The relationship between synaptic excitation and inhibition (E/I ratio), two opposing forces in the mammalian cerebral cortex, affects many cortical functions such as feature selectivity and gain1,2. Individual pyramidal cells show stable E/I ratios in time despite fluctuating cortical activity levels. This is because when excitation increases, inhibition increases proportionally through the increased recruitment of inhibitory neurons, a phenomenon referred to as excitation–inhibition balance3,4,5,6,7,8,9. However, little is known about the distribution of E/I ratios across pyramidal cells. Through their highly divergent axons, inhibitory neurons indiscriminately contact most neighbouring pyramidal cells10,11. Is inhibition homogeneously distributed12 or is it individually matched to the different amounts of excitation received by distinct pyramidal cells? Here we discover that pyramidal cells in layer 2/3 of mouse primary visual cortex each receive inhibition in a similar proportion to their excitation. As a consequence, E/I ratios are equalized across pyramidal cells. This matched inhibition is mediated by parvalbumin-expressing but not somatostatin-expressing inhibitory cells and results from the independent adjustment of synapses originating from individual parvalbumin-expressing cells targeting different pyramidal cells. Furthermore, this match is activity-dependent as it is disrupted by perturbing pyramidal cell activity. Thus, the equalization of E/I ratios across pyramidal cells reveals an unexpected degree of order in the spatial distribution of synaptic strengths and indicates that the relationship between the cortex’s two opposing forces is stabilized not only in time but also in space.
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We thank M. Chan, J. Evora, A. Linder and P. Abelkop for technical assistance; M. S. Caudill and S. R. Olsen for help with the in vivo physiology recording programme; E. Kim and A. Ghosh for pCAG-Kir2.1-T2A-tdTomato plasmid; J. Isaacson and H. Y. Zoghbi for comments on earlier versions of the manuscript; D. N. Hill, G. I. Allen, E. Arias-Castro and M. Wang for advice on statistical analysis; the members of the Scanziani and Isaacson laboratories for suggestions; and the University of California, San Diego Neuroscience Microscopy Facility (P30 NS047101) for imaging equipment. M.X. was supported by a fellowship from Jane Coffin Childs Memorial Fund for Medical Research. M.S. is an investigator of the Howard Hughes Medical Institute. This work was also supported by the Gatsby Charitable Foundation.
The authors declare no competing financial interests.
Extended data figures and tables
Extended Data Figure 1 Cre recombinase-expressing cells in the cortex of Scnn1a-Cre-Tg3 mice are layer 4 excitatory neurons.
AAV-CAGGS-Flex-ChR2-tdTomato, expressing ChR2-tdTomato fusion protein in a Cre-dependent manner, was injected into Scnn1a-Cre-Tg3 mice. a, Representative fluorescent images of a coronal section of V1 showing that the ChR2-tdTomato-expressing cells located primarily in layer 4 (n = 11 mice). Cortical layers are indicated on the right based on the DAPI staining pattern. L, layer; WM, white matter. b, Left, schematic of experiments. Right, a layer 2/3 pyramidal cell was voltage clamped at the reversal potential for excitation (+10 mV). Photoactivation of ChR2-expressing neurons in layer 4 elicited an IPSC (black trace), which was abolished by the glutamatergic receptor antagonists NBQX and CPP (red trace), indicating its disynaptic nature. c, Summary data: NBQX and CPP reduced IPSC amplitudes by 98.0 ± 0.6% (mean ± s.e.m., n = 8, P = 0.008) indicating that ChR2 was exclusively expressed in excitatory neurons.
Extended Data Figure 2 Characterization of the inter-cell variability of EPSCs, IPSCs and E/I ratios.
a, b, The inter-cell variability of EPSCs, IPSCs and E/I ratios among neighbouring pyramidal cells does not correlate with their inter-soma distances. a, The average relative deviations of EPSCs, IPSCs and E/I ratios from each experiment in Fig. 1f are plotted against the average inter-soma distance from the same experiment. The average inter-soma distance is the mean of the distances between each pair of pyramidal cells. For the experiments in which only two pyramidal cells were recorded, the inter-soma distance between the two pyramidal cells was used. Lines, linear regression fits. b, The absolute value of the logarithm of the ratio of EPSCs (or IPSCs or E/I ratios) simultaneously recorded in two pyramidal cells was plotted against the inter-somatic distance between the two cells. c, The distribution of E/I ratios across pyramidal cells varies less than if EPSCs and IPSCs were randomly paired between cells and less than the distributions of EPSC and IPSC amplitudes. To determine whether the precise E/I ratio recorded within each pyramidal cell minimizes the average relative deviation, we computed the E/I ratios from randomly but uniquely paired EPSCs and IPSCs within each of the 20 experiments from Fig. 1f. By randomizing within each experiment, we ensured that the average relative deviation was only modified owing to the pairing of EPSCs to IPSCs. Note that, for an experiment with N pyramidal cells, there were N! possible randomized pairings of EPSCs and IPSCs, and hence N! possible E/I ratio average relative deviations (referred to as random-E/I ratio average relative deviations). The distribution of the means of the random-E/I ratio average relative deviations (grey histogram) was constructed from the means of 10,000 samples. Each sample consisted of 20 random-E/I ratio average relative deviations, each of which was randomly chosen from the N! possible random-E/I ratio average relative deviations of each experiment. The grey vertical line represents the mean of the distribution. The distribution of the means of the E/I ratio average relative deviations (black histogram) was generated by bootstrapping (that is, resampling 10,000 times with replacement). Each resample consisted of 20 randomly chosen E/I ratio average relative deviations from the 20 experiments in Fig. 1f, and an E/I ratio average relative deviation was allowed to be repeated within one resample (that is, sampling with replacement). The black vertical line represents the mean of the experimentally obtained E/I ratio average relative deviations. The E/I ratio average relative deviations are smaller than the random-E/I ratio average relative deviations (P < 0.0001). The distributions of the means of the EPSC average relative deviations (red histogram) and the means of the IPSC average relative deviations (blue histogram) were generated by similar bootstrapping to the E/I ratio average relative deviations. The red and blue vertical lines represent the means of the experimentally obtained EPSC average relative deviations and IPSC average relative deviations, respectively. The E/I ratio average relative deviations are smaller than the EPSC average relative deviations (P < 0.0001) and the IPSC average relative deviations (P < 0.0001).
Fos–EGFP mice were crossed with Gad2-ires-Cre and Rosa-CAG-LSL-tdTomato−WPRE mice to generate Fos–EGFP, Gad2-ires-Cre, Rosa-CAG-LSL-tdTomato−WPRE mice. a, Representative fluorescent images showed a coronal section of V1. All neurons were visualized by NeuroTrace 435/455 blue fluorescent Nissl stain and GABAergic interneurons were labelled by tdTomato. EGFP was stained with an antibody against GFP and visualized with a secondary antibody conjugated with Alexa Fluor 647. Cortical layers are indicated on the left based on the Nissl staining pattern. b, Enlarged view of the boxed region in a. In layer 2/3 of V1, only 5.3 ± 0.9% (mean ± s.e.m., n = 10 sections from two mice) of EGFP+ neurons were GABAergic interneurons (two examples are indicated by arrowheads). GABAergic interneurons constitute 13.2 ± 0.6% (mean ± s.e.m., n = 14 sections from three mice including one Gad2-ires-Cre, Rosa-CAG-LSL-tdTomato−WPRE mouse) of all layer 2/3 neurons.
Extended Data Figure 4 Overexpression of Kir2.1 increases a Ba2+-sensitive K+ current and decreases neuronal excitability.
a, Schematics of experiments. Kir2.1 or a non-conducting mutant Kir2.1 (Kir2.1Mut) was overexpressed in a subset of layer 2/3 pyramidal cells by in utero electroporation. b, Membrane currents in response to a 5 s membrane potential ramp from −25 to −125 mV from an untransfected control pyramidal cell, a pyramidal cell overexpressing Kir2.1 and a pyramidal cell overexpressing Kir2.1Mut. The purple traces were recorded in control condition and the grey traces were recorded in the presence of 50 μM BaCl2, a concentration that primarily blocks the K+ channels of the Kir2 subfamily50. The blue traces were obtained by subtracting the grey traces from the purple traces, representing the Ba2+-blocked K+ currents. c, The exogenously overexpressed Kir2.1 increased not only the Ba2+-blocked inward current density at −125 mV (P = 0.01), but also the outward current density at −45 mV (P = 0.001) owing to its reduced inward rectification (see Methods). d, Kir2.1Mut can bind to the endogenous Kir2.1 to form non-conducting channels50, acting as a dominant negative to decrease the inward current density at −125 mV (P = 0.004) but without affecting the outward current density at −45 mV (P = 0.2). e, Membrane potentials (upper panels) in response to current injections (lower panels) from an untransfected control pyramidal cell, a pyramidal cell overexpressing Kir2.1 and a pyramidal cell overexpressing Kir2.1Mut. f–h, Overexpression of Kir2.1 hyperpolarized the resting membrane potential (f, P = 0.0003), decreased the resting input resistance (g, P < 0.0001) and increased the rheobase current (h, P < 0.0001). i–k, Overexpression of Kir2.1Mut increased the resting input resistance (j, P = 0.0002), but had no effects on the resting membrane potential (i, P = 0.5) and the rheobase current (k, P = 0.9). The numbers of recorded neurons are indicated on the bars. All data are expressed as mean ± s.e.m.
Extended Data Figure 5 Overexpression of Kir2.1Mut or mNaChBacMut in layer 2/3 pyramidal cells does not affect inhibition.
a, Left, schematic of experiments. Scnn1a-Cre-Tg3 mice with ChR2 in layer 4 excitatory neurons and Kir2.1Mut in a subset of layer 2/3 pyramidal cells. Right, monosynaptic EPSCs and disynaptic IPSCs from simultaneously recorded control and Kir2.1Mut neurons in response to layer 4 photoactivation. b–d, Summary graphs. b, Left, EPSC amplitudes in Kir2.1Mut neurons plotted against those in control neurons. Right, logarithm of the ratio between EPSC amplitudes in Kir2.1Mut and control neurons. Red, mean ± s.e.m. EPSC amplitudes are similar between Kir2.1Mut and control neurons (n = 23, P = 0.7). c, As in b, but for IPSCs. IPSC amplitudes are similar between Kir2.1Mut and control neurons (n = 22, P = 0.6). d, As in b, but for E/I ratios. E/I ratios are similar between Kir2.1 and control neurons (n = 22, P = 0.6). e, Left, schematic of experiments. Pvalb-ires-Cre mice with ChR2 in Pvalb cells and Kir2.1Mut in a subset of layer 2/3 pyramidal cells. Right, IPSCs from simultaneously recorded control and Kir2.1Mut neurons in response to Pvalb cell photoactivation. f, Summary graphs. Left, IPSC amplitudes in Kir2.1Mut neurons plotted against those in control neurons. Right, logarithm of the ratio between IPSC amplitudes in Kir2.1Mut and control neurons. Red, mean ± s.e.m. IPSC amplitudes are similar between Kir2.1Mut and control neurons (n = 14, P = 0.8). g, h, As in e, f, but for a non-conducting mutant mNaChBac (mNaChBacMut). IPSC amplitudes are similar between mNaChBacMut and control neurons (n = 16, P = 0.9).
a, Schematics of experiments. mNaChBac or a non-conducting mutant mNaChBac (mNaChBacMut) was overexpressed in a subset of layer 2/3 pyramidal cells by in utero electroporation. b, Membrane currents (upper and middle panels) in response to voltage steps (lower panels) from an untransfected control pyramidal cell, a pyramidal cell overexpressing mNaChBac and a pyramidal cell overexpressing mNaChBacMut. The endogenous voltage-gated inward Na+ current was fast inactivating and was blocked by tetrodotoxin (TTX, 1 μM), whereas the mNaChBac-mediated inward current was slow inactivating and insensitive to TTX. Inset, overlay of the two dashed boxes. Note that the fast component of the inward current representing the endogenous Na+ current was blocked by TTX. c, Membrane potentials (upper panels) in response to current injections (lower panels) from a control neuron, a mNaChBac neuron and a mNaChBacMut neuron. The mNaChBac neuron generated long-lasting action potentials and depolarizations, whereas the mNaChBacMut neuron generated action potentials similar to the control neuron. d, e, Overexpression of mNaChBac lowered the action potential threshold (defined as the membrane potential whose derivative reaches 2 V s−1) (d, P = 0.004) and decreased the rheobase current (e, P = 0.03). f, g, Overexpression of mNaChBacMut did not alter the action potential threshold (f, P = 0.9) and the rheobase current (g, P = 0.8). The numbers of recorded neurons are indicated on the bars. All data are expressed as mean ± s.e.m.
a, Constitutive overexpression of mNaChBac causes a neuronal migration defect. mNaChBac or mNaChBacMut was overexpressed in a subset of pyramidal cells by in utero electroporation of pCAG-mNaChBac-T2A-tdTomato or pCAG-mNaChBacMut-T2A-tdTomato, respectively, on embryonic day 15.5 (E15.5). Representative fluorescent images of coronal sections of V1 obtained at postnatal day 16 or 17 showing that mNaChBac-expressing neurons (left panels) resided not only in layer 2/3, but also in layers 4–6 (n = 7 mice), whereas mNaChBacMut-expressing neurons (right panels) are all located in layer 2/3 (n = 5 mice). Cortical layers are indicated on the right based on the DAPI staining pattern. b, Experimental procedures for conditional expression of mNaChBac or Kir2.1 in a subset of layer 2/3 pyramidal cells. Left, plasmids pAAV-EF1α-F-FLEX-mNaChBac-T2A-tdTomato or pAAV-EF1α-F-FLEX-Kir2.1-T2A-tdTomato together with pCAG–EGFP were electroporated in utero into V1 on embryonic day 15.5. Successful transfection is indicated by the expression of EGFP. Middle, AAV-hSynapsin-Flpo was injected postnatally into V1. Right, only those neurons that were transfected with either pAAV-EF1α-F-FLEX-mNaChBac-T2A-tdTomato or pAAV-EF1α-F-FLEX-Kir2.1-T2A-tdTomato and infected with AAV-hSynapsin-Flpo expressed mNaChBac-T2A-tdTomato or Kir2.1-T2A-tdTomato, respectively. c, Representative fluorescent images of coronal sections of V1 obtained at postnatal day 16 showing that without injection of AAV-hSynapsin-Flpo transfected neurons did not express mNaChBac-T2A-tdTomato (left panels, n = 2 mice). The expression of mNaChBac-T2A-tdTomato in transfected neurons was turned on by injection of AAV-hSynapsin-Flpo. These neurons were all properly located in layer 2/3 (right panels, n = 7 mice). Cortical layers are indicated on the right based on the DAPI staining pattern. d, Schematics of concurrent expression of mNaChBac or Kir2.1 in layer 2/3 pyramidal cells and ChR2 in Pvalb or Sst cells. Plasmids pAAV-EF1α-F-FLEX-mNaChBac-T2A-tdTomato or pAAV-EF1α-F-FLEX-Kir2.1-T2A-tdTomato were electroporated in utero together with pCAG–EGFP into V1 of Pvalb-ires-Cre or Sst-ires-Cre mice on embryonic day 15.5. AAV-EF1α-DIO-hChR2(H134R)-EYFP and AAV-hSynapsin-Flpo were injected postnatally into V1. ChR2 was conditionally expressed in Pvalb or Sst cells, whereas mNaChBac or Kir2.1 was conditionally expressed in a subset of layer 2/3 pyramidal cells.
Extended Data Figure 8 A Flpo recombinase-mediated FLEX (F-FLEX) switch for conditional gene expression.
a, DNA sequence of the F-FLEX switch cassette. The first F14 site and Frt site were constructed in the forward direction and were separated by a 50-base-pair linker. The second F14 site and Frt site were constructed in the reverse direction and were separated by another 50-base-pair linker. Multiple cloning sites were inserted between the first Frt site and the second F14 site. b, Principle of F-FLEX switch. The gene of interest is inserted between the first Frt site and the second F14 site of the F-FLEX switch cassette in an inverted orientation, and is driven by an EF1α promoter. Flpo-recombinase-mediated recombination first occurs between the two F14 sites or the two Frt sites that are in the opposite direction, leading to a reversible inversion of the inverted gene of interest. Flpo-mediated recombination then occurs between the two F14 sites or the two Frt sites that are now in the same direction, excising the Frt site or the F14 site between them, respectively. The resulting construct contains only one F14 site and one Frt site, and the gene of interest is permanently locked in the forward orientation. c, Flpo turns on F-FLEX switch. HEK cells were transfected with (1) Flpo, (2) F-FLEX-mNaChBac-T2A-tdTomato, (3) Flpo and F-FLEX-mNaChBac-T2A-tdTomato or (4) Cre and F-FLEX-mNaChBac-T2A-tdTomato. EGFP was co-transfected to monitor the transfection. There was no leaky expression of mNaChBac-T2A-tdTomato in the absence of Flpo. mNaChBac-T2A-tdTomato expression was switched on by the expression of Flpo, but not by Cre. Similar results were obtained with other F-FLEX constructs (n = 5). d, Flpo does not turn on Cre-dependent DIO switch46. HEK cells were transfected with (1) Cre, (2) DIO-hChR2(H134R)-EYFP, (3) Cre and DIO-hChR2(H134R)-EYFP or (4) Flpo and DIO-hChR2(H134R)-EYFP. mRFP was co-transfected to monitor the transfection. There was no leaky expression of hChR2(H134R)-EYFP in the absence of Cre. hChR2(H134R)-EYFP expression was switched on by the expression of Cre, but not by Flpo. Similar results were obtained with other DIO constructs (n = 2).
Extended Data Figure 9 Overexpression of Kir2.1 in a small subset of layer 2/3 pyramidal cells does not affect Pvalb-cell-mediated inhibition onto untransfected pyramidal cells.
a, Schematic of experiments. Unitary connection from a Pvalb cell onto nearby layer 2/3 pyramidal cells in control mice (left) and onto untransfected pyramidal cells in mice that were electroporated in utero with pCAG-Kir2.1-T2A-tdTomato (right). b, Connectivity rates from Pvalb cells to layer 2/3 pyramidal cells in control mice (95%, 57 out of 60) and to untransfected pyramidal cells in electroporated mice (93%, 52 out of 56) are similar (P = 0.7). c, Cumulative frequencies for uIPSC amplitudes (control: n = 57, median, 224.0 pA; untransfected: n = 52, median, 190.4 pA; P = 0.5). Inset, mean ± s.e.m. d, Summary graph for the average relative deviations of uIPSCs from 20 and 17 similar experiments as in a. Bars, mean ± s.e.m. (P = 0.6).
Schematic illustration of how pyramidal cell activity regulates the inter-cell variability of Pvalb-cell-mediated inhibition. Left, pyramidal cells with different activity levels (dark and light colours indicate high and low activity, respectively) receive different amounts of Pvalb-cell-mediated inhibition (long and short bars indicate more or less inhibition, respectively). Inhibition consists of an activity-dependent component (green bars) and an activity-independent component (blue bars). The activity-dependent component is positively regulated by the pyramidal cell activity and varies accordingly, whereas the activity-independent component is similar across neurons. Right, when the activity of pyramidal cells is suppressed by overexpression of Kir2.1, the activity-dependent component is diminished and the remaining inhibition is largely the activity-independent component. This flooring effect reduces the variability of uIPSC amplitudes among Kir2.1-expressing neurons.
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Xue, M., Atallah, B. & Scanziani, M. Equalizing excitation–inhibition ratios across visual cortical neurons. Nature 511, 596–600 (2014). https://doi.org/10.1038/nature13321
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