Tag: Computational biophysics

  • Self-organized patterning of crocodile head scales by compressive folding

    Self-organized patterning of crocodile head scales by compressive folding

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    Animal husbandry

    Fertilized crocodile eggs (imported from Seronera Crocodile Farm) were transported to the University of Geneva and incubated at 31 °C in moist vermiculite. All treated and non-treated crocodile embryos were fixed and stored in 10% neutral buffered formalin (NBF). All non-fluorescence imaging of embryonic crocodile samples was undertaken using the Keyence VHX 7000 digital microscope. Imaging of hatched crocodile specimens was undertaken using an overhead-mounted Nikon D800 camera. Maintenance of, and experiments with, crocodile embryos and juveniles were approved by the Geneva Canton ethical regulation authority (authorization GE10619B) and performed according to Swiss law. The sample sizes are specified in figure legends and the Supplementary Information. Randomization and blinding was not required.

    Nanoindentation

    A Piuma nanoindenter (Optics11) was used to acquire stiffness measurements (effective Young’s modulus, Pa) of embryonic crocodile skin surface. When comparing measurements in two skin samples, a change in epidermal keratinization will produce a change in surface stiffness, which is very likely to be correlated with a change of the same sign in the effective overall Young’s modulus of the whole multilayered epidermis. In other words, an increase in epidermal surface stiffness is very likely accompanied by an increased stiffness of the whole epidermis. Freshly dissected upper jaws were positioned lateral side upwards, submerged in PBS. A probe with a tip radius of 99 µm and stiffness rating of 0.48 N m−1 was used to indent at a depth of 2,000 nm. Only measurements from load-displacement curves with a Hertzian contact model fit of ≥95% were subsequently analysed. Each biological replicate for the embryonic nanoindentation series was indented 10 times (Fig. 1c) or 5 times (Fig. 2f). These indentation points were positioned in a single row with each point separated by 120 µm. Plots showing the mean effective Young’s modulus values for each biological replicate with s.d. are presented. Statistical analysis was undertaken in Prism 9 (GraphPad).

    Confocal microscopy

    Confocal microscopy was used for embryonic crocodile samples stained with the Fast Green FCF dye (Sigma-Aldrich) according to a protocol of whole-mount collagen staining25. Image acquisition was undertaken as previously described25, using the SP8 microscope (Leica Microsystems), with a ×63 oil-immersion objective (numerical aperture, 1.4). Fast Green was excited at 627 nm and the signal was detected in the range of 630–730 nm. Image reconstruction was undertaken using Imaris (Oxford Instruments).

    H&E staining

    Fixed embryonic crocodile samples were dissected and embedded in paraffin as previously described24. Paraffin sections were cut at 10 µm with a RM2255 microtome (Leica Microsystems) before staining with haematoxylin and eosin (H&E). Slides were imaged using an automated slide scanner (3DHISTECH).

    In ovo intravenous EGF injections in crocodiles

    The injection of crocodile eggs was undertaken in accordance with our previously published work20,21 (https://youtu.be/qCYWSgbffnY). Crocodile eggs were incubated until the appropriate developmental stage and then cleaned with 70% ethanol. Eggs were candled to identify a suitable vein for injection, and a detailing saw (Micromot 50/E, Proxxon) was used to remove the shell while keeping the underlying membrane intact. The eggshell was then removed using fine forceps, and mineral oil was applied to the membrane with a cotton bud, thereby increasing membrane transparency to allow clear visualization of the underlying veins. The samples were injected with either 30 µl of PBS as a control or 30 µl of PBS containing recombinant murine EGF (PeproTech). Different doses of EGF were injected (0.625 µg, 1.5 µg or 2 µg). Patent Blue was also added to the solution to enable visualization of the solution entering the vein during injection. Injections were undertaken using a Hamilton syringe attached to a micromanipulator (MM33 right, Marzhauser). Once injected, the eggs were cleaned to remove excess mineral oil, and the eggshell window was covered with adhesive tape. Treated embryos were then returned to their incubator. The samples were each injected three times over the course of 10 days for each experiment (Fig. 2a). At collection, the embryos were treated with an intravenous injection of EdU to label proliferating cells (Baseclick); embryo collection and fixation were undertaken 3 h after EdU injection. Some EGF-treated embryos were used for nanoindentation at the end of the experiment, and some others were incubated until hatching. Embryos were subsequently fixed in 10% NBF at 4 °C and imaged with a Keyence VHX 7000 digital microscope. Every embryo injected with EGF exhibited modified head-scale patterning. All of the replicates from these experiments are shown in Supplementary Fig. 4 and are summarized in Supplementary Table 1.

    The drug that we use here (EGF) has the remarkable property of specifically promoting epidermal growth and differentiation without exhibiting strong deleterious effects in other aspects of in vivo embryonic development. Further validation of the parameters involved in the compression-folding process of crocodile head-scale patterning will require the identification of other drugs that would specifically affect one parameter at the time. For example, it would be particularly interesting to pharmacologically perturb the 3D architecture of collagen in developing crocodile embryos to investigate the corresponding effects on skin folding of the dorsal versus lateral upper jaw surface. Unfortunately, drugs currently known to effect collagen organization (such as β-aminoproprionitrile, BAPN) are highly toxic in vivo as they strongly affect the development of multiple connective tissues such as skin, bones and blood vessels. Given the great difficulties of experimentation with crocodile embryos, the screening of drugs that could, in vivo, specifically affect one mechanical parameter at a time in the skin, could be initially performed in a more classical model (such as the chicken) with more reliable source of embryos.

    LSFM

    The upper and lower jaws of fixed embryonic crocodile samples were dissected, dehydrated into methanol, and bleached with hydrogen peroxide, before rehydration and permeabilization in PBS with Triton X-100 (Sigma-Aldrich) (PBST). For nuclear staining, the samples were incubated in either TO-PRO-3 iodide or YO-PRO-1 iodide (3:1,000, Thermo Fisher Scientific) for 6 h. EdU-positive cells (EdU+) were detected using the EdU detection kit manufacturer’s guidelines (Baseclick). The samples were then dehydrated into methanol and collagen staining was undertaken in anhydrous conditions with the same Fast Green protocol25 as for confocal microscopy (see above). Samples were then cleared according to the iDISCO+ protocol37. Upper and lower jaw samples were imaged separately using a light-sheet microscope (Ultramicroscope Blaze, Miltenyi Biotec). Selected specimens were restained with Alizarin Red in potassium hydroxide (KOH) and re-imaged to visualize the developing calcified bone matrix (Extended Data Fig. 1b). Image stacks were processed using ImageJ38, before rendering with the Redshift engine of Houdini (SideFX) and the Unreal Engine (Epic Games). A summary of replicates used for LSFM is shown in Supplementary Table 5. Each sample includes both upper and lower jaws, which we scanned separately.

    3D reconstructions of hatched crocodiles

    Using our custom-built imaging system39, combining a robotic arm, high-resolution camera and illumination basket of light-emitting diodes, we combine ‘photometric stereo’ and ‘structure from motion’ to reconstruct the precise 3D surface mesh and colour-texture of hatched crocodile heads (Fig. 5b–e and Extended Data Fig. 6a–d). To compare the polygonal scale sizes among individuals, we first compute the minimum principle curvature of the meshes. Then, the folding network of each sample is computed by applying a skeletonization algorithm40, followed by graph simplification (using MATLAB R2021a), on the negative curvature regions of the mesh. Using the colour texture of meshes, the folding networks were manually completed and cleaned using Houdini (SideFX).

    Segmentation of LSFM data

    Using TO-PRO-3, YO-PRO-1, EdU, Alizarin Red and Fast Green staining (see above), we segmented the light-sheet microscopy data to extract (in both the upper and lower jaws) the geometry of the epidermis, dermis and bone tissues (Supplementary Video 6), as well as the dominant orientations of the dermal collagen fibres, and the distribution of proliferating cells in the dermis and epidermis. The segmented data were used to build a finite element model (FEM, see below) of the crocodile head.

    Cell nuclei staining signal enables precise segmentation of the epidermis from the dermis because the former exhibits a higher cell density (Fig. 3a). More specifically, the 3D image generated by LSFM on the basis of the TO-PRO-3/YO-PRO-1 fluorescence signal was subjected to 3D Canny’s edge detection41 in MATLAB-R2021a, generating a 3D binary image in which non-zero voxels form point clouds corresponding to two 3D surfaces: the surface of the epidermis and the epidermis–dermis boundary. For each of these two surfaces, we compute at each point the surface normal vector from the intensity gradient. The position of points and their corresponding normal vectors are then fed to a screened Poisson surface reconstruction algorithm42 in Meshlab43 to reconstruct triangular surface meshes, which effectively represent the initial point clouds in a much lighter format: 3D meshes are much easier to manipulate, for example, with the Laplacian smoothing algorithm to filter out the artifactual stair-step patterns in the original voxelized data format. The epidermis surface and the epidermis–dermis boundaries allow for computing the epidermis thickness across each control and treated sample at different developmental stages.

    Collagen network 3D architecture is likely to become instrumental in biomechanical modelling25,26 because it endows tissues with distinctive mechanical properties such as anisotropic response to homogeneous stress. Thus, we assess the orientation(s) of collagen fibres in the dermis across the face and jaws of developing crocodile embryos (Fig. 3b). To this end, we use our recently published whole-mount Fast Green staining method, which provides unmatched visualization of 3D collagen network architecture via confocal or light-sheet microscopy25. In brief, (1) the two most dominant orientation(s) of populations of collagen fibres were identified by determining the dominant 3D Fast Fourier transform coefficients in each of 13,000 homogeneously distributed dermal samples (cubic patches of 50 × 50 × 50 voxels) of 3D light-sheet images (Supplementary Note 1); (2) smoothing of the spatial variation of fibres orientations was achieved with an exact optimization procedure using a fibre axis mismatch energy functional (Supplementary Note 2); and (3) the two dominant fibre orientations, both tangential to the dermis mid-plane, were interpolated using spectral least-squares approximation (Supplementary Note 3).

    After standard EdU labelling and detection (Supplementary Video 3), we used a 3D principal curvatures approach36 (on the fluorescence signal) to segment proliferating cells in the jaws of an embryonic crocodile at E51, that is, at the onset of head-scale emergence (Fig. 3c). This approach is highly efficient for individually segmenting cells when they are grouped (that is, in contact). As the signal intensity is embedded in a 3D domain, three signal principal curvatures k1,2,3 are computed (in MATLAB) for each voxel, and voxels characterized by ks > kthreshold, where \({k}_{s}={({k}_{1}^{+}{k}_{2}^{+}{k}_{3}^{+})}^{\frac{1}{3}}\) and \({k}_{i}^{+}=\max ({k}_{i},0)\) are stored. The centroid of the connected voxels is considered as the location of an EdU+ cell. We then compute the density of EdU+ cells, separately for the dermis and the epidermis, by choosing sampling points in the corresponding segmented tissue layers. The space surrounding each sampling point is limited to a box of 80 × 80 × 80 voxels clipped by the layer boundaries. The density of EdU+ cells at a sampling point is computed as the number of cells inside the clipped box divided by its volume. In our numerical model, densities of proliferating cells are represented as a space-dependent growth function. We transfer this information to the 3D model using a spectral least-squares approximation approach to interpolate data on the spatial modes of the target mesh (details are provided in Supplementary Note 3).

    For segmenting bone tissue, we use either the 3D Canny’s edge detection of the (very strong) Alizarin Red signal or a semi-automatic procedure for samples with (weaker) Fast Green or EdU signals. In the latter case, we (1) choose several sections in the x, y and z directions and manually mark the separation between the dermis and the bone, (2) store the coordinates of all profile points as a 3D point cloud and compute their normal with Variational Implicit Point Set Surface44 and (3) use screened Poisson surface reconstruction42 from Meshlab43 to generate the mesh corresponding to the bone surface.

    A biomechanical model of head-scale emergence

    We use the segmented data to build a 3D finite-element numerical growth model. Triangular meshes were generated, both for upper and lower jaws, at the surface boundaries of the epidermis, dermis and bone of embryos before the onset of head-scale patterning (Fig. 1b and see above). The epidermis surface and the epidermis–dermis interface were smoothed to remove any artificial local deformations associated with sample preparation, including dehydration into methanol. The 3D volume of each of the three layers was represented as a tetrahedral mesh generated with TetGen45 (Extended Data Fig. 8a).

    During simulated growth, the deformation of tetrahedral elements is realized through finite-strain theory in which the bulk material configuration at current time t is represented as the spatial coordinates of a collection of points in the form of a vector variable x = x(X,t), where X is the spatial coordinates of these points at a reference configuration, that is, at t = 0 (Extended Data Fig. 8b). The coordinates between the current and the reference configurations are connected by the deformation gradient map, F—that is, a second-order tensor that incorporates the elastic and growth deformations. The elastic energy and the mechanical stress stored in each tetrahedral element is then calculated from the neo-Hookean material model, known to behave appropriately under large deformations30,31,46, and allowing the incorporation of anisotropic material, such as collagen fibres47 (Supplementary Note 4). The direction of fibres, as well as the spatial pattern of cell proliferation density, both inferred from LSFM data (Fig. 3b,c), are fed to the mechanical model. However, the elastic moduli, fibre stiffness and final amount of growth are considered as unknown parameters. Note that the absolute values of stiffness are irrelevant in the numerical simulations as the model key parameters are the fibre stiffness relative to the dermis and epidermis moduli, as well as the ratio of epidermis to dermis stiffnesses (Young’s moduli).

    Numerical simulations and parameter optimization

    To perform numerical simulations, the mechanical model formulation described above is discretized for tetrahedral elements using the FEM and integrated with contact and viscous forces (Supplementary Note 5). The final model is then implemented in an in-house application that uses NVIDIA GPUs for high-performance computation. For that purpose, we used the CUDA programming language to develop intensive-computation kernels, whereas C++ is used for data management, geometry processing, input/output operations and the graphical user interface. Our application integrates the following open-source libraries: Dear ImGui (https://github.com/ocornut/imgui, MIT licence) for the graphical user interface, CUDA C++ Core Libraries (https://github.com/NVIDIA/cccl, Apache-2.0, FreeBSD, BSD-3-Clause licences) for parallel algorithms, Eigen (https://gitlab.com/libeigen/eigen, MPL-2.0, BSD licences) for linear algebra and libigl (https://github.com/libigl/libigl, GPL-3.0, MPL-2.0 licences) for geometry processing. The simulation input is a tetrahedral mesh that defines the geometry of the crocodile head (epidermis, dermis and bone layers). Moreover, a set of model parameters are used: in addition to the dermal collagen fibres orientation and stiffness, we include, both for epidermis and dermis, the Young’s modulus and Poisson’s ratio, the growth rate functions and the cell proliferation pattern. The deformation of the skin is then computed and the final geometry is generated as a tetrahedral mesh.

    The mechanical model is integrated with a Bayesian optimization process (bayesopt library from MATLAB R2021a with parallel sampling), that is, a machine-learning global minimization algorithm. The optimality criterion consists of the distance between the metrics (integrating multiple topological and geometrical features, see below) of the steady-state simulated geometry versus LSFM-acquired meshes. To compute the metrics of a folding network, we first compute the minimum principle curvature of the corresponding surface mesh representing the epidermis boundary. We then segment the skin folds by applying a skeletonization algorithm40, followed by graph simplification (using MATLAB R2021a), on the negative curvature regions of the mesh. Next, we compute the following geometrical and topological features of the network: number of domains (cycles), perimeters of domains, lengths of edges, curvatures of edges and lengths of incomplete edges. The final metrics is a vector of which the components are the means of these features, normalized to the diagonal length of its bounding box. Given that components within a metrics vector may differ significantly among each other, we need to normalize them properly. For this purpose, we use LSFM data to compute the metrics of controls at E64 and treated individuals (2 μg EGF) at E64. We then compute the interindividual (that is, among all individuals) mean and s.d. of each component (Fig. 2e). We finally normalize the components of any newly computed metrics by subtracting the interindividual mean and dividing by the interindividual s.d.

    Finding optimal parameter values for control and treated targets is performed in two steps. First, we use an E64 control target mesh and perform optimization on the six-dimensional parameter space, including epidermis Young’s modulus, Eepidermis (keeping Edermis = 1); epidermis and dermis Poisson’s ratios, vepidermis/dermis; dermis tangential growth values, \({G}_{T,{\rm{dermis}}}^{+/-}\) (keeping \({G}_{T,{\rm{epidermis}}}^{+/-}\) at 80% of the dermis values); and the fibre stiffness, k1 (k2 being set to 0). Second, using a 2 μg EGF-treated target, we perform another optimization on the three-dimensional parameter space including epidermis-related parameters, that is, Eepidermis, vepidermis and \({\lambda }_{T,{\rm{epidermis}}}^{{\rm{EGF}}}\) (additional epidermal tangential growth induced by EGF). See Supplementary Notes 4 and 6 for the definitions of parameters and Supplementary Table 4 for the complete list of parameter values. To minimize the distance between the metrics vectors of the simulated versus LSFM target geometry (control or treated), we use a Gaussian process (that is, a generalization of the multivariate normal distribution to infinite dimensions) in the optimization loop to approximate posterior mean and variance functions from which the objective function is sampled (Extended Data Fig. 8d). The posterior functions are updated at each iteration according to Bayesian inference and this information is then used to compute the expectation of the improvement function, which measures the chance of observing an objective (that is, the distance between simulation and observation) smaller than the minimum objective observed so far (Supplementary Note 7). The optimization process, which typically takes a few thousand iterations, continues until no more improvement is observed in the last 500 iterations.

    Reporting summary

    Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

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  • Mis-splicing of a neuronal microexon promotes CPEB4 aggregation in ASD

    Mis-splicing of a neuronal microexon promotes CPEB4 aggregation in ASD

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    Animals

    Cpeb4 KO mice45 and conditional transgenic mice overexpressing the human CPEB4 isoform that lacks exon 4 (TgCPEB4Δ4)2 both in a C57BL/6J background were used. All mice were bred and housed in the CBMSO animal facility. Mice were grouped four per cage with food and water available ad libitum and maintained in a temperature-controlled environment on a 12–12 h light–dark cycle with light onset at 8:00 and a relative humidity of 55 ± 10%. Animal housing and maintenance protocols followed local authority guidelines. Animal experiments were performed under protocols approved by the CBMSO Animal Care and Utilization Committee (Comité de Ética de Experimentación Animal del CBMSO, CEEA-CBMSO) and Comunidad de Madrid (PROEX 247.1/20).

    Generation of mEGFP–CPEB4 mice

    A synthetic sequence consisting of the mEGFP linker sequence flanked by short regions of 5′ homologous (238 bp) and 3′ homologous (99 bp) DNA was obtained (Twist Bioscience). PCR was carried out on the synthetic sequence using the following primers: Fw ssDNA-mGFP–CPEB4 (phosphorylated) tacttcaagcaaacatatttgagatacagggga; Rv ssDNA-mGFP–CPEB4 (thiol-protected) GGTGATGGTGTGGAGGCTGC. Single-stranded DNA (ssDNA) was generated from double-stranded DNA by lambda exonuclease digestion of the phosphorylated strand, followed by gel purification and column extraction. Animals were generated by electroporation of isolated mouse zygotes with ssDNA combined with Cas9 protein and guide/tracr RNA ribonuclear protein complexes (guide; C45gRNA ATCCTAAAAATAATAAATGG). The correct integration of the knock-in cassette was confirmed by PCR and sequencing of the region. The resulting positive mice were crossed with C57BL6/J mice to confirm germline transmission. The offspring were maintained in a C57BL/6J background, and routine genotyping was performed by PCR using the following genotyping primers: 5′-ACGTAGGGTGATAAGCTGTGAT3′ (Fw) and 5′-AGGGTCTTGTTGTTCTTGCTGT-3′ (Rv). Mice were maintained in a specific pathogen-free facility with a 12–12 h light–dark cycle at 21 ± 1 °C at a relative humidity of 55 ± 10% and given ad libitum access to standard diet and water. Animal handling and all experimental protocols were approved by the Animal Ethics Committee at the Barcelona Science Park and by the Government of Catalonia.

    Mouse mEGFP–CPEB4 striatal neuron extraction and culture

    mEGFP–CPEB4 mice over 6 weeks of age were crossed in timed matings. Females were weighed weekly to monitor gestation progression. Females with an increment over 3 g up to 18 days after a positive plug were euthanized and embryos were collected at embryonic day 18.5 in cold buffer containing 1× HBSS, 10 mM glucose and 10 mM HEPES. A tail sample was also collected for embryo genotyping. Brains were dissected in the aforementioned buffer on an ice-cold plate, and the striatum was extracted and chopped. Samples were centrifuged and digested with a previously heated solution containing 1× HBSS, 10 mM glucose, 10 mM HEPES, 12 U ml–1 papain (Worthington LS003180) and 5 mM l-cysteine for 15 min at 37 °C. Samples were then disaggregated in a buffer containing 1× DMEM/F-12, 2 mM glutamine, 1 mM sodium pyruvate, 20 mM glucose and 10% inactivated horse serum. Cells were seeded at a confluence of 25,000 cells per well in µ-Slide 8-well ibiTreat imaging plates (Ibidi, 80826) previously coated with poly-d-lysine. Cells were then incubated at 37 °C for 1 h. After this time, medium was exchanged with previously tempered medium containing 1× Neurobasal (Gibco, 21103049), 1× B27 with vitamin A (Gibco, 17504044), 2 mM glutamine and 0.5% penicillin–streptomycin (PS). Medium was refreshed every 2–3 days. Neurons were considered differentiated after 7 days of culture. After genotyping, homozygous mEGFP–CPEB4 mice and wild-type littermates were selected for imaging. When specified, cell depolarization was induced by the addition of 50 mM KCl with 1:3 medium dilution. Neurons were maintained in culture for up to 14 days.

    mEGFP–CPEB4 distribution in neurons

    Primary striatal neurons from mEGFP–CPEB4 mice were imaged at 7 days of differentiation using a LIPSI spinning disk microscope (Nikon). Image acquisition was performed using a fully incubated, high-content, high-speed screening LIPSI platform (Nikon) equipped with an Eclipse Ti2 inverted microscope and a Yokogawa W1 confocal spinning disk unit. The spinning disk unit with an Apo LWD ×40 water lens of 1.15 numerical aperture, and a 488 nm (20%) laser was used for acquisition on a Prime BSI Photometrics sCMOS camera. NIS Elements AR (v.5.30.05) software was used for acquisition, and Fiji/ImageJ software was used to adjust images for visualization.

    mEGFP–CPEB4 neuronal stimulation with NMDA

    Primary striatal neurons from mEGFP–CPEB4 mice were imaged at 14–21 days of differentiation, and where specified, neuron stimulation was induced by the addition of 20 µM NMDA (Tocris, 0114), a selective NMDA receptor agonist. Stimulated neurons were imaged using a fully incubated Zeiss Elyra PS1 LSM 880 confocal microscope with a Plan ApoChromat ×63/1.2 Imm corr oil objective. A 488 nm (50%) laser was used for acquisition on a Prime BSI Photometrics sCMOS camera. Images were captured every 15 min over the recording period. Zen Elements AR (v.5.30.05) software was used for acquisition, and Fiji/ImageJ software was used for image quantification and to adjust images for visualization. A tailor-made macro applying an intensity threshold was used to accurately segment cytoplasmic condensates and the whole cell for each time frame. The condensed fraction per frame was obtained as the sum of areas of condensates divided by the cell area. For representation, the values were normalized to that measured at the end of the stimulation period.

    nCPEB4 extraction from mouse brains

    To extract nCPEB4 from the brains of 6-month-old control mice, Cpeb4 KO mice and TgCPEB4Δ4 mice, around 500 mg of tissue was first collected and snap-frozen in liquid nitrogen. Each sample was homogenized in 5 ml lysis buffer (50 mM Tris, pH 7.7, 5% glycerol, 0.1% Triton X-100, 1% NP-40, 50 mM NaCl, 50 mM imidazole and Pierce protease inhibitor, EDTA-free) using a Polytron homogenizer and rotated for 30 min at 4 °C. The homogenate was moved to high-speed PPCO centrifuge tubes and centrifuged at 48,000g at 4 °C for 20 min. After this, the supernatant was retained while the resultant pellet was dissolved in 4 ml lysis buffer and homogenized further using the Polytron homogenizer with the same protocol. This process was repeated 3 times (with 1 ml reduction of lysis buffer after each round of homogenization) to maximize the extraction of nCPEB4. To further clarify the combined supernatants, they were filtered through a Miracloth membrane (Millipore) to remove lipids and then passed through a 0.45 μm filter. Exploiting the histidine-rich regions present in the sequence of nCPEB4 (23RFHPHLQPPHHHQN36 and 229LSQHHPHHPHFQHHHSQHQQ248), a 2-elution step Ni2+-affinity chromatography was carried out using a Histrap HP 5 ml (GE Healthcare) on a FPLC apparatus (ÄKTA Pure, GE Healthcare). The combined supernatants were injected into a column pre-equilibrated with binding buffer consisting of 50 mM Tris, pH 7.7, 50 mM NaCl and 50 mM imidazole. The bound fraction was initially washed in a high-salt buffer consisting of 50 mM Tris, pH 7.7, 1 M NaCl and 50 mM imidazole. This step is crucial as it removes a high-molecular-weight nonspecific binder that was detectable by western blotting (WB), even in the Cpeb4 KO mice. The removal of this nonspecific binder is important to ensure the integrity of subsequent analyses. Once the nonspecific binder was completely removed, nCPEB4 was eluted using a second buffer containing 50 mM Tris, pH 7.7, 50 mM NaCl and 500 mM imidazole. The non-bound, washed and eluted fractions were then analysed by WB using Bis-Tris 4–12% gradient gels. At this point, fractions containing nCPEB4, verified by WB in SDS–PAGE, were used for proteinase K digestion and SDS-resistance analysis using 1.5% SDD–AGE as previously described46. Here, the non-boiling proteins were transferred to a nitrocellulose membrane by capillary methods and probed with an anti-CPEB4 antibody. Samples identified as CPEB4 monomers and aggregates were selected for subsequent seeded aggregation assay. Additionally, to quantify the amount of CPEB4 aggregates, the same samples were injected into a Superdex 200 Increase 10/300 GL (GE Healthcare) column pre-equilibrated with 1× PBS, pH 7.5. The eluted fractions from the gel filtration chromatography were combined every 4 fractions (2 ml) and concentrated into 100 µl using a Pierce concentrator, PES, 30 K MWCO, 0.5 ml, to be ultimately analysed using 1.5% SDD–AGE. For all the blots described here, including SDS–PAGE, immunodot blots and SDD–AGE, a 1:2,000 dilution of polyclonal rabbit anti-CPEB4 antibody (Abcam, ab224162) and a 1:5,000 dilution of HRP-linked anti-rabbit IgG antibody (Cell Signaling Technology, CST-7074S) were used.

    Proteinase K digestion

    About 400 ng of total protein, estimated from BCA assays, containing endogenous nCPEB4 extracted from the brains of 6-month-old control mice, Cpeb4 KO mice and TgCPEB4Δ4 mice were digested with 0.1, 0.5, 1, 5 and 10 ng of proteinase K for 2 min at 37 °C. Proteinase K activity was stopped by heating the samples to 75 °C. Next, 2 μl of the enzyme-treated reaction mixture was manually applied to a nitrocellulose membrane. The membrane was blocked in 5% milk in TBS-T buffer and probed with anti-CPEB4 antibody (Abcam, ab224162).

    Seeded aggregation assay

    A concentration of 1% w/w of the seed, 40 ng of total protein containing nCPEB4 aggregates extracted from TgCPEB4Δ4 mouse brains, was incubated with the substrate, which consisted of 4 μg total protein containing soluble nCPEB4 extracted from wild-type (WT) mouse brains. Unless concentrated 100-fold, the seed used was not detectable by WB. The seeding reaction was carried out at 4 °C for 24 h during the time course experiment in 50 mM Tris, pH 7.7, and 50 mM NaCl. The seeded reactions, which were non-boiled, were analysed using 1.5% SDD–AGE as previously described46. The proteins were transferred to a nitrocellulose membrane by capillary methods and probed with anti-CPEB4 antibody (Abcam, ab224162) to follow the aggregation of WT nCPEB4 in a time-dependent manner.

    Proteostat staining and CPEB4 immunofluorescence

    Six-week-old TgCPEB4Δ4 mice (n = 4) and control littermates (n = 3) were anaesthetized by an intraperitoneal injection of pentobarbital and then transcardially perfused with PBS. Brains were immediately removed and each hemisphere placed in 4% paraformaldehyde overnight at 4 °C, followed by 3 PBS washes (10 min each) and then immersed in 30% sucrose in PBS for 72 h at 4 °C and them included in optimum cutting temperature compound (Tissue-Tek, Sakura Finetek Europe, 4583) and immediately frozen. Samples were stored at −80 °C until use.

    Brain hemispheres were cut sagittally at 30 µm on a cryostat (Thermo Scientific), and sections were stored (free floating) in glycol-containing buffer (30% glycerol and 30% ethylene glycol in 0.02 M PB) at −20 °C.

    For staining, sections (2 per mouse) were washed in PBS to eliminate the cryoprotective buffer and permeabilized in 0.2% Triton X-100 for 30 min at room temperature, and then stained with the dye Proteostat (Enzo51035-K100; 1:2,000) for 15 min at room temperature followed by 2 PBS washes (10 min each) and then 1% acetic acid for 30 min at room temperature, followed by 3 PBS washes (10 min each). For CPEB4 immunofluorescence, sections were immersed in blocking solution (2% NGS, 1% BSA and 0.2% Triton X-100 in PBS) for 1 h at room temperature and then incubated overnight at 4 °C with anti-CPEB4 primary monoclonal antibody (1:1,000, mouse monoclonal, homemade, ERE149C) in blocking solution. After 3 PBS washes (10 min each), sections were incubated with Alexa 488 donkey anti-mouse secondary antibody (1:500, Thermo Fisher, A-21202) for 1 h followed by 3 PBS washes (10 min each) and, finally, nuclei were stained by incubating with DAPI (1:10,000 in PBS, Merck) followed by 3 PBS washes (10 min each) and mounted with Prolong medium (Life Technologies).

    Images of the striatum were obtained with a vertical Axio Observer.Z1/7 laser scanning microscope (LSM 800, Carl Zeiss) at ×63 magnification with ×2 optical zoom and analysed by performing z stacks (11 optical sections with a thickness of 1 μm, spanning 6.6 μm on the z axis). Sequential scanning mode was used to avoid crosstalk.

    Medium-sized spiny neurons were distinguished by the morphology and size of the nucleus, and fields were selected to typically include 4–8 medium-sized spiny neurons. The number of Protesotat and CPEB4 double-positive foci was manually counted per cell fully included within the z stack. Typically, between 16 and 20 cells were analysed per mouse from a total of 50 control and 73 TgCPEB4Δ4 neurons.

    Significance for differences in the number of positive foci between control mice and TgCPEB4Δ4 mice was assessed using a generalized linear mixed model (family = Poisson(link = ‘identity’)) with mouse as the random effect (Supplementary Methods).

    Plasmids for expression in N2a cells

    Human nCPEB4 (UniProt identifier Q17RY0-1) FL open reading frame (ORF) was cloned into a pBSK vector. The me4 sequence (nucleotides 1258–1281) was deleted by PCR on a pBSK-nCPEB4 plasmid using Gibson assembly master mix (New England Biolabs, E2611S) following the manufacturer’s instructions. Mutagenesis of nCPEB4 phosphorylation sites was performed using a QuikChange Lightning Multi Site-Directed Mutagenesis kit (Agilent Technologies, 210513), with oligonucleotides purchased from Sigma-Aldrich, following the manufacturer’s instructions. ΔHC mutants were generated by PCR mutagenesis on a pBSK-nCPEB4 plasmid, with oligonucleotides purchased from Sigma-Aldrich. For cell transfection, nCPEB4 ORF, FL, NTD and mutants were cloned into pPEU4 and pPEU5 vectors, which contain a C-terminal eGFP or mCherry tag, respectively, by In-Fusion (BD Clontech) cloning reaction47. For BioID, xCPEB4 or BirA ORF was cloned into a pBSK vector. me4 was added to the xCPEB4 sequence by PCR on a pBSK-xCPEB4 plasmid using Gibson assembly master mix (New England Biolabs, E2611S) and following the manufacturer’s instructions. A MYC tag and BirA ORF were added at the N terminus of pBSK-xCPEB4 plasmid. For competition experiments, xCPEB1 RRMZZ and xCPEB4 RRM domains were cloned in pBSK, and a HA tag was added at the N terminus. pBSK-Emi2 3′ UTR was obtained from a previous study48.

    N2a cell culture, differentiation and DNA transient transfection

    N2a cells were grown in DMEM with 10% FBS, 1% PS and 2 mM l-glutamine for maintenance. For fixed-cell imaging, cells were seeded on 6-well plates with 12-mm-diameter poly-lysine-coated glass coverslips (Marienfeld Superior). For live-cell imaging, cells were seeded on µ-Slide 8-well ibiTreat plates. For differentiation, medium was exchanged with DMEM with 0.5% FBS, 1% PS, 2 mM l-glutamine and 1 µM retinoic acid and cells were grown for 48 h. They were then transfected at 60% confluence with 1.25 µg DNA using Lipofectamine LTX and Plus reagent (Thermo Fisher, 15338100) following the manufacturer’s protocol. When specified, N2a depolarization was induced as described for striatal neurons, specified in the section ‘Mouse mEGFP–CPEB4 striatal neuron extraction and culture’.

    N2a cell line characterization

    N2a cells, like neurons, express CPEB4 variants including and excluding me4 (nCPEB4 and nCPEB4Δ4, respectively), independently of their differentiation status (Extended Data Fig. 1e). By contrast, cell lines of non-neural origin only express nCPEB4Δ4. Inclusion of me4 in N2a cells correlates with the expression of the splicing factor SRRM4 but not with that of RBFOX1 (Extended Data Fig. 1f). Depletion of SRRM4 in N2a cells decreases the inclusion of me4, whereas overexpression of SRRM4 in the non-neuronal cell line 293T forces its inclusion5,49 (Extended Data Fig. 1g). N2a cells, therefore, recapitulate the neuron-specific regulation of CPEB4 alternative splicing.

    nCPEB4–GFP distribution in N2a cells

    Twenty-four hours after transfection, N2a cells were fixed with 4% paraformaldehyde (Aname, 15710) in PBS for 10 min at room temperature. They were then washed with PBS and incubated with 0.5 µg µl–1 DAPI (Sigma) for 15 min. Coverslips were rinsed with PBS and mounted on a glass slide with Prolong Gold Antifade mountant (P36934, Invitrogen). Image acquisition was performed with a Leica SP5 confocal microscope (Leica Microsystems), and z series stacks were acquired at 1,024 × 1,024 pixels using a ×63/1.4 numerical aperture oil immersion objective with a zoom factor of 2. Argon 488 nm (20%) and diode 405 nm (10%) lasers were used. Hybrid detectors for GFP (500–550 nm with 33% gain) and DAPI (415–480 nm, 33% gain) were used for acquisition. LAS AF Leica software was used to acquire 10–20 z stack slices per cell with a z step size of 0.5 µm. Fiji/ImageJ software was used to perform the image analysis. A tailor-made macro using BioVoxxel Toolbox and 3D object counter plug-ins was used to accurately segment and obtain the number and volume of foci per cell.

    Live-cell imaging of GFP-tagged CPEB4 variants in N2a cells

    Live imaging of overexpressed nCPEB4–GFP variants in N2a cells was performed 20 h after transfection, whereas primary striatal neurons from mEGFP–CPEB4 mice were imaged at 7 days of differentiation. For both types of cells, image acquisition was performed using a spinning disk microscope (Andor Revolution xD, Andor). A total of 24 images were taken per experiment (4 before the addition of the stimulus and 20 after), with 13 z stacks at 512 × 512 pixels of format resolution. Images were acquired with a step size of 0.5 μm. For acquisition, the typical frame rate was adjusted to 5 images per s at 50 ms integration time of the EMCCD camera (Andor). An argon 488 nm laser (20%) was used for acquisition with a 1.4 numerical aperture/×60 oil immersion objective. Fiji/ImageJ software was used to obtain a z projection of the z stacks and subsequent concatenation of images. The obtained time-lapse images were subsequently used for manual quantification of nCPEB4 dissolution events. Cells were manually classified into two categories depending on the existence of cytoplasmic foci at t = 60 min: cells with remaining foci or cells without. For nCPEB4 and nCPEB4Δ4 FL comparison, the percentage of cells with remaining cytoplasmic foci after the depolarizing stimuli (t = 60 min) was calculated from a pool of 7 experiments. Unless specified, the percentage of cells with remaining cytoplasmic foci after the depolarizing stimuli (t = 60 min) was calculated per each experiment. When specified, blind analysis and classification were performed independently by a group of four different people from a pool of experiments.

    FRAP in N2a cells

    A spinning disk microscope from Andor, equipped with a FRAPPA module, was used for FRAP experiments. A total of 350 images were taken per experiment (50 images before the bleaching and 300 after) at 512 × 512 pixels. The typical frame rate was set to the fastest (88 ms) with an exposure time of 50 ms on an EMCCD camera. An AOTF 488 nm laser (20%) was used for acquisition, and 50% laser intensity was set for bleaching in 2 repeats with a dwell time of 40 ms. Fiji/ImageJ software was used for FRAP analysis. Three regions of interest (ROIs) were defined per video: background, cell and bleaching area. The mean fluorescence intensity was obtained for the 3 ROIs for all 350 frames, and the output was exported in tabular format. Outputs were then entered on the easyFRAP website50. Full-scale normalization was selected, ‘initial values to discard’ was set to 20 and the curves obtained were fitted to a single exponential model. Fluorescence recovery curves, mobile fraction and half time of recovery were obtained for each experimental condition.

    Mapping of nCPEB4 post-translational modified sites by mass spectrometry

    Overexpressed nCPEB4–GFP and nCPEB4Δ4–GFP were immunoprecipitated from basal (–stim) and stimulated (+stim) N2a differentiated cells. Cells were lysed in ice-cold RIPA buffer containing 50 mM Tris HCl pH 8, 1% Nonidet P-40 (NP40), 0.1% SDS, 1 mM EDTA, 150 mM NaCl, 1 mM MgCl2, 1× EDTA-free complete protease inhibitor cocktail (Roche, 5056489001) and phosphatase inhibitor cocktails (Sigma, P5726 and P0044). Cells were subsequently sonicated for 5 min at low intensity with a standard bioruptor diagenode. Following centrifugation (4 °C for 10 min at maximum speed), supernatants were collected, precleared and immunoprecipitated overnight at 4 °C with 50 μl GFP-conjugated Dynabeads protein A (Invitrogen). Beads had previously been conjugated with 5 μl anti-GFP antibody (Invitrogen, A6455) diluted in 500 μl PBS 1× for 2 h at room temperature. After immunoprecipitation, beads were washed with cold RIPA buffer and eluted with Laemmli sample buffer. Eppendorf LoBind microcentrifuge tubes (Eppendorf, 30108116) were used for the entire protocol. The immunoprecipitated elutions were run on precast 4–20% gradient gels (Midi Criterion TGX, Bio-Rad) and stained with Coomassie blue for 1 h at room temperature. Bands at the expected nCPEB4–GFP molecular weight were cut, washed with 50 mM NH4HCO3 and acetonitrile, reduced with 10 mM DTT and alkylated with 50 mM IAA. Samples were digested with trypsin and digestion was stopped by the addition of 5% formic acid. Following evaporation, samples were reconstituted in 15 μl of 1% formic acid and 3% acetonitrile. Mass spectrometry analysis of nCPEB4 PTM sites was performed as previously described7 with some modifications. In brief, samples were loaded in a μ-precolumn at a flow rate of 250 nl min–1 using Dionex Ultimate 3000. Peptides were separated using a NanoEase MZ HSS T3 analytical column with a 60 min run and eluted with a linear gradient from 3 to 35% buffer B in 60 min (buffer A: 0.1% formic acid in H2O; buffer B: 0.1% formic acid in acetonitrile). The column outlet was directly connected to an Advion TriVersa NanoMate (Advion) fitted on an Orbitrap Fusion Lumos Tribrid (Thermo Scientific). Spray voltage in the NanoMate source was set to 1.7 kV. The mass spectrometer was operated in a data-dependent acquisition mode. Survey mass spectrometry scans were acquired in the orbitrap with the resolution (defined at 200 m/z) set to 120,000. The top speed (most intense) ions per scan were fragmented in the HCD cell and detected in the orbitrap.

    For peptide identification, searches were performed using MaxQuant (v.1.6.17.0) software and run against a target and decoy database to determine the false discovery rate. The database included proteins of interest sequences (nCPEB4–GFP and nCPEB4Δ4–GFP) and contaminants. Search parameters included trypsin enzyme specificity, allowing for two missed cleavage sites, oxidation in methionine, phosphorylation in serine, threonine and tyrosine, methylation and demethylation in lysine and arginine, and acetylation in the protein N terminus as dynamic modifications, and carbamidomethyl in cysteine as a static modification. Peptides with a q value lower than 0.1 and false discovery rate < 1% were considered as positive identifications with a high confidence level. Mass spectrometry spectra were searched against contaminants (released in 2017) and user proteins using Andromeda and MaxQuant (v.1.6.17.0) software. To accept a site as modified, PTM localization probability was set above 75%. For the differential expression analysis, a t-test on PTM site intensities from MaxQuant was applied for each site within nCPEB4 variants. For data visualization, two parameters were used for each PTM site, namely the sum of intensities of modified peptides that contain the specific PTM-site (Int_mod) and the PTM-to-base ratio, with the latter calculated as: Int_mod/Int_unmod, where Int_unmod is the sum of intensities of unmodified peptides that contain the site. For data visualization, the PTM-to-total ratio was calculated for each site as follows: PTM-to-total = Int_mod/(Int_mod + (Int_mod/PTM-to-base)).

    Effect of phosphorylations on condensate dissolution

    To strengthen the conclusion that phosphorylation of nCPEB4 does not promote condensate dissolution, we studied the behaviour in N2a cells of the condensates formed by phosphomimicking (S/T to D) and non-phosphorylatable (S/T to A) variants of nCPEB4(NTD), the phosphorylation status of which cannot be altered by depolarization. In agreement with our previous findings11, the former had a lower propensity to condense (Extended Data Fig. 2c) and, in agreement with our conclusion, both variants dissolved after depolarization (Extended Data Fig. 2d,e).

    Intracellular pH tracking

    Quantitative determination of intracellular pH (pHi) was performed using the cell-permeant ratiometric pH indicator SNARF-5F 5-(and-6)-carboxylic acid AM (Thermo Fisher) in live imaged N2a cells at 48 h of differentiation. In brief, for loading the pH indicator into cells, they were incubated with 10 µM SNARF-5F 5-(and-6)-carboxylic acid AM diluted in serum-free DMEM for 15 min at 37 °C. Cells were then washed and imaged in serum-free DMEM. A Zeiss Elyra PS1 LSM 880 confocal microscope using a Plan ApoChromat ×40/1.2 Imm corr DIC M27 water objective was used for acquisition at 2 emission wavelengths: −575 nm and 640 nm. Images were captured every 30 s over the recording period. pHi estimation was performed as described in previous publications51. In brief, in vivo pHi calibration was performed by fixing the pHi between 5.5 and 7.5 with a commercially available intracellular pH calibration buffer kit (Thermo Fisher). Valinomycin and nigericin were used to equilibrate the intracellular pH. The intensity of fluorescence emitted at the two wavelengths was used to calculate a ratio (RF640/F575) that is proportional to pHi. Fluorescence ratio values (RF640/F575) from cells with fixed pHi were used to obtain a calibration curve for each biological replicate. Experimental pHi estimation from the fluorescence ratio values was calculated using the following equation: pHi = (RF640/F575 + b)/m, where m is the slope from the calibration curve equation and b is the intercept.

    RNA extraction and real-time quantitative RT–PCR

    For N2a RNA extraction, cells were scraped into an ice-cold plate, collected and centrifuged at 500g for 5 min at 4 °C. For mouse tissue RNA extraction, organs were ground with a liquid-nitrogen-cooled mortar to obtain tissue powder. Total RNA was extracted from both cells and tissue powder using TRIsure reagent (Bioline, Ecogen, BIO-38033) following the manufacturer’s protocol and using phenol–chloroform. The RNA concentration was determined using a Nanodrop spectrophotometer (Nanodrop Technologies). Next, 1 μg of total RNA was reverse transcribed using RevertAid reverse transcriptase (Themo Fisher, EP0442) following the manufacturer’s recommendations and using oligodT and random hexamers as primers. Quantitative real-time PCR (qPCR) was performed in triplicate in a QuantStudio 6flex (Thermo Fisher) using PowerUp SYBR green master mix (Thermo Fisher, A25778). All quantifications of mRNA levels were first normalized to an endogenous housekeeping control (Tbp), and then mRNA relative quantities to a reference sample (brain, N2a undifferentiated) were calculated using the 2–ΔΔCt method. The following primers were used for qPCR: 5′-TGATTCCATTAAAGGTCGTCTAAACT-3′ (Fw) and 5′-GAAACAATGAAGACTGACCTCTCCTT-3′ (Rv) for Mm Cpeb4 isoform containing exons 3 and 4; 5′-TGATTCCATTAAAGCAAGGACTTATG-3′ (Fw) and 5′-GCTGTGATCTCATCTTCATCAATATC-3′ (Rv) for Mm Cpeb4 isoform lacking exon 3; 5′-TGATTCCATTAAAGGTCGTCTAAACT-3′ (Fw) and 5′-GGAAACAATGAAGACTGACCATTAAT-3′ (Rv) for Mm Cpeb4 isoform lacking exon 4; 5′-ATTCCATTAAAGGTCAGTCTTCATTG-3′ (Fw) and 5′-GCTGTGATCTCATCTTCATCAATATC-3′ (Rv) for Mm Cpeb4 isoform lacking exons 3 and 4; 5′-GGAAAGGGACCTTCAAAGCAGT-3′ (Fw) and 5′ CTCTGTCCTTGGCATCGGCT-3′ (Rv) for Mm Srrm4; and 5′-ACTTCTATGCAGGCACGGTG-3′ (Fw) and 5′-AGCCAGGCATTGCAGAAGTAT-3′ (Rv) for Mm Rbfox1. Mm JunB and cFos primers were obtained from a previous study5.

    Real-time semi-quantitative RT–PCR

    For CPEB4 splicing isoform amplification, specific primers were used in CPEB4 exon 2 (Fw primer) and exon 5 (Rv primer) as previously described2. PCR products conforming to the 4 isoforms of CPEB4 were resolved on a 2% agarose/GelRed gel run at 130 V for 2 h.

    WB analysis

    Cells were lysed in ice-cold buffer containing 1% NP40, 150 mM NaCl, 50 mM Tris HCl (pH 7.5), 2 mM EDTA, 2 mM EGTA, 20 mM sodium fluoride, 2 mM PMSF, 2 mM sodium orthovanadate, 1 mM DTT and 1× EDTA-free complete protease inhibitor cocktail. Lysed samples were then sonicated at medium intensity for 5 min with a standard bioruptor diagenode, and total protein content was quantified using a DC Protein assay (Bio-Rad, 5000113). Next, 15–30 μg of total protein lysate was resolved on SDS–PAGE gels and transferred to a nitrocellulose membrane (Cytiva, 10600001). After 1 h of blocking at room temperature in 5% non-fat milk, membranes were incubated overnight at 4 °C with primary antibodies and subsequently with secondary antibodies for 2 h at room temperature. Specific proteins were labelled using the following primary antibodies: CPEB4 (1:100, homemade, mouse monoclonal, ERE149C); GFP (1:2,000, Invitrogen, rabbit polyclonal, A6455); MYC (1:1,000, Abcam, goat polyclonal, ab9132); and β-actin (1:10,000, Abcam, mouse monoclonal, ab20272) or streptavidin (1:5,000, Thermo Fisher, S911). The following secondary antibodies were used: goat anti-mouse (1:300, Thermo Fisher, 31430); goat anti-rabbit (1:300, Thermo Fisher, G-21234); and donkey anti-goat (1:300, Abcam, ab6885). Membranes were then incubated for 3 min with Amersham ECL TM WB detection reagents (Sigma, GERPN2106) or for 5 min with Clarity Western ECL substrate (Bio-Rad, 1705061).

    nCPEB4 and nCPEB4Δ4 co-localization experiments in N2a cells

    mCherry red signals were acquired with a DPSS 561 excitation laser (9%) and a HyD2 detector set to 570–650 nm with a gain of 33%. DAPI and GFP signals were acquired using the settings specified in the section ‘nCPEB4–GFP distribution in N2a cells’. For measuring the extent of co-localization between the two channels, the ImageJ JaCoP plug-in was used to obtain Pearson’s correlation coefficients and Mander’s overlap coefficients per cell.

    Immunohistochemistry

    Mouse embryos at embryonic day 13.5 were fixed in 10% neutral-buffered formalin solution and embedded in paraffin. Rabbit polyclonal primary antibody anti-CPEB4 (Abcam, ab83009) was used at 1:1,000 dilution. Embryo sections were counterstained with haematoxylin.

    X.
    laevis oocyte preparation

    Stage VI oocytes were obtained from full-grown X.laevis females as previously described52. In brief, ovaries were treated with collagenase (2 mg ml–1; StemCell Technologies) and incubated in modified bath saline 1× medium with 0.7 mM CaCl2. Animal handling and all experimental protocols were approved by the Animal Ethics Committee at the Barcelona Science Park and by the Government of Catalonia.

    X.
    laevis BioID

    BioID was performed as previously described7. In brief, 150 stage VI X.laevis oocytes were microinjected with 50.6 nl of 50 ng μl–1 in vitro transcribed and polyadenylated RNAs corresponding to MYC-BirA-xCPEB4 variants. Oocytes were then incubated in 20 μM biotin (Merck) at 18 °C for 40 h. Oocytes were lysed in cold lysis buffer and centrifuged twice at 16,000g at 4 °C for 15 min. Cold BioID lysis buffer was added to cleared extract, and the resulting mixture was subjected to clearing with PD MiniTrap G-25 columns (GE Healthcare). Next, 1.6% Triton X-100 and 0.04% SDS were added, and extracts were incubated with MyOne Dynabeads Streptavidin C1 (Invitrogen). The beads were then washed with a subsequent sequence of wash buffers. The beads were resuspended in 3 M urea, 50 mM NH4HCO3, pH 8.0, and 5 mM DTT for 1 h at room temperature with orbital shaking and subsequently incubated in 10 mM iodoacetamide for 30 min at room temperature, and then DTT was added. Proteins were on-bead digested with trypsin (Promega) at 37 °C for 16 h with orbital shaking. Digestion was stopped by the addition of 1% formic acid. Mass spectrometry analysis of biotinylated proteins in xCPEB4 and xCPEB4 + Ex4 was carried out at the Mass Spectrometry Facility at IRB Barcelona as previously described7. In brief, samples were analysed using an Orbitrap Fusion Lumos Tribrid mass spectrometer (Thermo Scientific). The MS/MS spectra obtained were searched against the UniProt (Xenopodinae, release 2017_02) and contaminants databases, and proteins of interest sequences using Proteome Discoverer (v.2.1.0.81).

    Identification of the nCPEB4 isoform interactome by immunoprecipitation coupled to mass spectrometry

    Overexpressed nCPEB4–GFP, nCPEB4Δ4–GFP and GFP (control) were immunoprecipitated from differentiated N2a cells. Cells were lysed in ice-cold RIPA buffer containing 50 mM Tris HCl pH 8, 1% Nonidet P-40 (NP40), 0.1% SDS, 1 mM EDTA, 150 mM NaCl, 1 mM MgCl2, 1× EDTA-free complete protease inhibitor cocktail (Roche, 5056489001) and phosphatase inhibitor cocktails (Sigma, P5726, and P0044). Cells were subsequently sonicated for 5 min at low intensity with a standard bioruptor diagenode. Following centrifugation (4 °C for 10 min at maximum speed), supernatants were collected, precleared and immunoprecipitated overnight at 4 °C with 50 μl GFP-conjugated Dynabeads protein A (Invitrogen). Beads had previously been conjugated with 10 μl anti-GFP antibody (Invitrogen, A6455) diluted in 500 μl PBS 1× for 2 h at room temperature. After immunoprecipitation, beads were washed with cold RIPA buffer (containing 0.05% NP-40 and 0.1% SDS) and eluted with Laemmli sample buffer. Eppendorf LoBind microcentrifuge tubes (Eppendorf, 30108116) were used for the entire protocol. The immunoprecipitated elutions were shortly run on 8% acrylamide 0.75 mm gels until the whole individual samples were compacted at the upper part of the running gel. Then, gels were stained with InstantBlue Coomassie for 1 h at room temperature. Bands corresponding to elutions were cut, washed and digested with 0.1 μg μl–1 trypsin, (Promega). Samples were digested with trypsin and digestion was stopped by the addition of 5% formic acid. Following evaporation, samples were reconstituted in 12 μl of 1% formic acid and 3% acetonitrile. In brief, mass spectrometry analysis of immunoprecipitates was performed as follows: samples were loaded into an Evotip trap column (Evosep) at a flow rate of 250 nl min–1. Peptides were separated using a EV1137 analytical column (Evosep) with a 88-min run and eluted with buffer A (0.1% formic acid in H2O) and buffer B (0.1% formic acid in acetonitrile). The column outlet was directly connected to an Easyspray (Thermo Scientific) fitted on an Orbitrap Eclipse Tribrid (Thermo Scientific). Spray voltage in the Easyspray source was set to 2.5 kV. The mass spectrometer was operated in data-dependent acquisition mode. The top speed (most intense) ions per scan were fragmented in the HCD cell and detected in the orbitrap. For peptide identification, searches were performed using Proteome Discoverer (v.2.5.0.400) software and run against databases including universal contaminants, mouse from Swissprot (2023/04) and bait proteins. Search parameters included trypsin enzyme specificity, allowing for two missed cleavage sites, oxidation in methionine, acetylation in the protein N terminus, methionine loss in the N terminus, and methionine loss in and acetylation in the N terminus as dynamic modifications, and carbamidomethyl in cysteine as a static modification. Protein hits in co-precipitates from each isoform were determined using a differential analysis of protein abundance in nCPEB4–GFP or nCPEB4Δ4–GFP relative to GFP. Protein group abundance values from Proteome Discoverer were used for protein quantification, and cut-off values for the fold change (|FC| > 1.5) and adjusted P value (padj < 0.05) were applied to define over-abundant significant proteins. Significant hits included proteins with no missing values in the three conditions (nCPEB4, nCPEB4Δ4 or GFP) or in only one condition, for which value imputation was performed. Only significant hits were considered for subsequent analyses. Protein hits differentially represented in nCPEB4Δ4–GFP versus nCPEB4–GFP were determined by a differential abundance analysis between the two baits, applying fold change (|FC| > 1.5) and padj < 0.05) as cut-off values.

    Competition experiments

    Competition experiments were performed as previously described10 using 23 nl of 500 ng μl–1 in vitro transcribed and polyadenylated RNAs encoding for HA-tagged xCPEB1 and xCPEB4 RRMs and variants. Not injected was considered as 0% competition whereas HA-xCPEB1 RRM was considered as 100% competition.

    Plasmids for protein expression in Escherichia coli

    An insert codifying for the nCPEB4(NTD) protein sequence (UniProt identifier Q17RY0-2, residues 1–448) was ordered in GenScript subcloned in a pET-30a(+) vector. The His6 tag and S tag from the plasmid were removed by PCR using a NEB Q5 site-directed mutagenesis kit, with oligonucleotides purchased from Sigma-Aldrich. The histidine to serine mutants were ordered from GenScript subcloned in a pET-30a(+) vector in the NdeI and XhoI restriction enzymes positions. The nCPEB4Δ4, ΔHC and Δ4ΔHC mutants were generated by PCR mutagenesis on the nCPEB4(NTD) plasmid using a NEB Q5 Site-directed mutagenesis kit, with oligonucleotides purchased from Sigma-Aldrich. The sequences of the N-terminal domain of nCPEB4 and mutants used for the in vitro experiments are described in Supplementary Methods.

    Protein expression and purification for in vitro experiments

    E.coli B834 cells were transformed with the pET-30a(+) plasmids. For non-isotopically labelled protein, the cells were grown in LB medium at 37 °C until the optical density at 600 nm (OD600) was 0.6, and then the cultures were induced with 1 mM IPTG for 3 h at 37 °C. For 15N or 15N,13C isotopically labelled protein, the cells were grown in LB medium until OD600 = 0.6 and then transferred into M9 medium53 (3 litres LB for 1 litre M9) containing [15N]H4Cl or [15N]H4Cl and [13C]glucose, respectively, and then the cultures were induced with 1 mM IPTG overnight at 37 °C. The cultures were then centrifuged for 30 min at 4,000 r.p.m., and the cells were resuspended with lysis buffer (50 mM Tris-HCl, 1 mM DTT, 100 mM NaCl, 0.05% Triton X-100, at pH 8.0, and supplemented with 500 μl of PIC and 500 μl of 100 mM PMSF).

    The cells were lysed by sonication and centrifuged for 30 min at 20,000 r.p.m. The pellet was washed first with wash-1 buffer (20 mM Tris-HCl, 1 mM DTT, 1 M NaCl, 0.05% Triton X-100, at pH 8.0, and supplemented with 500 μl of PIC, 500 μl of 100 mM PMSF, and 50 μl of 5 mg ml–1 DNAse) and then with wash-2 buffer (20 mM Tris-HCl, 1 mM DTT, 0.1 M l-arginine, at pH 8.0). The pellet was resuspended with the nickel-A buffer (25 mM Tris-HCl, 1 mM DTT, 50 mM NaCl, 8 M urea and 20 mM imidazole, at pH 8.0) and centrifuged for 30 min at 20,000 r.p.m. The supernatant was injected at room temperature into a nickel affinity column and eluted with a gradient from 0 to 100% of nickel-B buffer (25 mM Tris-HCl, 1 mM DTT, 50 mM NaCl, 8 M urea and 500 mM imidazole, at pH 8.0). The fractions with protein were pooled, and 1 mM EDTA was added. The sample was injected into a size exclusion Superdex 200 16/600 (GE Healthcare) column, running at 4 °C in size exclusion buffer (25 mM Tris-HCl, 1 mM DTT, 50 mM NaCl and 2 M urea, at pH 8.0). The fractions with protein were pooled and concentrated to approximately 150 μM. The sample was dialysed against the final buffer (20 mM sodium phosphate, 1 mM TCEP and 0.05% NaN3, at pH 8.0), fast frozen in liquid nitrogen and stored at −80 °C.

    Peptide for in vitro experiments

    The me4(GS)3me4 synthetic peptide with amidated or Cy3-modified C terminus and acetylated N terminus was obtained as lyophilized powder with >95% purity from GenScript. The peptide was dissolved in 6 M guanidine thiocyanate and incubated with agitation overnight at 25 °C. The sample was then centrifuged at 15,000 r.p.m. for 10 min. The supernatant was extensively dialysed against the final buffer (20 mM sodium phosphate, 1 mM TCEP and 0.05% NaN3, at pH 8.0)54. The peptide sample was then manipulated in the same way as the protein samples, as detailed below.

    Sample preparation for in vitro experiments

    All samples were prepared on ice as follows. First, a buffer stock solution consisting of 20 mM sodium phosphate buffer with 1 mM TCEP and 0.05% NaN3 was pH adjusted to 8.0 (unless otherwise indicated) and filtered using 0.22 μm sterile filters (buffer stock). A 1 M NaCl solution in the same buffer was also pH adjusted to 8.0 (unless otherwise indicated) and filtered (salt stock). The protein samples were then thawed from −80 °C on ice, pH adjusted to 8.0 (unless otherwise indicated) and centrifuged for 5 min at 15,000 r.p.m. at 4 °C. The supernatant (protein stock) was transferred to a new Eppendorf tube, and the protein concentration was determined by measuring its absorbance at 280 nm. The samples were prepared by mixing the correct amounts of buffer stock, protein stock and salt stock, as well as other indicated additives in the experiments, to reach the desired final protein and NaCl concentrations.

    Apparent absorbance measurement as a function of temperature

    The absorbance of the samples was measured at 350 nm (A350 nm) using 1 cm pathlength cuvettes and a Cary100 ultraviolet–visible spectrophotometer equipped with a multicell thermoelectric temperature controller. The temperature was increased progressively at a ramp rate of 1 °C min−1. The cloud point (Tc) values were determined as the maximum of the first-order derivatives of the curves, and the absorbance increase (ΔA) represents the difference between the maximum and the minimum absorbance values of the samples during the temperature ramp.

    For the experiment to quantify the reversibility of condensation, a 20 μM protein with 100 mM NaCl sample was prepared on ice. It was then split into 4 Eppendorf tubes and a temperature ramp was carried out with the first one after centrifugation for 2 min at 5 °C and 15,000 r.p.m. Once the Tc and ΔA for condensation had been determined, the other 3 samples were heated 10 °C above the Tc for 2.5 min and then cooled to 10 °C below the Tc for 5 more min. This procedure was repeated 1, 2, or 3 times for each sample. Next, the samples were centrifuged for 2 min at 5 °C and 15,000 r.p.m., and a temperature ramp was carried out to determine their respective Tc and ΔA values (Extended Data Fig. 7d).

    Microscopy in vitro

    For microscopy imaging, 1.5 μl of sample was deposited in a sealed chamber comprising a slide and a coverslip sandwiching double-sided tape (3M 300 LSE high-temperature double-sided tape of 0.17 mm thickness). The coverslips used had been previously coated with PEG-silane following a published protocol55. The imaging was always performed on the surface of the coverslip, where the condensates had sedimented.

    The DIC microscopy images were taken using an automated inverted Olympus IX81 microscope with a ×60/1.42 oil Plan APo N or a ×60/1.20 water UPlan SAPo objective using the Xcellence rt (v.1.2) software.

    For fluorescence microscopy experiments, the purified proteins were labelled with DyLight 488 dye (DL488, Thermo Fisher Scientific) or Alexa Fluor 647 dye (AF647, Thermo Fisher Scientific). The labelling, as well as the calculation of the labelling percentage and the determination of the protein concentration, was performed following the provider’s instructions. The final samples contained 0.5 µM of labelled protein and/or peptide out of the total indicated concentrations.

    FRAP experiments were recorded using a Zeiss LSM780 confocal microscope system with a Plan ApoChromat ×63/1.4 oil objective. Condensates of similar size were selected, and the bleached region was 30% of their diameter. The intensity values were monitored for different ROIs: ROI 1 (bleached area), ROI 2 (entire condensate) and ROI 3 (background signal). The data were fitted using EasyFrap software50 to extract the kinetic parameters of the experiment (recovery half-time and mobile fraction).

    Super-resolution microscopy images of the multimers and their time evolution were taken at 25 °C in a Zeiss Elyra PS1 LSM 880 confocal microscope using the Fast Airyscan mode with an alpha Plan ApoChromat ×100/1.46 oil objective. The pixel size was kept constant at 40 nm.

    Fluorescence microscopy images of the condensates and aggregates were taken at 37 °C in a Zeiss Elyra PS1 LSM 880 confocal microscope with an Airyscan detector using a Plan ApoChromat ×63/1.4 oil objective. The quantification of the aggregation process was done by image analysis using Fiji/ImageJ. The regions with the fluorescence signal not stemming from the background or the spherical condensates were selected. The percentage of the area of the field of view occupied by this selection corresponds to the aggregation value of the sample. The partitioning of the proteins in the condensates was calculated by image analysis using Fiji/ImageJ. The partitioning for each condensate was calculated by dividing the mean intensity of the condensate by the mean intensity of a ring of 1 μm thickness around the condensate.

    RNA for in vitro experiments

    The RNA used for in vitro experiments is a fragment of the 3′ UTR of cyclin B1 mRNA from X.laevis containing only one CPE site56,57, 5′-AGUGUACAGUGUUUUUAAUAGUAUGUUG-3′. We used it as a control to study whether it influences the properties of the condensates. RNA caused a slight decrease in the phase-separation propensity of both isoforms, larger for nCPEB4(NTD) than for nCPEB4Δ4(NTD), which we attribute to interactions with positively charged amino acids involved in the intermolecular interactions driving condensation (Extended Data Fig. 5f). Notably, however, the presence of RNA in the samples did not alter their propensity to aggregate (Extended Data Fig. 5g).

    Saturation concentration measurements

    Saturation concentration measurements of nCPEB4(NTD) and the histidine to serine mutants were carried out by incubating the samples at 40 °C for 5 min, followed by centrifugation at 5,000 r.p.m. for 1.5 min at 40 °C. The concentration of protein in the supernatant (csat) was determined by absorbance measurement at 280 nm.

    NMR spectroscopy

    The samples were prepared as indicated in the section ‘Sample preparation for in vitro experiments’ using isotopically labelled protein (15N- or 15N,13C-labelled). The prepared final samples were again pH adjusted to the desired value immediately before measurement. All the measurements were acquired at 5 °C using 3 mm NMR tubes with a sample volume of 200 µl.

    All NMR experiments, except the diffusion measurements, were carried out on a Bruker Avance NEO 800 MHz spectrometer equipped with a TCI cryoprobe. All NMR samples contained 100 μM protein concentration (unless otherwise indicated) in 20 mM sodium phosphate buffer with 1 mM TCEP, 0.05% NaN3, 7% D2O and 2.5 μM DSS for referencing, at pH 8.0 (unless otherwise indicated). Samples with denaturant agent contained the indicated concentrations of d4-urea.

    A 15N,13C-labelled sample at 280 μM for nCPEB4(NTD) or 200 μM for nCPEB4Δ4(NTD) with 4 M urea at pH 7.0 was used for backbone resonance assignment. A series of nonlinear sampled 3D triple resonance experiments were recorded, including the BEST-TROSY version58 of 1HN-detected HNCO, HN(CA)CO, HNCA, HN(CO)CA, HNCACB, HN(CO)CACB and (H)N(CA)NH. Also, additional 1Hα-detected HA(CA)CON and (HCA)CON(CA)H experiments59 were measured for nCPEB4(NTD). Backbone resonance assignments were performed using CcpNmr60 (v.2.4.2). The NMR assignments are available from the Biological Magnetic Resonance Data Bank (identifiers 51875 and 52346 for nCPEB4(NTD) and nCPEB4Δ4(NTD), respectively).

    pH titrations from 7.0 to 8.0 were carried out to transfer NH assignments to the final experimental conditions. Standard 2D 1H,15N-HSQC or BEST-TROSY experiments were measured at 7.0 ≤ pH ≤ 7.25. 2D 1H,15N-CP-HISQC61 experiments were used at pH ≥ 7.5 to reduce the effects of chemical exchange with water. For the urea titrations from 0 to 4 M at pH 8.0, 1H,15N-CP-HISQC experiments were measured. In the 1H,15N-CP-HISQC for the detection of arginine side-chain resonances, the 15N carrier was placed at 85 ppm, and 13C pulses for decoupling were centred at the chemical shift of 13Cδ (42 ppm) and 13C (158 ppm) arginine side chains.

    Standard 2D 1H,13C-HSQC experiments of 500 μM 15N,13C-labelled nCPEB4(NTD) were measured in the absence and presence of 4 M urea to monitor specific amino acid side chains easily identifiable by their typical 1H and 13C random coil chemical shifts.

    For histidine pKa determination, 2D 1H,13C-HSQC spectra of 75 μM 15N,13C-labelled nCPEB4(NTD) were measured in the presence of 4 M urea at pH values between 5.58 and 8.31. The pH-induced changes of the chemical shifts of histidine side chains (1H and 13C, both aliphatic and aromatic) were fitted to a sigmoid function to obtain an apparent pKa for all these histidine resonances in nCPEB4(NTD).

    Non-uniform sampled experiments were processed using qMDD62 (v.3.2). 2D 15N-correlations (1H,15N-HSQC, 1H,15N-CP-HISQC, BEST-TROSY) and 2D 1H,13C-HSQC were processed using NMRPipe63 and Topspin (v.4.0.8) (Bruker), respectively.

    15N-edited X-STE diffusion experiments64 of 100 μM 15N-labelled nCPEB4(NTD) in the absence and presence of 2 M urea were performed on a Bruker Avance III 600 MHz spectrometer equipped with a TCI cryoprobe. An encoding/decoding gradient length of 4.8 ms and a diffusion delay of 320 ms were used. The hydrodynamic diameter of nCPEB4(NTD) was estimated using dioxane as a reference molecule. Diffusion measurements under identical experimental conditions were carried out for dioxane, using in this case the PG-SLED sequence65. A gradient time (δ) of 1.6 ms and a diffusion time (Δ) of 70 ms were used. Diffusion coefficients were obtained by fitting the data to a mono-exponential equation using MestreNova (v.14.2.1-27684).

    Dynamic light scattering

    Dynamic light scattering (DLS) measurements were taken with a Zetasizer Nano-S instrument (Malvern) equipped with a He-Ne of 633 nm wavelength laser. Immediately before the measurement, the prepared samples were centrifuged for 5 min at 15,000 r.p.m. at 4 °C, and only the supernatant was subjected to measurement. Three measurements were performed for each sample, each of the measurements consisting of 10 runs of 10 s each. The experiments were carried out at 5 °C unless otherwise indicated. The deconvoluted hydrodynamic diameters arise from the mean of the peak of the intensity deconvolution of the data.

    Size exclusion chromatography coupled to multi-angle light scattering

    Size exclusion chromatography coupled to multiangle light scattering (SEC–MALS) experiments were performed by loading a 160 μM nCPEB4(NTD) with 0 mM NaCl sample into a Superose 6 increase 10/300 GL column (GE Healthcare) mounted on a Shimadzu Prominence Modular HPLC with a SPD-20 UV detector (Shimadzu) coupled to a Dawn Heleos-II multi-angle light scattering detector (18 angles, 658 nm laser beam) with an Optilab T-rEX refractometer (Wyatt Technology). The SEC-UV/MALS/RI system was equilibrated at 25 °C with 20 mM sodium phosphate buffer with 1 mM TCEP and 0.05% NaN3 at pH 8.0. Data acquisition and processing were performed using Astra 6.1 software (Wyatt Technology).

    Liquid-phase transmission electron microscopy

    Transmission electron microscopy (TEM) experiments were performed on a 50 μM nCPEB4Δ4(NTD) sample with 0 mM NaCl. The sample was first imaged in solid-state TEM using the same set-up as described below for liquid-phase TEM (LPEM). Pre-screening samples in solid-state TEM before the LPEM imaging procedure is routinely done to pre-screen the structures that will be imaged in liquid later. The sample with no stain was deposited onto 400 mesh Cu grids, which were plasma discharged for 45 s to render them hydrophilic and to allow optimal sample wettability.

    LPEM imaging was performed using a JEOL JEM-2200FS TEM microscope. The system was equipped with a field emission gun operating at 200 kV and an in-column Omega filter. The images were acquired with a direct detection device, the in-situ K2-IS camera (Gatan). The Ocean liquid holder, from DENSsolutions, was used to image the structure and dynamics of the specimens. The liquid samples were encased into two silicon nitride (SiXNy) chips. These chips had a 50-nm-thick SiXNy electron-transparent window of dimensions 10 × 200 μm. One of these chips had a 200 nm spacer that acts as a pillar and defines the liquid cell thickness, that is, z height, and hence the liquid thickness in the experiments. The chips were cleaned in HPLC-graded acetone followed by isopropanol for 5 min each to remove their protective layer made of poly(methyl methacrylate). Afterwards, the chips were plasma-cleaned for 13 min to increase their hydrophilicity. Next, 1.5 μl of non-stained sample was deposited on the previously prepared 200-nm-spacer chip. The drop-casted sample was enclosed by the spacer-less chip, thus sealing the liquid chamber. Then, 300 μl of the sample solution was flushed in the liquid holder at 20 μl min–1 with a syringe pump to ensure that the liquid cell inlet and outlet pipes were filled with the solution. We waited 5 min after collecting the sample solution from the outlet tube to minimize the convection effects from the flowing process. The liquid holder was introduced in the microscope, where imaging was performed in TEM mode and static conditions, that is, not in flow. To limit the electron beam dose (20 e Å–2) on the specimen, images were collected at the minimum spot size (number 5) with a small condenser lens aperture (CLA number 3). For our investigations, dose fractionation videos were recorded in counted mode at 20 frames per s with the K2 camera. Every image was recorded in the format of 4-byte greyscale and required the full size of the detector.

    The images and videos recorded were corrupted by noise, which significantly reduced the quality of the images, complicating any further analysis. Therefore, the Noise2Void (N2V) machine learning-based approach was adopted to overcome this problem66. Unlike the conventional machine learning-based approach, N2V reduces the noise of an image without any need for the corresponding noiseless image. This requirement makes the N2V ideal to process LPEM images, as noiseless images in liquid TEM are impossible to record. However, N2V requires an extensive dataset (also known as a training set) to fulfil its task, a common requirement to machine-learning-based approaches. Conventionally, the training set has to contain thousands of hundreds of images recorded with the same imaging settings to produce high-quality estimation of the noise distribution. Unfortunately, in our case, only single videos (image sequence) recorded at different imaging conditions were available. Therefore, the training set was created by sampling the image sequence every two frames to not bias the training process of the N2V. The remaining half of the image sequence was processed and used to derive the presented results.

    To train the N2V, 3,050 frames were selected, extracting 128 different non-overlapping squared patches (that is, portions of the pixels of the image) of 64 × 64 pixels from each of them. Moreover, the N2V was iterated for 100 epochs, a trade-off value between performances and processing time. The training was performed by extracting 128 random patches (64 × 64 pixels) from each training image. These values produced the best results in a short processing time.

    Molecular simulations

    Molecular dynamics simulations were performed using the single-bead-per-residue model CALVADOS (v.2)22,23 implemented in OpenMM (v.7.5)67. All simulations were conducted in the NVT ensemble at 20 °C using a Langevin integrator with a time step of 10 fs and friction coefficient of 0.01 ps−1. In our simulations, pH was modelled through its effect on the charge of the histidine residues (qHis)68.

    Direct coexistence simulations were performed with 100 chains in a cuboidal box of side lengths [Lx, Ly, Lz] = [25, 25, 300] nm. Simulations were run in n = 3 independent replicas for at least 55 µs each. The systems readily formed a protein-rich slab spanning the periodic boundaries along the x and y coordinates. The initial 2 µs of the simulation trajectories were discarded, and time-averaged concentration profiles along the z axis were calculated after centring the condensates in the box as previously described22.

    To model protein multimers, 400 chains were initially placed at random positions in a cubic box of side length 188 nm and simulations were run in n = 2 replicas for 16 µs each. The formation and dissolution of protein multimers was monitored using a cluster analysis implemented in OVITO69. Proteins were clustered on the basis of the distances between their centres of mass, using a cut-off of 1.5 times the average radius of gyration of the protein. Contact maps were calculated between a chain in the middle of the condensate or multimer and the surrounding chains. Contacts were quantified using the switching function c(r) = 0.5 – 0.5 × tanh[(r – σ0)/r0], where r is the intermolecular distance between two residues, σ0 = 1 nm, and r0 = 0.3 nm.

    To match the conditions of the experiments with which the simulation results are compared, direct coexistence and multimer simulations were performed at ionic strengths of 150 mM and 60 mM, respectively. Configurations were saved every 2 ns for slabs and every 5 ns for multimer simulations.

    Simulation trajectories were analysed using MDTraj70 (v.1.9.6) and MDAnalysis71,72 (v.1.1). The molecular visualizations presented in Fig. 2j were generated using VMD73 (v.1.9.4).

    Characterization of the multimers

    To investigate which specific residues of nCPEB4(NTD) drive its condensation, we used solution NMR spectroscopy, a technique that can provide residue-specific information on the conformation and interactions of intrinsically disordered proteins74. Indeed, when conditions are insufficient for condensation, the same interactions driving this process can cause the monomer to collapse into a state that can be characterized at residue resolution, thus providing this key information75. Under such conditions (Supplementary Fig. 5a), nCPEB4(NTD) had a spectrum characteristic of a collapsed intrinsically disordered protein, in which only 13% of the NMR signals were visible (Supplementary Fig. 5b, in light green). We analysed the sample by DLS to confirm its monomeric nature, but we detected only nCPEB4(NTD) multimers with a hydrodynamic diameter of approximately 55 nm, which is much larger than that predicted for a monomer76 (approximately 11 nm) (Supplementary Fig. 5c).

    To characterize the multimers, also known as clusters, which have also been observed for phase-separating proteins with intrinsically disordered domains77,78,79,80, we first determined whether their formation is reversible. To this end, we performed DLS analysis of increasingly diluted samples of nCPEB4(NTD) under the same solution conditions. We observed that at 0.5 µM, the multimers seemed to be in equilibrium with a species with a hydrodynamic diameter close to that predicted for the monomer (Extended Data Fig. 3e, in green). Next, at this concentration, we modified solution conditions to favour condensation by increasing the temperature and ionic strength, as well as by decreasing the pH. In all cases, we observed a decrease in the signal corresponding to the monomer and an increase in that corresponding to multimers, thus indicating a shift of the multimerization equilibrium (Extended Data Fig. 3e). This result suggests that the nCPEB4(NTD) multimers are stabilized by the same types of interactions as the condensates (Extended Data Fig. 1m and Fig. 2e,k).

    These findings prompted us to study whether these multimers grow over time to become condensates observable by optical and fluorescence microscopy, that is, whether they represent intermediates in the condensation pathway. To this end, we first analysed, over 15 h, samples of freshly prepared nCPEB4(NTD) multimers by DLS. We observed a progressive increase in size and polydispersity up to an average hydrodynamic diameter of approximately 90 nm and a polydispersity index of approximately 0.10 (Supplementary Fig. 5d). We also determined the morphology of the multimers at the nanoscale by LPEM, confirming that they are spherical and have a diameter of 30–50 nm (Extended Data Fig. 3f and Supplementary Fig. 5e). Finally, super-resolution microscopy confirmed that the multimers grow with time, thus becoming larger spherical particles resembling condensates (Extended Data Fig. 3g). It is possible that the nCPEB4 multimers here identified correspond to mesoscopic condensates, equivalent to those observed by optical microscopy, albeit smaller; however, as their dimensions preclude their thorough physical characterization, we consider it appropriate to consider them distinct species in this work.

    We next carried out experiments to determine the nature of the species giving rise to the residue-specific NMR signals observed in the presence of multimers. To this end, we analysed a sample of multimers by SEC–MALS. This approach showed that the multimers are assemblies of approximately 350 nCPEB4(NTD) molecules (Supplementary Fig. 5f), corresponding to a molecular weight of approximately 1.7 × 107 Da. Next, we performed 15N-edited X-STE experiments to measure the diffusion coefficient of the species giving rise to the signals detected by NMR, from which we derived that they diffuse much more slowly than a monomer, with a value in semi-quantitative agreement with that obtained by DLS and LPEM (Supplementary Fig. 5g), thereby indicating that they correspond mainly to multimers. We concluded that solution NMR can be used to identify the most flexible regions of the nCPEB4(NTD) sequence under conditions in which it forms multimers, presumably corresponding to those least involved in the interactions stabilizing them81,82,83.

    To assign the NMR signals to specific residues, we progressively added urea and observed that at 1.5–2 M, the urea concentration necessary to dissociate the multimers, the signals of most residues could be detected (Extended Data Fig. 3h,i and Supplementary Fig. 5b) and stemmed from a species with the diffusion coefficient expected for a nCPEB4(NTD) monomer (Supplementary Fig. 5g). A comparison of the spectra obtained in the absence and presence of denaturant revealed that the signals observed for the multimer corresponded to residues between positions approximately 50 and 150 in the sequence of nCPEB4(NTD): this region of sequence is devoid of aromatic and positively charged residues and instead rich in negatively charged ones (Extended Data Fig. 3h,j). Despite the presence of 4 M urea, the spectrum of monomeric nCPEB4(NTD) had a wide range of intensities. An analysis of signal intensity as a function of residue type revealed particularly low values for histidine and arginine (Extended Data Fig. 3k), which suggested that these residue types are involved in transient interactions and explain the very low signal intensity of the histidine-rich HClust (residues 229–252) and the arginine-rich me4 (residues 403–410) (Extended Data Fig. 3h).

    To facilitate the interpretation of these results, we monitored the formation of nCPEB4(NTD) multimers in molecular simulations performed using the CALVADOS model22,23. Contacts calculated between a chain in the centre of the multimer and the surrounding chains in assemblies of 130–170 chains showed that the C-terminal region, including HClust and me4, is more involved in intermolecular interactions than the N-terminal region rich in aspartate and glutamate residues (positions 72–147) (Extended Data Fig. 3l). The simulations therefore support the conclusion that the decreased NMR signal intensity in the C-terminal region reflects an increased number of contacts of these residues within the condensates. Finally, to further characterize the interactions stabilizing the multimers, we performed 1H,13C-HSQC experiments to analyse the intensity of side-chain signals without urea, when nCPEB4(NTD) is multimeric, and in 4 M urea, when nCPEB4(NTD) is instead monomeric (Extended Data Fig. 3m and Supplementary Fig. 5h–j). We observed that the intensities, especially those of the signals corresponding to histidine, tryptophan and arginine residues, are lower for the former than for the latter. We also performed 1H,15N-CP-HISQC experiments to study the arginine side-chain NH signals in the same samples and found that they are undetectable in the absence of the denaturant but can be observed in its presence (Supplementary Fig. 5k). Taken together, our results indicate that the multimers formed by nCPEB4(NTD) on the condensation pathway are stabilized mainly by interactions involving histidine and arginine residues, which are predominantly located in the C-terminal region (Supplementary Fig. 5l).

    Protein sequence analysis

    Cprofiler (http://www.cprofiler.org/) was used to determine the enrichment score of each amino acid type in the protein sequence compared with the DisProt3.4 database84,85. The protein sequences analysed correspond to residues 1–448 for nCPEB4(NTD) (UniProt identifier Q17RY0-2), residues 1–311 for CPEB2(NTD) (UniProt identifier Q7Z5Q1-3) and residues 1–452 for CPEB3(NTD) (UniProt identifier Q7TN99-1).

    Reporting summary

    Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

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  • Calcium-permeable AMPA receptors govern PV neuron feature selectivity

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    Mice and marmosets

    All procedures were approved by the Johns Hopkins Animal Care and Use Committee and conducted per the guidelines of the National Institutes of Health and the Society for Neuroscience. Hippocampal imaging experiments were carried out according to German national and institutional guidelines and approved by the ‘Tierversuchskommission’ of the Regierungspräsidium Freiburg (license number G16/037). Marmoset post-mortem tissue was obtained from terminal experiments approved by NIH Institutional Animal Care and Use Committees. The following mouse lines were used: PV-Cre30 (Jackson Laboratory (JAX), 008069), lsl-eGFP51 (JAX, 010701), lsl-eGFP-GluA2 (Extended Data Fig. 5), GluA2 KO39 (JAX, 002913), and GluA1 KO52 (JAX, 024422). We generated the ROSA26-lsl-eGFP-GluA2 mouse line by electroporating mouse embryonic stem (ES) cells with an engineered construct containing ROSA26-CAG-loxP-STOP-loxP-eGFP-Gria2-WPRE (adapted from targeting vector used to generate Ai14 mice53) and homologous recombination (Extended Data Fig. 5). We generated PV-Cre;lsl-eGFP-GluA2 (and PV-Cre;lsl-eGFP) mice from crosses with PV-Cre mice, born at Mendelian ratios. GluA2/– pups displayed lower body weight compared with wild-type littermates. They displayed occasional mortality, mitigated by separating the littermates from the parents to reduce litter sizes39. All lines were maintained on a mixed background composed primarily of C57BL/6J, and mice of both sexes were used for experiments. We maintained all animals on a 12-h light–dark cycle at 20–26 °C and 30–70% relative humidity.

    Constructs

    We used Q/R and R/G RNA-edited flip-isoform short c-tail rat Gria2 cDNA sequences for mutant animal generation and viruses unless otherwise stated. SEP-GluA2 and GFP-GluA2 fusion constructs were generated by amino-terminal insertion of SEP or GFP at four amino acids after the signal peptide padded with linker sequences, as in previously published constructs54. We generated the FUW-Cre construct by replacing the eGFP in FUGW with the Cre recombinase gene.

    pAAV.Syn.Flex.NES-jRGECO1a.WPRE.SV40 (ref. 55) was a gift from D. Kim and the GENIE Project (Addgene, plasmid 100853). The loxP/lox2272 sequences in the Flex cassette were inverted or exchanged with lox511/loxFAS to mitigate compatibility with other DIO AAVs. pAAV-CW3SL-eGFP56 was a gift from B.-K. Kaang (Addgene, plasmid 61463).

    To deliver large genes, such as the SEP-GluA2 fusion gene, with the high tropism and low cytotoxicity provided by AAV vectors, we heavily optimized vector components to allow larger transgene size. Using the short hSyn1 promoter (469 bp), abbreviated linker sequences and DIO sequences and an optimized WPRE+polyA signal (CW3SL, 425 bp)56, we generated a pan-neuronal Cre-dependent AAV expression vector with a minimal backbone (1,350 bp from inverted terminal repeat (ITR) to ITR without cargo) and large cargo capacity size (about 3.65 kb; based on an earlier estimation of 5 kb AAV genome size limit57; 3.85 kb when Cre dependency is not required). The loxP/lox2272 sites were spaced by a minimal 64 bp (5′ end-to-5′ end) to set the second recombination event distance (128 bp) above 118 bp, at which inefficient recombination has been reported, but at an exact multiple of the helical repeat length (10.6 bp). This repeat length allowed better-aligned loxP sites after DNA looping, thereby maximizing the efficiency of Cre-mediated excision58.

    As proof of principle, this study showed that SEP-GluA2 (3,378 bp), a large fusion protein previously only expressed through electroporation or lentiviral transfection, can be strongly expressed with this vector both in vitro and in vivo (Extended Data Fig. 7). The DIO-SEP-GluA2Q vector harboured Gria2 cDNA unedited at the Q/R editing site (R607Q)59. GluA2 Q/R RNA editing occurs at the pre-mRNA stage and requires a hairpin structure in the adjacent intron, which is absent in this vector. This structure bypasses RNA editing and expression of a calcium-permeable GluA2Q subunit. The DIO-eGFP control virus was similarly generated, replacing SEP-GluA2 with eGFP, for use as a control. These plasmids have been deposited to Addgene for distribution to the scientific community.

    AAV was produced by HHMI-Janelia Viral Tools using a PEI triple transfection protocol into AAV293T cells (an ITR-containing plasmid, 2/9 capsid helper from UPenn Vector Core and the E1-deleted pHelper plasmid from Agilent). The cells were grown under serum-free conditions (three 150 mm culture dishes at about 3 × 107 cells per dish for each 100 µl batch), purified by two rounds of CsCl density gradient centrifugation and exchanged into storage buffer (1× PBS, 5% sorbitol and 350 mM NaCl). Virus titres (GC per ml) were determined by qPCR targeting the AAV ITRs.

    Stereotaxic cranial surgeries

    We used stereotaxic surgery to inject viruses and to implant 4 mm square cranial windows over the left V1. Mice of mixed sex (>6 weeks old) were given carprofen (5 mg kg–1) or buprenorphine (sustained release; 0.5–1.0 mg kg–1) and dexamethasone (4 mg kg–1) for analgesia and were anaesthetized using avertin or isoflurane (1.5–2.5%). We made a craniotomy with a number 11 scalpel blade centred at 2.5 mm lateral and 3.4 mm posterior to bregma.

    For AAV injections, viruses were diluted with sterile PBS to 1–5 × 1013 GC per ml. We injected the solution at 5–10 sites spanning the posterior central area of the craniotomy (corresponding to the V1) with about 100 nl injections at each site at 250 μm below the dura surface. Injections were made using a bevelled glass pipette and a custom mineral oil-based injection system over 2–4 min. We left the pipette in place for another 2–3 min to allow diffusion and to prevent backflow.

    We placed a 4 mm square glass coverslip over the craniotomy and attached a stainless-steel head bar to the skull during surgery to allow rigid head-fixation during imaging. We allowed mice to recover for 1–2 weeks before imaging and handled them extensively to alleviate experiment-related stress.

    For hippocampal experiments, virus injections and cortical excavation or window implantation were done in separate surgeries. We made a small craniotomy over the hippocampus and injected 500 nl of AAV into the CA1 (anterior–posterior (AP): −2.0 mm; medial–lateral (ML) 2.0 mm; dorsal–ventral (DV): −1.4 mm). In the same surgical session, we implanted mice with a stainless-steel head plate (25 × 10 × 0.8 mm with an 8 mm central aperture) horizontally. We allowed mice to recover from surgery for at least 5 days before training sessions. We continued postoperative analgesic treatment with carprofen (5 mg kg–1 body weight) for 3 days after surgery.

    Cortical excavation and hippocampal imaging window implantation were performed >10 days after the initial virus injection per published protocols41. We made a craniotomy (diameter 3 mm) centred at AP −1.5 mm and ML −1.5 mm. Parts of the somatosensory cortex and posterior parietal association cortex were gently aspirated while irrigating with chilled saline. We continued aspiration until the external capsule was exposed. We then gently peeled away the outer part of the external capsule using fine forceps, leaving the inner capsule and the hippocampus undamaged. The imaging window implant consisted of a 3 mm diameter coverslip (CS-3R, Warner Instruments) glued to the bottom of a stainless-steel cannula (3 mm diameter 1.2–1.5 mm height). The window was gradually lowered into the craniotomy using forceps until the glass was in contact with the external capsule. The implant was then affixed to the skull using cyanoacrylate. We allowed mice to recover from window implantation for 2–3 days.

    Awake in vivo 2P fluorescence imaging

    We performed retinotopic mapping60,61 to verify the location of the V1 using optimized protocols and software (https://github.com/ingiehong/retinotopy). We conducted awake in vivo 2P imaging with a custom-built, resonant/galvo 2P laser-scanning microscope (Sutter Instrument) controlled by ScanImage (Vidrio Technologies) and light-proofed to allow imaging in ambient light during visual stimulation. The designs for the head-fixed imaging platform and lightproofing apparatus are available online (https://github.com/ingiehong/StackGPS). We imaged neurons in the L2/3 of monocular V1 expressing eGFP or SEP and jRGECO1a using a ×20/1.0 NA water-immersion objective (Zeiss) and a Ti:Sapphire laser (Coherent Chameleon Ultra; Spectra-Physics Insight X3) tuned at 930 nm or 1,040 nm, respectively, with 20–100 mW of power delivered to the back-aperture of the objective.

    We corrected the lateral motion of acquired image sequences using a rigid motion correction algorithm (NoRMCorre62). Neuronal somata with calcium transients were segmented using a constrained non-negative matrix factorization algorithm63. The source-separated GCaMP or jRGECO1a signal from each neuron was used to estimate various visual response properties of L2/3 neurons.

    Visual stimulation

    Visual stimuli were presented on a gamma-corrected 27″ LED monitor placed 22 cm in front of the centre of the eye contralateral to the hemisphere in which imaging was performed. The visual stimuli consisted of full-screen drifting gratings (4 s of duration, sinusoidal, 0.05 cycles per degree, 1 Hz, 100% contrast) following a 4-s iso-luminant grey screen. Six orientation gratings spaced at 30° were presented drifting in both directions orthogonal to the gratings (total of 12 directions) in a pseudo-randomized order to characterize sensory tuning using Psychtoolbox-3 (ref. 64) and FocusStack/Stimserver65. We used the average response during the 4 s of stimuli across 9–11 presentations to calculate visual responsiveness and orientation and direction selectivity. Visually responsive neurons were defined as cells with significant stimulus-related fluorescence changes (ANOVA across blank and 12 direction periods, P < 0.05)66.

    The orientation and direction tuning curve was constructed by measuring the mean ΔF/F, averaged over the stimulus period for each grating drifting direction θ, denoted as R(θ). The OSI was calculated for visually responsive units21,66,67 with slight modifications on previous definitions67 to avoid values outside the intended interval ([0 1]) and to accommodate occasional bona fide negative responses68,69,70. The preferred drifting direction (θpref) of the cell was determined as the stimuli that induced the greatest responses, \(R({\theta }_{{\rm{pref}}})\) and \({R(\theta }_{{\rm{oppo}}})\), as a sum where \({\theta }_{{\rm{oppo}}}={\theta }_{{\rm{pref}}+18{0}^{^\circ }}\), \(R({\theta }_{{\rm{pref}}}) > R({\theta }_{{\rm{oppo}}})\). The OSI was defined as follows:

    $$\begin{array}{c}{\rm{OSI}}=\frac{R({\theta }_{{\rm{pref}}})+R({\theta }_{{\rm{oppo}}})-R({\theta }_{{\rm{ortho}}+})-R({\theta }_{{\rm{ortho}}-})}{R({\theta }_{{\rm{pref}}})+R({\theta }_{{\rm{oppo}}})},\end{array}$$

    where θorth+ = θpref+90°, θorth– = θpref–90°. All response values were subtracted by the most negative R(θ) when negative responses were present (Rcorrected), which effectively ensured that the relative dynamic range of responses were reflected in the index for which they would otherwise distort the index (leading to values outside [0 1]), or be clipped (when negative values were discarded). Formally,

    $${R}_{{\rm{corrected}}}(\theta )=R(\theta )-\min (0,R({\theta }_{{\rm{pref}}}),R({\theta }_{{\rm{oppo}}}),R({\theta }_{{\rm{orth}}+}),R({\theta }_{{\rm{orth}}-}))$$

    Empirically, this modified index correlates tightly with the OSI calculated using the previous definition67 of orientation index and OSI, is bounded by [0 1] and accommodates tuning curves that are partially or entirely negative. Notably, the trends and results of statistical comparisons in this work did not change with the choice of index definition. The DSI, global OSI (gOSI) and global DSI (gDSI) were defined as follows:

    $${\rm{DSI}}=\frac{R({\theta }_{{\rm{pref}}})-R({\theta }_{{\rm{oppo}}})}{R({\theta }_{{\rm{pref}}})}$$

    $${\rm{gOSI}}=\frac{\left|{\sum }_{k}R({\theta }_{k}){e}^{i2{{\theta }}_{k}}\right|}{{\sum }_{k}R({{\theta }}_{k})}$$

    $${\rm{gDSI}}=\frac{\left|{\sum }_{k}R\left({\theta }_{k}\right){e}^{i{\theta }_{k}}\right|}{{\sum }_{k}R({\theta }_{k})}$$

    gOSI and gDSI gave the same conclusions as OSI and DSI (data not shown). Note that \({R}_{{\rm{corrected}}}\left(\theta \right)\) can also be used in gOSI and gDSI, with the same benefits.

    Head-fixed navigation and hippocampal imaging

    Mice implanted with hippocampal imaging windows were subjected to a custom head-fixed virtual reality environment as previously described41. It consisted of a spherical treadmill monitored by an optical sensor that translated motion on the treadmill into forward motion through the virtual environment. We adjusted the forward gain so that 4 m of distance travelled along the circumference of the treadmill equalled one full traversal along a simulated linear track displayed on monitors surrounding the mouse. The track consisted of textured walls, floors and other 3D-rendered objects at the sides of the track as visual cues. To motivate consistent behaviour, we administered soy-milk rewards (4 µl) when the animal traversed certain locations that were spread at fixed distances along the track, and animals were trained for 5–10 days until they displayed consistent running behaviour before commencing imaging experiments.

    Imaging was performed using a resonant/galvo high-speed laser scanning 2P microscope (Neurolabware) with a frame rate of 30 Hz for bidirectional scanning and a power of 5–20 mW measured at the objective front aperture. The microscope had an electrically tunable, fast z-focusing lens (Optotune, Edmund optics) to switch between z planes within less than a millisecond. Images were acquired through a ×16 objective (Nikon, 0.8 N.A., 3 mm WD). eGFP and jRGECO1a were excited at 930 nm or 1,040 nm, respectively, with a femtosecond-pulsed 2P laser (Mai Tai DeepSee, Spectra-Physics). We scanned 3 imaging planes (about 25 µm z spacing between planes) in rapid alternation so that each plane was sampled at 10 Hz. The planes spanned 300–500 µm in the x/y direction and were placed so that as many labelled neurons as possible were captured. We attached the animal’s head plate to the bottom of an opaque imaging chamber before each experiment to block ambient light from the photodetectors. We fixed the chamber in the behavioural apparatus with the animal. A ring of black foam rubber between the imaging chamber and the microscope objective blocked any remaining stray light.

    Spatial tuning analysis

    We motion-corrected all imaging data line-by-line71 with a 2D hidden Markov model using the software package SIMA71 or with block-wise non-rigid registration through the software package Suite2P72. If no suitable motion correction could be achieved, we discarded the data. To segment interneuron somata, regions of interest (ROIs) were manually drawn using ImageJ (NIH) or automatically drawn by applying Suite2P72. For automated ROI settings, the experimenter subsequently inspected individual ROIs. The average jRGECO1a signal over time was then obtained from each ROI for all runs. We restricted our analysis to mouse running periods with a minimum speed of 5 cm s−1. To obtain baseline-normalized ΔF/F calcium traces, we examined the fluorescence value distribution of the jRGECO1a signal and subtracted and divided the entire trace by the eighth percentile value of this distribution73. In rare instances, individual datapoints were below zero after baseline subtraction, and we set these negative values to zero for further calculations.

    To compute spatial vector tuning, we plotted the mean activity (ΔF/F) of each spatial bin at its respective angle from the start position on the circular track into a polar coordinate system (Fig. 4e and Extended Data Fig. 15c). We then computed the circular mean of this distribution to obtain the mean tuning vector length and angle of the cell. Spatial coherence (Fig. 4f) was determined as the correlation (Pearson’s R) between the mean fluorescence value in each 5-cm bin on the track and its two nearest neighbours, measuring the local smoothness of the spatial tuning curve74. To calculate spatial information (SI; Extended Data Fig. 15e), we computed the average calcium activity (mean ΔF/F) for each 5-cm-wide bin along the linear track to approximate the average firing rate of neurons in that location. SI was then calculated for each cell as \({\rm{SI}}=(\,{\sum }_{i=1}^{N}{\lambda }_{i}{\log }_{2}\frac{{\lambda }_{i}}{\lambda }{p}_{i})\) / λ, where λi and pi are the average calcium activity and fraction of time spent in the ith bin, respectively, λ is the overall calcium activity averaged over the entire linear track, and N is the number of bins on the track. Given the distribution of the underlying values, we plotted the log10 of SI values and compared them statistically (Extended Data Fig. 15e).

    To assess the stability of the spatial representation of a cell within a session, we divided the track into 5-cm bins and calculated the mean ΔF/F value for each bin while the animal was moving on the track with a speed >5 cm s–1 to obtain activity maps for each individual cell. This mapping was done separately for the first and second half of the recording session. We then computed the within-session stability as the cross-correlation between the mean activity maps of the first and second half of the session (Extended Data Fig. 15b,f). We also computed population vector correlations as a function of position in the first and second half of the recording (Extended Data Fig. 15g) to visualize the local similarity of population activity across time. Before computing these correlations, we re-normalized the map of each neuron by subtracting the mean over space and dividing by the standard deviation (z scoring) to mitigate the potential effects of mean rate differences between cells on assessing local population vector similarity.

    Quantification of Gria2 mRNA A-to-I editing rates

    We mapped the raw sequencing reads from a mouse brain scRNA-seq dataset (n = 1,679)14 to the mouse reference genome (GRCm38) with a gene annotation, GENCODE (v.M16)75, using STAR76. The uniquely mapped reads whose sequencing qualities (Phred score) were greater than 20 were counted for the QR and RG RNA-editing sites in Gria2. We filtered out samples if the proportions of the sequencing read with A or G alleles together accounted for less than 95% to avoid potential sequencing errors. We defined the RNA-editing rate for a given site as a ratio of the number of sequencing reads showing G relative to the number of reads with either A or G.

    FACS-assisted RNA-seq of PV interneurons

    To assess transcriptional changes specifically in PV interneurons after removing CP-AMPARs with RNA-seq, we sorted dissociated cortical PV interneurons by their GFP fluorescence using FACS. Dissociation of adult mouse brain neurons leads to a rapid decimation of viable PV interneurons77,78,79, which potentially biases downstream analyses to a select subpopulation of PV interneurons. Various proposed methods to mitigate PV interneuron loss failed to recover them at native cell frequencies in adult mice80. Several fixation-based FACS approaches have been proposed to target immune cells and neurons, but crosslinking leads to lower RNA yield for RNA-seq.

    We developed and used a brain-slice optimized workflow, FICSR-seq (Extended Data Fig. 11a), which recovers PV interneurons vulnerable to dissociation at native cell frequencies. We cut brain slices from adult mice (113.1 ± 11.6 days old) in NMDG cutting solution + trehalose77 and diced them into small pieces <1 mm3. Extracellular proteins were digested with pronase (2 mg ml–1; 8 U µl–1) at 34–37 °C, after which the slice pieces were fixed in 4% paraformaldehyde (PFA) in PBS (with 0.1 U ml–1 RNase inhibitor, Promega) for 15 min and dissociated into single cells through careful trituration. We filtered the single cells through a 40-μm filter, labelled them with the cell-permeable nuclear dye DRAQ5 (1:1,000 dilution) to identify nuclei-containing cells and then subjected them to FACS. DRAQ5+GFP+ or DRAQ5+GFP cells were sorted, and more than 20,000 cells were collected per mouse cortex to provide extensive coverage of low-expressing PV interneuron transcripts.

    We treated the fixed cells with proteinase K before RNA extraction (RecoverAll Total Nucleic Acid Isolation kit for FFPE, Thermo Fisher Scientific) to liberate RNA from protein–protein and protein–nucleic acid crosslinks generated by fixation. We prepared cDNA libraries from GFP+ and GFP samples (NEBNext Ultra RNA Library Prep kit for Illumina, NEB) from RNA enriched with mRNA through bead-based polyA selection. cDNA libraries were barcoded and sequenced together on an Illumina Hiseq 2500 sequencer, generating 150-bp paired-end reads. We processed RNA-seq reads with bcbio-nextgen (v.1.2.3; https://doi.org/10.5281/zenodo.3564938)81, aligning to GRCm38 with the STAR aligner76 and quantifying counts per gene with Sailfish82 using the Ensembl annotation. We used DESeq2 (ref. 83) to analyse differential expression.

    Brain slice preparation and whole-cell patch-clamp recordings

    To test post-critical period electrophysiological properties and to maintain consistency within experiments, we used mice of either sex, aged postnatal day 32 (P32)–P62 for studies of synaptic properties and aged P69–P77 for studies of intrinsic properties. We first anaesthetized mice of either sex using isoflurane. We rapidly removed their brains in an ice-cold sucrose solution containing the following (in mM): 76 NaCl, 25 NaHCO3, 25 glucose, 75 sucrose, 2.5 KCl, 1.25 NaH2PO4, 0.5 CaCl2 and 7 MgSO4, pH 7.3, 315 mOsm. We hemisected the brain along the midline and mounted one or both hemispheres on a 30° ramp. We then sectioned acute parasagittal slices of the visual cortex, 300-μm thick, in the same ice-cold sucrose-cutting solution using a vibratome (VT-1200s, Leica). Slices were incubated in warm (32–35 °C) sucrose solution for 30 min and then transferred to warm (32–35 °C) artificial cerebrospinal fluid (aCSF) composed of the following (in mM): 125 NaCl, 26 NaHCO3, 2.5 KCl, 1.25 NaH2PO4, 1 MgSO4, 20 d-(+)-glucose, 2 CaCl2, 0.4 ascorbic acid, 2 pyruvic acid and 4 l-lactic acid, pH 7.3, 315 mOsm. Slices were then allowed to cool to room temperature. For rectification measurements, we cut coronal slices with a NMDG-based cutting solution and incubated them for >15 min. Then we transferred them to aCSF (see the section ‘Analysis of AMPAR rectification’). All solutions were continuously equilibrated with 95% O2 and 5% CO2.

    We transferred slices to a submersion chamber on an upright microscope (Zeiss AxioExaminer; ×40 objective, 1.0 NA) and continuously superfused (2–4 ml min–1) them with warm (about 32–34 °C) oxygenated aCSF. We visualized neurons with a CCD camera (Sensicam QE, Cooke) using either infrared differential interference contrast (IR-DIC) microscopy or epifluorescence. The visual cortex was identified based on the relative position of the cortex and hippocampus and the anatomical borderline between the visual cortex and retrosplenial dysgranular cortex. We selected slices in which the apical dendrites of infragranular pyramidal neurons ran parallel to the plane of the slice up through L2/3 in the area targeted for recording. PV interneurons were targeted for recording based on eGFP or SEP-GluA2 expression along with unlabelled L2/3 pyramidal neurons. We filled patch pipettes (2–4 MΩ) pulled (P-97, Sutter Instrument) from borosilicate capillary glass (Sutter Instrument) with an internal solution containing (in mM): 2.7 KCl, 120 KMeSO3, 9 HEPES, 0.18 EGTA, 4 ATP magnesium salt, 0.3 GTP sodium salt and 20 phosphocreatine disodium salt, adjusted to pH 7.3, 295 mOsm. For recordings of PV interneurons, the internal solution included 0.25% w/v biocytin. Whole-cell patch-clamp recordings were obtained using Multiclamp 700B amplifiers (Molecular Devices) and digitized using an Instrutech ITC-18 (HEKA) and software written in Igor Pro (Wavemetrics). All signals were low-pass filtered at 10 kHz and sampled at 20–100 kHz. Neurons with an access resistance >30 MΩ or a resting membrane potential greater than −60 mV were not used for further recordings or analyses. The access resistance was not compensated in current clamp, and recordings were not corrected for the liquid junction potential.

    Analysis of intrinsic excitability, synaptic connectivity and synaptic plasticity

    We measured the resting membrane potential (RMP) shortly after establishing the whole-cell current-clamp recording configuration. A 1-s hyperpolarizing current (−100 pA) pulse was used to calculate the input resistance of recorded neurons. To assess the spiking behaviour of the cell, we injected 1-s depolarizing current steps into the recorded neurons. We measured the current–spike frequency relationship with a range of depolarizing current steps presented in pseudorandom order (1-s long, 40-pA increments, 5-s inter-stimulus intervals). Each current intensity was tested three times. For each current intensity, we counted the total number of action potentials exceeding an amplitude of 0 mV generated during each current step, then averaged the values across the three trials. We determined the rheobase by first probing the response of the neuron with 1-s-long depolarizing steps (5-s inter-stimulus intervals) to define a small range of current steps that bounded the rheobase. We then tested the neuron response within this range using 1-s-long depolarizing steps with 1-pA increments. We measured action potential properties from single spikes evoked by rheobase current injections. To compare the current–spike frequency relationship and rheobase between cells from the same baseline, we held cell membrane potentials at −70 mV when injecting depolarizing current steps. We performed all electrophysiological recordings that were assessing the intrinsic properties of PV interneurons in the presence of the following blockers of glutamate and GABA receptors (all from Tocris Bioscience): 5 µM NBQX (AMPA receptor antagonist); 5 µM (RS)-3-(2-carboxypiperazin-4-yl)-propyl-1-phosphonic acid (NMDA receptor antagonist); and 10 µM 6-imino-3-(4-methoxyphenyl)-1(6H)-pyridazinebutanoic acid hydrobromide (SR95531; GABAA receptor antagonist).

    To determine the properties of unitary synaptic connections among neurons, we generated two action potentials in the presynaptic neuron by injecting short, depolarizing current steps (3-ms pulse duration, 20 Hz, 10-s inter-trial interval). We held pyramidal neurons and PV interneurons at approximately −55 mV and −70 mV during synaptic connectivity tests to detect inhibitory postsynaptic potentials (IPSPs) and EPSPs, respectively. We assessed synaptic connectivity (EPSP or IPSP) with an average of 10–50 trials. A synaptic connection was detected if the first response amplitude of the average trace was >3 times the root mean squared of the average trace during baseline conditions and visually verified. We calculated the paired-pulse ratio by dividing the amplitude of the second postsynaptic potential by the first.

    We subjected a subset of connected pyramidal→PV pairs, all of which exhibited an average EPSP amplitude of >0.3 mV at baseline, to an anti-Hebbian protocol. After recording 50 traces (6 Hz) as a baseline, we induced synaptic plasticity by pairing 400 presynaptic action potentials delivered at 5 Hz with continuous hyperpolarization of the postsynaptic PV interneuron to –90 mV25,84. After induction, EPSPs were recorded under the same conditions as the baseline measurement (50 traces in response to presynaptic action potentials, 6 Hz).

    Analysis of AMPAR rectification

    To measure AMPAR rectification85,86,87,88, we cut coronal brain slices in ice-cold cutting solution containing (in mM) 96 NMDG, 2.5 KCl, 1.25 NaH2PO4, 25 NaHCO3, 25 d-(+)-glucose, 10 MgSO4, 0.5 CaCl2, 96 HCl, 20 HEPES, 12 N-acetylcysteine and 5 sodium l-ascorbate, and oxygenated with carbogen gas (95% O2 and 5% CO2). The 300-µm-thick slices were kept in aCSF (125 NaCl, 2.5 KCl, 2 MgCl2, 2 CaCl2, 1.0 NaH2PO4, 26.2 NaHCO3 and 11 glucose) and oxygenated with carbogen gas at 23–25 °C until they were transferred for recording to a submerged chamber superfused with aCSF (1–3 ml min–1) supplemented with about 50 µM picrotoxin and 100 μM APV (2-amino-5-phosphonovaleric acid) to isolate AMPAR-mediated excitatory synaptic transmission.

    We made targeted whole-cell recordings of eGFP/SEP-GluA2-positive L2/3 PV interneurons using pipettes of 3–5 MΩ resistance. The intracellular solution contained (in mM): 115 CsMeSO4, 0.4 EGTA, 5.0 TEA-Cl, 1 QX314, 2.8 NaCl, 20 HEPES, 3.0 ATP magnesium salt, 0.5 GTP sodium salt, 10 phosphocreatine disodium salt and 0.1 spermine and was adjusted to pH 7.2, 285–290 mOsm. When we achieved whole-cell mode, we allowed >5 min for dialysis of the intracellular solution before collecting data. We held cells at −70 mV holding potential and recorded them at room temperature. We left the junction potential (about 11 mV) uncorrected. Signals were measured with a MultiClamp 700B amplifier, digitized using a Digidata 1440A digitizer (Molecular Devices) at 20 kHz and acquired with pClamp 10 software (Molecular Devices). We recorded AMPAR currents at 11 membrane potentials to construct a current–voltage (IV) plot (Vh = −60 to +60 mV, except for a subset of pyramidal neurons recorded for comparison up to +50 mV). We calculated the rectification index as a weighted ratio of negative (−60 mV) and positive (+60 mV) currents. We compensated for the junction potential (11 mV): rectification index (RI) = (I–60 mV/–71)/(I+60 mV/49). An AMPAR rectification index of 1 represented perfect linearity, whereas values <1 indicate inward rectification. We estimated the reversal potential (Erev) by cubic polynomial regression that fitted the linear, rectifying and double-rectifying AMPAR IV curves well.

    Immunohistochemistry

    We deeply anaesthetized mice with isoflurane then transcardially perfused them with PBS and 4% PFA. We removed and post-fixed the brain in 4% PFA–PBS for >2 h. We sectioned the brain coronally into 25 μm slices using a vibratome (VT-1000, Leica). We acquired marmoset brains post-mortem from terminal experiments and sliced them into 40 µm sections. Free-floating sections underwent antigen retrieval using LAB solution (Polysciences) when necessary and were blocked and permeabilized in 3% BSA with 0.3% Triton X-100 in PBS for 1 h at room temperature. We incubated sections with primary antibodies overnight at 4 °C, washed them with PBS 3 times for 5 min, and then incubated them with secondary antibodies for 2 h at room temperature. After another round of washes, we mounted the slices on glass slides in PermaFluor mounting medium (Thermo Fisher Scientific) and imaged them using a laser scanning confocal microscope (Zeiss LSM880). Controls were carefully carried out, including antibody staining of homozygous knockout mice (Extended Data Fig. 2) to ensure antibody specificity. For GluA1 and GluA2 quantification, ROIs were made around cell somas, and the background signal was subtracted to estimate protein levels.

    The following primary antibodies were used: rabbit anti-parvalbumin (1:2,000, PV25, Swant); goat anti-parvalbumin (1:1,000, PVG-213, Swant); rat anti-somatostatin (1:200, MAB354, Chemicon); mouse anti-CaMKIIα (1:1,000, sc-32288, Santa Cruz); rabbit anti-GluA1 (1:1,000, JH4294, generated in-house); mouse anti-GluA2 (1:5,000; clone 15F1, gift from E. Gouaux); chicken anti-GFP (1:1,000, GFP-1020, Aves); and rabbit anti-dsRed2 (1:1,000, 632496, Clontech). The following secondary antibodies were used: Alexa Fluor 405 donkey anti-goat (1:1,000, ab175665, Abcam); Dylight 405 goat anti-mouse IgG2a (1:1,000, 115-477-186 Jackson ImmunoResearch); Alexa Fluor 488 goat anti-mouse IgG2a (1:1,000, A-21131, Thermo Fisher Scientific); Alexa Fluor 488 goat anti-chicken (1:1,000, A-11039, Thermo Fisher Scientific); Alexa Fluor 546 goat anti-rabbit (1:1,000, A-11035, Thermo Fisher Scientific); Alexa Fluor 568 goat anti-mouse IgG1 (1:1,000, A-21124, Thermo Fisher Scientific); Alexa Fluor 568 goat anti-rabbit (1:500, Thermo Fisher Scientific); Texas Red donkey anti-goat (1:1,000, SAB3700332, Millipore Sigma); Alexa Fluor 647 goat anti-rabbit (1:1,000, A-21245, Thermo Fisher Scientific); Alexa Fluor 647 goat anti-mouse IgG2a (1:1,000, A-21241, Thermo Fisher Scientific); Alexa Fluor 647 donkey anti-goat (1:1,000, A-21447, Thermo Fisher Scientific); and Alexa Fluor 647 goat anti-rat (1:500, A-21247, Thermo Fisher Scientific).

    Computational modelling

    The low feature selectivity of PV neurons17,18,19,20,21,89 (but see refs. 22,90,91,92) and the enhancement in PV-Cre;lsl-eGFP-GluA2 mice could result from several mechanisms. We used computational models to identify which mechanisms are consistent with the observed link between CP-AMPARs and feature selectivity. We examined the impact of three observed electrophysiological circuit changes: (1) increased intrinsic excitability (Extended Data Fig. 10o); (2) the loss of inward-rectifying AMPARs (Extended Data Fig. 7e,f); and (3) enhanced LTD (Extended Data Fig. 10l). Each mechanism was incorporated into a variation of a common base model. This model comprises a single PV neuron receiving excitatory inputs from a set of presynaptic pyramidal neurons with predefined stimulus tuning (Fig. 5a). The output of the PV neuron is a firing rate that is computed as a weighted sum of the inputs. Negative inputs are rectified to ensure a positive firing rate. To endow the PV neuron with stimulus tuning, pyramidal–PV connectivity was modelled as bell-shaped around the preferred orientation of the PV neuron (Fig. 5b), which enabled these neurons to inherit their tuning from pyramidal cells (Fig. 5c). We adjusted the parameters of pyramidal selectivity and connectivity to match the observed PV (and pyramidal) selectivity in the data.

    Modelling increased intrinsic excitability

    PV interneurons without CP-AMPARs showed increased intrinsic excitability (Extended Data Fig. 10o). PV neuron activation typically requires the coincident activation of multiple excitatory synaptic inputs93,94. However, the reduced rheobase, and increased RMP and input resistance in PV-Cre;lsl-eGFP-GluA2 mice suggested some strong synapses may reach the activation threshold unilaterally, which may increase selectivity95. To test whether this alone could account for the increased stimulus selectivity of PV interneurons, we increased the excitability of the PV model neuron by introducing a positive baseline current to the PV cell, mirroring the empirical shift of the frequency–current (FI) curve (Extended Data Fig. 16a,b). We discovered that increased excitability reduced stimulus selectivity, contradicting the experimental observation. The response of the PV neuron was increased for all stimuli, thereby reducing the relative magnitude of the preferred response when compared with non-preferred responses (Extended Data Fig. 16c). This held for any rise in intrinsic excitability, regardless of a potential reduction in unitary EPSP amplitude (Extended Data Fig. 10f) when implemented as synaptic scaling (Extended Data Fig. 16d). We also simulated a scenario whereby enhanced intrinsic excitability was adjusted such that it homeostatically maintained the mean rate of the neuron by compensating for a multiplicative decrease in EPSPs (Extended Data Fig. 16e). In this scenario, stimulus selectivity was also reduced (Extended Data Fig. 16f–h). In conclusion, nonselective mechanisms such as increased intrinsic excitability and synaptic downscaling are insufficient to increase stimulus selectivity in the model.

    Modelling removal of inward-rectifying AMPAR current

    CP-AMPARs are inward-rectifying, which means that their conductance decreases with increasing postsynaptic potential (Extended Data Fig. 7e,f). This implies that they could become less effective for coincident stimuli that induce a strong postsynaptic response. To model this effect, we introduced a dependence of synaptic weights on the postsynaptic potential of the PV interneuron. In this model, we used conductance instead of current-based synapses to allow for a better comparison with experimentally measured current–voltage relationships. We modelled each synaptic weight as the sum of two components (Fig. 5d). The first represents CP-AMPARs and weakens with increasing postsynaptic potential. The second symbolizes other calcium-impermeable AMPARs unaffected by postsynaptic potential (Fig. 5d, dashed line), except due to changes in synaptic drive. We systematically varied the amount of CP-AMPARs relative to calcium-impermeable AMPARs and the membrane potential at which they inactivate (inactivation threshold). The intuition behind CP-AMPARs influencing stimulus selectivity is that they should remain open for weak (that is, non-preferred) stimuli but deactivate for strong (that is, preferred) stimuli. PV neurons fire at high frequencies, which makes this more relevant, and compartmentalized dendritic depolarizations could further exacerbate this effect. This would selectively enhance the response to non-preferred stimuli, thus reducing stimulus selectivity. Conversely, eliminating CP-AMPARs would enhance stimulus selectivity. Indeed, we observed that removing the CP-AMPAR component reduced the response to non-preferred stimuli without affecting preferred stimuli, thereby increasing stimulus selectivity (Fig. 5e,f and compare with Extended Data Fig. 9c and Fig. 2e). This effect was robust to variations in the relative abundance of the CP-AMPARs and their inactivation threshold (Fig. 5g).

    A qualitatively similar outcome emerged from applying a previously measured empirical IV curve from Gria2–/– mice96 to estimate inward rectification (Extended Data Figs. 16 and 7e,f). Systematically varying the proportion of CP-AMPARs in the PV neuron model revealed that orientation selectivity monotonically decreases as the proportion of CP-AMPARs increases (Extended Data Fig. 16f). Two previous papers have examined the potential impact of CP-AMPARs on postsynaptic activation from slightly different perspectives of EPSC kinetics and dendritic summation sublinearity93,97, and both arrived at conclusions similar to ours. In conclusion, increased stimulus selectivity may be due to the removal of CP-AMPAR-mediated inward rectification.

    Modelling increased LTD

    Pyramidal–PV connections exhibited exaggerated LTD in PV-Cre;lsl-eGFP-GluA2 mice compared with control mice (Extended Data Fig. 10l). This could enhance selectivity by weakening synaptic inputs from pyramidal cells tuned to non-preferred stimuli. We modelled this scenario by introducing synaptic plasticity in the pyramidal–PV synapses. Synaptic weights changed according to a Bienenstock–Cooper–Munro (BCM) rule, which has been broadly studied as a model for the development of stimulus selectivity98. The BCM learning rule is an associative rule that changes synapses when the presynaptic (pyramidal) neuron and the postsynaptic (PV) neuron are simultaneously active. However, the direction of the change is determined by the postsynaptic firing rate. When PV activity is below a threshold, synaptic efficacy decreases. If PV activity surpasses the threshold, synaptic efficacy increases (Fig. 5h). Here we used a fixed instead of the typical activity-dependent threshold in the classical BCM model. This allowed us to test the effect of increased LTD by varying the threshold. Specifically, we increased the LTP–LTD threshold to model the exaggerated LTD in PV-Cre;lsl-eGFP-GluA2 mice (Fig. 5h and Extended Data Fig. 10l). This weakened synapses from pyramidal cells activated for stimuli that elicit only a weak response in the PV cell (Fig. 5i). The exaggerated LTD consequently reduced the PV response to non-preferred stimuli (Fig. 5j) while enhancing its response to preferred stimuli. The resulting boost in selectivity was observable across a wide range of LTD–LTP thresholds as long as the threshold was within the range of PV responses (Fig. 5k). We conclude that increased selectivity could arise from changes in synaptic plasticity if this plasticity, in a BCM-like manner, can generate both potentiation and depression, and if depression is exaggerated after the removal of CP-AMPARs.

    Conclusions of modelling studies

    These modelling studies demonstrate that the inward-rectifying nature of the CP-AMPAR ion channel and the exaggerated LTD observed in PV-Cre;lsl-eGFP-GluA2 mice can both effectively reduce responses to non-preferred stimuli, thereby accounting for the increases in orientation selectivity. However, neither the rise in intrinsic excitability nor a potential general reduction in excitatory input in PV interneurons due to GluA2 expression can explain the increase in orientation selectivity. These modelling findings imply that acute rectification and cumulative plasticity triggered by resident CP-AMPARs may sufficiently account for their role in maintaining low selectivity. Determining the extent of contribution of these two mechanisms to sensory selectivity in vivo poses a challenging question, which will necessitate rigorous empirical investigation in the future.

    Network modelling architecture

    The model was a feed-forward rate network of n presynaptic pyramidal neurons and a single postsynaptic PV neuron. We first describe the base model and then its elaborations. The presynaptic pyramidal neurons were tuned to stimulus direction and orientation according to a mixture of von Mises distributions. Specifically, the response of the ith pyramidal cell to a moving grating with direction θ was given by the following:

    $${r}_{i}(\theta )\propto (1-\alpha )\cdot \exp (\kappa \cdot \cos (\theta -{\theta }_{i})+\alpha \cdot \exp (\kappa \cdot \cos (\theta -{\theta }_{i}-180))$$

    The proportionality sign indicates a normalization between a minimum of 0 and a maximum of 1 across stimuli. Here θi is the preferred direction of the cell, κ determines its tuning width and α controls the strength of direction tuning (κ = 2 and α = 0.5). The preferred directions of the pyramidal cells were equally spaced in the interval [0,2π). The tuning of the PV cell was determined by the pyramidal tuning and the pyramidal-to-PV connectivity. Without loss of generality, we defined the preferred orientation of the PV cell to be 0°. The connectivity from the ith pyramidal cell onto the PV cell was given by a single von Mises distribution:

    $${w}_{i}\propto \exp (\kappa \cdot \cos (-{\theta }_{i})),\kappa =3$$

    Weights were normalized across presynaptic cells, such that the minimum and maximum weights were equal to 0 and 1, respectively. The connectivity and pyramidal response together defined the PV voltage and rate using the following equations:

    $$\tau \frac{{\rm{d}}u}{{\rm{d}}t}=-\,u\left(t\right)+\mathop{\sum }\limits_{i=1}^{n}\,{w}_{i}{r}_{i}\left(\theta \right)$$

    Here, τ = 10 ms denotes the membrane time constant. To simulate the PV activity from these equations, we used forward Euler discretization with a time step Δt = 1 ms. We simulated a time T = 100 ms unless specified otherwise and confirmed that the system had reached its steady state. This steady-state activity was used to compute tuning curves.

    Intrinsic excitability

    We fitted the change in the empirical IF curve by numerically finding the shift that minimized the squared difference between the PV-Cre;lsl-eGFP-GluA2 and the PV-Cre;lsl-eGFP mean values. This was done using the minimize_scalar method of SciPy99 with the shift as the optimization parameter. In the model, we increased the intrinsic excitability by adding an untuned positive baseline input I0:

    $$\tau \frac{{\rm{d}}u}{{\rm{d}}t}=-\,u\left(t\right)+\mathop{\sum }\limits_{i=1}^{n}\,{w}_{i}{r}_{i}\left(\theta \right)+{I}_{0}.$$

    We varied I0 between 0 and 10. Note that firing rates, membrane potential, weights and currents are unitless in our model. This does not alter the results, because orientation tuning is assessed based on relative rates. Decreases in unitary EPSPs were modelled by downscaling the synaptic weights with a factor p:

    $$\tau \frac{{\rm{du}}}{{\rm{d}}t}=-\,u\left(t\right)+p\cdot \mathop{\sum }\limits_{i=1}^{n}\,{w}_{i}{r}_{i}\left(\theta \right)+{I}_{0}.$$

    We downscaled the weights in two different ways. In Extended Data Fig. 16d, we used p = 0.62, reflecting the mean empirical reduction in EPSPs (Extended Data Fig. 10f). To investigate the effect of homeostatic increases in excitability, we used the minimize_scalar function to find the scaling that would keep the average PV rate constant given a specific increase in its excitability I0.

    Inward rectification

    We modelled the inward-rectifying calcium currents by adding a voltage-dependent weight scaling p(u) to the PV dynamics. We also introduced conductance-based synapses to allow for a better comparison with experimental data:

    $$\tau \frac{{\rm{d}}u}{{\rm{d}}t}=-\,u\left(t\right)+p\left(u\right)\cdot \mathop{\sum }\limits_{i=1}^{n}\,{w}_{i}{r}_{i}\left(\theta \right)\cdot \frac{{u}_{0}-u}{{u}_{0}}.$$

    Here, u0 = 30 is the reversal potential. In our simulations, the precise value of u0 and the choice for conductance versus current-based synapses scale the postsynaptic responses without strongly affecting relative stimulus tuning in different conditions. The scale p smoothly increases for decreasing voltages:

    $$p(u)=1+\frac{A}{2}\cdot [\tanh (\,-\,\beta (u-M))+1].$$

    This is a decreasing sigmoid function between 1 and A, with a slope β and a midpoint M. The midpoint M describes the threshold potential at which the CP-AMPARs deactivate, and β how sensitive the inactivation is to the membrane potential. A quantifies the abundance of rectifying AMPARs relative to the number of non-rectifying AMPARs. We varied A between 0 and 3 and M between 0 and 5; we fixed β to 0.5. The removal of CP-AMPARs was modelled by fixing p to 1. We increased the width of the presynaptic tuning to κ = 3.6 to achieve approximately equal selectivity in the presence of rectification.

    In addition to this idealized model of inward rectification, we also simulated a data-driven model. Our starting point were previously measured current–voltage relationships96 (Extended Data Fig. 16i). These data were collected in excitatory cells of wild-type and Gria2–/– mice, which allowed for a direct comparison of calcium permeable (CP) and calcium-impermeable (CI) receptors. Specifically, we used these published measurements96 to estimate the normalized conductance at each voltage as the ratio I/V (Extended Data Fig. 16j). We did this for both wild-type and GluA2 traces, and normalized each between 0 and 1. This resulted in scaling factors \({p}_{{\rm{CP}}}\left(u\right)\) and \({p}_{{\rm{CI}}}\left(u\right)\) that represent the strength of CP and CI receptors, respectively, in our model (Extended Data Fig. 16k). Their convex sum determined the total synaptic rectification:

    $$p\left(u\right)=\lambda {\cdot p}_{{\rm{CP}}}\left(u\right)+\left(1-\lambda \right)\cdot {p}_{{\rm{CI}}}\left(u\right).$$

    We found that orientation selectivity slowly but monotonically decreased with increasing λ (Extended data Fig. 16l–n). In the data-driven model, neurons with a larger relative abundance of CP receptors therefore have a weaker orientation selectivity, consistent with the idealized model and with our experimental findings.

    Plasticity

    We modelled synaptic plasticity using a plasticity rule inspired by BCM theory98. According to BCM, the change in synaptic efficacy is given by:

    $$\Delta w=\eta \cdot {r}_{\text{pre}}\cdot {r}_{\text{post}}\cdot ({r}_{\text{post}}-{\theta }_{{\rm{BCM}}}).$$

    Here η = 0.02 is a small learning rate that controls the speed of learning but does not affect the outcome. rpre and rpost are the presynaptic and postsynaptic rates, respectively, and θBCM is the threshold between LTD and LTP. In most applications of the BCM rule, this threshold is adaptive and depends on the recent PV activity. Here we fixed it to a single value per experiment to allow full control over the amount of LTD. Specifically, LTD was implemented by increasing the threshold from 8 to 10 Hz. We further varied the threshold between 6.5 and 11 Hz. As the empirical response distribution seems to be largely unaffected by CP-AMPAR removal, we added synaptic scaling100 to keep the mean postsynaptic rate constant:

    $$w\to w\cdot \frac{{r}^{* }}{\bar{r}}.$$

    Here r* is the target mean rate, which we fixed to the mean rate across stimuli before the onset of plasticity. The mean rate \(\bar{r}\) was computed after every weight update by averaging across all stimuli. In the plasticity experiments, we first simulated T = 100 time steps without plasticity to allow the system to reach a steady state. At subsequent time steps, we computed Δw for each individual stimulus, and used the average Δw across stimuli to update the weights. This continued until the weights and rates converged to a new steady state.

    Statistical analysis and reproducibility

    We performed statistical tests in Matlab (Mathworks), Prism (GraphPad) or R. Data distributions were tested for normality using Shapiro–Wilk test. We used parametric tests if the data were normally distributed and nonparametric otherwise, as detailed in the text describing each comparison. For parametric tests, we used unpaired or paired t-tests and one-way or two-way ANOVA tests with Tukey’s post hoc multiple comparison correction (all two-sided). For data that did not follow normal or log-normal distributions, we used the following statistical tests where appropriate: Mann–Whitney U-test (Wilcoxon rank-sum test), Kruskal–Wallis one-way ANOVA with Dunn’s post hoc multiple comparison correction (all two-sided). For categorical data, we used Fisher’s test or χ2 with or without Yates correction according to degrees of freedom and sample size. We report centre and spread values as the mean ± s.e.m. or median ± interquartile range unless otherwise stated. We did not use statistical methods to plan sample sizes, but used sample sizes similar to those frequently used in the field. The text or figure legends include the number of animals and cells. We did not use randomization, and data collection and analyses were not performed blind to the conditions of the experiments unless otherwise stated. P values < 0.05 were considered to be significant. When we used a statistical test, the P value is noted either in the manuscript text or depicted in figures and legends as follows: *P < 0.05, **P < 0.01, ***P < 0.001, ****P < 0.0001, NS, not significant, P ≥ 0.05. Representative examples such as traces and micrographs were chosen from at least three or more independent experiments.

    Reporting summary

    Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

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