectively). Uncaging laser power was adjusted to produce responses mimicking average quantal EPSPs amplitudes at the corresponding dendritic locations (Figure S3; see STAR Methods). Consistent with model predictions, PV-INs showed strong sublinear re-

sponses to distal dendritic stimulation, while integration was mostly linear with proximal stimulation (Figures 1K and 1L). Conversely, supralinear responses were still observed in SST-INs at distal dendritic locations using quantal-adjusted EPSPs (Figure 1L). Importantly, differences in dendritic integration
A

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B

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Proximal dendrite

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C

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D

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E

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F

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G

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Martinotti Cell

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synapses •

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H

Basket Cell

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full dendritic branch

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proximal segments

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distal segments

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I

linear density distributions

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J

synaptic count distributions

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between PV- and SST-INs could not be attributed to differences in dendritic diameter along their length, as both cell types exhibited similar dendritic diameter profiles (Figure S4). Overall, these findings reveal distinct dendritic integration properties between PV- and SST-INs, with PV-INs exhibiting distal-dependent sublinear integration consistent with passive integration in thin dendrites.²,³³ while SST-INs show NMDAR-dependent supralinear integration throughout their entire dendritic arbor.

## Distinct spatial distribution of synapses along the dendrites of PV- and SST-INs

Integration of synaptic inputs is determined by the activation, timing, and location of active synapses along the dendritic tree.⁴⁰,⁴¹ Previous work has shown that synapse density gradients can greatly alter dendritic responses.⁴¹,⁴² However, it is unknown whether glutamatergic synapses distribute along the dendritic tree similarly in PV- and SST-INs. We thus investigated the synaptic distributions along the dendritic tree of PV- and SST-INs in L2/3 of S1 (Figure 2A). To estimate the density of glutamatergic synapses we used transgenic mice in which PSD95 (a protein involved in the structure of glutamatergic synapses) was conditionally tagged with a fluorescent marker, mVENUS.⁴⁰,⁴³ PSD95 puncta along different dendritic locations in both PV- and SST-INs were imaged using immunohistochemistry and confocal/stimulated emission depletion (STED) microscopy. To probe whether synapse density was uniform or variable across the dendritic tree, we compared PSD95 puncta density at proximal (<40 µm from soma) and distal (~100 µm from the soma) dendritic regions. We found that glutamatergic synapse density in PV-INs was higher in proximal than distal dendrites (Figures 2B and 2C). Conversely, SST-INs exhibited a consistent synapse density throughout the length of their dendritic tree (Figures 2D-2F).

We further investigated such differences in synapse distribution using a publicly available electron microscopy (EM) dataset from the Allen Brain Institute, corresponding to the full reconstruction of a 1 mm³ sample of the mouse visual cortex⁴⁴⁻⁴⁶ (Figures 2G and 2H, see STAR Methods). We focused on morphologically identified basket and Martinotti cells as proxies for PV- and SST-INs respectively, because they represent the majority of those molecularly-defined classes.²,⁴⁷

Consistent with our PSD95 quantifications the synaptic distribution peaks in the very proximal regions, exhibiting a strongly negative slope and highly skewed distributions (Figures 2H-2J). On the other hand, in Martinotti cells synaptic distribution was more constant along the entire dendritic length (medial peak location, negligible slope, and weakly-skewed distributions, Figures 2H-2J). Thus, the key dendritic integration properties of PV- and SST-INs (Figure 1) are associated to strikingly distinct synapse distributions, pointing to two fundamentally different morpho-functional organization principles in these IN subtypes.

## Two different strategies to enhance EPSP-spike coupling in thin dendritic structures

How do dendrites with proximally distributed, NMDAR-poor synapses integrate simultaneous inputs as compared with dendrites with uniformly distributed, NMDAR-enriched synapses? To investigate this, we built detailed biophysical models of PV- and SST-INs using morphological reconstructions of basket and Martinotti cells, respectively, incorporating their synaptic distributions as determined by EM (Figures 2G and 2H). Synaptic and biophysical properties were constrained by experimental measures (Tables S1-S3). To evaluate each dendritic integration strategy, we compared it to a “null” model without the IN-specific feature: for SST-INs, this involved removing NMDARs; for PV-INs, synapses were redistributed uniformly along dendrites (Figures 3A and S5).

In the case of PV-INs, we hypothesized that asymmetric synaptic distributions along dendritic branches could serve to normalize the influence of synapses at varying locations on dendritic nonlinearities, as observed in Cornu Ammonis area 1 (CA1) neurons.⁴¹ To test this, we randomly selected a sparse subset of synapses (4%; see also Figure S6) located within either a distal (160–200 µm) or proximal (20–60 µm) dendritic segment (Figure 3A) to probe local dendritic integration. This resulted in a small number of synapses (from 2 to 8, depending on local density, see Figure 3A) that we activated independently and quasi-synchronously (0.5 ms delay) to simulate a spatially and temporally clustered input. We then simulated the expected and

<caption>**Figure 2.** Distinct synaptic distributions in the dendritic trees of PV- and SST-INs as well as in the morphologically defined basket and Martinotti INs</caption>

(A) Illustration of the experimental strategy used to quantify glutamatergic synapse distribution along dendrites of SST- and PV-INs in S1. PSD-95 was selectively labeled in these INs and quantified at two defined distances along individual dendritic branches.

(B) (Left) Overview image of PV-INs with proximal dendrites labeled with tdTomato (green) and PSD95venus (red). (Middle) STED image of dendritic location defined on the left. (Right) Merged image between tdTomato obtained in confocal mode (green) and PSD95venus (red) labeling obtained in STED.

(D and E) Same as (B) but for SST-INs.

(C and F) Summary of PSD-95 puncta density at proximal (<40 µm) and distal (~100 µm) dendrites in PV- and SST-INs ($PV_{proximal}$, *n* = 33; $PV_{distal}$, *n* = 12, *p* < 0.001; $SST_{proximal}$, *n* = 21; $SST_{distal}$, *n* = 14, *p* > 0.05, Mann-Whitney U test).

(G) Examples of reconstructed basket and Martinotti INs from EM mouse visual cortex data,⁴⁴ with blue dots marking identified synapse locations along their dendrites.

(H) Illustration of synapse distribution along individual dendritic branches from cells shown in (G), highlighting synapses across entire branches as well as at proximal and distal segments.

(I) Linear synapse density distributions (left) for all basket (*n* = 59) and Martinotti (*n* = 41) cells as a function of the distance from soma. (Right) Violin plots of distribution peaks (basket vs. Martinotti, *p* < 0.0001, Mann-Whitney U test) and distribution slopes expressed as percentage variation in linear density per 100 µm (basket vs. Martinotti, *p* < 0.0001, Mann-Whitney U test) for the plots on the left.

(J) Similar to (I), but for synapse counts (left) and corresponding analyses of distribution peaks (basket vs. Martinotti, *p* < 0.0001, Mann-Whitney U test) and distribution skewness (basket vs. Martinotti, *p* < 0.0001, Mann-Whitney U test).

See also Figure S5.
<figure><img src="image_26.png" /><figcaption>Figure 3. PV- and SST-INs display distinct strategies to improve synaptic efficacy and distal transmission: Proximal synapse bias in PV-INs vs. NMDAR-dependent integration in SST-INs</figcaption></figure>

(A) Morphology of EM-reconstructed basket (i) and Martinotti (ii) cells, used as PV- and SST-IN models, respectively. Insets display actual synapse distributions (colored bars) on a representative dendritic branch, alongside uniform-distribution surrogates (gray bars). The table highlights the sparse synapse subsets recruited in the distal (green) and proximal (pink) segments.

(B) Example numerical simulations of Vm responses following quasi-synchronous stimulation of selected synapses in proximal (pink) and distal (green) dendritic segments for PV-IN (i) and SST-IN (ii) models. The observed response (solid line) and the expected response (dashed line), derived from the linear sum of individual event responses, are shown. Each model is compared with its control condition: (i) gray for uniform distribution and (ii) purple for no-NMDA.

(C) Quantification of EPSP amplitude suppression resulting from clustered synapse activation, for the conditions described in (B), compared with the linear prediction.

(D) Suppression ratio between distal and proximal segments in the PV-IN (i: red; uniform control in gray, *n* = 6 branches, *p* < 0.001) and SST-IN model (ii: orange; no-NMDA control in purple, *n* = 6 branches, *p* < 0.05, Wilcoxon test).

(legend continued on next page)
observed responses for such clustered inputs in each activated dendritic segment (Figure 3B).

For PV-INS modeled with the uniform-distribution surrogate, clustered synaptic activation in distal segments resulted in classical sublinear behavior of passive dendrites³⁹ (Figure 3B). However, using the real synapse distribution (based on EM data, Figures 3A and S6), the lower density of distal synapses reduced the overall input strength within the 4% cluster (2 vs. 5 synapses in the uniform model; Figure 3A). This reduced synaptic saturation as well as sublinear integration in distal segments (Figures 3B and 3C). In proximal segments, the higher synapse density (7 vs. 4 in the uniform model; Figure 3A) did not significantly affect sublinearity (Figure 3C). Therefore, proximally biased synapse distributions can effectively limit distal signal loss (Figure 3C) and equalize distal/proximal engagement of sublinear dendritic integration (Figure 3D) by reducing the size of active synaptic clusters in distal dendritic regions.

In the case of SST-INS, the no-NMDA control condition exhibited the expected distance-dependent sublinear integration, indicative of predominantly passive dendritic processing (Figure 3Bii). Introducing NMDARs completely abolished the distal suppression (Figure 3Cii) due to the recruitment of the slow NMDAR excitatory conductance (Figure 3Bii) during cluster input activation. Consistent with our glutamate uncaging data, increasing the number of active synapses—particularly in distal dendrites—led to supralinear integration (Figure S6). Therefore, in SST-INS, distal signal loss was also limited (Figure 3Cii) but through a different mechanism than that used by PV-INS. SST-INSs use an NMDAR-dependent integration, similarly to PNs²¹ (Figure 3Dii).

We next examined how the distinct anatomical and functional synaptic properties of PV and SST cells influenced their firing dynamics. Specifically, we tested the ability of synchronous synaptic activations to elicit action potentials on a per branch basis. Neuronal activity was simulated in response to increasing synapse number *n*<sub>syn</sub> randomly selected across the entire branch (with *n*<sub>syn</sub> < 10% of all synapses), superimposed on *in vivo*-like excitatory and inhibitory background activity (Figure 3E, see STAR Methods). PV-INSs responded to real (asymmetric) synaptic activation more effectively than uniform distribution (Figures 3F and 3G). Likewise, SST-INSs exhibited a substantial decrease in spiking probability in response to synapses devoid of NMDARs (Figures 3F and 3G), even with a boost in AMPAR conductance to match excitatory postsynaptic potential (EPSP) size to –60 mV (see STAR Methods).

We conclude that the distinct morpho-functional dendritic integration strategies of L2/3 PV- and SST-INSs represent two separate mechanisms for enhancing synaptic efficacy. PV-INSs arrange their synapses to reduce sublinear integration, particularly in distal dendritic regions, whereas SST-INSs leverage

NMDARs to amplify coincident dendritic activity throughout their entire dendritic arbor.

## Specific dendritic integration mechanisms of PV- and SST-INSs preserve input release dynamics

Dendritic integration in thin dendrites can significantly influence the readout of presynaptic short-term plasticity (STP) by either amplifying or dampening the postsynaptic integration of release probability variations.²²,⁴⁰ PV- and SST-INSs are recruited by glutamatergic inputs that display opposite STP characteristics: inputs to PV-INSs typically exhibit short-term depression, while inputs to SST-INSs often show short-term facilitation associated with low release probability.²,¹⁵ Yet, whether and how dendritic integration properties influence the readout of presynaptic dynamics in both subtypes of INS is not known.

We reasoned that the influence of dendritic integration on the readout of STP could be further enhanced if excitatory inputs onto PV- and SST-INSs involve not only changes in release probability but also multivesicular release (i.e., quantal content greater than one) at individual synaptic sites. The integration of such closely timed and spatially adjacent released events would increase the likelihood of recruiting nonlinear dendritic mechanisms²² (Figure 1). We thus first probed whether glutamatergic synapses onto PV- and SST-INSs exhibited multivesicular release in response to a single action potential. To test this, we used the genetically encoded glutamate sensor iGluSnFR⁴⁸ to monitor glutamate release from L2/3 PN axonal boutons targeting PV- and SST-INSs *in vitro* (Figure 4A). iGluSnFR was expressed in either SST- or PV-INSs. We filled individual L2/3 PNs with Alexa 594 via the whole-cell pipette, and we used two-photon imaging to identify putative points of contact between presynaptic axons and iGluSnFR-expressing IN dendrites (Figures 4A and 4B). To elicit glutamate release, we evoked action potentials in presynaptic L2/3 PNs (7 APs at 10 Hz) via injection of brief current pulses (Figure 4A). We successfully identified specific functional synaptic contacts, enabling the detection of glutamate release events even within individual recording sweeps (Figures 4B and 4C).

As expected for synapses with low release probability, inputs to SST-INSs displayed higher failure rates than those to PV-INSs, both at 2 mM and at the more physiological 1.2 mM extracellular calcium levels (Figures 4C and S7). Consistently, SST-IN inputs showed higher coefficients of variation (CV). The number of release sites (N) defines the maximum number of synaptic vesicles that could be released per action potential at individual synaptic locations.⁴⁹ To estimate N, we performed optical fluctuation analysis⁵⁰,⁵¹ (see STAR Methods), assuming a binomial distribution of release events. We found that N was quite variable

<footnote>(E) Somatic Vm responses to background and stimulus-evoked activity in the dendritic branch shown in (A), with quasi-synchronous activation of increasing numbers of randomly selected synapses. Responses shown for the PV-IN model (red, with its uniform distribution control in gray) and SST-IN model (orange, with its no-NMDA control in purple).</footnote>

<footnote>(F) Spike probability (50 ms post-stimulus) plotted against number of stimulated synapses (*n*<sub>syn</sub>).</footnote>

<footnote>(G) Onset response level in the PV-IN model (red, with its uniform distribution control in gray, *p* < 0.001, *n* = 6 branches, Wilcoxon test) and SST-IN model (orange, with its no-NMDA [AMPA+] control in purple, *p* < 0.001, *n* = 6 branches, Wilcoxon test). Onset level is defined as the input level where the “Erf” fit goes above spike probability = 0.05. Results are shown as mean ± SEM over *n* = 6 branches in (C), (D), (F), and (G). See also Figure S6 and Tables S1–S3.</footnote>
<figure><img src="image_27.png" /><figcaption>Figure 4. Multivesicular release is differentially processed by PV- and SST-INs dendrites, suggesting that dendritic properties differently influence short-term plasticity readout in both IN populations</figcaption></figure>

(A) (Top) Methodology to study glutamate release at individual synaptic contacts between PNs and PV- or SST-INs using iGluSNFR-A184V. Glutamate release was evoked from L2/3 PNs via current injection. (Bottom) 2PLSM images displaying a patch-loaded PN axon (red) and SST-INs expressing iGluSnFR-A184V (green).

(B) Averaged line scan (10 images) of iGluSnFR-A184V fluorescence (green) at contact sites between L2/3 PN boutons and PV/SST-IN dendrites following 7 action potentials at 10 Hz. Time-series traces (10 trials) show mean fluorescence over a 1 µm region (white line); black trace indicates the average ΔF/F.

(C) Summary of failure rates and coefficient of variation for L2/3 PN synapses onto SST-INs (n = 8) and PV-INs (n = 9), including release probability (P<sub>Ves</sub>) and maximum vesicles released per action potential (AP) (N<sub>maxVes</sub>) (*p* < 0.05, Mann-Whitney test).

(D) (Left) 2PLSM image of an SST-IN loaded with Alexa 594, with glutamate uncaging at three dendritic sites. (Right) Somatic EPSC recordings from photolysis at two pulse durations, mimicking one or two quantal events, at the indicated dendritic locations. EPSC traces are shown with raw amplitudes (top) and normalized to the first peak (bottom).

(E) (Left) Summary of single and double-quanta photolysis-evoked EPSCs amplitude ratio for SST-INs. (Right) Photolysis-evoked EPSCs amplitude ratio binned by distance from soma for SST-INs.

(F) Similar analysis as (E) but for experiments performed in the presence of NMDARs, alone (left) or voltage-gated calcium channel (VGCC) blockers (right), (*p* < 0.05, ** *p* < 0.01, Kruskal-Wallis test with Dunn's correction).

(G and H) Similar to (D) and (E) but for PV-INs (** *p* < 0.01, **** *p* < 0.00001, Kruskal-Wallis test with Dunn's correction).

(I) (Left) Similar experiments as in (F) but for PV-INs in the presence of TEA (5 mM) (left) or by reversing the order of P1 and P2 pulses mimicking short-term depression (right). (* *p* < 0.05, ** *p* < 0.01, Kruskal-Wallis test with Dunn's correction.) Data are mean ± SEM.
See also Figures S7 and S8.

between individual points of contact, like previously reported in
hippocampal INs,⁵² with a mean value per action potential close
to 2 for both SST- and PV-INs (Figure 4C). Overall, our results re-
veal that multivesicular release can occur at individual glutama-

tergic inputs into both SST- and PV-INs and thus could be sub-
ject to dendritic nonlinear readout.

To assess how single-synapse multivesicular release is
integrated in PV- and SST-IN dendrites, we used quantal
A

<figure><img src="image_28.png" /></figure>

B

STP
stochastic
model

pre APs

events

glut releases

<figure><img src="image_29.png" /></figure>

trials

<figure><img src="image_30.png" /></figure>

PV

average

<figure><img src="image_31.png" /></figure>

SST

average

<figure><img src="image_32.png" /></figure>

C

<figure><img src="image_33.png" /></figure>

D

<figure><img src="image_34.png" /></figure>

E

<figure><img src="image_35.png" /></figure>

F

<figure><img src="image_36.png" /></figure>

G

<figure><img src="image_37.png" /></figure>

(legend on next page)
size-adjusted pEPSCs to compare responses to single vs. double quanta at individual dendritic sites (Figures 4D–4I, see STAR Methods). Dendrites of SST-INs integrated double quanta uniformly all along the dendritic tree (Figures 4D and 4E). This integration profile was also observed in current-clamp configuration (Figure S8) and depended on NMDARs but was unaffected by the blockade of other voltage-gated channels (Figure 4F). Conversely, PV-IN dendrites exhibited a progressive somatodendritic attenuation of double-quanta pEPSCs as expected for a passive cable (Figures 4G and 4H; Abrahamsson et al.²²). In agreement, blocking potassium channels with tetraethylammonium (TEA) did not reduce the sublinear integration of double quanta along dendrites in cortical PV-INs (Figure 4I) suggesting that the observed sublinear effect is driven purely by passive properties. Importantly, reversing the order of the double and single quantum pulses still reveals that the amplitude difference between the two pulses decreases along dendritic branches (Figure 4I). Thus, PV dendritic input resistance is sufficient to engage sublinear integration following the activation of a single synapse during STP at distal synaptic contacts.

Our findings suggest that PV- and SST-INs have evolved distinct dendritic mechanisms to reliably read out target-specific dynamics of neurotransmitter release.

## Specific dendritic integration properties of PV- and SST-INs result in temporally distinct output firing dynamics

IN-specific mechanisms that reduce the cable filtering properties of thin dendrites and preserve the readout of presynaptic release dynamics could result in different spiking responses to the same input stimuli. To test this hypothesis, we used numerical simulations in our IN models in the presence and absence of STP (Figures 5A–5C).

Modeled SST-INs responded to a short pulse (50 ms, step 1, Figure 5A, see STAR Methods) with delayed and long-lasting activity, which exceeded the NMDAR decay time constant (Figures 5A and 5D, ~200 ms vs. $τ_{decay}$ = 80 ms). This prolonged response resulted from the temporal broadening of NMDAR-related events by excitatory/inhibitory synaptic fluctuations⁵³ as it disappeared with NMDAR removal (Figures 5A and 5D, green curve). Conversely, modeled PV-INs responded rapidly,

and the firing remained confined within the pulse duration (Figure 5E).

Furthermore, PV and SST models also exhibited distinct input sensitivities. The PV-IN model showed near-linear spiking responses, closely matching the stimulus width and amplitude (Figures 5A and 5D, pink), with strong correlations between input steps and output rates (Figure 5F). In contrast, the SST model had a greater response to prolonged stimuli at a given amplitude (Figure 5A, brown, step 2 vs. step 3: Figures 5D and 5G). This preference for long-lasting stimuli was due to NMDAR-mediated integration dynamics, as it was eliminated when NMDARs were removed (Figure 5A, green, step 2 vs. step 3; Figures 5D and 5G).

We next explored how IN-specific presynaptic STP interacted with dendritic properties to further shape the temporal processing of INs. To this purpose, we developed a simple model of synaptic dynamics capturing the stochastic nature of vesicle release at the single trial level (see STAR Methods, Figure 5B). We constrained model parameters with our experimental results (Figure S9), which allowed us to reproduce the established depressive and facilitatory behavior of glutamatergic inputs into PV- and SST-INs, respectively⁵⁴⁻⁵⁶ (Figure 5B). In terms of input-output transformation, we found that the inclusion of STP strengthened and expanded the different temporal processing of the two IN models. Importantly, those simulations demonstrated a synergistic interaction between facilitation and NMDAR dynamics, as facilitation alone yielded a significantly lower firing output response (Figures 5D and 5G). The increased depolarization and the increased likelihood of coincident inputs during facilitating periods indeed specifically engage NMDAR to strengthen the low-frequency selectivity of the SST-full model (Figures 5C, 5D, and 5G). In contrast, modeled PV-INs strongly decreased the overall response to long-lasting (>200 ms) stimuli (Figures 5C, 5D, and 5G, red vs. pink curves) and thus track changes of input stimulus rather than representing stimulus duration (Figure 5F, 1 s, red vs. pink bars).

Taken together, these results suggest that the distinct dendritic and synaptic properties of PV- and SST-INs are tuned to produce two opposing temporal processing modes. PV-INs generate rapid and brief response times (Figure 5E, peak response with a delay of <10 ms; Figure 5F, tracking fast inputs; Figure 5G, tuned to fast input variations), making them ideal for

<caption>**Figure 5.** Detailed models of dendritic integration predict temporally distinct spiking dynamics in PV- and SST-INs</caption>

(A) Example simulations for step-waveform input integration in IN models without STP (see STAR Methods). (Top to bottom) (1) Input rate waveform (gray), (2) excitatory/inhibitory events (green/red) and Vm dynamics for a single trial, and (3) rate output from peri-stimulus time histograms (PSTH) over 100 trials. The step decreases in amplitude (step 1 to 2: 3.5× to 2× step-to-baseline factor) and then increases in duration (step 2 to 3: 50 to 250 ms).

(B) Illustration of the experimentally constrained STP stochastic model capturing the release dynamics of excitatory synapses into PV- and SST-INs (see Figure S9 for the parameters optimization). The model response to 8 presynaptic action potentials at 20 Hz over 10 trials is shown, with release events (single quanta: light gray; double quanta: dark gray) and glutamate release traces for individual trials (thin lines) and the trial average (thick black line).

(C) Same as (A) but for models with STP. Note the extended stimulus windows (step 1,2: 100 ms, step 3: 500 ms) and longer timescales than in (A).

(D) Summary data for the firing responses to step-waveform inputs in all IN models ($n$ = 6 branches per model, see also Figure S10). The step decreases in amplitude (step 1 to 2: 4× to 3× step-to-baseline factor) and then increases in duration (step 2 to 5: 50 ms to 1 s).

(E) Delay after stimulus onset to reach 80% peak firing response in all models.

(F) Step correlations for short (50 ms, left) and long (1 s, right) steps in all models, defined as the square root of the sum of squared rate responses (from E) after min-max normalization.

(G) Mean firing in response to steps of varying durations for the 6 different models (at the 3× step-to-baseline factor shown in D). To capture evoked firing over different temporal windows in the models, the firing response was evaluated as the mean firing in the interval where the firing exceeds twice the baseline firing. In (D)–(G), results are shown as mean ± SEM over $n$ = 6 branches for each model.

See also Figures S9 and S10.
<figure><img src="image_38.png" /><figcaption>Figure 6. The distinct inhibitory dynamics observed during visual processing of natural movies in PV- and SST-INs can be explained by their respective dendritic integration properties</figcaption></figure>

(A) Schematic overview of the Neuropixels dataset from Siegle et al.⁵⁷

(B) Example data from recording sessions in PV-Cre (i) and SST-Cre (ii) mice. Top-left: photo-tagging trials; bottom-left: classification of photo-tag-positive vs. photo-tag-negative units (see STAR Methods). Right: Spike rasters and PSTHs showing responses of PV⁺ (red), SST⁺ (orange), and tag-negative (gray) units aligned to stimulus onset.

(C) Cross-correlation function between firing rates of tag-negative units and PV⁺ (red) or SST⁺ (orange) populations during natural movie #1. Units from different sessions were pooled to increase spike-rate sampling.

(D) Half-width of the cross-correlation function for positive and negative units (Lorentzian fit), using pooled units from individual sessions. PV-Cre: *N* = 9 sessions × 2 movies; SST-Cre: *N* = 12 sessions × 2 movies. Kruskal-Wallis test with Dunn's correction: PV⁺ vs. PV⁻, *p* = 1.0; SST⁺ vs. SST⁻, *p* < 0.05; PV⁻ vs. SST⁻, *p* > 0.05; PV⁺ vs. SST⁺, *p* < 0.001.

(E) Example simulations using PV-full (red) and SST-full (orange) INs models driven by synaptic activity constrained by experimentally derived rates obtained from non-tagged units during natural movie presentation (see B, STAR Methods, and Figure S11). (1) Input rate waveform (gray), (2) excitatory (green) and inhibitory (red) synaptic events with corresponding Vm dynamics for a single trial, and (3) firing rate output from PSTH over 40 trials.

(F and G) Same as (C) and (D) but for simulations described in (E). Half-width of the cross-correlation function between input and output rates (Lorentzian fit) for the different IN models. Data are shown as mean ± SEM over *n* = 6 branches per model. Statistical comparisons were made using a Student's t test with Bonferroni correction: PV-noSTP vs. PV-full, *p* > 0.05; PV-full vs. SST-full, *p* < 0.0001; SST-full vs. SST-noNMDA, *p* < 0.0001; SST-full vs. SST-noSTP-noNMDA, *p* < 0.0001; SST-noNMDA vs. SST-noSTP-noNMDA, *p* < 0.0001.

See also Figure S11.

representing rapid changes in sensory stimuli. In contrast, SST-INs exhibit slower, sustained responses with delayed peaks (≥100 ms; Figure 5E), enabling them to represent the duration of ongoing stimuli and respond preferentially to slower input fluctuations (Figures 5F and 5G).

## PV- and SST-INs display distinct inhibitory dynamics during visual processing in awake mice

Our numerical simulations predict distinct processing of input signals in PV- and SST-INs. Next, we tested those specific processing predictions during sensory integration in the visual cortex of awake mice. We analyzed a publicly available dataset from the Allen Brain Institute, which contains single-unit recordings from the mouse visual cortex in response to natural movie presentations. This dataset includes firing activity of photo-tagged PV- and SST-INs⁵⁷ (Figure 6A, see STAR Methods). Specifically, we computed the time-varying firing rate of each IN type by pooling

photo-tagged units of a single session. We also estimated local excitatory activity by computing the time-varying rate of 100 randomly picked, photo-tag-negative units in the recordings that we assumed to largely originate from PNs (Figure 6B). To quantify the IN-specific temporal features of evoked activity during movie presentations, we computed the cross-correlation function (CCF) between excitatory and IN activity (Figure 6C). We observed a wider temporal window for SST-INs in the CCF, as compared with PV-INs (Figure 6C). This observation was highly consistent across sessions and movies, as measured by the half-width of the CCF (Figure 6D, see STAR Methods). We generated predictions from our IN models to investigate whether PV- and SST-IN-specific dendritic integration mechanisms could explain different temporal input-output firing dynamics. Because both PV- and SST-INs are primarily driven by local cortical excitation,⁵⁸ we used the average rate of photo-tag-negative units to generate excitatory/inhibitory synaptic inputs, and we simulated
the single-neuron dynamics over different trials to obtain aver-
age output rates (Figures 6E and S11, see STAR Methods).
PV-INs generated sharp, fast responses with narrow CCFs, while
SST-INs showed broader, sustained activity and wider CCFs
(orange vs. red, Figures 6E–6G). Notably, these model predic-
tions closely matched experimental data both at the population
level (Figures 6F vs. 6C) and across sessions (Figures 6G vs.
6D), with comparable CCF widths (PV model, 0.21 ± 0.02 s;
SST model, 0.41 ± 0.02 s; PV neuropixels data, 0.23 ± 0.05 s;
SST neuropixels data, 0.56 ± 0.05 s). STP slightly sharpened
the CCF in PV-INs (Figure 6G, pink vs. red) while the broadening
was due to the combination of STP and NMDAR dynamics in
SST-INs (Figure 6G, green vs. purple vs. orange). We conclude
that the distinct spiking dynamics during the processing of nat-
ural movies of visual cortical PV- and SST-INs can largely be
explained by their different dendritic integration properties.

NMDARs control the *in vivo* response dynamics of SST-INs in response to visual stimuli

To test the crucial role of NMDARs in specifically shaping SST-IN activity *in vivo*, we performed two-photon Ca²⁺ imaging from SST- and PV-INs to record their activity in response to visual stimuli. Full-field static gratings were presented for 2 s while we recorded visually evoked activity in INs using a genetically encoded Ca²⁺ sensor (GCaMP6s/8s) (Figures 7A and 7B). Fluorescence signals were deconvolved to remove sensor dynamics. We generated model predictions by simulating IN responses to a two-component waveform mimicking the grating-evoked activity (Figures 7C and S13, see STAR Methods). As predicted by the model (Figure 7C), visual stimulation produced significantly delayed peak onsets and sustained activity (measured between 0.8 and 2 s after stimulation) in SST-INs, as compared with PV-INs (Figure 7D). The model also predicted that NMDARs regulate SST-IN recruitment. Indeed, NMDAR removal resulted in a >10-fold decrease in evoked spiking and it was paralleled by a reduction in the sustained component of SST firing (Figure 7C). To test this prediction experimentally, we selectively removed NMDARs from SST-INs using SST::GluN1-KO mice (see Figure1 and STAR Methods) and monitored SST-INs activity using two-photon calcium imaging (Figure 7B). Importantly, genetic removal of NMDARs did not affect glutamatergic transmission and STP at L2/3 PN-SST-IN synapses (Figure S12). However, these mice exhibited a marked reduction in SST-IN responsiveness to both half- and full-contrast visual stimuli (Figure 7E), supporting the crucial role of NMDARs in SST-IN recruitment by visual input. In line with our model predictions (Figure 7C), the reduced visually evoked recruitment of SST-INs in SST::GluN1-KO mice was associated with a faster response decay compared with their wild-type littermates (Figure 7E). These perturbation experiments confirm that NMDARs contribute causally to the characteristically broad temporal dynamics of SST-IN activation, validating our computational model and highlighting the importance of NMDAR-mediated signaling in shaping SST-IN response properties.

DISCUSSION

PV-INs have been characterized by their fast synaptic kinetics,
depressing STP, and rapid voltage-gated ion channel activation,

supporting the view that they encode temporally precise informa-
tion with millisecond resolution. However, their thin, electrotoni-
cally compact dendrites exhibit passive properties that can
dampen and temporally smear EPSPs, potentially constraining
their ability to integrate input with the temporal precision tradition-
ally ascribed to them. Similar dendritic limitations in SST-INs have
been proposed to suppress facilitation at excitatory synapses,²²
raising broader questions about how IN dendrites impact circuit
computations. Despite their central role in visual cortical function,
how dendritic properties shape the temporal tuning of PV- and
SST-INs has remained poorly understood. We now show that
dendritic integration mechanisms critically shape the distinct
temporal response profiles of PV- and SST-INs.

Differential dendritic mechanisms in PV and SST-INs

PV-INs exhibit sublinear integration, consistent with PV-INs den-
drites functioning primarily as passive cables, whereas SST-INs
display NMDAR-dependent supralinear dendritic integration. In-
terestingly, our model simulations predict that variations in the
density of synaptic NMDARs represent a major contributor for
such differential dendritic integration properties. Previous
studies have shown that NMDAR density varies across IN
classes,³⁸,⁵⁹ but the functional significance of these differences
remained unclear. We suggest that variations in the synaptic
NMDAR content across different populations of INs contribute
to functional diversity in their dendritic operations, ultimately
shaping their roles during *in vivo* network activity.

Surprisingly, we found that the different dendritic integration
modes of PV- and SST-INs were associated with different dis-
tributions of glutamatergic inputs along their dendritic trees. In
particular, we observed a non-uniform pattern along the den-
dritic branches of PV-INs. Synaptic density was reduced in
the distal dendritic compartments where synaptic integration
is strongly sublinear. In the cerebellum, gap junctions have
been reported to compensate for sublinear integration.²⁹
Here, we propose that gradients of synapse distributions in
PV-INs may have a similar effect by reducing the number of co-
active synapses in distal dendritic regions, where input resist-
ance is particularly elevated and dendritic saturation is easily
achieved. An important inference from our data is also that
the asymmetric positioning of synapses, placing a large frac-
tion of synaptic inputs in somatically close dendritic segments,
will attenuate the filtering effect of passive integration on STP
(Figure 4; Abrahamsson et al. ²⁵) and thus increase the sensitiv-
ity of PV-INs to presynaptic short-term dynamics. Interestingly,
in dendrites of SST-INs where synapses contain higher density
of NMDARs, this effect was much less pronounced. Altogether,
our data suggest a general scenario in which INs vary both their
synaptic receptor compositions and synaptic organization
patterns along their dendrites to generate temporally distinct
responses while maintaining the efficiency of synaptic
transmission.⁶⁰

Different integration modes generate distinct inhibitory
dynamics

The present results suggest that, in addition to the known mor-
phological, transcriptomic, and electrophysiological differences,
dendritic integration properties vary across the distinct
<figure><img src="image_39.png" /><figcaption>Figure 7. Two-photon imaging during gratings presentation confirms the rapid recruitment of PV-INs and the NMDAR-dependent sustained activations of SST-INs</figcaption></figure>

(A) Representative 2PLSM image (left, mean image) and time-series traces (right) of GCaMP8s fluorescence in PV- and SST-INs (top and bottom, respectively), displayed as ΔF/F₀ (green), along with their corresponding deconvolution traces (PV in red, SST in orange) during the presentation of static gratings at half and full contrast.

(B) Same as (A) but showing GCaMP6s fluorescence of SST-INs in SST-Cre and SST-Cre::GluN1flox mice (orange and purple, respectively).

(C) Predictions from the different models (SST-full, SST-noNMDA, and PV-full) for the output firing rate in response to a two-component waveform input simulating the activity induced by grating stimulation (see also Figure S13).

(D) Peak-normalized deconvolved responses of GCaMP8s signals in responsive ROIs following stimulus presentation (at full contrast, averaged across all orientations) are shown as mean ± SEM over *N* = 22 sessions for PV-INs (*n* = 429 ROIs, 9 mice) and *N* = 15 sessions for SST-INs (*n* = 382 ROIs, 7 mice). Mean values in the [0.8,2] s interval (highlighted by a gray line): 0.68 ± 0.02 (SST-Cre, *N* = 15) vs. 0.40 ± 0.03 (PV-Cre, *N* = 22), Mann-Whitney U test: *p* < 0.001. The inset shows a zoom of the [−0.1, 0.3] s window. Delays to peak onset: 0.19 ± 0.01 s (PV-Cre, *N* = 22) vs. 0.63 ± 0.14 s (SST-Cre, *N* = 15), Mann-Whitney U test: *p* < 0.001.

(E) Fraction of responsive ROIs in at least one orientation at half (top) and full (bottom) contrast in SST-Cre (orange, *n* = 490 ROIs, 18 sessions in 7 mice) and SST-Cre::GluN1flox mice (purple, *n* = 319 ROIs, 14 sessions in 5 mice).

(F) Same as (D) but for deconvolved GCaMP6s signals in SST-INs from SST-Cre (*N* = 18, orange) and SST-Cre::GluN1flox (*N* = 14, purple) mice. Mean levels in the [0.8,2] s interval (highlighted with a gray line): 0.67 ± 0.03 (WT, *N* = 18) vs. 0.48 ± 0.03 (KO, *N* = 14), Mann-Whitney U test: *p* < 0.001. See also Figures S12 and S13.

populations of cortical interneurons. Numerical simulations highlight that such a variability in integration properties plays a crucial role in shaping the distinctive functional characteristics of the

specific PV- and SST-IN classes. The dendritic properties of PV-INs allow a precise temporal response to variations in pyramidal cell activity. They seem to be particularly well tailored for
PV-INs to fulfill their important role as fast coincidence detectors, to sharpen sensory inputs through powerful and precise feedforward inhibitory networks and to drive fast cortical brain oscillations.⁵ Previous studies have shown that dendritic conductances as well as synaptic AMPA receptor composition in PV-INs favor fast signaling.¹⁴,⁶¹,⁶² Our results reveal that the dendritic integration mechanisms, notably the low synaptic composition of NMDA-type receptors and the proximal location of excitatory inputs along dendrites, are tailored to generate fast PV-IN activity dynamics. Conversely, in SST-INs, the presence of slow NMDARs along dendrites extends the window of temporal integration and increases the efficacy of synaptic activity in driving SST-IN firing. This extended temporal window appears important for providing feedback inhibition to cortical microcircuits using glutamatergic synapses that are known to be particularly inefficient because of low release probability.¹⁵,⁵⁴

## Distinct inhibitory dynamics subserve different neuronal computations

Studies in the neocortex and hippocampus indicate that differences in STP of glutamatergic inputs onto PV- or SST-INs enable each inhibitory circuit to extract distinct temporal features from ongoing activity.¹²,¹³ In the neocortex, increased dendritic activity in PNs has been linked to bursting, which preferentially recruits SST-INs through synaptic facilitation while reducing PV-IN activity due to their short-term depression. Through this mechanism, PV- and SST-IN activity have been suggested to reflect the somatic and dendritic activity in PNs, providing in return compartment-specific feedback inhibition.¹²,¹³ Our new findings are compatible with such a model where PV- and SST-INs extract the different temporal features of input dynamics. Overall, both presynaptic and postsynaptic mechanisms appear to converge to support distinct modes of cortical inhibition. Somatic inhibition, mediated by PV-INs is finely tuned to precisely regulate spike timing and frequency in PNs. In contrast, delayed dendritic inhibition mediated by SST-INs appears particularly suited to controlling burst firing in PNs via sculpting dendritic computations as NMDAR-dependent plateau potentials. We conclude from our observations that, alongside STP, PV- and SST-INs have developed distinct dendritic integration mechanisms specifically tailored to provide different temporal dynamics of inhibition. Further research is still needed to fully understand how the routing of inhibition across separate modules with distinct dynamics serves the computational properties of cortical assemblies.

## RESOURCE AVAILABILITY

### Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Nelson Rebola (nelson.rebola@icm-institute.org).

### Materials availability

This study did not generate unique reagents.

### Data and code availability

* All data reported in this paper will be shared by the lead contact upon request.

* The code for the data analysis (EM dataset, neuropixels dataset, and imaging dataset) and numerical simulations (simplified morphological model, detailed biophysical and morphological models) of this study are publicly available at the following links: https://github.com/yzerlaut/pv-sst-dendrites and https://doi.org/10.5281/zenodo.15341533.

* Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

* The two-photon data in SST and SST:GluN1-KO are publicly available on the EBrain database (https://doi.org/10.25493/MVCK-4YH).

## ACKNOWLEDGMENTS

This study was supported by the Centre National de la Recherche Scientifique "Investissements d'avenir" ANR-10-IAIHU-06, Agence Nationale de la Recherche (to N.R.; ANR-16-CE16-0007-02, ANR-18-CE16-0011-01, ANR-20-CE16-0011-01; ANR-24-CPJ1-0124-01 to Y.Z.; ANR-22-CE37-0008-01 to A. B.; ANR-DecoSensoMol1 to N.R. and A.B.; ANR-17-CE16-0026-01 to A.B. and D.D.; and ANR-13-BSV4-0016, ANR-17-CE16-0019, and ANR-18-CE16-0018 to D.A.D.), ANR-23-CE16-0003 to N.R. and D.A.D. and ANR-16-CE19-0003-01 to G.M., the Émergence programme par l'Alliance Sorbonne Université (J.L.); the European Research Council (ERC-STG-678250 to N.R.); the European Union's Horizon 2020 research and innovation program (Marie Skłodowska-Curie Grant 892175 "InProsMod" to Y.Z.); the Paris Brain Institute and the Fonderie pour la Recherche Médicale (FRM; fellowship ARF201909009117 to Y.Z.); Equipes FRM - DEQ20150331684; Equipes FRM - EQU201903007860 to A. B.); NIH (1R01MH124867-02) to P.P.; the NeuroCure Cluster of Excellence Berlin; the Deutsche Forschungsgemeinschaft (DFG), SFB-1315 "Brenda Milner Award" to A.T.; and Région Ile-de-France (DIM-ELICIT grant to G.M. and N.R. and DIM C-BRAINS PhD fellowship to C.M.P.). We thank the Paris Brain Institute core facilities, namely iVector and ICMice PHENOPARC and ICM.Quant. We are very grateful to Casey Schneider-Mizell, Forrest Collman, and Emily Joyce for sharing material and guiding us in the analysis of the MICrONs dataset and to Kathleen Cho and Hillel Adesnik for comments on the manuscript.

## AUTHOR CONTRIBUTIONS

Conceptualization, A.M., Y.Z., A.B., D.A.D., J.L., and N.R.; methodology and visualization, A.M., Y.Z., D.D., E.B., C.M.P., A.T., G.M., L.C., P.P., A.B., D.A. D., J.L., and N.R.; investigation, A.M., Y.Z., D.D., E.B., C.M.P., A.T., G.M., J. L., and N.R.; funding acquisition, Y.Z., D.D., G.M., A.B., J.L., and N.R.; project administration, N.R.; supervision: A.B., D.A.D., J.L., and N.R.; writing—original draft, review & editing, A.M., Y.Z., A.T., P.P., A.B., D.A.D., L.C., J.L., and N.R.

## DECLARATION OF INTERESTS

Authors declare that they have no competing interests.

## STAR★METHODS

Detailed methods are provided in the online version of this paper and include the following:

* KEY RESOURCES TABLE

* EXPERIMENTAL MODEL AND STUDY PARTICIPANT DETAILS

* Mice

* METHOD DETAILS

* Slice preparation

* Electrophysiology

* Transmitted light and fluorescence imaging

* Stereotaxic viral injections

* Estimation of quantal miniature EPSCs

* Glutamate uncaging

* iGluSnFR imaging

* PSD95 labeling in cortical interneurons

* Surgery for *in vivo* 2P imaging

* *In vivo* 2P Ca2+ imaging
* Visual stimulation

* Reduced model of dendritic integration

* Stochastic release model of short-term plasticity

* Detailed digital models of PV- and SST-INS

* **QUANTIFICATION AND STATISTICAL ANALYSIS**

* Synapse distribution analysis

* Visually-evoked spiking dynamics of PV- and SST-INS during natural movies

* Analysis of fluorescence signals

* Optical fluctuation analysis

* PSD-95 Venus puncta detection

* Statistics

## SUPPLEMENTAL INFORMATION

Supplemental information can be found online at https://doi.org/10.1016/j.neuron.2025.05.029.

Received: September 4, 2024

Revised: April 10, 2025

Accepted: May 30, 2025

Published: June 30, 2025

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## STAR★METHODS

### KEY RESOURCES TABLE

<table><thead><tr><th>REAGENT or RESOURCE</th><th>SOURCE</th><th>IDENTIFIER</th></tr></thead><tbody><tr><td colspan="3">Antibodies</td></tr><tr><td>Anti-GFP Nanobody coupled to ATTO 647N</td><td>ChromoTek</td><td>GBA647N-100; RRID: AB_2629215</td></tr><tr><td colspan="3">Bacterial and virus strains</td></tr><tr><td>pAAV.CAG-FLEX.SF-iGluSnFR.A184V</td><td>Marvin et al.<sup>48</sup></td><td>Addgene:106187</td></tr><tr><td>AAV9.Syn-Flex-GCaMP6s-WPRE-SV40</td><td>Chen et al.<sup>63</sup></td><td>Addgene:100845</td></tr><tr><td>AAV9.pGP-AAV-syn-FLEX-jGCaMP8s-WPRE</td><td>Zhang et al.<sup>64</sup></td><td>Addgene:162377</td></tr><tr><td>AAV1.Flex.tdTomato</td><td>gift Edward Boyden</td><td>Addgene: 28306</td></tr><tr><td>AAV-Syn-PSD95.FingR-eGFP-CCR5TC</td><td>Bensussen et al.<sup>65</sup></td><td>Addgene:125693</td></tr><tr><td colspan="3">Chemicals, peptides, and recombinant proteins</td></tr><tr><td>D-AP5</td><td>Hello Bio</td><td>HB0225</td></tr><tr><td>NBQX disodium salt</td><td>Tocris; Hello Bio</td><td>Cat. No. 1044; HB0443</td></tr><tr><td>Alexa Fluor 594 hydrazide, sodium salt</td><td>Invitrogen</td><td>A10438</td></tr><tr><td>(+)-MK 801 maleate</td><td>Hello Bio</td><td>HB0004</td></tr><tr><td>MNI-caged-L-Glutamate</td><td>Tocris</td><td>Cat. No. 1490</td></tr><tr><td>Picrotoxin</td><td>Abcam</td><td>Ab120315</td></tr><tr><td>Tetrodotoxin citrate</td><td>Hello Bio</td><td>HB1035</td></tr><tr><td>QX 314 chloride</td><td>Hello Bio</td><td>HB1030</td></tr><tr><td>Tetraethylammonium chloride</td><td>Millipore Sigma</td><td>6614-25G</td></tr><tr><td colspan="3">Deposited data</td></tr><tr><td>MICRONS dataset</td><td>https://doi.org/10.1038/s41586-025-08790-w</td><td>N/A</td></tr><tr><td>Proofread cellular annotations of the MICRONS dataset</td><td>https://zenodo.org/record/7641781#collapseTwo</td><td>N/A</td></tr><tr><td>Two-photon in vivo data in WT and GluN1-KO mice</td><td>https://doi.org/10.25493/MVCK-4YH</td><td>N/A</td></tr><tr><td colspan="3">Experimental models: Organisms/strains</td></tr><tr><td>C57BL/6NRj N/A</td><td>Janvier Labs</td><td>N/A</td></tr><tr><td>Ssttm2.1 cre)Zjh/J (SST-IRES-Cre)</td><td>Jackson Laboratory</td><td>JAX 013044</td></tr><tr><td>Pvalbtm1(cre)Arbr/J (PV-Cre)</td><td>Jackson Laboratory</td><td>JAX 008069</td></tr><tr><td>B6.Cg-Gt(ROSA)26Sortm9(CAG-tdTomato) Hze/J (td-tomato)</td><td>Jackson Laboratory</td><td>JAX007909</td></tr><tr><td>B6;129-Dlg4tm1.1Hnz/J (PSD 95 enabled)</td><td>Jackson Laboratory</td><td>JAX 026092</td></tr><tr><td>GluN1 Flox (NR1-2lox)</td><td>Niewoehner et al., 2007</td><td>N/A</td></tr><tr><td colspan="3">Software and algorithms</td></tr><tr><td>pClamp</td><td>Molecular Devices</td><td>N/A</td></tr><tr><td>IGOR Pro 8</td><td>WaveMetrics</td><td>N/A</td></tr><tr><td>NeuroMatic</td><td>http://www.neuromatic.thinkrandom.com/<sup>66</sup></td><td>N/A</td></tr><tr><td>Fiji</td><td>ImageJ</td><td>N/A</td></tr><tr><td>GraphPad Prism 9</td><td>https://www.graphpad.com</td><td>N/A</td></tr><tr><td>Affinity Designer</td><td>https://affinity.serif.com/fr/designer/</td><td>N/A</td></tr><tr><td>Prairie View 5.4</td><td>Bruker</td><td>N/A</td></tr><tr><td>Python Programming Language</td><td>https://www.python.org/</td><td>N/A</td></tr><tr><td>Cloud-volume</td><td>https://github.com/seung-lab/cloud-volume</td><td>N/A</td></tr></tbody></table>

(Continued on next page)
Continued

<table><thead><tr><td>REAGENT or RESOURCE</td><td>SOURCE</td><td>IDENTIFIER</td></tr></thead><tbody><tr><td>MeshParty</td><td>https://github.com/CAVEconnectome/MeshParty</td><td>N/A</td></tr><tr><td>CAVEclient</td><td>https://github.com/CAVEconnectome/CAVEclient</td><td>N/A</td></tr><tr><td>Custom code for analysis and simulations</td><td>https://doi.org/10.5281/zenodo.15341533</td><td>N/A</td></tr><tr><td>suite2p</td><td>https://github.com/MouseLand/suite2p</td><td>N/A</td></tr><tr><td>brian2</td><td>https://brian2.readthedocs.io</td><td>N/A</td></tr></tbody></table>

## EXPERIMENTAL MODEL AND STUDY PARTICIPANT DETAILS

### Mice

Animals (C57BL/6 background) were housed in the Paris Brain Institute animal facility accredited by the French Ministry of Agriculture for performing experiments on live rodents under normal light/dark cycles. Work on animals was performed in compliance with French and European regulations on care and protection of laboratory animals (EC Directive 2010/63, French Law 2013-118, February 6th, 2013). All experiments were approved by local the Ethics Committee #005 (authorizations APAFIS #51086-2024091315255171-v5 and #38114-2022120614459263-v6) and by the French Ministry of Research and Innovation. Experimental data was obtained from adult (P25-P70) mice. Both male and female mice were used with the following genotypes: SST-IRES-Cre (SSTtm2.1(cre)Zjh/J; JAX 013044) X Ai9 (Gt(ROSA)26Sortm9(CAG-tdTomato); JAX 007909); PV-Cre (Pvalbtm1(cre)Arbr/J; JAX 008069) X Ai9 (Gt(ROSA)26Sortm9(CAG-tdTomato); SST-IRES-Cre (SSTtm2.1(cre)Zjh/J; JAX 013044) X PSD-95-ENABLED (B6;129-Dlg4tm1.1Hnz/J; JAX 026092); PV-Cre (Pvalbtm1(cre)Arbr/J; JAX 008069) X PSD-95-ENABLED (B6;129-Dlg4tm1.1Hnz/J; JAX 026092); SST-IRES-Cre (SSTtm2.1(cre)Zjh/J; JAX 013044) X GluN1 Flox (Niewoehner et al., 2007). Animals were maintained on a 12-h light/dark cycle with food and water provided ad libitum.

### METHOD DETAILS

#### Slice preparation

Acute parasagittal (S1) or coronal (V1) slices (320 µm) were prepared from adult mice, aged between postnatal days 25 and 70. Mice were deeply anesthetized with a mix of ketamine/xylazine (mix of i.p. ketamine 100 mg/kg and xylazine 13 mg/kg) and perfused transcardially with ice-cold cutting solution containing the following (in mM): 220 sucrose, 11 glucose, 2.5 KCl, 1.25 NaH2PO4, 25 NaHCO3, 7 MgSO4, 0.5 CaCl2. After the perfusion the brain was quickly removed and slices prepared using a vibratome (Leica VT1200S). Slices containing S1 barrel field or V1 were transferred to ACSF solution at 34°C containing (in mM): 125 NaCl, 2.5 KCl, 2 CaCl2, 1 MgCl2, 1.25 NaH2PO4, 25 NaHCO3, 15 Glucose for 15-20 min. After the period of recovery, slices were kept at room temperature for a period of 5-6 h.

#### Electrophysiology

Whole-cell patch-clamp recordings were performed close to physiological temperature (32-34°C) using a Multiclamp 700B amplifier (Molecular Devices) and fire-polished thick-walled glass patch electrodes (1.85 mm OD, 0.84 mm ID, World Precision Instruments); 3.5-5 MΩ tip resistance. For voltage-clamp recordings, cells were whole-cell patched using following intracellular solution (in mM): 90 Cs-MeSO3, 10 EGTA, 40 HEPES, 4 MgCl2, 5 QX-314, 2.5 CaCl2, 10 Na2Phosphocreatine, 0.3 MgGTP, 4 Na2ATP (300 mOsm pH adjusted to 7.3 using CsOH). Extracellular synaptic stimulation was achieved by applying voltage pulses (20 µs, 5-50 V; Digitimer Ltd, UK) via a second patch pipette filled with ACSF and placed 20-40 µm from soma. For voltage and current clamp glutamate uncaging experiments patch pipettes were filled with the following intracellular solution (in mM): 135 K-gluconate, 5 KCl, 10 HEPES, 0.01 EGTA, 10 Na2phosphocreatine, 4 MgATP, 0.3 NaGTP (295 mOsm, pH adjusted to 7.3 using KOH). The membrane potential (Vm) was held at -60 mV, if necessary, using small current injection (typically in a range between -50 pA and 200 pA). Recordings were not corrected for liquid junction potential. Series resistance was compensated online by balancing the bridge and compensating pipette capacitance. For glutamate uncaging experiments Alexa 594 (20 µM) was added to the intracellular solution daily. In all experiments data were discarded if series resistance, measured with a -10 mV pulse in voltage clamp configuration, was >20 MΩ or changed by more than 20% across the course of an experiment. For current clamp experiment cells were excluded if input resistance varied by more than 25% of the initial value. AMPA-EPSCs were recorded at -70 mV in the presence of the GABAA blocker picrotoxin (100 µM, Abcam). To record NMDA-EPSCs, NBQX (10 µM, Tocris) was added to the ASCF and the resting membrane potential changed to +40 mV. All recordings were low-pass filtered at 10 kHz and digitized at 100 kHz using an analog-to-digital converter (model NI USB 6259, National Instruments, Austin, TX, USA) and acquired with NeuroMatic software⁶⁶ running in Igor PRO (Wavemetrics, Lake Oswego, OR, USA). For all the experiments L2/3 PV-INs and L2/3 SST-INs were identified using PV-Cre and SST-Cre mice crossed with the reporter mouse line (Ai9, (ROSA)26Sortm9 (CAG-tdTomato)Hze/J; JAX 007909). The intracellular
solution used for the experiments in which a presynaptic cell was depolarized by a train of action potentials to induce neurotransmitter release on a postsynaptic cell/element was (in mM): 130 K-MeSO3, 4 MgCl2,10 HEPES, 0.01 EGTA, 4 Na2ATP, 0.3 NaGTP (300 mOsm, pH 7.3 adjusted with NaOH). Paired recordings connections were probed using a train of 5/9 action potentials at frequency of 20 Hz. APs were initiated by brief current injection ranging from 1000–2000 pA and 1–5 ms duration. After a clear identification of synaptic connection (mean of 30 sweeps with clear AMPA current), post-synaptic cell membrane potential was brought from the initial -70 mV membrane potential to +40 mV to record the NMDAR-EPSCs in the presence of blockers as described before. To visualize single boutons in the experiments targeting SFiGluSnFR.A184V positive dendritic elements, we added 40 µM Alexa 594 in the intracellular solution.

## Transmitted light and fluorescence imaging

Neurons were visualized using infrared Dodt contrast (Luigs & Neumann, Ratingen, Germany) and a frame transfer CCD camera (Infinity-Lumenera). These components were mounted on an Ultima two-photon laser scanning head (Bruker, USA) based on an Olympus BX61W1 microscope, equipped with a water-immersion objective (60x, 1.1 numerical aperture, Olympus Optical, Japan). The somas of SST- and PV-INS were identified using a td-Tomato reporter mouse line (see animals) combined with fluorescence imaging. Two-photon excitation was performed with a pulsed Ti:Sapphire laser (DeepSee, Spectra-Physics, France) tuned to 810 or 840 nm for imaging neuronal morphology. Individual neurons were patch-loaded with Alexa 594 (20 µM). In some instances, we used a transmitted light PMT mounted after the Dodt tube to acquire a laser-illuminated contrast image simultaneously with the 2PLSM image. This dual imaging mode was used to position stimulation electrodes of sucrose puffing pipettes close to a spatially isolated dendrite, identified from maximal intensity projections of 2PLSM images. In addition to the light collected through the objective, the transmitted infrared light was collected through a 1.4 NA oil-immersion condenser (Olympus), and reflected on a set of substage photomultiplier tubes (PMTs). SFiGluSnFR.A184V fluorescence were filtered using hq525/70 nm bandpass filters (Chroma) and detected with gallium arsenide phosphate-based PMTs (H10770PA-40, Hamamatsu Photonics), and Alexa Fluor 594 fluorescence were filtered using hq607/45 bandpass filters (Chroma) and detected using gallium arsenide phosphate-based PMTs (H10770PA-40, Hamamatsu Photonics). 200 nm yellow-green fluorescent beads (Life Technologies) were used to estimate the point spread function (PSF) of the microscope system. The measured PSF at 810 nm had lateral dimensions of 368 ± 5.19 nm (full width at half maximum, n =20).

## Stereotaxic viral injections

Mice were initially anesthetized with Isoflurane. Induction of anaesthesia was performed at 4% isoflurane, Iso-Vet, and an air flow of 250ml/min. Mice were then placed in a stereotactic device (Kopf) kept at 37°C using a regulated heating blanket and a thermal probe and maintained under anaesthesia using 1-2% Isoflurane and an air flow of 250 ml/min until the end of the surgery. Adult mice were then bilaterally injected in the S1-BF by or unilaterally in V1 using a 10 µl Hamilton syringe (1701RN; Phymep, France) with a borosilicate glass capillary (O.D. 1.0mm; I.D.0.50mm; 10 cm length item #: BF100-50-10 WPI) pulled and beveled mounted on automatic injector used to infuse between 100 and 450 nl of virus at a rate of 60 nl/min using the following coordinates relative to Bregma: S1 anterior-posterior [AP], -0.5mm; medial lateral [ML], ± 3.2 mm and dorso ventral [DL] -0.2 mm relative to brain surface; V1(anterior-posterior [AP], -4.1mm; medial lateral [ML], ± 2.8 mm and the dorso ventral [DL], -0.2 mm relative to brain surface. Following the injection, the beveled glass capillary was left in place for 4 minutes to allow full diffusion of the viruses. Ex vivo electrophysiology experiments were performed at least 2/3 weeks after the surgery. For monitoring glutamate release at individual glutamatergic synapses, PV- or SST-cre mice were stereotaxically injected with AAV9.CAG-FLEX.SFiGluSnFR.A184V (Addgene plasmid #106205). For in vivo two photon calcium imaging mice were injected with AAV9 Syn-Flex-GCaMP6s-WPRE-SV40 (2.5x1013 AddGene-100845) or AAV9 pGP-AAV-syn-FLEX-jGCaMP8s-WPRE (2.5x1013 AddGene-1162377). To trace dendritic elements from SST or PV positive neurons in the STED experiment, we injected AAV1.Flex.tdTomato (Addgene-28360) in S1-BF.

## Estimation of quantal miniature EPSCs

The morphology of L2/3 SST- and PV-INS was visualized using fluorescence imaging of patch-loaded Alexa 594 (20 µM). The extracellular solution was modified to contain in mM: 0 CaCl2 and 3 MgCl2 in the presence of TTX 0.5 µM.⁶⁷ Neurons were patch loaded with Alexa 594 for at least 20 min to visualize cell morphology using two-photon microscopy with a laser tuned to 820 nm and modulated using a Pockels cell (Conoptics, Danbury, CT). This strategy allowed us to identify the proximal and distal dendrites of the patched neuron. A puff pipette was then placed at 20-30 µm from the selected dendrite where an extracellular hypertonic sucrose solution (350 mOsm) was puffed for 2 seconds at 0.40 bar positive pressure. Single evoked miniature events were then isolated from the 2 second sucrose puffing period recorded in 20 sweeps. On average 120 events were used for analysis. For single experiments rise time estimation was performed by fitting single events with a triexponential function. Fitted events have been subsequently aligned for their respective 10% rise time which finally resulted in the reported amplitude and kinetics values (Figure S3). To reduce possible contamination of distally recorded events by spontaneous proximal events in PV-INS due to their elevated basal rate of mEPSCs we used an exclusion criteria based on rise times. During estimation of sucrose evoked mEPSCs in distal dendritic regions in PV-INS we excluded events whose rise time was within mean+2SD the rise time of the sucrose mEPSCs obtained on the same cell
at proximal locations. These criteria allowed us to remove spontaneous proximal events that occurred during the sucrose puffing period. The distance used for proximal and distal evoked events was respectively 13.55 ± 3.46 and 113.6 ± 4.89 nm for PV-INs and 22.51 ± 2.60 and 124.2 ± 9.61 nm for SST-INs.

## Glutamate uncaging

L2/3 PN and L2/3 INs morphology was visualized using fluorescence imaging of patch-loaded Alexa 594 (20 µM). The output of two pulsed Ti:Sapphire (DeepSee, Spectra Physics) lasers were independently modulated to combine uncaging of MNI-glutamate and Alexa 594 imaging. The imaging laser beam was tuned to 820 nm and modulated using a Pockels cell (Conoptics, Danbury, CT). For uncaging, the intensity and duration (0.5ms or 1ms for single and double quanta experiment) of illumination of the second Ti:Sapphire laser tuned to 720 nm was modulated using an acousto-optic modulator (AA Opto-Electronic, France). MNI-caged-L-glutamate (10 mM) was dissolved in a solution containing (in mM): NaCl 125, glucose 25, KCl 2.5, HEPES 10, CaCl2 2 and MgCl2 1 (pH 7.3) and constantly puffed using a glass 1.5–2 MΩ resistance pipette placed in the proximity of a selected dendrite. Multiple uncaging locations (6–12) were placed adjacent to visually identified spines for PNs or in proximity to the shafts for INs (1 µm) and not closer to each other than 2 µm to reduce possible effect of glutamate spillover between locations. For the uncaging experiments in INs the uncaging spots were placed along the dendritic shaft at the level of synaptic “hot-spots” identified by single events rise time as described in.²²,⁶⁸ For experiments in the primary visual cortex, locations of glutamatergic synapses in interneuron dendrites were visualized using fibronectin antibodies against PSD-95.⁶⁹ To achieve this, PV-Cre and SST-Cre mice were injected with AAV-SyN-PSD95.FingR-eGFP-CCR5TC (Addgene #125693) in the visual cortex two weeks prior to glutamate uncaging experiments. Laser intensity was adjusted to obtain individual pEPSP of a variable amplitude. The arithmetic sum (always corrected for not perfect simultaneous activation) was used to compare the obtained values (expected) versus the recorded EPSP elicited by an increasing number of inputs recruited by glutamate uncaging. An input-output curve was obtained by plotting the amplitude of the expected EPSP versus the amplitude of recorded EPSP. Non-linearity was calculated as previously described.⁷⁰ Different inter event time intervals were tested during the quasi simultaneous activation of inputs: 0.12 and 1, 5 or 8 ms. In a subset of experiments laser power used to evoke glutamate uncaging was adjusted in order to obtain pESPCs with similar amplitudes than the mean amplitude of the quantal miniature EPSCs recorded during sucrose puff at proximal and distal locations. This initial calibration was performed in the voltage clamp configuration. Amplitude of quantal adjusted pEPSPs (qEPSPs) was also obtained in a separate group of experiments by shifting the recording conditions to the current clamp configuration while maintaining uncaging location and laser intensity. This allowed us to obtain the following values: qEPSCs PV-INs proximal= 32.90 ± 1.27 pA, qEPSPs PV-INs proximal 0.73 ± 0.06 mV; qEPSCs PV-INs distal= 16.40 ± 1.39 pA, qEPSPs PV-INs distal 0.47 ± 0.06 mV; qEPSCs SST-INs distal= 17.06 ± 0.17 pA, qEPSPs SST-INs distal 0.83 ± 0.17 mV. The drugs used for uncaging experiments were placed in the puff pipette and in the bath. In glutamate uncaging experiments involving specific receptor antagonists and/or channel blockers, the drugs were present in both the puff pipette solution and the bath solution. The concentration of NMDA blockers, D-AP5 and MK-801, used in the puff pipette solution was 500 µM and 50 µM respectively following the conditions described in.²¹ In the bath solution concentration of D-AP5 and MK-801 used was 50 µM and 20 µM respectively. In a subset of experiments, we also blocked voltage gated calcium and sodium channels in addition to NMDARs (described as “blockers cocktail”). For that TTX 1µM, NiCl 100µM, Nifedipine 30µM were added to the puff and bath solution.

## iGluSnFR imaging

Acute brain slices from animals previously injected with AAV9.CAG-FLEX.SFiGluSnFR.A184V were performed as described above. L2/3 PNs were subsequently patch loaded with Alexa 594 (40 µM) and the axon visualized using two-photon imaging. Axonal boutons were easily identified after 30-40 min of intracellular loading in whole cell patch-clamp configuration. Using simultaneous two-photon imaging of Alexa 594 and iGluSnFR fluorescence signals, putative points of contact were first identified at 820nm. The genetically encoded glutamate sensor, iGluSnFR-A184V was selectively expressed in SST- or PV-INs. Presence of positive synaptic connections was probed by placing a linescan (~7 µm at 0.76 ms per line) over the identified potential synaptic connection and variation of iGluSnFR fluorescence signals (imaged at 920 nm) monitored in response to evoked action potentials via current injection in the presynaptic L2/3 PN. Trains of 7 action potentials at 10 Hz repeated at a frequency of 0.33Hz were used to image glutamate release into PV- and SST-INs. Variations in iGluSnFR fluorescence were expressed as ΔF/F time series traces constructed from linescan images. The fluorescence as a function of time was averaged over visually identified pixels corresponding to width of the presynaptic bouton (identified using Alexa 594 fluorescence and overlapping with the iGluSnFR expressing dendrite) and then averaged over individual trials, resulting in a single fluorescence trace as a function of time $F_{dendrite}(t)$. The background fluorescence $F_{back}(t)$ was estimated similarly (identical spatial line length), but from a location not on a labeled structure. This $F_{back}(t)$ trace was then fitted with a single exponential function and then subtracted from $F_{dendrite}(t)$ in order to correct for bleaching. The background corrected traces $F(t)$ was then converted to the final ΔF/F(t) according to Equation 1:

$$ \frac{\Delta F}{F}(t) = \frac{F(t) - F_{rest}}{F_{rest}} $$

where $F_{rest}$ is the time averaged (100 ms window) fluorescence before stimulation and $F(t)$ is the time-dependent fluorescence transient.
## PSD95 labeling in cortical interneurons

We examined the distribution of excitatory synaptic inputs along the somatodendritic compartment in SST- and PV-INs using transgenic mouse lines that conditionally express Venus-tagged PSD95 under the control of the SST- or PV- promoter (PSD95-Enabled⁴³ × SST Cre or PV-Cre, respectively). Stereotaxic viral injections of AAV1.Flex.tdTomato was used to visualize IN morphology in such transgenic mouse lines. Two/three weeks after stereotaxic viral infections, SST-PSD-95-CreNABLED and PV-PSD-95-CreNABLED adult mice were deeply anesthetized with a mix of ketamine/xylazine (mix of i.p. ketamine 100 mg/kg and xylazine 13 mg/kg) and perfused transcardially with ice-cold PBS 1X (ET330-A) followed by ice-cold PFA 4% freshly prepared. At least 30 ml of PFA was used per animal. After extraction, brains were immersed in PFA 4% for an additional 2 hours, at 4°C, and sliced on the same day as the perfusion. Parasagittal slices (100 um) containing S1 were prepared at 4°C using a vibratome (Leica VT1200S). Slices were kept at 4°C in a PBS-Azide 0.4% solution. In order to amplify the endogenous PSD95-mVenus fluorescence signal brain sections were immunostained with an anti-GFP Nanobody coupled to ATTO 647N (GBA647N-100, ChromoTek). For that brain sections were washed for 10 minutes in Phosphate Buffer (PB) 0.1M, followed by three 10 min incubations in Tris Buffer Saline (TBS). Sections were subsequently incubated for 1 hour in a blocking solution composed of 10% Normal Goat Serum (NGS), 0.2% triton 100-X in TBS. Directly after the blocking solution, brain sections were incubated for 2 hours in a solution of 2% NGS, 0.2% triton 100-X, GFP-Booster ATTO647N (GBA647N-100, ChromoTek), 1:2000 in TBS. Sections were then washed (3 X 10 minutes) in TBS and rinsed in PB 0.1M and mounted on microscope slides using ProLongGlass Antifade Mountant (ProLong Glass, Invitrogen P36982). Fluorescence images were acquired at least 3 days after mounting to allow mounting medium to cure. Brain slices were imaged with a Stimulated Emission Depletion (STED) fluorescence microscope (expert line - Abberior Instruments) using an Olympus 100X/1.4 NA oil objective lens and 775 nm STED Laser line. Excitation laser lines were at 561nm and at 640nm respectively for TdTomato and Atto 647N. STED Images were analyzed using Fiji.⁵⁸

## Surgery for in vivo 2P imaging

Mice were initially anesthetized with Isoflurane. Induction of anaesthesia was performed at 4% isoflurane, Iso-Vet, and an air flow of 250ml/min. Mice were then placed in a stereotactic device (Kopf) kept at 37°C using a regulated heating blanket and a thermal probe and maintained under anaesthesia using 1-2% Isoflurane and an air flow of 250 ml/min until the end of the surgery. For calcium imaging, cranial window implantation and AAV viral stereotaxic injection was performed in the same surgical procedure. In order to prevent brain swelling and post-operative pain, anti-inflammatory (Dexamethasone, 2 µg/g Dexadreson, MSD) and analgesic drugs (Buprenorphine, 0.1 mg/kg Buprecare) were injected subcutaneously. After shaving the scalp, the skin was cleaned by wiping multiple times with an antiseptic solution and 70% alcohol. After injecting a local anaesthetic under the scalp (lidocaine, 10mg/kg - Xylovet or Laocaine) a skin incision was performed using surgical scissors. The periosteum was then carefully removed and the skull was scrapped using a dental drill, in order to remove all residues. The surface of the skull was subsequently thoroughly cleaned and dried using cotton swabs and a physiological saline solution. Using the stereotactic device, the center of the cranial window was marked and a circular piece of bone was removed using a 3 mm biopsy punch (LCH-PUK-30 Kai Medical). This step of the surgical procedure was considered critical since damage to the dura would result in rapidly opacifying cranial windows. Once the brain was exposed, the AAV viral vectors carrying the genetically encoded calcium indicators (GCaMP6s or GCaMP8s) were stereotactically injected (AAV9 Syn-Flex-GCaMP6s-WPRE (2.5x10¹³ AddGene-100845) or AAV9 Syn-Flex-GCaMP8s-WPRE (2.7x10¹³ AddGene-162377) respectively). Using a 10uL Gastight syringe 1701N (Hamilton), 200 nL of virus were injected in the visual cortex (from bregma: 3.0 RC; 2.4 ML) at a rate of 1 nL/s followed by a 5 minutes waiting period to prevent backflow. A round of 3mm glass coverslip (CS-3R Warner Instruments) was then placed over the craniotomy and glued in place using dental cement (Superbond). A stainless-steel head post (Luigs & Neumann) was then attached to the skull also using dental cement. For 3 days following the cranial windows surgery, mice were injected once a day with a mix of anti-inflammatory (Dexamethasone, 2 µg/g Dexadreson, MSD) and analgesic drugs (Buprenorphine, 0.1 mg/kg Buprecare). One week after the surgery, animals were transferred into an inverted light-dark cycle housing. Two weeks after surgery, mice were first habituated to the experimenter by handling and the following days, mice were head-fixed in the acquisition setup for increasing periods of time (5-45 minutes). The habituation of animals to the experimental setup lasted at least 5 days with a minimum of 5 sessions. At the end of the habituation period animals spontaneously transitioned between rest and running periods in the circular treadmill. Animals were imaged between Zeitgeber time 12 and 24. Imaging sessions lasted between 30 to 60 min and animals were imaged between 3-5 days. The location of the injection site in V1 was confirmed with intrinsic imaging experiments⁷¹ as performed in our previous work.⁷²

## In vivo 2P Ca2+ imaging

In vivo two-photon calcium imaging was performed with an Ultima IV two-photon laser-scanning microscope system (Bruker) as part of the Paris Brain Institute Quantitative Cellular and Molecular Imaging Core Facility (RRID:SCR_026393), using a 20X, 1.0 N.A. water immersion objective (Olympus) with the femtosecond laser (MaiTai DeepSee, Spectra Physics) tuned to 920 nm for imaging of cells expressing GCaMP6s or GCaMP8s. Fluorescence light was separated from the excitation path through a long pass dichroic (660dcxr; Chroma, USA), split into green and red channels with a second long pass dichroic (575dcxr; Chroma, USA), and cleaned up with band pass filters (hq525/70 and hq607/45; Chroma, USA). Fluorescence was detected using both proximal epifluorescence photomultiplier tubes (gallium arsenide phosphide, H7422PA-40 SEL, Hamamatsu). Time-series movies of neuronal populations
expressing GCaMP6s/GCaMP8s were acquired at the frame rate of 30Hz (512 × 512 pixels field of view; 1.13 µm/pixel). During the recording periods animals were free to run on a circular treadmill covered with a soft foam.

## Visual stimulation

Visual stimuli were presented at 60Hz on a Dell-2020 LED screen and synchronized to imaging and behavioral data via a photodiode (placed on the top right of the screen) that recorded the timing of each stimulus onset. Visual stimulation was controlled via the OpenCV library ( opencv-python, version 4.10.0). Full-field static gratings were presented for 2s (interleaved with 4s interstim intervals) with 2 contrast levels (half-contrast and full contrast), 8 different orientations evenly spaced from 0° to 157.5° and a spatial frequency of 0.04 cycle/degree. For two-photon experiments, the power source of the LED backlight of the monitor was synchronized to the resonant scanner turnaround points (when data were not acquired) to minimize light leak from the monitor<sup>73</sup>.

## Reduced model of dendritic integration

Adapting the work of W. Rall,<sup>74</sup> we studied dendritic integration by implementing cable theory in a simplified model of the dendritic arborization. The overall dendritic structure is schematized in Figure 1I, the morphology is made of 4 generations of branches with length 50µm. At the end of each generation b, each branch divides into two branches of a smaller diameter $D_{b+1}=T \cdot D_b$ where T is the tapering factor. The root diameter ($D_r$) was set to 1.0µm to match our proximal measurements (Figure S4) and the tapering factor was set to T=0.7 so that the diameter reached $D_3=0.5\mu m$ in the [100,150] µm of our distal measurements (Figure S4). An isopotential spherical compartment of radius 15µm was added to model the soma. The membrane leak conductance was adjusted to $g_L=2.5pS/\mu m^2$ to match the ~100MΩ input resistance for PV+ cells while the other cable properties were fixed to classical values with the membrane capacitance set to $c_m=1\mu F/cm^2$ and the intracellular resistivity to $R_i=150\Omega.cm$. Synaptic integration was tested by adding synaptic conductance events with an instantaneous rise of amplitude 1nS and an exponential decay of $\tau=5ms$. The reversal potential of the associated synaptic current was set to $E_{rev}=0mV$. This morphology and electrical properties were implemented in the brian2 simulator<sup>75</sup> and simulated with a time step dt=0.025ms and a spatial discretization of n=20 steps per branch.

## Stochastic release model of short-term plasticity

We derived a simplified model able to capture both the short-term dynamics and the stochastic nature of synaptic release at excitatory synapses in interneurons. This model was made of two-components: 1) a time-varying dynamics for the release probability and 2) a stochastic scheme allowing the release (or failure) of multiple vesicles.

The release probability p follows a first order dynamics given by:

$$ \frac{dp}{dt} = \frac{p_0 - p(t)}{\tau_p} - \sum_{spike} \delta p \cdot \left( \frac{p_{\infty} - p(t)}{|p_0 - p_{\infty}|} \right) \cdot \delta(t - t_{spike}) $$

where $p_0$ is the probability at zero frequency stimulation (infinitely spaced events), $p_{\infty}$ is the probability at infinite frequency stimulation (null spaced events), $\delta p$ is a strictly positive probability increment following every presynaptic event with constraint $\delta p \le |p_0 - p_{\infty}|$ and $\tau_p$ is the recovery time constant to go back to $p_0$ level. Synaptic depression corresponds to the setting: $p_0 \ge p_{\infty}$ and synaptic facilitation corresponds to the setting: $p_0 < p_{\infty}$.

We designed an event-based implementation by using, for a set of presynaptic event {$t_i$}, the iterative expression:

$$ p_i = p_0 + \left( p_{i-1} + \delta p \cdot \left( \frac{p_{\infty} - p_{i-1}}{|p_0 - p_{\infty}|} \right) - p_0 \right) \cdot e^{\frac{t_i - t_{i-1}}{\tau_p}} $$

Next, the stochastic release scheme is the following. For a presynaptic event at time $t_i$ and current probability $p_i$, we draw a random number $r_i$ from a uniform distribution between 0 and 1. We release n single-vesicles ($n \in [0,N]$), where N is the maximum number of vesicles, if:

$$ H(N-n) \cdot \binom{N}{n} \cdot p_i^n \cdot (1-p_i)^{N-n} < r_i \le \binom{N}{n-1} \cdot p_i^{n-1} \cdot (1-p_i)^{N-(n-1)} $$

where H is the right-continuous Heaviside function (i.e. $H(x \ge 0)=1$ and $H(x<0)=0$).

We show in Figure S9 that this simple model can cover a large spectrum of short-term dynamics behavior. For comparison with numerical simulations (Figure S9), we also used the analytic expression of the average release:

$$ R_{(i)} = \sum_{n \in [1,N]} n \cdot w \cdot \binom{N}{n} \cdot p_i^n \cdot (1 - p_i)^{N-n} $$

Following the results of our optical fluctuation analysis (Figures 4A–4C), we fixed the maximum number of vesicles to N=2 for both PV and SST INs. The recovery time constant $\tau_p$ was also fixed to 1s following previous estimates of STP dynamics<sup>76</sup> and we found that it captured well the dynamics in our recordings (Figure S9). The remaining parameters ($p_0, p_{\infty}, \delta p$) were constrained by our experimental recordings in PV and SST INs. The parameters were determined by minimizing the sum of the square residuals between paired recording data (9 APs at 20 Hz, to constraint the temporal dynamics of STP) and glutamate sniffer data (7 APs at 10 Hz, to
constrain the absolute probability) and average model release using the Nelder-Mead method of the `scipy.minimize` module (see Figure S9). The values were $p_0=0.65$, $p_\infty=0.28$, $\delta p=0.10$ for the PV model and $p_0=0.10$, $p_\infty=0.60$, $\delta p=0.05$ for the SST model. The contribution of a single vesicle was set by the unitary quantal weights of glutamatergic synapses (see Table S3).

## Detailed digital models of PV- and SST-INs

### Numerical simulations of morphologically-detailed PV- and SST-IN models

The morphologically-detailed models were implemented within the NEURON simulation environment,⁷⁷ version 8.2.3. From the Electron-Microscopy dataset of Schneider-Mizell et al.⁴⁶, we took the detailed morphological reconstructions of the Basket (cell-ID: 864691135396580129) and Martinotti (cell-ID: 864691135571546917) example cells shown in Figure 2G for the PV-IN and SST-IN models respectively. To focus on dendritic integration and for numerical simulation efficiency, axonal compartments were removed from the reconstructions and only the somatic and dendritic compartments were simulated. Numerical simulations were performed with the default first-order numerical scheme of NEURON and a time step of 0.025ms.

### Electrophysiological properties

The passive properties of the models were constrained from experimental measurements and literature estimates, see Table S1. Figures 3A–3D relies on passive properties only. To investigate the spiking output properties following dendritic integration, we next added a minimal set of active currents in Figure S 3E–3G and 5–7 for each model (Table S2). The action potential currents were made of a fast voltage- dependent sodium channel (“gnafin”) and a delayed rectifier potassium channel (“gkdrin”) with densities adjusted to match the rheobase of experimentally recorded cells (Table S2). For the PV-IN model, we also added A-type potassium channels (Table S2) as this was shown to strongly participate in dendritic integration in PV-INs.³³ For SST-INs, we also added M-type potassium channels in the soma (Table S2) as those shape the regular-spiking response characterizing SST-INs spiking profile. Action potentials were detected as a positive crossing of the 0mV threshold.

### Synaptic input distributions

For each morphologically-detailed model, we manually defined n=6 dendritic branches that corresponded to a unique straightforward path starting near the soma (<30µm) and ending in a distal branch termination (>200µm). Branches were ensured not to overlap with each other. Synapses were inserted on the morphology according to their locations on the dendritic tree on the Electron-Microscopy dataset. Per dendritic branch, a uniform-distribution surrogate was also created by randomly picking locations from a uniform distribution of distance to the soma along the branch (see insets of Figure 3A).

### Synaptic currents

Synaptic currents from AMPA, GABA and NMDA receptors were taken from refs.³³,⁷⁸ and inserted in the IN models (see properties in Table S3). For simplicity, NMDAR currents were only included in the SST-IN model and not in the PV-IN model (Table S3; see also Figure 1G). For the SST-IN model in absence of NMDAR (condition “no-NMDA, AMPA+”, Figures 3E–3G and 5–7), the AMPA weight was increased by 50% to match the peak amplitude of PSPs at -60mV.

### Synaptic activity: Stimulus on top of background activity

Background activity in Figures 3E–3G was achieved by stimulating all synapses of a branch with independent homogeneous Poisson point processes. Rates of Poisson processes were adjusted to bring the neurons in the -60mV range. For the PV-IN model, this was achieved with $F_{inh}=2.25Hz$ per synapses and $F_{exc}=3Hz$ per synapse. For the SST-IN model, this was achieved with $F_{inh}=8Hz$ per synapses and $F_{exc}=1Hz$ per synapse. The stimulation consisted in the synchronous activation of $n_{syn}$ synapses randomly picked from the synapses on the branch. In Figure 3F, spiking response curves were fitted to the function:

$$F(n_{syn}) = A \cdot \text{Erf} \left( \left( n_{syn} - n_{syn}^{1/2} \right) / \sigma \right)$$

Where Erf is the error function (fitting with the Nelder-Mead method from the `scipy'), minimize` function).

### Synaptic activity: Step-like time-varying inputs

In Figure 5, the synapses were driven by inhomogeneous Poisson processes controlled by a time-varying rate $R(t)$ built from a step-like waveform (Figure 5, filled grey curve). Independently for each synapse, a set of release events was generated according to a Poisson process probability (i.e. at time $t$ with rate $R(t)$, the event probability was $R(t) \cdot dt$). The step waveform was parametrized by a baseline rate level $R_b$ and a step factor increase $F_s$, i.e. the rate reached the level $R_b \cdot F_s$ during the step. We varied the magnitude of the step amplitude ($F_s$ from 2 to 4) as well as its duration (from 50ms to 1s) and we looked for the value of $R_b$ that would bring the model’s firing response in the [5,80]Hz range. This was achieved for $R_b=8.5Hz$ for the PV models (both with and without STP) and for $R_b=1.2Hz$ for the SST models (SST-full, SST-noSTP). Despite the AMPA boost (see above), a steady current of 40 pA was necessary to achieve the same range of firing in the SST model without NMDA (SST-noNMDA, SST-noNMDA-noSTP) for $R_b=1.2Hz$. Simulations were performed on a single branch basis, i.e. stimulating the synapses of a single branch (see Figure S5) where 80% of the synapses were set as excitatory and 20% as inhibitory. The output rate function was then obtained by binning spikes from n=160 trials (“psth: peri-stimulus time histogram”) and smoothing the resulting trace with a Gaussian filter of width 10ms. Simulations were repeated over the n=6 branches for the PV and SST models (Figure S10 and Figure 5D).

### Synaptic activity: Dynamics during visual processing of natural images

In Figure 6, we stimulate the IN models with an input rate following the spiking activity recorded by neuropixels probes during the presentation of natural images in the visual cortex (see below). The input rate waveform was computed as the average of all
phototagging-negative spiking rates across sessions and generated synaptic activity according to an inhomogeneous Poisson process (see above). To minimize effects related to input-output non-linearity in differently shaping the firing dynamics, we ensured that all considered models had similar spiking levels in those simulations. Because input rates were fixed by experimental data, we used two other parameters to control the output firing levels. We varied the fraction of inhibitory synapses $F_{inh}$ using the [5, 10, 15, 20] % values and the fraction of considered synapses $F_{syn}$ using the [8.3, 12.5, 25, 50] % values (i.e. for $F_{syn}$=25% we randomly pick 25% of the synapses per branch shown in Figure S5). For all models, we selected the ($F_{inh}$, $F_{syn}$) pair leading to an output firing of 5Hz as this output firing could be reached in all models and also fell in the approximate range of IN firing observed experimentally (Figure 6, 9 ±7Hz for SST INs and 13±8Hz for PV INs). We show in Figure S11 the result of this minimization procedure together with examples of single branch simulations for all models. The output rate function was obtained by binning spikes from n=40 trials and by smoothing the resulting trace with a Gaussian filter of width 10ms. The positive part of the cross-correlation functions between input and output rates were fitted to a Lorentzian function (constrained fitting with the L-BFGS-B method from the scipyImprove.minimize function) and the half-width parameter provides an estimate of the temporal extent of the correlations to the input signal (Figure 6G).

## Synaptic activity: Dynamics during visual processing of grating stimuli

In Figure 7, we stimulate the IN models with a rate input reproducing the activity evoked by a static grating presentation of 2s duration.⁷⁹ The rate input was thus designed to include both a fast ~400ms wide high-amplitude transient followed by a lower amplitude long-lasting (up to stimulus end) component. Such constraints were achieved with a waveform given by the equation (Figure 7C):

$$S(t) = R \cdot \left[ \text{Erf}\left(\frac{0.2 - t}{0.08}\right) \cdot \text{Erf}\left(\frac{0.45 - t}{0.35}\right) + 0.4 \cdot \text{Erf}\left(\frac{0.7 - t}{0.3}\right) \cdot \text{Erf}\left(\frac{2.1 - t}{0.2}\right) \right]$$

where R is a factor scaling the amplitude of the synaptic activity rates. For the SST models (SST-full and SST-noNMDA as in Figure 5), The factor R was set to 1.1 Hz for the SST models (the minimum to reach suprathreshold responses in absence of NMDAR, see SST-noNMDA in Figure 7C) and to 11.0 Hz in the PV-full model. Simulations were performed on a single branch basis, 80% of the synapses were set as excitatory and 20% as inhibitory. The output rate function was then obtained by binning spikes from n=100 trials and by smoothing the resulting trace with a Gaussian filter of width 10ms. Simulations were repeated over the n=6 branches for the PV and SST models (Figure S13 and Figure 7C).

## QUANTIFICATION AND STATISTICAL ANALYSIS

### Synapse distribution analysis

We analyzed synaptic distributions on IN dendrites in a publicly-available 1mm³ reconstruction of the mouse visual cortex from a serial section transmission Electron Microscopy volume,⁴⁵ i.e. a reconstruction with synaptic resolution. To specifically analyze INs, we also benefited from the manual proofread annotations of morphologically-identified INs found in Schneider-Mizell et al.⁴⁶ available at https://zenodo.org/record/7641781#collapseTwo. As a proxy for PV- and SST-INs, we considered the most numerous morphological type in each of those molecular classes, i.e. Basket and Martinotti cells respectively. From Schneider-Mizell et al.⁴⁶, n=59 Basket cells and n=41 Martinotti cells were available. For each cell, we benefited from a mesh reconstruction of its whole morphology as well as the set of synapses targeting this cell (“pre”) or targetted by this cell (“post”) with their localization in the volume.⁴⁶ In Figures 2G and 2H, we show such mesh reconstruction with the “pre” synapses (note the presence of both the axonal and dendritic trees). As a first step, we converted the mesh reconstructions of each cells into a “skeleton”, i.e. a set of segments with diameters, using the package MeshParty (https://meshparty.readthedocs.io/, version 1.16.4) as this enables to measure quantities such as “path length” along the dendritic tree.⁴⁵ Next, we splitted axonal and somato-dendritic compartments based on the density of “pre” and “post” synapses per compartment (“pre” is high in dendrites/soma, “post” is high in axons) using the function meshwork.algorithms.split_agon_by annotation from MeshParty. The few synapses (<1%) located on the axonal compartments were excluded from further analysis. We next focused only on the somato-dendritic compartments only. To analyze synapses along the dendritic path (Figures 2I and 2J), the somato-dendritic skeleton of each cell was divided into a set of “dendritic cover paths” covering the full dendritic tree (without any overlap). On all segments of this unique “dendritic cover path”, we could compute the “path distance to soma” and count the number of synapses in the segment to report either the linear density of synapses (Figure 2I) or the absolute count (Figure 2J) as a function of the distance to soma.

### Visually-evoked spiking dynamics of PV- and SST-INs during natural movies

To analyze the temporal dynamics of the spiking activity in PV- and SST-INs, we re-analyzed the publicly-available Visual Coding dataset from Siegle et al.⁵⁷ of Neuropixels recordings with visual stimulation and phototagging of INs. We considered the sessions in both the “brain_observatory1.1” and the “functional_connectivity” datasets performed on Pvalb-IRES-Cre;Ai32 (N=8 session) and Sst-IRES-Cre;Ai32 mice (N=12 sessions). We first restricted the analysis to spiking units in the visual cortex (i.e. annotated as belonging to one of the visual areas: “VISp”, “VISal”, “VISam”, “VISI”, “VISli”, “VISmma”, “VISmmp”, “VISp”, “VISpm”, “VISr”, see Siegle et al.⁵⁷). We then splitted single units into positive and negative units with respect to the molecular marker for INs. To this purpose, we analyzed the phototagging protocol (specifically the 10ms light pulse stimulation) and computed the firing in the pre-stimulus [-10,0] ms and post-stimulus [0,10]ms window. Units were defined as positive if their post-stimulus firing was above 20Hz and twice larger than the pre-stimulus firing (see “phototagging” insets in Figure 6B). Using this criterion, we found n=146 PV-positive units over N=6
sessions (n=24±14 units/session, two sessions in Pvalb-IRES-Cre;Ai32 mice were excluded from the analysis because they had less than 2 positive units) and n=97 SST-positive units over N=12 sessions (n=8±6 units/session). To estimate local cortical activity, we considered a random subset of n=100 negative units in each session (out of the n=259±41 negative units/session in Pvalb-IRES-Cre; Ai32 mice and the n=308±108 negative units/session in Sst-IRES-Cre;Ai32 mice). We next analyzed the spiking dynamics during the two natural movies that were presented in all sessions: “natural one” and “natural movie three”. For each movie, we concatenated the spike times of the different units and different movie presentations to build an average time-varying rate for a specific IN population (see Figure 6B). This time-varying rate resulted in a trace of ~5min duration (5 x 30s movie presentation + 2s interstimulus interval) and was smoothed by a Gaussian kernel of width 10ms. We pooled all units of all sessions for a single stimulus to show a high-sampling estimate (shown in Figure 6C) or we pooled units on a per-session basis (shown in Figure 6B) to be able to analyze properties across sessions (Figure 6D). Cross-correlation functions were computed from the 5min traces of negative and positive rates. As in the model (Figure 6G), the single-session cross-correlation functions were fitted to a Lorentzian curve to estimate the temporal extent of correlations (Figure 6C).

## Analysis of fluorescence signals

Two-photon imaging recordings of calcium activity were preprocessed with the suite2p software⁸⁰ to perform the registration and the extraction of calcium signals. Identification of SST+ cells were performed using the cellopose algorithm⁸¹ on the time-averaged image of the field of view. Raw fluorescence traces were corrected for neuropil contamination by subtracting Suite2p-neuropil traces using a fixed scaling coefficient of 0.7.⁸¹ To be able to compare activity across cells and mouse lines, fluorescence signals were normalized. To do this we used the ΔF/F0 method, calculated using the following formula: (F-F₀)/F₀, where F is the fluorescence and F0 is the time-varying baseline fluorescence evaluated as the lowest 5th percentile with a 2min sliding window. After neuropil subtraction, calcium signals were deconvolved using the deconvolution algorithm oasis from ref. ⁸² with kernel time constants of 1.5s and 0.8s for the GCaMP6s and GCaMP8s indicators respectively. Visually responsive cells were defined as cells displaying a significant increase (Anova test, p<0.05) over the n=10 stimulus repetitions between the intervals [-1,0]s and [1,2]s preceding and following stimulus presentation respectively.

## Optical fluctuation analysis

The estimation of number release sites ($N_{ves}^{max}$) and probability of release ($P_{ves}$) from single boutons using iGluSnFR fluorescence signals was performed using fluctuation analysis inspired in the method previously described for estimating number and open probability of voltage gated calcium channels (VGCCs; ⁵⁰,⁵¹). We considered simplistically that if neurotransmitter release at single point of contact is governed by binomial statistics, then the coefficient of variation of the dark/shot noise subtracted iGluSnFR fluorescence variance is given by:

$$CV_{F,\Delta iGluSnFR} = \frac{\sqrt{\sigma_F^2 - \sigma_d^2 - \sigma_{sn}^2}}{\langle \Delta F \rangle}$$

where $\sigma_F$ is the total signal variance, $\sigma_d$ is the dark noise and $\sigma_{sn}$ represents the shot noise contributions, where the shot noise variance was calculated by imaging a pipette filled with Alexa 488 with varying laser intensities. To ensure that variance was related to fluctuations in neurotransmitter release and to minimize other sources of variance, including optical drift we corrected the variance with a trial to trial correction for drift as reported in⁸³ by using the equation:

$$\sigma_F^2 = \frac{1}{2(n-1)} \sum_{i=1}^{n-1} (\Delta F_{i+1} - \Delta F_i)^2$$

where n represents the number of trials. This normalization minimizes the variance increase given by a run up or run down of fluorescence during the recording. Recordings in which the baseline variance (calculated from a 100 ms window before AP induction) was larger than the 99% confidence interval of the shot noise expected variance were not included in the analysis. Failure rate estimation was defined using a thresholding approach on the F(t) trace. We systematically tested multiple different thresholds. To this purpose, we compared the post-AP iGluSnFR fluorescence (i.e. averaged in a 10 ms window following the evoked APs) to the mean + 0.5, 1 or 2 times the SD of the baseline (i.e. preceding presynaptic APs). Release successes were defined if iGluSnFR fluorescence value after AP was larger than threshold. In order to optimally define the best threshold for each individual experiment we computed variance from the failure trials defined for the different thresholds and compared to predicted shot noise variance. The largest threshold value that resulted in a variance within the 99% confidence interval of the expected shot noise variance was used to define release successes. All successes were further analyzed as ΔF/F. To estimate the amplitude of release successes, we fit ΔF/F traces with the following equation,⁸⁴ using a least-square algorithm implemented in IgorPro (Wavemetrics):

$$\frac{\Delta F}{F}(t) = \left(1 - \exp\left(\frac{-(t - t_0)}{\tau_{rise}}\right)\right)^n \left(A_1 \exp\left(\frac{-(t - t_0)}{\tau_{decay1}}\right) + A_2 \exp\left(\frac{-(t - t_0)}{\tau_{decay1}}\right)\right)$$
Assuming that neurotransmitter release at single point of contact is governed by binomial statistics the probability that an action potential fails to release any synaptic vesicle is given by the equation:

$$P(0) = (1 - p)^N$$

where p is the release probability of individual vesicles and N is the number of release sites. Equation 5 together with $CV_{F,iGluSnFR}$ can be used to solve for N and p (solved numerically using Newton-Raphson method).

$$P(0) = \left( \frac{CV_{F,iGluSnFR}^2}{1 + CV_{F,iGluSnFR}^2} \right)^N \quad \text{and} \quad p = \frac{1}{1 + N \cdot CV_{F,iGluSnFR}^2}$$

## PSD-95 Venus puncta detection

PSD-95 puncta quantification was performed in dendrites simultaneously labeled with td-Tomato. Td-Tomato fluorescence allowed effective dendrite tracing in order to estimate PSD-95 puncta density relative to soma distance. For individual dendritic branches, image acquisitions were performed proximally (less than 40µm away from the soma) and distally (approximately 100µm away from the soma). To avoid errors while defining distal and proximal dendritic segments, we only imaged dendrites that did not cross other dendritic branches in the fields of view. In addition, PSD95 quantification was performed in single images and not in z-stacks. Image acquisition was performed for both td-tomato (excitation peak at 555nm) and ATTO647N for mVenus (excitation peak at 647nm). Images were subsequently analyzed using Fiji software using the Analyze Particles plugin. PSD-95 mVenus fluorescence images were first filtered using Fast Fourier transforms using the Fiji FFT BandPass Filter function. Large structures (low frequency) were filtered down to 60 pixels, small structures (high frequency) were filtered up to 2 pixels. The images were thresholded using a minimum intensity threshold of the mean plus three times the standard deviation of the background. Puncta detection was conducted using the Analyze Particles plugin in Fiji, considering puncta with areas larger than 0.01 square micron. No maximal size limit was defined. Puncta density was calculated by dividing the number of puncta by the length of the analyzed dendritic segment. The length of the dendritic segment was defined on the td-Tomato fluorescence channel.

## Statistics

Statistical tests were performed using a non-parametric Wilcoxon-Mann-Whitney two-sample rank test for unpaired, a Wilcoxon signed-rank test for paired comparisons, and a Kruskal-Wallis test followed by Dunn's test with Bonferroni correction for multiple comparisons. For data in Figure S12 involving multiple comparisons within multiple groups we used the Mann Whitney test and to correct for the false discovery rate in multiple comparisons we applied Benjamini-Krieger-Yekutieli correction. To compare numerical simulation data across the different initial settings illustrated in Figure 6, we used a parametric Student's t-test with Bonferroni correction to account for multiple comparisons. No statistical methods were used to pre-determine sample sizes, but our sample sizes were similar to those used in previous publications. Allocation into experimental groups was not randomized. Data collection and analysis were not performed blind to the experimental conditions. Data analysis was performed using IGOR Pro (Wave Metrics) or custom python code with numpy,⁸⁵ version 1.13.25, and scipy,⁸⁶ version 1.10.1. All the statistical analysis was performed and graphs were created using Prism 8 (GraphPad) or the scipy.stats and matplotlib modules. Most data are represented as mean ± SEM or using box and scatter plots depicting the median, the interquartile ranges as well as individual values. Significance was conventionally set as ****p<0.0001 **p < 0.001, **p < 0.01 and *p < 0.05.
Supplemental information

Distinct dendritic integration strategies control
$dynamics of inhibition in the neocortex$

Annunziato Morabito, Yann Zerlaut, Dhanasak Dhanasobhon, Emmanuelle Berthaux, Cibele Martins Pinho, Alexandra Tzilivaki, Gael Moneron, Laurence Cathala, Panayiota Poirazi, Alberto Bacci, David A. DiGregorio, Joana Lourenço, and Nelson Rebola
Supplemental Information

<figure><img src="image_40.png" /><figcaption>Figure S1</figcaption></figure>

Dependence of synaptic integration in PN, SST- and PV-INs on the time interval between uncaging events and differences in dendritic integration in PV- and SST-INs in the primary visual cortex. Related to Figure 1. A) Population average pEPSPs recorded at soma in response to 20 (PN) or 10 uncaging spots (PV and SST-INs) activated with 8 ms inter pulse interval. Recorded average is presented in color while the linear sum is depicted in grey. B) Summary plot of non-linearity obtained across the different population of cells using 8ms interpulse interval. Data are presented as average ± SEM with single experiment quantified as dotted color (PN: 96.36±57.88%, n=4; SST: +35.08±6.69%, n=5; PV:-2.32 ± 3.25, n=6; PN vs SST p>0.99; PN vs PV p=0.02; SST vs PV p=0.03; Kruskal Wallis test with Dunn's correction). C, D) Same as A and B, but for 5 ms interpulse interval (PN:89.66±34.39, n=4; SST: 42.36±4.45, n=6; PV:-14.64±4.68, n=6; PN vs SST p=0.83; PN vs PV p=0.003; SST vs PV p=0.046; Kruskal Wallis test with Dunn's correction). E, F) Same as A and B, but for 1 ms interpulse interval (PN:78.85±41.01, n=4; SST: 30.41±5.83, n=5; PV:-20.49±1.47, n=6; PN vs SST p>0.99; PN vs PV
p=0.01; SST vs PV p= 0.03; Kruskal Wallis test with Dunn's correction). G) (top left) Two-photon laser scanning microscopy (2PLSM) image (maximum-intensity projection, MIP) of a PV-IN dendrite in L2/3 of V1 loaded with Alexa-594 (10 µM). (bottom left) Fluorescence image from the dendrite shown on top but for PSD95-FingR-eGFP signal. The expression of fibronectin intrabodies against PSD95 allowed us to identify location of glutamatergic synapses in PV and SST-INs dendrites. The target cross dots indicate the used uncaging sites for 7 synapses. (Right) Example of photolysis-evoked EPSP in a PV dendrite with the quasi-simultaneous (0.12 ms intervals) activation of the 7 synapses illustrated on the left. The trace compares the calculated linear sum of individual responses to the recorded response from quasi-synchronous synapse activation. H) Same as G but for SST-INs. I) Summary plot of non-linearity obtained across PV- and SST-INs in the primary visual cortex using 0.12 ms interpulse interval. p<0.0001, Mann-Whitney test. Data are presented as average ± SEM with single experiment quantified as dotted color.
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B

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PN

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PN

PN

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SST

PN

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PV

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C

PV

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10 pA + DAP5

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SST

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+ DAP5

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20 pA

D

SST

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PV

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AMPA+NMDA

NMDA

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NMDAR

AMPAR

<caption>Figure S2</caption>

Different synaptic AMPA-to-NMDA EPSC ratio in SST- and PV-INs. Related to Figure 1.
A) (top) Schematic representation of the experimental approach used to monitor unitary EPSCs between individual L2/3 PNs and different postsynaptic partners. Unitary AMPA- and NMDA-EPSCs were separately recorded by varying the holding membrane potential of the postsynaptic potential from -70 mV (uAMPA-EPSCs) to + 40 mV (uNMDA-EPSCs). NBQX was added to the recording solution at positive potentials to block AMPA+Kainate receptors. Synaptic currents were recorded in response to a presynaptic train of action potential evoked at 20 Hz through current injection. (bottom) Representative AMPA- and NMDA-EPSCs (average of 30 sweeps) obtained for the different postsynaptic partners. B) Summary plots for the experiments illustrated in A reported as uNMDA to AMPA ratio (PN n=10; SST n=14; PV n=14). The data are reported as mean ± SEM (PN: 0.67 ± 0.13; SST: 0.44 ± 0.06; PV:0.23 ± 0.05; PN vs SST p=0.94; PN vs PV, p= 0.004; SST vs PV p= 0.04, Kruskal Wallis test with Dunn's correction C) Example traces for miniature EPSCs (mEPSCs) recorded at -30mV in a PV(red) or SST(orange) INs in control conditions and in the presence of NMDA blocker D-AP5. D) Average of aligned mEPSC events recorded in both SST and PV cells under control conditions (AMPAR+NMDAR), as well as after bath application of D-AP5 (AMPAR only). The subtraction between these two conditions allowed for isolating the slow component, representing the contribution of NMDAR alone (NMDA). Summary plot of the NMDAR- and AMPAR-mediated components of mEPSCs recorded in SST- and PV-INs determined using the subtraction described on the left (SST NMDA vs PV NMDA p<0.001; SST AMPA vs PV AMPA p>0.05, Mann-Whitney test). The data are presented as average ± SEM.
A

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B

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C

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D

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<figure><img src="image_66.png" /><figcaption>Figure S3</figcaption></figure>

Experimental estimation of single quanta EPSC (qEPSC) amplitude for proximal and distal dendritic locations in SST- and PV-INs. Related to Figure 1. A) Graphical representation of the experiment used to monitor qEPSC at different dendritic locations. Quantal responses were obtained by local perfusion of a hypertonic sucrose solution placed at proximal or distal dendritic locations using two-photon imaging (see Methods). B) Top: Example traces of recorded EPSCs during a 3 sec puff application of sucrose. Bottom: Magnification of recorded segment showing the sucrose evoked events in SST and PV cells. C) Example traces of detected and aligned sucrose-evoked EPSCs. Average mEPSC is shown in color. D) Quantification of the amplitude of average mEPSCs obtained for proximal (square) and distal (circle) dendritic locations in both SST (orange) and PV cells (red) plotted in function of the rise time. The values are reported as color-coded for single experiments with the average and SEM in black (SST proximal: 34.59±4.40 pA; SSTdistal: 20.15±2.18 pA; PVproximal: 31.66±1.74 pA; PVdistal: 17.21±0.83 pA).
<figure><img src="image_67.png" /><figcaption>Figure S4</figcaption></figure>

Dendritic diameters can not explain the qualitative difference in dendritic integration properties between PV- and SST-INs. Related to Figure 1. A) Example of a single 2P image capturing SST-INs distal dendritic branches. The orange square defined the dendritic location used to create the intensity profile shown and quantified below by using full width half maximum (FWHM) to define the relative diameter. B) Top: Distribution of dendrite diameters for proximal (<40µm) PV- (red) and SST-INs (orange) dendritic segments. Bottom: Summary plot of average proximal dendrite diameters obtained for PV and SST-INs. The data are presented as individual values and population median (black line). PV median:0.82 mm, n=35; SST median:0.87 mm, n=32; p=0.07 Mann Whitney test. C) Top: Same as in B but for distal (>100µm) dendritic locations. In gray the distribution for the detected diameter of 0.25 µm beads, used to inform about lateral resolution of the 2P system. Bottom: Same than in B but for distal dendritic locations. The data are presented as single values and the median (black line). PV median: 0.59 mm, n=58; SST median: 0.66 mm, n=59; p<1e-4 Mann Whitney test. D) Variations of dendritic diameters in the range of the experimentally-measured differences of C predicts minor impact on the dendritic integration mode in the simplified morphological model (see Methods). The root diameter of the morphological model is kept identical between the PV and SST model following the data of B. The tapering factor (the factor between the diameter of the children branches and the parent branch) was increased by 12% following the data of C. The average response over the 4 locations shown in Fig. 1I is shown. The change in non-linearity between the PV and the SST morphologies is 2.3%.
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<figure><img src="image_70.png" /><figcaption>Figure S5</figcaption></figure>

Dendritic branches used for numerical simulations in the PV-IN and SST-IN models. Related to Figure 2. A) Morphology of a V1 basket cell reconstructed from serial electron microscopy imaging highlighting the six distinct dendritic branches used for numerical simulations of the PV-IN model.
Histogram (top inset) of the real synapse distribution (colored) and its uniform-distribution surrogate (gray, see Methods) for the different individual dendritic branches. **B)** Same as **A** but for the Martinotti cell used in the SST-IN model. **C)** Distributions slopes (of the synaptic count vs distance to soma) in the real synaptic distributions and uniform surrogates. Basket cell, real: -21.1±3.7 syn./100µm, uniform: 0.8±0.6 syn./100µm, n=6 branches, p=3e-2, Wilcoxon test. Martinotti cell, real: -3.6±0.7 syn./100µm, uniform: -0.5±0.5 syn./100µm, n=6 branches, p=6e-2, Wilcoxon test.
<figure><img src="image_71.png" /><figcaption>Figure S6</figcaption></figure>

Distal and proximal integration upon increasing number of co-active inputs in dendritic segments of the morphologically-detailed interneuron models. Related to Figure 3.
We vary the sparsening variable that sets synaptic recruitment from 2% (left) to 8% (right) in the PV-model (A) and SST-model (B) with their respective control (see main text, "uniform" distribution for the PV-model and "no-NMDA" setting for the SST-model. Note the very high level of suppression (>50%) for sparsening above 4% in the PV-model. Note also the appearance of supra-linear integration (suppression <0%) in the distal segment of the SST-model in presence of NMDAR at a sparsening of 8%. C) Example V<sub>m</sub> response in a branch in the SST-model at a sparsening of 8%. Integration from the distal segment stimulation exhibits supra-linear integration (suppression <0%).
<figure><img src="image_72.png" /><figcaption>Figure S7</figcaption></figure>

Quantification and analysis of iGluSnFR fluorescence events. Related to Figure 4.

A) Upper left: MIP of a L2/3 PN axon patch loaded with Alexa 594. Upper middle: Positive iGluSnFR dendrites present in the same field of view as the image on the left. iGluSnFR was selectively expressed in PV-INs using PV-Cre transgenic mice. Bottom left: Point of contact between the Alexa 594 fluorescence (axon) and iGluSnFR signal (putative PV-dendrite) where release of glutamate was monitored using 2P linescan. Bottom middle: Average 2P linescan (10 sweeps) obtained from point of contact illustrated in merged image. The increase in iGluSnFR fluorescence observed upon presynaptic firing of the individual L2/3 PNs is restricted to a narrow (~ 1 µm) dendritic space. Right: Time series traces are mean fluorescence of individual images over 1 µm (red and blue line), and the trace is the average of all 10 traces. B) Single trial iGluSnFR fluorescence signal after conversion to ΔF/F in a PV(red) and a SST(orange) postsynaptic dendrite in the presence of 1.2 mM extracellular Ca2+. In black the average of 10 sweeps C) Histogram of ΔF/F amplitude distributions for PV (red) and SST-INs (orange) iGluSnFR events in 2mM extracellular [Ca2+]. D) Same as C but for 1.2 mM extracellular calcium. E) Summary of failure rates and coefficient of variation for L2/3 PN synaptic contacts in SST-(n=8) and PV-INs (n=9) for experiments performed in 1.2 mM external calcium. Data include release probability (Pves) and maximum vesicles released per AP (N max Ves). The data are presented as mean±SEM, (*p<0.05, Mann-Whitney test). F) Left: Mean ± SEM of the ΔF/F values obtained per AP. Right: normalized ΔF/F values from the experiments on the right. Recordings were performed at 2 mM extracellular [Ca2+]. G) Example of iGluSnFR fluorescence recorded for 70 APs (grey). Average trace is shown in black. The dotted line represents the time interval (5ms) and the location in the events used
for measuring baseline and peak fluorescence values. On the right the graphical representation of the mean-variance plot for the baseline (black circle) and the peak fluorescence values (black). The magenta circle represents the mean-variance plot obtained by imaging the patch pipette at different laser powers to estimate variance expected from shot noise. In dotted black the 99% confidence interval for the measurement (see methods). H) Left: Example of iGluSnFR fluorescence signals recorded for 70 APs (grey) evoked in a single presynaptic L2/3 PNs. Average response is shown in black. The two colored 5 ms windows represent the location for the baseline and peak fluorescence measurements. Center: Example of failure rate detection obtained using two different amplitude thresholds. The success detection was performed using a thresholding method comparing amplitude in peak window + SD of baseline (baseline average±0.5 or 1 SD of the baseline; see methods). Different multiple factors of SD were used and best value was chosen using mean-variance plots like illustrated in right. Right: Mean-variance plot for baseline and peak windows on the traces illustrated in the left using baseline± 0.5 or 1 SD. The empty circles represent the peak values and the full circle the baseline. Based on the peak variance detection the value to be used for the failure detection is baseline ± 0.5 SD. In this case the experiment presents a failure rate of 32.8%.

A

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B

<figure><img src="image_75.png" /><figcaption>Figure S8</figcaption></figure>

Integration of single and double quanta in SST+ dendrites in the current-clamp configuration.

Related to Figure 4. A) Example pEPSP traces of single and double quanta integration, separated by 50 ms (in gray), along an SST+ IN dendrite. In black the isolated second pEPSPs after subtraction of the first evoked response. B) Quantification of double quanta integration at different dendritic locations (n=16) expressed as paired-pulse ratio. In black the linear fit.
<figure><img src="image_76.png" /><figcaption>Figure S9</figcaption></figure>

**Stochastic release model of Short-Term Plasticity (STP) and calibration on experimental data for PV- and SST-INs. Related to Figure 5.**

A) Release probability following presynaptic events (shown as black dots) in 4 examples settings of the short-term dynamics model: faithful transmission (i.e. no stochasticity and no dynamics), stochastic transmission (i.e. with stochasticity but with stationary release probability), synaptic depression (stochasticity release and release probability decrease with activity) and synaptic facilitation (stochasticity release and release probability increase with activity).

B) Illustration of the stochastic STP model for a few example model settings. From left to right we show: the parameters of the model setting, the presynaptic events over time (x-axis) across trials (y-axis), the release events (dots, the number of released vesicles in color coded, see annotations), the release dynamics (i.e. the released events convolved with a 5ms exponential kernel) and the average of the release dynamics over n=100 trials together with the analytical predictions at release time (see Methods).

C) Experimental data used for the calibration of model parameters in SST (top) and PV (bottom) INs. We used the paired recording data (left, 9 APs at 20 Hz) to constraint the temporal
dynamics of STP and the sniffer data (right, 7 APs at 10 Hz) to constrain the absolute probability levels. We show the model predictions after parameter fitting (see Methods) in the PV and SST models in pink. D) Same as B for the parameters of the SST (top) and PV (bottom) models.

<figure><img src="image_77.png" /><figcaption>Figure S10</figcaption></figure>

Firing rate responses to steps of synaptic activity with various durations (from 50ms to 1s) and various step amplitudes (increasing the step-to-baseline factor from 2 to 4). Related to Figure 5.

A) Responses of the PV IN models, with STP (red, PV-full) and without STP (pink, PV-noSTP). B) Responses of the SST IN models, with STP and NMDAR (orange, SST-full), without STP and with NMDAR (SST-noSTP, brown), without STP and with NMDAR (SST-noSTP, brown), without STP and without NMDAR (SST-noSTP-noNMDA, green). Data shown as mean +/- SEM over n=6 branches for each model.
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<figure><img src="image_84.png" /><figcaption>Figure S11</figcaption></figure>

Simulations of detailed digital models of interneurons in response to spiking activity extracted from recordings during visual processing of natural movies. Related to Figure 6. A) Parameter scan to bring output spiking activity in a similar range (see Methods). We varied the fraction of inhibitory
synapses $F_{inh}$ using the [5, 10, 15, 20] % values and the fraction of considered synapses $F_{syn}$ using the [8.3, 12.5, 25, 50] % values and computed the output rate (color-coded). Note that the 5Hz value can be reached for all models and was therefore used as a target output rate. We highlight the selected ($F_{inh}$, $F_{syn}$) pair in each model as a red square. **B)** Example simulations in all models: PV IN models, with STP (red, PV-full) and without STP (pink, PV-noSTP), SST IN models, with STP and NMDAR (orange, SST-full), without STP and with NMDAR (SST-noSTP, brown), without STP and with NMDAR (SST-noSTP, brown), without STP and without NMDAR (SST-noSTP-noNMDA, green). **C)** Comparison of cross-correlation functions between input and output rates in the models shown in **B**.

<figure><img src="image_85.png" /><figcaption>Figure S12</figcaption></figure>

**Absence of synaptic NMDARs but intact short-term plasticity at glutamatergic inputs onto SST-INs in SST-Cre::GluN1flox transgenic mice. Related to Figure 7.**

**A)** (Top) Illustration of the genetic mouse model approach to selectively remove NMDARs from SST-INs (see also Methods). (Bottom) Representative traces of EPSCs indicating the selective absence of NMDAR-EPSCs in SST-INs in SST-Cre::GluN1flox mice as reported before [51]. NMDAR-EPSCs were recorded by holding the cell at +40mV and blocking AMPA/Kainate receptors with NBQX (10 uM) **B)** Quantification of the NMDA/AMPAR ratio recorded in SST-INs in WT and in SST-Cre::GluN1 flox mice. Note the selective removal of NMDAR-mediated EPSCs in SST-INs from SST-Cre::GluN1 flox mice. NMDA/AMPAR ratio, SST:cre: 0.68 ± 0.17; n=9 vs and SST-Cre::GluN1 KO: 0.05 ± 0.03, n=6, p<0.001, Mann-Whitney. **C)** Representative traces of uEPSCs recorded in a postsynaptic L2/3 SST-IN held at -70 mV in WT (left) and in SST-Cre::GluN1flox mice after a train of action potentials (9 at 40 Hz) induction in a presynaptic L2/3 pyramidal neuron (PN). **D)** Summary plot of short-term plasticity, uEPSCs amplitude and failures rate (first EPSC of the train of stimulation) for the unitary connection between L2/3 PN and L2/3 SST-INs in WT (n = 14) and in SST-Cre::GluN1flox mice (n = 9). Data are presented as mean (circles) ± SEM (bars). Single data points from all three datasets (STP, EPSC amplitude, and failure rate) were analyzed using a Mann-Whitney test with multiple comparisons, adjusted for false discovery rate using the Benjamini-Krieger-Yekutieli method (Q = 5%). No significant differences were found (p > 0.05).
<figure><img src="image_86.png" /><figcaption>Figure S13</figcaption></figure>

Example simulations of detailed digital IN models in response to inputs reproducing the activity evoked by a 2s-long grating presentation. Related to Figure 7. From top to bottom, we show the rate input, the excitatory/inhibitory synaptic events and the $V_m$ dynamics associated to a single trial, the output rate computed from trial-averaged spiking data. From left to right we show the SST-full model (i), the SST-noNMDA model (ii, same as in Fig. 5, with AMPA-boosted synaptic weight, but without additional current injection) and the PV-full model (iii).
<table><caption>**Table S1:** Passive properties of interneuron models. Related to Figure 3.</caption><thead><tr><th>Property</th><th>Soma</th><th>Proximal dendrite</th><th>Distal dendrite</th><th>Constraint/Reference</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-weight: bold;">PV model</td></tr><tr><td>Leak conductance (g<sub>pas</sub>)</td><td>4.37 10<sup>-4</sup> S.cm<sup>-2</sup></td><td>4.37 10<sup>-4</sup> S.cm<sup>-2</sup></td><td>4.46e-5 S.cm<sup>-2</sup></td><td>Adjusted to get a somatic input resistance of 100MΩ while keeping the prox./dist ratio of [S2]</td></tr><tr><td>Resting Membrane Potential (e<sub>pas</sub>)</td><td>-70 mV</td><td>-70 mV</td><td>-70 mV</td><td>[S1], [S3]</td></tr><tr><td>Membrane capacitance (c<sub>m</sub>)</td><td>1.2 μF.cm<sup>-2</sup></td><td>1.2 μF.cm<sup>-2</sup></td><td>1.2 μF.cm<sup>-2</sup></td><td>[S4]</td></tr><tr><td>Axial Resistance (R<sub>a</sub>)</td><td>172 Ω.cm</td><td>142 Ω.cm</td><td>142 Ω.cm</td><td>[S4]</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">SST model</td></tr><tr><td>Leak conductance (g<sub>pas</sub>)</td><td>3.5e-5 S.cm<sup>-2</sup></td><td>3.5e-5 S.cm<sup>-2</sup></td><td>3.5e-5 S.cm<sup>-2</sup></td><td>Adjusted to get a somatic input resistance in 300 +/- 40 MΩ [S1], here 285MΩ</td></tr><tr><td>Resting Membrane Potential (e<sub>pas</sub>)</td><td>-60 mV</td><td>-60 mV</td><td>-60 mV</td><td>[S1], [S3]</td></tr><tr><td>Membrane capacitance (c<sub>m</sub>)</td><td>1.2 μF.cm<sup>-2</sup></td><td>1.2 μF.cm<sup>-2</sup></td><td>1.2 μF.cm<sup>-2</sup></td><td>[S4]</td></tr><tr><td>Axial Resistance (R<sub>a</sub>)</td><td>172 Ω.cm</td><td>142 Ω.cm</td><td>142 Ω.cm</td><td>[S4]</td></tr></tbody></table>
<table><caption>**Table S2:** Active current densities in interneuron models. Related to Figure 3.</caption><thead><tr><th>Current</th><th>Soma</th><th>Proximal dendrite</th><th>Distal dendrite</th><th>Constraint/Reference</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-weight: bold;">PV model</td></tr><tr><td>Fast Sodium current</td><td>3.4 10<sup>-1</sup><br>S.cm<sup>-2</sup></td><td>0 S.cm<sup>-2</sup></td><td>0 S.cm<sup>-2</sup></td><td>Adjusted to match rheobase in 216 +/- 40 pA <sup>[S5]</sup>,<br>here 229.3 pA</td></tr><tr><td>Delayed rectifier<br>Potassium current</td><td>9.60 10<sup>-2</sup><br>S.cm<sup>-2</sup></td><td>0 S./cm<sup>-2</sup></td><td>0 S.cm<sup>-2</sup></td><td>Keeping ratio with sodium current of <sup>[S2]</sup></td></tr><tr><td>A-type Potassium<br>current (proximal)</td><td>0 S.cm<sup>-2</sup></td><td>1.0 10<sup>-3</sup><br>S.cm<sup>-2</sup></td><td>0 S.cm<sup>-2</sup></td><td><sup>[S2]</sup></td></tr><tr><td>A-type Potassium<br>current (distal)</td><td>0 S.cm<sup>-2</sup></td><td>9.0 10<sup>-4</sup><br>S.cm<sup>-2</sup></td><td>2.2 10<sup>-3</sup><br>S.cm<sup>-2</sup></td><td><sup>[S2]</sup></td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">SST model</td></tr><tr><td>Fast Sodium current</td><td>7.0 10<sup>-1</sup><br>S.cm<sup>-2</sup></td><td>0 S/cm2</td><td>0 S/cm2</td><td>Adjusted to match rheobase 76.9 +/- 35 pA <sup>[S6]</sup>,<br>here 93.1pA</td></tr><tr><td>Delayed rectifier<br>Potassium current</td><td>4.0 10<sup>-1</sup><br>S.cm<sup>-2</sup></td><td>0 S/cm2</td><td>0 S/cm2</td><td>Keeping ratio with sodium current of <sup>[S2]</sup></td></tr><tr><td>M-type Potassium<br>current</td><td>2.0 10<sup>-3</sup><br>S.cm<sup>-2</sup></td><td>0 S/cm2</td><td>0 S/cm2</td><td></td></tr></tbody></table>
<table><caption>**Table S3:** Synaptic properties of the interneuron models. Related to Figure 3.</caption><thead><tr><th>Receptor</th><th>Quantal</th><th>Decay</th><th>Constraint/Reference</th></tr></thead><tbody><tr><td colspan="4" style="text-align: center; font-weight: bold;">PV model</td></tr><tr><td>AMPA</td><td>0.8 nS</td><td>2 ms</td><td>[S7]</td></tr><tr><td>GABA</td><td>2 nS</td><td>5.5 ms</td><td>[S7]</td></tr><tr><td colspan="4" style="text-align: center; font-weight: bold;">SST model</td></tr><tr><td>AMPA</td><td>0.8 nS</td><td>2 ms</td><td>[S7]</td></tr><tr><td>NMDA</td><td>1.2 nS</td><td>80 ms</td><td>Constrained from NMDA/AMPA ratio=1.5</td></tr><tr><td>GABA</td><td>2 nS</td><td>5.5 ms</td><td>[S7]</td></tr></tbody></table>

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