Astrocyte morphogenesis requires self-recognition

Self-recognition is a fundamental cellular process across evolution and forms the basis of neuronal self-avoidance1–4. Clustered protocadherins (Pcdh), comprising a large family of isoform-specific homophilic recognition molecules, play a pivotal role in neuronal self-avoidance required for mammalian brain development5–7. The probabilistic expression of different Pcdh isoforms confers unique identities upon neurons and forms the basis for neuronal processes to discriminate between self and non-self5,6,8. Whether this self-recognition mechanism exists in astrocytes, the other predominant cell type of the brain, remains unknown. Here, we report that a specific isoform in the Pcdhγ cluster, γC3, is highly enriched in human and murine astrocytes. Through genetic manipulation, we demonstrate that γC3 acts autonomously to regulate astrocyte morphogenesis in the mouse visual cortex. To determine if γC3 proteins act by promoting recognition between processes of the same astrocyte, we generated pairs of γC3 chimeric proteins capable of heterophilic binding to each other, but incapable of homophilic binding. Co-expressing complementary heterophilic binding isoform pairs in the same γC3 null astrocyte restored normal morphology. By contrast, chimeric γC3 proteins individually expressed in single γC3 null mutant astrocytes did not. These data establish that self-recognition is essential for astrocyte development in the mammalian brain and that, by contrast to neuronal self-recognition, a single Pcdh isoform is both necessary and sufficient for this process.

plasma membrane, promoting trans interactions between processes expressing the same but not different combinations of isoforms 6,15,16 .As non-self processes all have different combinations of isoforms, mismatches prevent interactions between partially matching sets of Pcdh proteins on opposing membranes 6,15 .This cis-mediated mechanism plays a key role in regulating self-recognition speci city.
In the course of analyzing transcriptomic data from the cortex [17][18][19] , we were surprised to nd that one Pcdh isoform, γC3, exhibited high and preferential expression in mature astrocytes in both mice and humans (Fig. 1b,c).Although neurons, oligodendrocytes, and microglia in mice also express γC3, they do so at much lower levels and, in addition, express other isoforms 5,[20][21][22] (Fig. 1b).γC3 in mouse is the predominant isoform expressed in astrocytes across 13 different brain regions 23 (Fig. 1c).This isoform is also selectively expressed in human astrocytes (Fig. 1c).Thus, whereas most neurons express different combinations of Pcdh isoforms in a largely probabilistic fashion 5,6 , astrocytes express γC3 in a deterministic fashion in both mouse and human.This striking difference in the mode of expression of γC3 and its conservation between mouse and human led us to assess the role of γC3 in the developing mouse visual cortex.

γC3 is required for astrocyte morphogenesis
We rst sought to determine the consequence of γC3 loss in mice that lacked γC3 in all cell types 24 .γC3 knockout (KO) mice were viable and fertile and exhibited no gross signs of developmental abnormalities or neuronal cell death 24 .To explore the role of γC3 in astrocytes we sparsely labeled them through injection of PHP.eB AAVs into the retro-orbital sinus of neonatal mice at post-natal day 1 (P1) (Fig. 2a).This virus, encoding a membrane targeted GFP (Lck-GFP) driven by an astrocyte-speci c sequence (GfaABC 1 D 25,26 ), drives brain-wide labeling of astrocytes 23,27 (Fig. 2b).Viral delivery at P1 resulted in robust astrocyte-speci c Lck-GFP expression in the visual cortex at P8, which persisted through later developmental stages (Extended Data Fig. 1).
We examined the development of WT and γC3 null mutant astrocytes in xed thick tissue preparations of V1 using confocal microscopy.We used the fast optical tissue clearing protocol (FOCM) 28 to e ciently clear thick tissues (Extended Data Fig. 2) allowing us to assess overall shape and approximate the volume of astrocytes and compared these features in different genetic backgrounds.Astrocyte processes typically undergo extensive branching between P8 and P21 [29][30][31] (Fig. 2c-f).Abnormal morphology was seen at all stages of development (Fig. 2c-f).Mutant astrocytes displayed abnormal morphology, apparent clumping of processes and reduced apparent volume (Fig. 2c-f and Extended Data Fig. 3a,b).These phenotypes were reminiscent of clumping of axon terminals and dendrites in different neuron types observed in deletions removing Pcdhα and Pcdhγ clusters, respectively 5,7 .

γC3 is required cell-autonomously in astrocytes
We next sought to assess whether γC3 acts autonomously to regulate astrocyte morphology.To do this we selectively removed the entire Pcdhγ cluster from astrocytes using the Cre-LoxP method regulated temporally by tamoxifen and assessed morphology with and without co-expression of a γC3 cDNA in these cells (Fig. 3a).Here we generated viruses expressing a spaghetti-monster uorescent protein (smFPs) each modi ed with an array of small peptide epitopes to enable immunolabeling with commercially available tag-speci c antibodies 32 .To enhance the labeling of ne astrocyte processes, an N-terminal membrane targeting sequence was fused to the smFP proteins enabling their targeting to the plasma membrane.The astrocyte phenotypes associated with removal of the Pcdhγ cluster selectively from astrocytes in early postnatal life (P1-P3) were similar to the phenotypes in γC3 KO mice (Fig. 3b,c).By contrast, targeted expression of a γC3 cDNA (or to a lesser extent a PcdhγA1 (γA1) cDNA) in an astrocyte-speci c Cre-dependent fashion from the ROSA26 locus in these mutant astrocytes rescued the phenotype (Fig. 3b,c; for genotypes see Methods).The less e cient rescue of γA1 may re ect differences in cell surface expression levels or unique features of γC3.Importantly, these data established that γC3 is required in a cell-autonomous fashion to regulate astrocyte morphogenesis.These data are consistent with astrocyte morphogenesis relying on γC3-mediated interactions between processes of the same astrocyte or alternatively γC3-mediated interactions between astrocytes and surrounding neurons.
To determine whether γC3 is required in cells other than astrocytes (e.g.neurons) for normal astrocyte development, we employed a viral gene delivery strategy to selectively restore γC3 expression only in astrocytes in γC3 KO mice.We generated an AAV construct encoding a full-length γC3 cDNA fused with a C-terminal 3xV5 tag (γC3FL, Fig. 4a) under the control of the astrocyte-speci c GfaABC 1 D promoter and coinjected this into retro-orbital sinus with a virus to visualize astrocyte morphology.Astrocytes expressing γC3 (i.e.detected with the anti-V5 antibody; Extended Data Fig. 4) substantially rescued the γC3 KO mutant astrocyte phenotype (Fig. 4d,e).Thus, expression of γC3 molecules in astrocytes only is su cient for astrocyte morphogenesis.
γC3 mutants lacking homophilic binding do not rescue astrocyte morphology in γC3 mutants If homophilic binding is required for γC3 function in astrocytes, then the genetic analysis suggests that γC3 may promote interactions between processes of the same astrocyte.It is possible, however, that γC3 recognizes a different, yet to be identi ed, protein on the surface of astrocytes, embedded in the extracellular matrix or on the surface of other cortical cell types that regulate astrocyte morphogenesis.If this were the case, point mutations disrupting homophilic binding would not be expected to disrupt astrocyte morphogenesis.To test this, we designed two single-point mutations in γC3 predicted to disrupt homophilic binding (Fig. 4a-c).Pcdhs form trans dimer interfaces with their N-terminal EC1-EC4 extracellular domains binding in an anti-parallel orientation 6,15,33 .Both the EC1::EC4 and EC2::EC3 interfaces must be formed for binding to occur.To disrupt binding we designed two mutants where hydrophobic residues Leu 87 and Leu 342, which are buried within the EC1::EC4 interface, were replaced with negatively charged glutamate (Fig. 4c).Both mutant proteins (γC3 EC1-EC4 L87E, and γC3 EC1-EC4 L342E) were monomers as determined by analytical ultracentrifugation (AUC) (Fig. 4b).We subsequently incorporated these single point mutations into full-length γC3 proteins modi ed with C-terminal 3xV5 epitopes (Fig. 4a).These constructs were virally introduced via retroorbital injection to transduce the cortical astrocytes of γC3 KO mice at P1 and the phenotypes were assessed at P21.Like WT γC3, mutant γC3 proteins were expressed and colocalized with membrane-tethered Lck-smMyc (Extended Data Fig. 5a,b).By contrast to WT γC3, neither the γC3-L87E nor γC3-L342E mutant proteins rescued the γC3 null phenotype; the astrocytes transduced with these constructs exhibited morphology defects indistinguishable from γC3 null mutants (Fig. 4d,e).These data are consistent with a requirement for γC3 to mediate interactions between processes of the same astrocytes through homophilic interactions.
Interactions between γC3 proteins on processes of the same astrocyte are required for astrocyte morphogenesis To determine whether γC3 binding between processes of the same cell is required for astrocyte morphogenesis, we designed pairs of novel γC3 variants that bind to each other, but not to themselves, and tested their ability to rescue the γC3 mutant phenotype when co-expressed in the same mutant astrocyte (Fig. 5).That is, we converted homophilic binding into heterophilic binding.We used a similar strategy previously to demonstrate that Dscam1 isoforms in Drosophila promote interactions between processes of the same neuron 34 .
Our approach to doing this was based, in large part, on the design of chimeras formed by combining domains of γC3 with those of either γC4 or γC5 and the introduction of additional amino acid substitutions to stabilize these interactions (Extended Data Fig. 6 and 7).Swapping two domains of γC3 (blue) with two domains from γC4 (green) yielded chimeras that were monomeric in solution (Fig. 5a,b for M1; and the other chimera generated in the swap shown in Extended Data Fig. 7c, and Supplementary Table 1).Based on interactions between complementary domains alone we would have expected these chimeras to bind to each other (i.e.heterophilically).However, they did not (Extended Data Fig. 7d).We, thus, set out to modify the interfaces with amino acid substitutions to selectively promote heterophilic binding.This required introduction of multiple mutations into prospective heterophilic pairs guided by reiterative testing, visual inspection, and computational analysis.The detailed approach used to generate these pairs is described in Methods (Extended Data Fig. 7-9 and Supplementary Table 2).Two different chimeric pairs exhibited heterophilic binding, concomitant with the loss of homophilic binding.The M1::M6 and M3::M8 pairs of the EC1-EC4 trans binding domain fragments had K D values of 32 μM and 80 μM, respectively (Fig. 5b and Supplementary Table 1).These K D estimates are in the range of most cell adhesion molecules and are stronger than the K D for γC3 (115 μM).
We next sought to assess whether the γC3 mutant astrocyte phenotypes were rescued by co-expression of heterophilic binding pairs.We incorporated the M1, M3, M6, and M8 EC1-EC4 chimeras into full-length γC3 protein variants.Each chimera was also tagged with a C-terminal 3xHA or 3xV5 epitope (Fig. 5a) to assess expression in vivo using antibody staining (Fig. 5c).These chimeras were expressed using the astrocyte-speci c GfaABC 1 D promoter and incorporated into AAVs for in vivo expression.At P1, γC3 KO mice received injections of either a single chimera (M1, M3, M6, or M8) or a complementary pair of chimeras (M1::M6 or M3::M8 pairs) (Fig. 5d).Only astrocytes positive for staining for the epitope tags were analyzed.Single chimera lacking the ability to form homodimers did not rescue the astrocyte morphology phenotype (Fig. 5d).By contrast, heterophilic binding pairs (M1::M6 or M3::M8) when introduced as pairs provided substantial rescue (Fig. 5d,e).Thus, interactions between γC3 proteins on the surface of processes of the same astrocyte promote normal astrocyte morphology.

Discussion
The γC3 isoform from the Pcdhγ cluster is selectively expressed in both mouse and human astrocytes.We show that γC3 is necessary for astrocyte morphogenesis and through the analysis of mutant isoforms of γC3 with altered binding speci cities, we provide evidence that this relies on γC3 interactions between processes of the same cell.The selective expression of γC3 in human astrocytes suggests that this function is evolutionarily conserved.
The key to establishing that γC3 mediates interactions between processes of the same astrocyte was the generation of γC3 mutants in which homophilic binding was converted to heterophilic binding.The primary challenge in generating these mutants was that different isoforms of Pcdhγ form trans dimers with rather distinct structures precluding simply achieving heterophilic speci city by combining different domains.Indeed, there are marked variations in surface interactions for Pcdhs (e.g.resulting in substantial deviations up to 4.5Å RMSD) 35 .Our analysis predicted that the EC2EC3 orientation in the γC3 trans dimer is different than that of γC4, which affects the contacts in the interface.By contrast, γC5 is expected to align closely with γC4 orientation.To accommodate these differences, we successfully created heterophilic recognition molecules by introducing targeted mutations to force the modeled chimeras to adapt trans dimer structures analogous to γC4.
The complexity of astrocyte morphology poses a challenge in critically assessing how γC3 contributes to astrocyte development.The loss of γC3 could lead to a collapse of astrocyte processes onto themselves or a failure of branches to segregate from each other as they extend from branch points.These phenotypes would be consistent with a repulsive function.Alternatively, interactions between astrocyte processes may be crucial to elaborate speci c features of astrocyte morphology, and these interactions may be of an adhesive nature, perhaps only transiently, promoting speci c interactions between processes to drive morphogenesis.A more detailed analysis of developing normal and γC3mutant astrocytes, both in vivo and in vitro, may provide ways to discriminate between these mechanisms.Regardless of the nature of the output of γC3 binding on opposed membranes, our data strongly support the conclusion that interactions between processes of the same astrocyte play a crucial role in astrocyte morphogenesis.
Although there is considerable evidence for a repulsive function of Pcdhg proteins, several studies are consistent with Pcdhg acting in an adhesive fashion.Previous studies demonstrated that the Pcdhg locus acting in astrocytes and neurons promotes the formation of both inhibitory and excitatory synapses 36 .These proteins localize in both neurons and astrocytes in close proximity to synapses 36 .It is not known, however, whether this activity is restricted to γC3 or whether this is a general property of Pcdhg proteins.In a more recent study, γC3 has been shown to promote interactions between pre-and postsynaptic neurons in the spinal cord and these are likely to be adhesive 9 .γC3 is also required in cortical pyramidal neurons to promote dendritogenesis, and the removal of γC3 from astrocytes leads to a similar phenotype in neurons 37 .This may re ect non-speci c effects of changes in astrocyte morphology on dendritogenesis or, more interestingly, an adhesive function for γC3 in astrocytes directly regulating dendritogenesis in neurons.Thus, like many other cell surface axon guidance and recognition molecules, γC3 may function in an adhesive or repulsive way in a context-dependent fashion.
By contrast to the cell-type speci c expression of γC3 in astrocytes, the probabilistic expression of Pcdh isoforms occurs in most neurons.As a consequence, each cell acquires a unique identity and this, in turn, allows neurites to distinguish between sister neurites (i.e.neurites of the same cell) from those of others.
This typically leads to self-avoidance, allowing neurites to uniformly cover receptive elds and prevent interactions (e.g.formation of autapses) between them [5][6][7] .Why would astrocytes utilize γC3 selectively rather than adopt the probabilistic expression of different isoforms as neurons do?We suggest two possibilities.First, astrocytes express very high levels of γC3 transcripts, some two orders of magnitude greater than expression in neurons.This high level of expression may be necessary to support interactions between the vast number of processes and thus the massive surface area of astrocytes.Speci c regulatory mechanisms may have evolved to support this function.Alternatively, as the γC3 sequences in the juxtramembrane domain are different from other Pcdhγ isoforms, these may promote interactions between astrocyte-speci c proteins, which act together to pattern astrocyte morphology-either through distinct complexes on the cell surface or the activation of distinct intracellular signaling pathways.Previous studies demonstrated that a speci c isoform in the Pcdha complex, PcdhαC2, is selectively expressed in serotonergic neurons and promotes axon tiling 8 .The prominent role of Pcdhs in many cell types to promote self-non-self discrimination, and the use of some isoforms in cell-type speci c ways is similar to the diverse roles of different Dscam proteins in Drosophila neurodevelopment 34,[38][39][40][41][42] .
In summary, the conservation of the selective expression of γC3 isoforms in mouse and human astrocytes, and the function we describe here for γC3 to regulate mouse astrocyte morphology argues for an evolutionarily conserved role for this isoform in regulating astrocyte development.
Declarations antibodies (Invitrogen, 1:500) or anti-RFP nanobody (FluoTag®-X4 anti-RFP, 1:200) for mCherry immunostaining.When necessary, tissues were treated with a nuclear counterstain, either DAPI (Invitrogen, 1:1000) or NeuroTrace Green (Invitrogen, 1:500), for 48 hours at 37°C.Finally, tissues were washed six times for 4 hours with 1X PBS and mounted on glass slides using a holder.The holder was lled with FOCM reagent, and the brain section was incubated for 15 minutes.Once the tissues became optically cleared, a glass coverslip was placed on the holder and sealed with nail polish for imaging.

Generation of γC3 Single-Point Mutants
Two γC3 single-point mutants, γC3-L87E and γC3-L342E, were designed by introducing an unsatis ed negative charge at the EC1::EC4 interface of the γC3 homodimer (Fig. 4C).The biophysical characteristics of these homophilic binding de cient mutants were then assessed in the context of the γC3 EC1-EC4 construct (Table S1).QuickChange site-directed mutagenesis kit from Strategene was used to introduce point mutations on the full-length γC3 cDNA with fused C-terminal 3xV5 tags following the mutagenesis PCR protocol.The resulting AAV.GfaABC1D.γC3-L87E and AAV.GfaABC1D.γC3-L342E constructs were veri ed by sequencing.

AAV Production and administration
Neonatal mice were gently removed from their holding cages and positioned on their side.Sterile saline and a cotton-tipped applicator were used to clean the injection site.A 33-gauge needle attached to the Hamilton microinjection syringe was inserted at a 45° angle into the left retro-bulbar sinus of the neonatal mice.A total injection volume of 10 µl virus diluted in 1X PBS was delivered into the retro-orbital bulbar sinus.After viral injection, mild pressure was applied at the injection site to minimize back ow of the injected viruses.AAVs were administered at an approximate viral titer of 1x10^11 vg per mouse.All injections were performed on postnatal day 1-2.Mice were sacri ced at designated time points in accordance with approved animal protocols and procedures.
To assess the effects of homophilic binding de cient mutants, separate litters of WT and γC3 KO mice each received AAV.GfaABC 1 D.γC3FL, AAV.GfaABC 1 D.γC3-L87E, or AAV.GfaABC 1 D.γC3-L342E.All groups were also injected with AAV.GfaABC 1 D.Lck-smMyc to label astrocyte morphology.In the heterophilic binding chimera experiment, the litter of γC3KO mice was equally divided to evaluate the effect of each heterophilic binding pair.To evaluate the phenotypic effect of the M1+M6 heterophilic binding chimera, the litters were equally divided to receive either AAV.GfaABC

Confocal Imaging and Morphology Analysis
Confocal images were acquired by a Zeiss LSM 880 confocal microscope equipped with Zen digital imaging software.Images were acquired at several microscope magni cations including 4x, 20x, 40x with each image frame of 1024 pixels by 1024 pixels and acquired at 4x, 20x, or 40x magni cations.Z stacks images were obtained to capture the entirely of single astrocyte volume based on uorescence signals.The acquired astrocyte z-stack confocal images were rst analyzed to compute the functional surface, which was then used to extract a range of morphometric parameters for individual astrocytes.The functional surface was by creating a region of interest (ROI) that encapsulated the entirety of each individual astrocyte based on uorescence signal.The background signal was eliminated by adjusting the threshold level.The uorescence intensities of the GFP or smFPs used to image astrocyte morphology were equivalent across all experimental groups.For 2D morphological analysis, various morphology parameters such as Feret max, Feret min, aspect ratio, territory size, roundness, and circularity, were performed in accordance with established protocols 23,44 .This assessment was carried out using maximum intensity projections, and each morphological parameter was quanti ed using ImageJ software.

Building trans dimer models
We used a crystal structure of γC4 (PDBID: 7JGZ) 35 as a template to build models of trans dimers for γC3 wild-type (WT), γC5 WT, the single point mutants to explain their effects on binding (γC3 L87E, γC3 L342E, γC4 E78A) and the chimeras (Mi, i =1, 2, 3, 6, 8) designed for exclusive heterophilic binding.Sequences of all modelled EC1-EC4 fragments (residues 1-421, numbering as in PDBID: 7JGZ) are juxtaposed with the template in a supplementary Fig. S10.Multiple sequence alignment shown in Fig. S10 was generated with Clustal Omega 45 and visualized via https://espript.ibcp.fr/ESPript/ESPript/ 46.The variants were modelled by mutating γC4 amino acids of the template structure into amino acids of the target proteins using BuildModel utility in FoldX 47 .This method ensures the backbone of the modeled proteins mirrors the template (γC4), gauging their propensity to form a γC4-like trans dimer.For instance, to build models of γC3 and γC5 wild-type trans dimers, we made 215 and 194 mutations to each γC4 protomer within a γC4::γC4 trans dimer, yielding DDG values of 27.2 and 5.9 kcal/mol, respectively.Here, DDG denotes the interaction energy of the trans dimer, derived from its total folding energy using AnalyseComplex utility in FoldX.The chimeras exhibited destabilization in a γC4-dictated trans dimer conformation by 16-18 kcal/mol, similar to γC3.These modelled trans dimers and their binding energies relative to γC4 are shown in Fig. S9A.Of note, the gure shows the precursor chimera models corresponding to merging EC1EC2 (residues 1-205) and EC3EC4 (residues of 206-421) fragments of γC3 (blue) with either γC4 (green) or γC5 (red).Only M1 and M3 match the precursor chimera in sequence.Mi chimeras (where i=2,6,8) carry additional point mutations atop the precursor chimeras, introduced via FoldX to bolster trans dimerization (detailed further in 'Design of chimeras').

Design of chimeras
Utilizing FoldX, we rst modelled heterophilic protocadherin chimeras combining sequences of γC3 with either γC4 or γC5 (refer to 'Building trans dimer models').Subsequent mutations were introduced to correct the non-complementary surfaces.Largely positive relative FoldX energies of the initial chimera models (Fig. S9A) suggested interface issues that might hinder gC4-like heterophilic chimera binding.
By examining all model structures, we identi ed problematic chemical interactions, especially those between polar/charged and hydrophobic residues.A comparison of these destabilizing contacts with the template interactions revealed speci c issues.For instance, Fig. S9B shows a ribbon representation of a γC4 trans dimer (template, green) and a model of a γC3 trans dimer (forced to have a backbone identical to γC4, blue).The amino acids at the EC2-EC3 boundary of γC4 are mostly hydrophobic (see labelled residues shown as sticks in a diamond-shaped area, shaded in grey) whereas γC3 has polar/charged residues (N299 and E301, underlined in cyan) that are incompatible with the neighboring hydrophobic residues (L204, A118, L117).Furthermore, a hydrophobic contact in a γC4 dimer formed by two valine residues (V206) was missing in γC3 (as it has Ala in place of Val).Hence, A206, N299, and E301 residues of γC3 would likely destabilize binding in a γC4-like orientation due to polar-hydrophobic mismatches at the EC2::EC3 interface.This logic extends to chimeras containing γC3 fragments.Of note, γC5 interface is similar in chemical composition to that of γC4 featuring V206 and PAM (299-301) (Fig. S9C and Fig. S10).
To validate our observations, we employed computational mutagenesis via FoldX.We mutated residues of the precursor chimera models to make the trans dimer interface at the EC2-EC3 boundary more hydrophobic (see details on computational mutagenesis procedure in 48 ).Predictions con rmed that A206V, N299P and E301M mutations would stabilize the interface (Table S2).
The E78A mutation enhances homophilic binding in γC4 35 .The biophysical effect of this mutation is explained in Fig. S7.The E78A mutation was introduced to M2 and M6 chimera featuring fragments of γC4 .The N299P and E301M mutations were introduced to M6 and M8 chimeras together with a predicted neutral (Table S2) P300A mutation (as a triple NPE®PAM mutation) to minimize the number of cloning events in the chimera generation.The A206V mutation was effectively introduced by a shift in the EC2-EC3 domain boundary (i.e.we merged the domains to preserve the Val-Val contact by keeping Val206 of γC4 or γC5 and cutting out Ala206 of γC3, see Fig. S7 for the chosen domain boundary between EC1EC2 and EC3EC4 fragments in the Mi chimeras).The NPE®PAM mutation differentiates M6 (with) from M2 (without) and M8 (with) from M4 (without), and it is crucial for restoring hydrophobic complementarity at the EC2-EC3 boundary in the heterophilic chimeric trans dimers (Fig. S9C) as M1::M6 and M3::M8 both formed heterodimers in AUC whereas M1::M2 and M2::M3 did not (Table S1).

Sedimentation equilibrium measurements
Experiments were performed in a Beckman XL-A/I analytical ultracentrifuge (Beckman-Coulter, Palo Alto CA, USA), utilizing six-cell centerpieces with straight walls, 12 mm path length and sapphire windows.All proteins were dialyzed over-night and then diluted in TRIS 10 mM, NaCl 150 mM, CaCl2 3 mM pH 8.0, 250 mM imidazole.Samples were diluted to 1.1, 0.73 and 0.37 mg/mL in channels A, B and C, respectively.Dilution buffer were used as blank.All samples were run at four speeds, 11000, 14000, 17000 and 20000 rpm, at 25 o C. The lowest speed was held for 20 h after which four measuring scans were taken with 1 h interval, the second lowest speed held for 10 h, followed by four scans as above, the third lowest and the highest speed performed identically as the second lowest speed.All measurements were done at 25 o C, and detection was by interference at 675 nm.Solvent density and protein v-bar were determined using the program SednTerp.(Alliance Protein Laboratories, Corte Cancion, Thousand Oaks, CA, USA) For calculation of dimeric K D and apparent molecular weight, all useful data were used in a global t, using the program SedPhat, obtained from National Institute of Health (www.nibib.nih.gov).All measurements are summarized in Table S1.
Protein production cDNA for mouse Pcdh ectodomain fragments, excluding the predicted signal sequence, were cloned into a pαSHP-H mammalian expression vector (from Daniel J. Leahy, John Hopkins University), modi ed with the BiP signal peptide (BiP: MKLSLVAAMLLLLSAARA) and a C-terminal octahistidine tag.The signal sequence was predicted using the SignalP 4.0 server.Point mutations were introduced into the constructs using the KOD hot start polymerase (Novagen) following the standard Quikchange protocol (Stratagene).
The constructs were expressed in suspension-adapted HEK293 Freestyle cells (Invitrogen) in serum-free media using polyethyleneimine as a transfectant (Polysciences).Media was supplemented with 10 mM CaCl2 4hr after transfection.Conditioned media was harvested 5 days after transfection, and the secreted proteins were puri ed by nickel a nity chromatography followed by size exclusion chromatography in 10 mM Tris, pH 8.0, 150 mM sodium chloride, 3 mM calcium chloride, and 250 mM imidazole, pH 8.0.The puri ed proteins were concentrated to > 3 mg/mL before sedimentation equilibrium AUC experiments.

Statistical Analyses
Data were analyzed using a two-tailed Mann-Whitney test for the comparisons between two groups and one-way ANOVA analysis, followed by Tukey's post hoc analyses, to assess for signi cant differences between more than two groups.All statistical analyses were performed using GraphPad Prism version 5.0c.Data are expressed as mean ± SEM.Asterisks in the gures denote the following signi cance levels: *p < 0.05; **p < 0.01; ***p < 0.001.In all cases, p < 0.05 was considered signi cant.Astrocyte morphology is disrupted in γC3 KO mice.AAV vectors expressing Lck-GFP, controlled by an astrocyte-speci c promoter were retro-orbitally injected into P1 neonates (see methods).b, Sparse labeling of astrocytes across all cortical layers (P14 mouse cortex).c,Comparison of astrocyte morphology in P8 WT and γC3 KO mutants labeled with AAV expressing a myristoylated GFP (Lck-GFP) which localizes to the cytoplasmic face of the plasma membrane.Quanti cation of astrocyte volumes (see Methods).WT: L2/3, n=7; L4, n=8; and L5/6, n=49 astrocytes each from three mice.γC3KO mice: L2/3, n=6; L4, n=8;and L5/6, n=75 astrocytes each from three mice.d, Astrocytes in P21 WT and γC3KO

Supplementary Files
This is a list of supplementary les associated with this preprint.Click to download. ExtendedDataFigsandSupplementaryTables.docx 1 D.M1, AAV.GfaABC 1 D.M6, or AAV.GfaABC 1 D.M1+ AAV.GfaABC 1 D.M6 constructs.Following a similar experimental design, other γC3 KO litters were equally divided to receive AAV.GfaABC 1 D.M3, AAV.GfaABC 1 D.M8, and AAV.GfaABC 1 D.M3+M8 treatments to evaluate the effect of M3 and M8 heterophilic binding pairs on astrocyte morphology.Of note, the same WT and γC3 KO control groups were shown in both Fig. 4E and Fig 5D.All AAV viruses were produced by the Janelia Viral Vector Core.Viral titers were measured using reverse transcription PCR (RT-PCR) to quantify the viral particle concentration in the nal virus preparations.

Figure 3 Replacement
Figure 3