Juan Du

Dejian Wang

Hongcheng Fan

Chanjuan Xu

Linhua Tai

Shuling Lin

Shuo Han

Qiuxiang Tan

Xinwei Wang

Tuo Xu

Hui Zhang

Xiaojing Chu

Cuiying Yi

Peng Liu
email: hliu@simm.ac.cn

Xiaomei Wang

Yu Zhou

Jean-Philippe Pin

Philippe Rondard

Hong Liu

Jianfeng Liu
email: jfliu@mail.hust.edu.cn

Fei Sun
email: feisun@ibp.ac.cn

Beili Wu
email: beiliwu@simm.ac.cn

Qiang Zhao
email: zhaoq@simm.ac.cn.

Structures of human mGlu2 and mGlu7 homo-and heterodimers

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cryo-electron microscopy (cryo-EM), X-ray crystallography, and functional studies to solve structures of mGlu2 and mGlu7 in both homo-and heterodimeric organizations and provide valuable insights into mGlu activity modulation.

Structure determination of mGlu2 and mGlu7

For structure determination of inactive mGlu2 and mGlu7 homodimers, a modified mGlu2 or mGlu7 was purified in presence of its selective negative allosteric modulator (NAM) [NAM563 (ref. 5) for mGlu2; MMPIP [START_REF] Suzuki | In vitro pharmacological characterization of novel isoxazolopyridone derivatives as allosteric metabotropic glutamate receptor 7 antagonists[END_REF] for mGlu7] (see Methods for construct design and function characterization; Extended Data Fig. 1a-l). The stable agonist-bound mGlu2 was obtained by co-purifying another modified receptor with the agonist LY354740 (ref. 7), the positive allosteric modulator (PAM) JNJ-40411813 (ref. 8), and the nanobody DN13 that acts as an mGlu2 PAM [START_REF] Scholler | Allosteric nanobodies uncover a role of hippocampal mGlu2 receptor homodimers in contextual fear consolidation[END_REF] (Extended Data Fig. 1e,i,). To solve the mGlu2-7 heterodimer structure, an FK506 binding protein (FKBP)-tagged mGlu2 and a rapamycin binding fragment (FRB)-tagged mGlu7 were co-purified in the presence of NAM563 and MMPIP (Extended Data Fig. 1r and Supplementary Fig. 1). The inactive structures of mGlu2, mGlu7, and mGlu2-7 and the agonist/PAM-bound mGlu2 structure were determined by cryo-EM with overall resolutions of 3.6 Å, 4.0 Å, 3.9 Å, and 3.1 Å, respectively, and the resolutions in the ECDs of mGlu7 and mGlu2-7 were further improved to 3.6 Å and 3.5 Å, respectively (Extended Data Figs. 2 and3; Extended Data Table 1). To provide high-resolution molecular details of NAM binding mode, we also solved two crystal structures of the mGlu2 TMD bound to two NAMs, NAM563 and NAM597 (ref. 10), at 2.5 Å and 2.7 Å resolution, respectively (Extended Data Table 2).

The inter-VFT disulfide bonds (mGlu2, C121-C121; mGlu7, C136-C136; mGlu2-7, C121-C136) were resolved in all the structures, but exhibit distinct conformations (Extended Data Fig. 3). Compared to the inactive mGlu2 structure, the junction loop between the disulfide bond and B helix in the VFT adopts a more extended conformation in the inactive structures of mGlu7 and mGlu2-7, resulting in a higher position of this disulfide bond (Extended Data Fig. 4a). Associated with the conformational rearrangement of the VFTs upon agonist binding, the disulfide bond undergoes an upward movement in the agonist/PAM-bound mGlu2 structure relative to the inactive state (Extended Data Fig. 4b), which may be consistent with previous observation that the intersubunit disulfide bond stabilizes the receptor active state [START_REF] Levitz | Mechanism of assembly and cooperativity of homomeric and heteromeric metabotropic glutamate receptors[END_REF] .

Multiple dimerization modes of inactive mGlus

Similar to the previously published inactive structures of mGlu5 [START_REF] Koehl | Structural insights into the activation of metabotropic glutamate receptors[END_REF] and mGlu2-VFT [START_REF] Chappell | Discovery of (1S,2R,3S,4S,5R,6R)-2-Amino-3-[(3,4difluorophenyl)sulfanylmethyl]-4-hydroxy-bicy clo[3.1.0]hexane-2,6-dicarboxylic Acid Hydrochloride (LY3020371.HCl): A Potent, Metabotropic Glutamate 2/3 Receptor Antagonist with Antidepressant-Like Activity[END_REF] , the inactive mGlu2 and mGlu7 structures reveal an open conformation of the VFTs and a common homodimer interface at the apex of the VFTs (Extended Data Fig. 4c,d). In contrast, the CRDs adopt distinct relative positioning in the inactive structures of mGlu2, mGlu5, and mGlu7, with the CRDs in mGlu2 exhibiting the closest positions (Extended Data Fig. 4e).

This difference is associated with the distinct dimerization modes of the receptor TMDs, where close contact is observed in mGlu2 but is absent in mGlu5 and mGlu7 (Fig. 2a). The TMDs of mGlu5 and mGlu7 are completely separated with helices V in the two subunits facing each other, while the TMDs in the inactive mGlu2 form extensive interactions along the whole length of helix IV (Figs. 1a, b and2a). This dimerization mode is supported by previous crosslinking studies, showing that helices IV and V of mGlu2 are involved in intersubunit interaction in basal or inactive state [START_REF] Xue | Major ligand-induced rearrangement of the heptahelical domain interface in a GPCR dimer[END_REF] . The additional involvement of helix V in dimerization suggests a dynamic nature of the dimer interface.

The different dimerization modes of the inactive mGlus agree with previous investigation of inter-TMD interaction, in which the mGlu2 TMD showed a higher proportion of dimers compared to that of mGlu1, mGlu3, or mGlu5 [START_REF] Gutzeit | Conformational dynamics between transmembrane domains and allosteric modulation of a metabotropic glutamate receptor[END_REF] , suggesting subtype-specific inter-TMD interaction strength of mGlus. In the inactive mGlu2, the TMD dimer interface is mainly mediated by helix IV and the extracellular tip of helix III through hydrophobic contacts (Fig. 2b,c). Mutations of most of the key residues in the dimer interface resulted in an elevated constitutive activity (Fig. 2d and Extended Data Table 3), and the full dose-response curves excluded the possible effects of increased glutamate potency and maximal activation potentially induced by the environmental glutamate (Extended Data Fig. 1s and Extended Data Table 3). Furthermore, a substantially impaired receptor activity was observed when the inactive dimer interface is locked through a disulfide bridge by introducing a cysteine substitution, L698 4.51 C or V699 4.52 C (Extended Data Fig. 1u, v and Supplementary Fig. 1). These data imply that the helix IV-mediated dimerization plays a role in stabilizing the receptor inactive conformation.

The mGlu2 residues that participate in dimerization are poorly conserved between mGlus (Extended Data Fig. 5), suggesting that the mGlu2 dimer interface along helix IV may be subtype-dependent. Some of the key residues such as L684 4.37 , L692 4.45 , L698 4.51 , and V699 4.52 are substituted by phenylalanine or residues with small side chains in other mGlus, which may disturb the dimer interface by introducing a spatial hindrance or disrupting the hydrophobic interaction. Replacing these residues with their counterparts in other mGlus increased the receptor basal activity (Fig. 2d, Extended Data Fig. 1t, and Extended Data Table 3), further reflecting the disturbance of the inactive state. In contrast, a wild-type level of basal activity was observed for the mGlu7 mutants in helices III and IV (Fig. 2e). These data support that the dimer interface along helix IV in the inactive mGlu2 homodimer is subtype-specific. However, this does not rule out the possibilities of specific inactive conformation that is required for facilitating conformational change upon receptor activation and structural constraints coming from the specific conformation of the VFTs and CRDs in different mGlus.

Intersubunit interactions upon activation

Comparison of the inactive and agonist/PAM-bound structures of mGlu2 revealed a closure of the VFTs and CRDs upon receptor activation (Fig. 1b,c; Extended Data Fig. 4f,g), leading to a dimer interface mediated by a hydrophobic interaction core at the apex of the CRDs (Extended Data Fig. 4h). Locking this interface by introducing a disulfide bond resulted in constitutive activation of mGlu2 and mGlu7 (Extended Data Fig. 1w,x), consistent with previous studies showing that a precise association of the two CRDs in an mGlu dimer is required for full receptor activation [START_REF] Huang | Interdomain movements in metabotropic glutamate receptor activation[END_REF] .

Similar to what was observed for mGlu5 [START_REF] Koehl | Structural insights into the activation of metabotropic glutamate receptors[END_REF] , in the agonist/PAM-bound mGlu2 structure the CRD and ECL2 are in proximity (Extended Data Fig. 6a and Extended Data Fig. 3c).

Disturbing the interaction interface by introducing alanine mutation(s) or removing the ECL2 residues R714 and E715 substantially reduced the maximal response (E max ) of the receptor in the agonist-induced inositol phosphate (IP) accumulation assay but had no effect on the PAM-induced receptor signalling (Extended Data Fig. 1y, z; Extended Data Table 3). A similar detrimental effect was also shown when residues at the apex of ECL2 in mGlu7 (T737-E741) were removed (Extended Data Fig. 1x and Extended Data Table 3). These data suggest that the CRD and ECL2 may play a similar role in transmitting signal from the VFT to the TMD in different mGlus.

Upon receptor activation, the helix IV-mediated dimeric association of mGlu2 switches to an active state mainly contributed by helix VI (Fig. 1b,c), a hallmark of class C GPCR activation [START_REF] Koehl | Structural insights into the activation of metabotropic glutamate receptors[END_REF][START_REF] Xue | Major ligand-induced rearrangement of the heptahelical domain interface in a GPCR dimer[END_REF] . An increased constitutive activity of mGlu7 mutant A812 6.61 C was observed (Extended Data Fig. 1x), suggesting that helix VI is most likely also involved in mGlu7 dimerization in the active state. Despite a similar dimer interface along helix VI in mGlu2 and mGlu5, the agonist/PAM-bound mGlu2 structure reveals a slight movement of the TMDs relative to the mGlu5 structure, leading to additional contacts between residues V782 6.59 and V789 7.27 at the extracellular tips of helices VI and VII (Extended Data Fig. 6b). Our cysteine crosslinking and signalling studies showed that in contrast to mutant C121A, additional introduction of mutations V782 6.59 C and V789 7.27 C in the two subunits, respectively, displayed an increased dimer proportion in presence of agonist and PAM (Extended Data Fig. 1u and Supplementary Fig. 1) and an elevated constitutive activity (Extended Data Table 3), which reflect the close contact between helices VI and VII in the active state and importance of such contact in stabilizing the receptor active conformation.

Intrasubunit conformational change of mGlu2

Following the relative movement of the two subunits, further conformational change within the TMD of one subunit occurs, resulting in G protein activation 16 . The crystal structures of the mGlu2-TMD bound to NAM563 and NAM597 (Extended Data Fig. 6c) and our recently determined structure of the fully active mGlu2-G i complex [START_REF] Lin | Structures of G i -bound metabotropic glutamate receptors mGlu2 and mGlu4[END_REF] allowed us to obtain molecular details of the conformational changes required for receptor activation within the receptor TMD.

In mGlu2, NAM563 and NAM597 bind to a cavity mainly formed by helices III and V-VII, which is similar to the NAM-binding pockets previously observed in mGlu1 [START_REF] Wu | Structure of a class C GPCR metabotropic glutamate receptor 1 bound to an allosteric modulator[END_REF] and mGlu5 [START_REF] Dore | Structure of class C GPCR metabotropic glutamate receptor 5 transmembrane domain[END_REF] and the ligand-binding sites in some class A GPCRs (Extended Data Fig. 6d). These two NAMs exhibit similar binding patterns that share many common interactions with the receptor but are distinct on the extracellular side, with the trifluoromethyl-morpholin group of NAM563 squeezing into a gap between helices VI and VII while the methyl-pyrazol group in NAM597 extending in an opposite direction to enable extra interactions with helix II and ECL2 (Extended Data Fig. 6c). This may account for the slightly higher activity of NAM597 in inhibiting receptor signalling (Extended Data Fig. 1m and Extended Data Table 3). The binding modes of these two NAMs are supported by a 5-1,000-fold reduction of their inhibitory activity associated with mutations within the binding pocket, which had a weak effect on agonist-induced receptor signalling (Extended Data Table 3).

Compared to the inactive structures of mGlu2 and mGlu2-TMD-NAMs, the pronounced outward movement of helix VI, a hallmark of receptor activation for classes A and B GPCRs, was not observed in both the G i -bound and -free structures of agonist-bound mGlu2 (Extended Data Fig. 6e). Instead, helix VI in the G i -bound subunit of the mGlu2-G i complex undergoes a downward shift towards the intracellular surface by half a helical turn (Extended Data Fig. 6f). However, neither the G protein-free agonist/PAM-bound structure nor the G ifree subunit in the mGlu2-G i structure displays such conformational change, suggesting that this movement is associated with G protein binding. Close inspection of the mGlu2-TMD-NAM and mGlu2-G i structures revealed a rotamer conformational change of the highly conserved class C GPCR residue W 6.50 with its side chain rotating downwards by approximate 90° in the G i -bound structure, which may release the transmembrane helical bundle from its inactive state by disrupting an interaction core involving helices III and V-VII and potentially leads to the downward shift of helix VI (Extended Data Fig. 6g). In the structures of mGlu2-TMD-NAMs, the NAMs form a close contact with W773 6.50 , constraining the conformational change of the side chain to stabilize the receptor in the inactive state (Extended Data Fig. 6c).

Although not directly involved in G protein binding of mGlu2 [START_REF] Lin | Structures of G i -bound metabotropic glutamate receptors mGlu2 and mGlu4[END_REF] , helix VI may play a role in modulating receptor activation by altering the interaction network on the intracellular surface of the receptor to facilitate G protein recognition. A salt bridge between the highly conserved residues K 3.50 and E 6.35 , which is known as the 'ionic lock' of class C GPCRs [START_REF] Wu | Structure of a class C GPCR metabotropic glutamate receptor 1 bound to an allosteric modulator[END_REF][START_REF] Dore | Structure of class C GPCR metabotropic glutamate receptor 5 transmembrane domain[END_REF] , and another ionic interaction formed by the less well conserved residue R656 3.53 in helix III and E754 in ICL3 are intact in both mGlu2-TMD-NAM structures but broken in the G i -bound subunit of the mGlu2-G i complex likely due to the downward shift of helix VI and rearrangement of ICL3 (Extended Data Fig. 6h). Our signalling assay showed an increased constitutive activity resulted from mutation E754A (Extended Data Table 3), implying that the salt bridge between R656 3.53 and E754 may act as a secondary 'ionic lock' to stabilize the inactive conformation of mGlu2.

Heterodimerization of mGlu2 and mGlu7

It was recently found that mGlu2 can associate with mGlu7 in hippocampus, suggesting a physiological relevance of such a heterodimer [START_REF] Habrian | Conformational pathway provides unique sensitivity to a synaptic mGluR[END_REF] . The mGlu2-7 heterodimerization was further confirmed by our tr-fluorescence resonance energy transfer (tr-FRET) assay (Extended Data Fig. 7a,b). Like the homodimers, the VFTs in the mGlu2-7 heterodimer adopt a similar open conformation forming contacts mainly through the B and C helices (Extended Data Fig. 4i,j), suggesting a conserved VFT dimerization mode shared by the mGlu homo-and heterodimers.

In addition to this common dimer interface, extra contacts between the mGlu7 residue R191 and the mGlu2 residues D174 and S176 were observed in the heterodimer (Fig. 3a). Similar interactions also exist in the inactive mGlu2 homodimer, but not in the inactive mGlu7 homodimer due to the substitution of S176 (mGlu2) with R190 (mGlu7), which repels the residue R191 in the opposite subunit (Fig. 3a). Compared to the heterodimer mutant that lacks the inter-VFT disulfide bond, further introduction of mutation D174C or S176C in mGlu2 and mutation R191C in mGlu7 greatly increased the dimer proportion in our crosslinking studies (Extended Data Fig. 1aa and Supplementary Fig. 1), supporting the close contacts between these residues. A substantially reduced potency of both the mGlu2 and mGlu7 agonists was observed for the crosslinked heterodimer mutants and mutants with the mGlu2 residues D174 and S176 replaced with arginines or alanine mutation(s) introduced to disrupt the inter-VFT interactions (Extended Data Fig. 7c-g), suggesting that this heterodimer interface may play a role in modulating receptor activation.

The interaction difference in the top lobes of the VFTs brings the rest of the heterodimer in closer distance compared to that in the mGlu7 homodimer (Fig. 3a). While the TMDs in the mGlu2 and mGlu7 homodimers adopt distinct dimerization modes, the TMDs in the mGlu2-7 heterodimer assemble in a similar manner to that in the mGlu7 homodimer with helices V facing each other (Fig. 1d), implying that mGlu7 may be more dominant in controlling heterodimer assembly. Previous investigations of mGlu homo-and heterodimerization suggested that mGlu2 dimerized with mGlu7 with a lower propensity compared to that of mGlu2 homodimerization 2 . This is likely due to the distinct dimerization modes of the TMDs, which form extensive contacts in the mGlu2 homodimer but not in the mGlu2-7 heterodimer. Asymmetric activation has been observed for some mGlu heterodimers [START_REF] Levitz | Mechanism of assembly and cooperativity of homomeric and heteromeric metabotropic glutamate receptors[END_REF][START_REF] Liu | Allosteric control of an asymmetric transduction in a G protein-coupled receptor heterodimer[END_REF] . The mGlu2-7 heterodimer displayed a 3-fold higher E max than the mGlu7 homodimer when activated by the mGlu7 agonist L-AP4 (ref. 22) (Fig. 3c), which indicates that the heterodimerization boosts the G protein activation even when one of the subunits is not occupied with agonist, demonstrating a clear cooperativity between the two subunits. Further investigation of heterodimer signal transduction showed an agonist-induced response comparable to the controls when the mGlu2 subunit carried mutation F756S in ICL3 that blocks the G protein coupling [START_REF] Francesconi | Role of the second and third intracellular loops of metabotropic glutamate receptors in mediating dual signal transduction activation[END_REF] , while no response was observed if the mutation was introduced in the mGlu7 subunit (Fig. 3b,c). Such data imply that the mGlu7 subunit is mainly responsible for G protein activation within the mGlu2-7 heterodimer, consistent with previous observation that the group III mGlu subunit plays a predominant role in mediating signal transduction in the heterodimers between groups II and III mGlus [START_REF] Liu | Allosteric control of an asymmetric transduction in a G protein-coupled receptor heterodimer[END_REF] . Furthermore, a recovery of agonist-induced response was observed in presence of the mGlu2 PAM JNJ-40411813 with the heterodimer containing the blocked mGlu7 subunit (Fig. 3d,e), demonstrating that the mGlu2 subunit within the mGlu2-7 heterodimer is capable of G protein coupling when its TMD activation is facilitated by a PAM. However, the signal transduction could not be redirected to mGlu2 if the mGlu7 blocked subunit was locked in its inactive state with a selective NAM (Fig. 3d and Extended Data Fig. 7h). This is in contrast to the previous finding on the mGlu2-4 heterodimer, in which mGlu2 took over for G protein activation when an mGlu4 NAM was used [START_REF] Liu | Allosteric control of an asymmetric transduction in a G protein-coupled receptor heterodimer[END_REF] . These observations suggest subtype-specific manners of signal transduction within different mGlu heterodimers.

Figure legends

Methods

Construct design and expression of mGlu2, mGlu7, and mGlu2-7

To solve the inactive mGlu2 structure, the human mGlu2 gene was cloned into a modified pTT5 vector with a hemagglutinin (HA) signal peptide and a Flag-tag at the N terminus and a PreScission protease (PPase) site and a 10 × His-tag at the C terminus. For the inactive mGlu7, the human mGlu7 gene was cloned into the same vector with the HA signal peptide at the N terminus and the PPase site, 2 × Strep-tag, and Flag-tag at the C terminus. The flexible C termini of the two receptors were truncated with different lengths, among which removing 47 residues (V826-L872) in mGlu2 and 56 residues (K860-I915) in mGlu7 produced the most optimal protein yield and homogeneity (Extended Data Fig. 1a,b). To further improve stability of the inactive receptors, mutation N 3.52 Y was introduced in both receptors as suggested by previous structural studies of mGlu5-TMD [START_REF] Dore | Structure of class C GPCR metabotropic glutamate receptor 5 transmembrane domain[END_REF] . Furthermore, mutation H815 7.53 Y in mGlu2 and mutations G722 4.52 I, I775 5.59 F, and P789 6.38 Y in mGlu7 were designed by replacing these residues with their counterparts in other mGlus to potentially increase stability of the transmembrane helical bundle by introducing extra intraand/or inter-helical contacts through larger side chains (Extended Data Fig. 5). With these mutations, the protein yield and homogeneity were greatly improved (Extended Data Fig. 1c,d). To assess effects of the truncations and mutations on receptor function, we performed IP accumulation assay and a bioluminescence resonance energy transfer (BRET) assay using TRUPATH biosensors [START_REF] Olsen | an open-source biosensor platform for interrogating the GPCR transducerome[END_REF] , which measures the proximal interaction between the α and γ subunits upon G i activation. The results confirmed that these modifications had little effect on receptor signalling and NAM activity (Extended Data Fig. 1e-j).

For structural studies of agonist-bound mGlu2, the wild-type receptor was modified by introducing a mutation S601A, which, together with the C-terminal truncation (residues V826-L872), greatly improved protein yield (Extended Data Fig. 1n) but did not alter receptor activation and PAM activity (Extended Data Fig. 1e,i,o,p). In addition, the Cterminal His-tag was replaced by a 2 × Strep-tag to facilitate protein purification.

To aid formation of mGlu2-7 heterodimer, two fusion proteins FKBP and FRB, which form an interaction pair to stabilize the heterodimerization [START_REF] Fegan | Chemically controlled protein assembly: techniques and applications[END_REF] , were linked to the C termini of mGlu2 (E19-V825) and mGlu7 (Q35-R859), respectively. FRET analysis indicates that these fusions do not affect heterodimerization between these two mGlus (Extended Data Fig. 7a,b).

To allow tandem affinity-chromatography, 10 × His-tag and 2 × Strep-tag were added to the C terminus of mGlu2-FKBP and the N terminus of mGlu7-FRB, respectively. The mGlu2 mutations N655 3.52 Y and H815 7.53 Y and the mGlu7 mutations G722 4.52 I, I775 5.59 F, and P789 6.38 Y were introduced to facilitate expression and purification of the heterodimer.

All the constructs were expressed in HEK293F cells (Invitrogen) with the starting density at 1.2 × 10 6 cells ml -1 in 5% CO 2 at 37 °C. For the mGlu2-7 heterodimer, the mGlu2 and mGlu7 constructs were co-expressed with a plasmid ratio of 1:1 and 100 nM rapamycin was added during expression. The cells were harvested by centrifugation (1,000g for 15 min) after 48 h transfection and stored at -80 °C until use.

Purification of mGlu2 and mGlu7 homo-and heterodimers

The cells expressing mGlu2, mGlu7, or mGlu2-7 were lysed in a hypotonic buffer containing 10 mM HEPES, pH 7.5, 10 mM MgCl 2 , 20 mM KCl, and EDTA-free protease inhibitor cocktail tablets (Roche). Extensive washes of membranes were performed by repeated dounce homogenization and centrifugation (160,000g for 30 min) in the hypotonic buffer and a high-osmotic buffer (hypotonic buffer supplemented with 1 M NaCl). The purified membranes were suspended in 10 mM HEPES, pH 7.5, 10 mM MgCl 2 , 20 mM KCl, and 30% glycerol and stored at -80 °C until use.

The membranes were thawed and incubated with different ligands [50 µM NAM563 for inactive mGlu2; 50 µM MMPIP for inactive mGlu7; 50 µM LY354740, 50 µM JNJ-40411813, and DN13 (prepared as below) (DN13 : mGlu2 = 3:1) for agonist/PAM-bound mGlu2; 50 µM NAM563 and 25 µM MMPIP for mGlu2-7 heterodimer], 1mg ml -1 iodoacetamide (Sigma), and EDTA-free protease inhibitor cocktail tablets at 4 ºC for 1 h.

After that, equal volume of solubilization buffer containing 100 mM HEPES, pH 7.5, 300 mM NaCl, 1% (w/v) n-dodecyl-β-D-maltopyranoside (DDM, Anatrace) and 0.2% (w/v) cholesteryl hemisuccinate (CHS, Sigma) was added to the membranes and incubated at 4 ºC for 3 h. The supernatant was then isolated by centrifugation at 160,000g for 30 min, and incubated with TALON resin (Clontech) (for the inactive mGlu2 and mGlu2-7) or STREP resin (IBA) (for the agonist/PAM-bound mGlu2 and inactive mGlu7) at 4 ºC overnight.

To purify the inactive mGlu2 homodimer, the TALON resin was washed with 10 column volumes of 0.05% (w/v) DDM, 0.01% (w/v) CHS, 25 mM HEPES, pH 7.5, 150 mM NaCl, 30 mM imidazole, and 50 µM NAM563. Then the detergent was exchanged to glycodiosgenin (GDN, Anatrace) by incubating the resin with a buffer containing 50 mM HEPES, pH 7.5, 0.25% (w/v) GDN, 150 mM NaCl, 30 mM imidazole, and 50 µM NAM563 at 4 ºC for 2 h. The resin was then washed by another 10 column volumes of wash buffer containing 25 mM HEPES, pH 7.5, 0.01% (w/v) GDN, 150 mM NaCl, 30 mM imidazole, and 50 µM NAM563. The protein was then eluted by the wash buffer supplemented with 300 mM imidazole. The imidazole was removed using a PD MiniTrap G-25 column (GE healthcare), and the protein was treated with His-tagged PPase (custom-made) at 4 ºC overnight. Ni-NTA Superflow resin (Qiagen) was used to remove the cleaved His-tag and PPase. The final sample was concentrated to about 5 mg ml -1 .

For the inactive mGlu7 homodimer, the STREP resin was washed with 10 column volumes of wash buffer containing 25 mM HEPES, pH 7.5, 0.05% (w/v) DDM, 0.01% (w/v) CHS, 150 mM NaCl, and 50 µM MMPIP. The detergent was exchanged to GDN following the same protocol mentioned above. The protein was eluted by 200 mM Tris, pH 8.0, 0.01% (w/v) GDN, 150 mM NaCl, 50 mM biotin, and 50 µM MMPIP, and concentrated to about 5 mg ml - 1 .

The agonist/PAM-bound mGlu2 homodimer was purified following the same protocol of inactive mGlu7 except that the ligands 50 µM LY354740 and 50 µM JNJ-40411813 were used throughout the whole process.

Tandem affinity-chromatography was performed to prepare the mGlu2-7 heterodimer sample. In brief, the TALON resin was washed with 10 column volumes of 25 mM HEPES, pH 7.5, 0.05% (w/v) DDM, 0.01% (w/v) CHS, 150 mM NaCl, 30 mM imidazole, 50 µM NAM563, and 25 µM MMPIP. Then, the detergent was exchanged to GDN and the protein was eluted by 25 mM HEPES, pH 7.5, 0.01% (w/v) GDN, 150 mM NaCl, 300 mM imidazole, 50 µM NAM563, and 25 µM MMPIP. The elution was then incubated with the STREP resin to remove mGlu2 homodimer. The final concentration of mGlu2-7 heterodimer was about 7 mg ml -1 .

Expression and purification of DN13

The nanobody DN13 was prepared as previously described [START_REF] Scholler | Allosteric nanobodies uncover a role of hippocampal mGlu2 receptor homodimers in contextual fear consolidation[END_REF] . In brief, DN13 was cloned into the pET32a vector and transformed into E. coli BL21DE3 strain for expression. The transformed cells were cultured in LB media supplemented with 100 µg ml -1 ampicillin, 0.1% (w/v) glucose and 1 mM MgCl 2 at 37 °C until the OD 600 reached 0.7. Then the cells were induced with 1 mM IPTG and grown at 28 °C overnight. The cells were collected by centrifugation at 4,000g for 15 min and resuspended in ice-cold TES buffer containing 200 mM Tris, pH 8.0, 0.5 mM EDTA, and 0.5 M sucrose. After incubation at 4 °C for 2 h, same volume of a diluted TES buffer (TES buffer : double distilled water = 1:3) was added for further incubation for 2 h. The periplasmic extract was collected by centrifugation at 50,000g for 30 min and incubated with the TALON resin at 4 °C overnight. The resin was then washed with 20 mM Tris, pH 8.0, 100 mM NaCl, and 30 mM imidazole and eluted by the same buffer supplemented with 300 mM imidazole. The protein was concentrated to about 10 mg ml -1 and stored at -80 °C with addition of 20% glycerol until further use.

Cryo-EM sample preparation, data acquisition and processing

Using Vitrobot Mark IV (ThermoFisher), 3 μl of protein sample were applied to glowdischarged 300 mesh amorphous NiTi foil 1.2/1.3 (Au) [START_REF] Huang | Amorphous nickel titanium alloy film: A new choice for cryo electron microscopy sample preparation[END_REF] (mGlu2 homodimers), Quantifoil R1.2/1.3 (Au) (mGlu7 homodimer), or CryoMatrix R0.6/1 (Au) (mGlu2-7 heterodimer) grids.

The grids were blotted at 4 °C and 100% humidity for 4 s, 6 s and 1 s, respectively, and rapidly plunged into liquid ethane for vitrification.

For mGlu2, all datasets were collected on a 300-kV Titan Krios G2 electron microscope (FEI) equipped with K2 Bioquantum direct electron detector (Gatan) and GIF Quantum energy filter. The defocus range varied from -1.2 µm to -2.2 µm and the dose was 1.75 electrons per frame. 10,137 and 2,425 movies of inactive mGlu2 were collected by SerialEM [START_REF] Mastronarde | Automated electron microscope tomography using robust prediction of specimen movements[END_REF] with a pixel size of 0.82 Å and 1.04 Å, respectively. A total of 6,989 movies of the agonist/PAM-bound mGlu2 were collected with a pixel size of 1.04 Å. All movies were subjected to beam-induced motion correction and dose-weighting using RELION's implementation [START_REF] Scheres | implementation of a Bayesian approach to cryo-EM structure determination[END_REF] . Contrast transfer function (CTF) parameters for each micrograph were estimated by Gctf [START_REF] Zhang | Gctf: Real-time CTF determination and correction[END_REF] . Gautomatch (developed by K. Zhang, MRC Laboratory of Molecular Biology, Cambridge, UK; http://www.mrc-lmb.cam.ac.uk/kzhang/Gautomatch/) was used to pick particles for topaz training [START_REF] Bepler | Positive-unlabeled convolutional neural networks for particle picking in cryoelectron micrographs[END_REF] and CryoSPARC 31 was used to generate initial models. Total 1,711,322 particles and 1,076,522 particles were picked for inactive and agonist/PAMbound mGlu2, respectively. 801,134 particles of inactive mGlu2 were subjected to threedimensional (3D) auto-refinement after 3D classification, followed by Bayesian polishing and magnification CTF refinement to yield a 3.4-Å resolution map. Four rounds of TMDmasked 3D classification were performed to improve the map quality of the TMDs and the best class was selected to run 3D auto-refinement with C2 symmetry and Sidesplitter refinement [START_REF] Ramlaul | Mitigating local over-fitting during single particle reconstruction with SIDESPLITTER[END_REF] . A 3.6-Å map was obtained. For the agonist/PAM-bound mGlu2, total 440,306 particles were selected after 3D classification. A similar data processing procedure was followed as above. Final 365,101 particles were selected and subjected to several refinements and yielded a 3.1-Å resolution map. Both maps were post-processed with LocSpiral [START_REF] Kaur | Local computational methods to improve the interpretability and analysis of cryo-EM maps[END_REF] and further locally filtered according to the local resolution values for the following model building and refinement.

The datasets of mGlu7 were collected on a 200-kV Talos Arctica electron microscope (FEI) equipped with K2 Bioquantum direct electron detector (Gatan) and GIF Quantum energy filter. The defocus range varied from -0.5 µm to -2.0 µm and the dose was 1.47 electrons per frame. A total of 13,282 movies were collected by SerialEM 27 with a physical pixel size of 0.8 Å. All movies were subjected to beam-induced motion correction and doseweighting using RELION's implementation [START_REF] Scheres | implementation of a Bayesian approach to cryo-EM structure determination[END_REF] . CTF parameters for each micrograph were estimated by Gctf [START_REF] Zhang | Gctf: Real-time CTF determination and correction[END_REF] . Particle selection was performed using template-free auto-picking in RELION-3.0. A total of 3,051,969 particles were extracted and then subjected to three rounds of reference-free two-dimensional classification and four rounds of 3D classification. The best-looking classes with 1,011,214 particles were selected for 3D auto-refinement and Bayesian polishing with C2 symmetry imposed to yield a 4.0-Å resolution map. Focused refinement of the ECDs was performed, which further improved the ECD map resolution to 3.6 Å. A composite map was generated in UCSF Chimera 34 using 'vop maximum' command and used for model building and refinement.

For the mGlu2-7 heterodimer, the data were collected on a 300-kV Titan Krios G3 electron microscope (FEI) equipped with K3 Summit direct electron detector (Gatan) and GIF Quantum energy filter. The final magnified pixel size was 1.045 Å in the super-resolution counting mode. Each movie stack was dose-fractionated over 32 frames with the dose of 2.2 electrons per frame. The defocus values of all movie stacks varied from -1.3 µm to -2.3 µm.

A total of 18,547 movies were collected by SerialEM [START_REF] Mastronarde | Automated electron microscope tomography using robust prediction of specimen movements[END_REF] . Beam-induced motion and drift correction were performed using MotionCor2 35 . The CTF parameters for each micrograph were determined by Gctf [START_REF] Zhang | Gctf: Real-time CTF determination and correction[END_REF] . Particle selection was performed using template-free auto-picking in RELION 3.0 (ref. 28). A total of 6,587,999 particles were extracted and then subjected to three rounds of reference-free 2D classification and six rounds of 3D classification. The best classes with 1,113,538 particles were selected and subjected to 3D auto-refinement and Bayesian polishing to get a 3.9-Å resolution map. Focused refinement of the ECDs was performed, which further improved the ECD map resolution to 3.5 Å. A composite map was generated in UCSF Chimera 34 using 'vop maximum' command and used for subsequent model building and analysis. The maps of mGlu2 and mGlu7 homo-and heterodimers exhibit a higher resolution in the VFT region compared to that in the CRDs and TMDs, indicating that these regions are more structurally dynamic.

Cryo-EM model building and refinement

The structures of inactive mGlu2 and mGlu7 were built using the inactive mGlu5 structure (PDB ID: 6N52) as an initial model. The structure of agonist/PAM-bound mGlu2 was built using the agonist/PAM-bound mGlu5 structure (PDB ID: 6N51) as an initial model. The model of the inactive mGlu2-7 heterodimer was built using the solved structures of inactive mGlu2 and mGlu7. All the models were docked into the cryo-EM density maps using Chimera [START_REF] Pettersen | UCSF Chimera--A Visualization System for Exploratory Research and Analysis[END_REF] , followed by iterative manual adjustment in Coot [START_REF] Emsley | Features and development of Coot[END_REF] and real space refinement in Phenix [START_REF] Adams | PHENIX: a comprehensive Python-based system for macromolecular structure solution[END_REF] . The crystal structures of mGlu2-TMD-NAM complexes (see below for materials and methods) were used to aid refinement of the TMDs in the inactive mGlu2 structure due to a relatively low resolution of the cryo-EM map in this region. The model quality was validated using MolProbity [START_REF] Chen | MolProbity: all-atom structure validation for macromolecular crystallography[END_REF] . The final refinement statistics are provided in Extended Data Table 1. The final models include most of residues in the receptors and the agonist LY354740 and nanobody DN13 in the agonist/PAM-bound mGlu2 structure. The mGlu2 NAM NAM563 (inactive mGlu2 and mGlu2-7), mGlu7 NAM MMPIP (inactive mGlu7 and mGlu2-7), mGlu2 PAM JNJ-40411813 (agonist/PAM-bound mGlu2), and the FKBP and FRB fusion proteins in the C termini of the mGlu2-7 heterodimer were not modeled due to the relatively low resolution in the TMD region.

Expression, purification, and crystallization of mGlu2-TMD-NAM complexes

The gene of mGlu2-TMD (residues 556-845) was modified by introducing the mutations N655 3.52 Y and H815 7.53 Y and replacing residues 663-670 at ICL2 with a fusion protein flavodoxin [START_REF] Chun | Fusion Partner Toolchest for the Stabilization and Crystallization of G Protein-Coupled Receptors[END_REF] , and cloned into a modified pFastBac1 vector with the HA signal sequence and Flag-tag at the N terminus and the PPase site followed by a 10 × His-tag at the C terminus.

The optimized mGlu2-TMD construct was expressed in Spodoptera frugiperda (Sf9) (Invitrogen) insect cells using the Bac-to-Bac Baculovirus Expression System (Invitrogen).

Sf9 cells at a cell density of 2 × 10 6 cells per ml were infected with high-titer virus at a MOI (multiplicity of infection) of 5. Cells were harvest 48 h post infection by centrifugation.

The cells expressing mGlu2-TMD were lysed in the hypotonic buffer containing 10 mM HEPES, pH 7.5, 10 mM MgCl 2 , 20 mM KCl, and EDTA-free protease inhibitor cocktail tablets (Roche). Extensive washing of the membranes was performed by repeated dounce homogenization and centrifugation in the hypotonic and high-osmotic buffers. Purified membranes were suspended in the hypotonic buffer with addition of 30% glycerol, 20 μM NAM563 (ref. 5) or NAM597 (ref. 10) (provided by Merck), and EDTA-free protease inhibitor cocktail. After incubation at 4 ºC for 1 h, the complex was extracted by adding equal volume of solubilization buffer containing 100 mM HEPES, pH 7.5, 1 M NaCl, 1% (w/v) DDM, and 0.2% (w/v) CHS. After incubation at 4 ºC for 3 h, the supernatant was isolated by centrifugation at 160,000g for 30 min and incubated with TALON resin (Clontech) at 4 ºC overnight. The resin was washed with 25 column volumes of wash buffer containing 25 mM HEPES, pH 7.5, 500 mM NaCl, 0.05% (w/v) DDM, 0.01% (w/v) CHS, 10% glycerol, 50 µM NAM563 (or NAM597), and 30 mM imidazole, and eluted by increasing the concentration of imidazole to 300 mM. PD MiniTrap G-25 column (GE Healthcare) was then used to remove imidazole. The sample was supplemented with 100 µM NAM563 (or NAM597) and incubated with His-tagged PPase (custom-made) at 4 ºC overnight to cut off His-tag. The Ni-NTA resin (Qiagen) was added to remove the cleaved His-tag and PPase. The purified sample was concentrated to 20-30 mg ml -1 with a 100-kDa molecular weight cut-off concentrator (Millipore).

The mGlu2-TMD-NAM complexes were crystallized using the lipidic cubic phase (LCP) method [START_REF] Caffrey | Crystallizing Membrane Proteins Using Lipidic Mesophases[END_REF] . The proteins were mixed with lipid (monoolein/cholesterol 10:1 by mass) at a ratio of 1:1.5 (w/w) using a syringe lipid mixer. The LCP mixture was dispensed onto 96-well glass sandwich plates (Shanghai FAstal BioTech) in 35 nl drop and overlaid with 800 nl precipitant solution using a Gryphon robot (Art-Robbins). The crystals of mGlu2-TMD-NAM563 appeared in 100 mM HEPES, pH 7.0, 100-200 mM NaCl, 100-200 mM MgCl 2 , and 20-30% (v/v) PEG 400 after 1 day and reached full size in 4-8 days. The crystals of mGlu2-TMD-NAM597 grew in 100 mM MES, pH 6.0-6.5, 50-200 mM NaCl, 50-150 mM MgCl 2 , 20%-35% (v/v) PEG 400 and reached full size in 7 days. Crystals were harvested using 50-75 µm micro mounts (M2-L19-50/150, MiTeGen) and immediately flash-frozen in liquid nitrogen.

X-ray data collection, processing, and structure determination of mGlu2-TMD-NAMs

Crystal diffraction data collection was performed at the SPring-8 beam line 41XU, Hyogo, Japan, using a Pilatus3 6M detector (X-ray wavelength 1.0000 Å). The crystals were exposed with a 10 μm × 8 μm mini-beam for 0.2 s and 0.2° oscillation per frame. Due to radiation damage, data collection was limited to 10-15° per crystal. HKL2000 [START_REF] Otwinowski | Processing of X-ray diffraction data collected in oscillation mode[END_REF] residues of mGlu2 (G564-V825) and 147 residues of flavodoxin (A1-I147). In both crystal structures, the receptor TMDs form dimers through a dimer interface mediated by helices I, VI, and VII, which is likely resulted from crystal packing.

IP accumulation assay

Flag-tagged wild-type and mutant mGlu2 and mGlu7 receptors were cloned into the pTT5 vector and expressed in HEK293F cells. Cells were co-transfected with the plasmids of receptor, glutamate transporter EAAC1, and a chimera G protein Gα qi9 , which allows efficient signalling through the phospholipase C pathway [START_REF] Xue | Major ligand-induced rearrangement of the heptahelical domain interface in a GPCR dimer[END_REF] , at a ratio of 2:1:2. Cells were harvested 48 h post transfection. The surface expression of receptors was measured with the Monoclonal Anti-Flag M2-FITC antibody (Sigma; 1:100 diluted in TBS+4% BSA) using a flow cytometry reader (Millipore). IP1 accumulation was measured using IP-One G q assay kit (Cisbio Bioassays) following the manufacturer's instructions.

For LY354740-induced IP accumulation of mGlu2, the cells expressing the wild-type mGlu2 or mutants (18,000 cells per well) were incubated with increasing concentrations of LY354740 (1.58 pM -25 µM) at 37 ºC for 45 min. For glutamate-induced IP accumulation of mGlu7, the cells expressing the wild-type mGlu7 or mutants (12,000 cells per well) were incubated with 2.5 µM VU0422288 (mGlu7 PAM) [START_REF] Jalan-Sakrikar | Identification of positive allosteric modulators VU0155094 (ML397) and VU0422288 (ML396) reveals new insights into the biology of metabotropic glutamate receptor 7[END_REF] and increasing concentrations of Lglutamate (1.58 µM -100 mM) at 37 ºC for 1 h. To measure the basal activity of mGlu2 and mGlu7, cells were incubated with stimulation buffer at 37 ºC for 90 min. Inhibition of IP accumulation by the NAMs of mGlu2 and mGlu7 was measured by incubating the cells with the agonist at EC 80 concentration (100 nM LY354740 for mGlu2; 10 mM glutamate for mGlu7) and increasing concentrations of NAMs (0.13 nM -50 µM NAM563; 0.76 nM -50 µM MMPIP) for 90 min. Cells were then incubated with cryptate-labelled anti-IP1 monoclonal antibody (1:20 diluted in lysis and detection buffer) and IP1-d2 antibody (1:20 diluted in lysis and detection buffer) for 1 h at room temperature. Fluorescence signal was measured using a Synergy II (Bio-Tek) plate reader with excitation at 330 nm and emission at 620 nm and 665 nm. The accumulation of IP1 was calculated according to a standard doseresponse curve using GraphPad Prism 8.0 (GraphPad software). The basal activity was calculated by subtracting the IP production measured in the control (Gα qi9 alone) for the WT receptor and all the mutants.

BRET assay using TRUPATH biosensors

To measure G i protein activation, a BRET assay using TRUPATH biosensors [START_REF] Olsen | an open-source biosensor platform for interrogating the GPCR transducerome[END_REF] , which measures the proximal interaction between the α and γ subunits, was performed. In brief, HEK293T cells (Invitrogen) were plated in 6-well plates at a density of 6-7 × 10 5 cells per well one day before transfection. Then, the cells were co-transfected with plasmids of receptor, Gα-RLuc8, Gβ, and Gγ-GFP2 [TRUPATH was a gift from Bryan Roth (Addgene kit # 1000000163)] at a ratio of 1:1:1:1 (500 ng per plasmid). After 24 h post transfection, cells were digested by 0.25% Trypsin-EDTA (Thermo Fisher Scientific) and plated in poly-D-lysine-coated white 96-well assay plates (Corning) at a density of 2-5 ×10 4 cells per well.

After 24 h, the culture medium was replaced with 60 µl of assay buffer [1 × Hank's balanced salt solution (HBSS), 20 mM HEPES, pH 7.4, and 0.1% BSA), followed by adding 10 µl freshly prepared 50 µM coelenterazine 400a (Nanolight Technologies) and equilibrating for 5 min. Then, plates were measured by Synergy II (Bio-Tek) plate reader with 410 nm (RLuc8coelenterazine 400a) and 515 nm (GFP2) emission filters for 5 min. The cells were then treated with 30 µl ligand for 5 min and continued to read serially 8 times. The last measurements were used in all analyses. The BRET ratios were calculated as the ratio of the GFP2 emission to RLuc8 emission.

Intracellular calcium release measurement

The Intracellular calcium release was measured as describe before [START_REF] Liu | Allosteric control of an asymmetric transduction in a G protein-coupled receptor heterodimer[END_REF] . In brief, the HEK293 cells (ATCC, CRL-1573) were transfected with the chimeric G protein Gα qi9 and the glutamate transporter EAAC1 together with the mGlu constructs. The transfected cells were loaded in 96-well plates with 1 μM Fluo4-AM in fresh buffer (20 mM HEPES, pH 7.4, 130 mM NaCl, 5.1 mM KCl, 0.42 mM KH 2 PO 4 , 0.32 mM Na 2 HPO 4 , 5.27 mM glucose, 3.3 mM Na 2 CO 3 , 0.1% BSA, and 2.5 mM probenecid) for 1 h at 37 °C. The fluorescence (excitation 485 nm, emission 525 nm) was measured for 60 s by a FlexStation 3 microplate reader (Molecular Devices, Sunnyvale, CA, USA). The ligand was injected at 20 s during recording.

tr-FRET measurement and ELISA

HEK293 cells were transiently transfected with indicated plasmids and plated in 96-well plates at 10 5 cells per well. After 24 h transfection, the cells were washed with PBS and incubated with fluorophore-conjugated antibodies HA-Tb cryptate antibody (Pekin Elmer; The expression levels of different proteins were evaluated by ELISA. The transfected cells were fixed for 5 min with paraformaldehyde (4%), then blocked with PBS containing 1% fetal bovine serum (FBS) and incubated for 30 min with monoclonal anti-HA horseradish peroxidase (Roche; 1:2,000 diluted in PBS+1% FBS) or anti-Flag horseradish peroxidase (Sigma; 1:20,000 diluted in PBS+1% FBS). Bound antibody was detected using a SuperSignal substrate (Pierce) and a Tecan infinite 200Pro plate reader.

Cysteine crosslinking and fluorescent-labelled blot experiments

Crosslinking of mGlu2 and mGlu2-7 mutants were measured by fluorescent-labelled blot as previously described [START_REF] Xue | Major ligand-induced rearrangement of the heptahelical domain interface in a GPCR dimer[END_REF] . After 48 h transfection, the HEK293 cells plated in 12-well plates were incubated in GlutaMAX medium (Gibco) overnight. Then, the cells were labelled with 100 nM SNAP-Surface 647 (NEW ENGLAND BioLabs Inc.) in culture medium at 37 °C for 1 h. Cells were then washed once with PBS and crosslinked with 1.5 mM CuP in crosslinking buffer (16.7 mM Tris, pH 8.0, 100 mM NaCl, 1 mM CaCl 2 , and 5 mM MgCl 2 ) at room temperature for 20 min. After incubation with 10 mM N-ethylmaleimide at 4 °C for 15 min to stop the crosslinking reaction, cells were lysed with lysis buffer (50 mM Tris, pH 7.4, 150 mM NaCl, 1% Nonidet P-40, and 0.5% sodium deoxycholate) at 4 °C for 1 h. After centrifugation at 12,000g for 30 min at 4 °C, supernatants were mixed with loading buffer at 37 °C for 10 min. Equal amounts of proteins were resolved by 6% SDS-PAGE. Proteins were transferred to nitrocellulose membranes (Millipore). Membranes were imaged by Odyssey CLx imager (LI-COR Bioscience, Lincoln, NE, USA).

Correspondence and requests for materials should be addressed to H.L., J.L., F.S., B.W. 762 or Q.Z. 763 5299. The mutant C121A/V782 6.59 C-C121A/V789 7.27 C was tested using an optimized GABA B quality control system, in which the C-terminal tails of the two mGlu2 subunits were replaced by the modified C1 and C2 domains of GABA B1 and GABA B2 , respectively, to only allow the mGlu2 dimers containing the C1-C2 dimer reach the cell surface [START_REF] Huang | Interdomain movements in metabotropic glutamate receptor activation[END_REF] . The WT and mutant C121A were tested in parallel as controls. Three independent experiments were performed with similar results. Results from a representative experiment are shown. For gel source data, see Supplementary Figure 1. v, LY354740-induced IP accumulation assay of mGlu2 in presence of the oxidant CuP. Surface expression levels of the mGlu2 mutants are reported as percent compared to the WT from at least three independent measurements performed in duplicate (% of WT): C121A, 100 ± 6; C121A/L698 4.51 C, 84 ± 11; C121A/V699 4.52 C, 92 ± 9. w, LY354740-induced IP accumulation assay of the mGlu2 mutants in the CRD. See Extended Data Table 3 for detailed statistical evaluation and expression level. x, Glutamate-induced IP accumulation assay of WT mGlu7 and mutants in presence of VU0422288. See Extended Data Table 3 for detailed statistical evaluation and expression level. y, LY354740-induced IP accumulation assay of mGlu2 mutants in the CRD and ECL2. See Extended Data Table 3 for detailed independent experiment numbers (n), statistical evaluation, and expression level. z, JNJ-40411813-induced IP accumulation assay of WT mGlu2 and the mutant in ECL2. aa, Crosslinking of the mGlu2-7 mutants C121A/D174C (mGlu2)-C136A/R191C (mGlu7) and C121A/S176C (mGlu2)-C136A/R191C (mGlu7). The crosslinking studies were carried out using the GABA B C1-C2 quality control system that allows cell surface targeting of the heterodimer only [START_REF] Liu | Allosteric control of an asymmetric transduction in a G protein-coupled receptor heterodimer[END_REF] . The WT heterodimer and mutant C121A (mGlu2)-C136A (mGlu7) were tested in parallel as controls.

Four independent experiments were performed with similar results. Results from a representative experiment are shown. For gel source data, see Supplementary Figure 1. and active mGlu2 structures. The mGlu2-TMD-NAM563 structure and the G i -bound subunit in the mGlu2-G i structure are colored cyan and dark red, respectively. The residue W773 6.50 in the two structures and the residues that form interactions with W773 6.50 in the mGlu2-TMD-NAM563 structure are shown as sticks. The red arrow indicates the rotamer conformational change of W773 6.50 in the active structure relative to the inactive structure. h, Comparison of the ionic locks in the inactive and active mGlu2 structures. The mGlu2-TMD-NAM563 structure is colored cyan. The G i -bound subunit and G i protein in the mGlu2-G i structure are colored dark red and green, respectively. The residues K653 3.50 , R656 3.53 , E754, and E758 6.35 that form ionic interactions in the inactive structure are shown as sticks in both structures. The ionic interactions in the inactive structure are shown as red dashed lines and the interaction between R656 3.53 and Gα i in the active structure is shown as a blue dashed line.

Extended Data

Extended Data Table 3 | IP accumulation assays of wild-type (WT) and mutant mGlus

using a chimeric Gα protein Gα qi9 † The basal activity was calculated by subtracting the IP production measured in the control (Gα qi9 ) for the WT receptor and all the mutants, and is presented as percent of WT activity. ‡ Data are shown as mean ± SEM from at least three independent experiments. nd (not determined) refers to data where a robust concentration response curve could not be established within the concentration range tested. ***P<0.001 by one-way ANOVA followed by Dunnett's post-test compared to the response of WT. § Sample size, the number of independent experiments performed in technical triplicate.

||

Protein expression levels of mGlu2 and mGlu7 constructs at the cell surface were determined in parallel by flow cytometry with an anti-Flag antibody (Sigma) and reported as percent compared to the WT from at least three independent measurements performed in duplicate. ¶ The mutations were introduced in the wild-type receptor.

# The span is defined as the window between the maximal agonist response (Emax) and the vehicle (no agonist/PAM). † † The IC 50 ratio (IC 50(mutant) /IC 50(WT) ) characterizes the effect of mutations on inhibitory activity of NAMs. ‡ ‡ n=29.

Fig. 1 |

 1 Fig. 1 | Maps and structures of mGlu2 and mGlu7. The maps and structures are colored

Fig. 2 |

 2 Fig. 2 | Inactive mGlu structures. a, Comparison of the TMDs in the inactive structures of

Fig. 3 |

 3 Fig. 3 | Structure and activation of mGlu2-7 heterodimer. a, Structural comparison of

  was used for integrating and scaling data from 21 mGlu2-TMD-NAM563 crystals and 26 mGlu2-TMD-NAM597 crystals. Both structures were solved by molecular replacement with Phaser 42 using mGlu1-TMD (PDB: 4OR2) and flavodoxin (PDB: 1I1O) structures as searching models. The correct molecular replacement solutions contained one mGlu2-flavodoxin molecule in the asymmetric unit. Refinements were performed with Refmac5 43 , Buster 44 , and Phenix 37 followed by manual examination into |2F o | -|F c | and |F o | -|F c | maps with Coot 36 . The final models of the mGlu2-TMD-NAM563 and mGlu2-TMD-NAM597 complexes contain 262

1 :

 1 160 diluted in Tris KREBS buffer) and Flag-d2 antibody (Pekin Elmer; 1:267 diluted in Tris KREBS buffer) overnight at 4 . The fluorescence of the cryptate (620 nm) and d2 (665 nm) was measured 40 µs after excitation at 337 nm using PheraStar instrument (BMG Labtechnologies). tr-FRET signals were expressed as ΔF% = [(665/620) sample -(665/620) mock ] × 100 / (665/620) mock .

Extended Data Fig. 2 |

 2 Cryo-EM processing and 3D reconstruction workflow. a-f, Results of the inactive mGlu2 homodimer. a, Processing workflow. b, Representative cryo-EM image from four independent experiments with similar results. c, 2D averages. d, Cryo-EM map colored according to local resolution (Å). e, Gold-standard FSC curve showing an overall resolution at 3.6 Å. f, Cross-validation of model to cryo-EM density map. FSC curves for the final model versus the final map and half maps are shown in black, red, and green, respectively. g-l, Results of the inactive mGlu7 homodimer. g, Processing workflow. h, Representative cryo-EM image from five independent experiments with similar results. i, 2D averages. j, Cryo-EM map colored according to local resolution (Å). k, Gold-standard FSC curves showing an overall resolution at 4.0 Å and a resolution at 3.6 Å for the ECDs. l, Cross-validation of model to cryo-EM density map. m-r, Results of the agonist/PAM-bound mGlu2 homodimer. m, Processing workflow. n, Representative cryo-EM image from three independent experiments with similar results. o, 2D averages. p, Cryo-EM map colored according to local resolution (Å). q, Gold-standard FSC curve showing an overall resolution at 3.1 Å. r, Cross-validation of model to cryo-EM density map. s-x, Results of the inactive mGlu2-7 heterodimer. s, Processing workflow. t, Representative cryo-EM image from four independent experiments with similar results. u, 2D averages. v, Cryo-EM map colored according to local resolution (Å). w, Gold-standard FSC curves showing an overall resolution at 3.9 Å and a resolution at 3.5 Å for the ECDs. x, Cross-validation of model to cryo-EM density map. Extended Data Fig. 3 | Cryo-EM density maps of mGlu2 and mGlu7 homo-and heterodimers. The models are shown as cartoon and sticks. The density maps are colored gray. a, Map and model of the inactive mGlu2 structure shown for all transmembrane helices, B and C helices in VFTs, CRDs, and intersubunit disulfide bond. The model is colored blue (molecule A) and gray (molecule B). b, Map and model of the inactive mGlu7 structure and mGlu7 are shown as spheres. The distance between the Cα atoms of the cysteine residues in each structure is indicated by a dashed line and colored blue (mGlu2), magenta (mGlu5), or orange (mGlu7). The red arrow indicates the movement of the CRDs in mGlu5 and mGlu7 relative to that in mGlu2. f, Comparison of VFT conformations in agonist-bound mGlu structures. The structures of LY354740/JNJ-40411813-bound mGlu2, L-quisqualate/CDPPBbound mGlu5 (PDB ID: 6N51), LY354740-bound mGlu2-VFT (PDB ID: 4XAQ), and glutamate-bound mGlu2-VFT (PDB ID: 5CNI) are shown in cartoon representation and colored blue, magenta, red, and light gold, respectively. g, Comparison of the CRDs in the agonist/PAM-bound mGlu2 and mGlu5 structures. The structures are shown in both side and extracellular views. h, Interactions between the CRDs in the agonist/PAM-bound mGlu2 structure. The residues that are involved in dimerization are shown as blue and gray sticks, respectively. The disulfide bonds are shown as yellow sticks. i, Comparison of VFT conformations in the inactive mGlu2 and mGlu7 homo-and heterodimers. j, VFT dimer interface in the inactive mGlu2-7 heterodimer structure. The residues that are involved in dimerization are shown as sticks. Extended Data Fig. 5 | Sequence alignment of the TMDs of human mGlus. Colors represent the similarity of residues: red background, identical; red text, strongly similar. The red arrows indicate the positions with mutations in the inactive mGlu2 and mGlu7 structures (2, mGlu2; 7, mGlu7). The mGlu2 residues that are involved in TMD dimerization in the inactive mGlu2 structure are indicated by green arrows. The conserved residues with the modified Ballesteros-Weinstein numbers for class C GPCRs, 1.50, 2.50, 3.50, 4.50, 5.50, 6.50, and 7.50, are indicated by black arrows. The alignment was generated using UniProt (http://www.uniprot.org/align/) and the graphic was prepared on the ESPript 3.0 server (http://espript.ibcp.fr/ESPript/cgi-bin/ESPript.cgi).

Fig. 7 |

 7 tr-FRET and functional assays of mGlu2 and mGlu7 homo-and heterodimers. a, Validation of mGlu2-7 heterodimer and construct used for structural determination by tr-FRET assay. The signals were measured using the N-terminal HA-and Flag-tags in each subunit. In each panel, cartoons illustrating the dimer compositions are shown at the bottom. Data are displayed as mean ± SEM (bars) from three independent experiments performed in technical triplicate with individual data points shown (dots). b, Cell surface expression of homo-and heterodimers quantified by ELISA. Data were calculated as the fold of mock. Data are displayed as mean ± SEM (bars) from three independent experiments performed in technical triplicate with individual data points shown (dots). c-g, Calcium release assays of mGlu2-7 heterodimer. Data are shown as mean ± SEM from at least three independent experiments performed in technical triplicate and correspond to the peak response. The numbers of independent experiments (n) are shown in the parentheses. c, e, and f, LY354740-induced calcium release of wild-type (WT) mGlu2-7 heterodimer and mutants. d, g, L-AP4-induced calcium release of WT mGlu2-7 heterodimer and mutants. h, LY354740-induced G i activation of mGlu2-7 × in presence of LY354740, LY354740+mGlu2 PAM (JNJ-40411813), or LY354740+mGlu7 NAM (MMPIP, ADX71743, or MDIP) measured by the BRET assay. Data are shown as mean ± SEM from at least three independent experiments performed in technical duplicate. The numbers of independent experiments (n) are shown in the parentheses. Extended Data Table 1 | Cryo-EM data collection, refinement and validation statistics * For inactive mGlu2, different datasets were collected with different magnification of 165,000 and 130,000, corresponding to different pixel sizes of 0.82 Å and 1.04 Å, respectively. † Particles picked from different datasets with different pixel sizes. The particles were then combined using RELION 3.1. ‡ n.a., not applicable. The LocSpiral performs the local map enhancement based on thresholding of amplitudes, which are obtained by using the spiral phase transformation. The algorithm does not estimate or use the B factor. Extended Data Table 2 | Data collection and structure refinement statistics of mGlu2-TMD-NAM563 and mGlu2-TMD-NAM597 complexes * Numbers in parentheses refer to the highest-resolution shell.

L684 4. 37

 37

L691 4. 44

 44

L692 4. 45

 45

A677 4. 30

 30

L684 4. 37

 37

L691 4. 44

 44

L692 4. 45

 45

  --------------------------------------------------------------------------------

Acknowledgements

The cryo-EM studies were performed at the Center for Biological Imaging (CBI, http://cbi.ibp.ac.cn), Institute of Biophysics, Chinese Academy of Sciences and the EM facility of Shanghai Institute of Materia Medica (SIMM), Chinese Academy of Sciences. We thank B. Zhu, X. Huang, X. Li, L. Chen, and X. Niu from CBI and Q. Wang from SIMM for their help with cryo-EM data collection. The synchrotron radiation experiments were performed at the BL41XU of SPring-8 with approval of the Japan Synchrotron Radiation Research Institute (Proposal no. 2019A2543, 2019B2543, 2019A2541, and 2019B2541). We thank the beamline staff members K. Hasegawa, N. Mizuno, T. Kawamura, and H. Murakami of the BL41XU for help with X-ray data collection. We thank Merck for providing the mGlu2 NAMs NAM563 and NAM597. This work was supported by the National Key R&D Program of China 2018YFA0507000 (Q.Z., B.W., and J.L.), National Science Foundation of China grants 31825010 (B.W.), 81525024 (Q.Z.), 31830020 (F.S.), and 81720108031 (J.L.), and CAS Strategic Priority Research Programs XDB37030100 (Q.Z. and B.W.) and XDB37040102 (F.S.).

Data availability

Atomic coordinates and cryo-EM density maps for the structures of inactive mGlu2, agonist/PAM-bound mGlu2, inactive mGlu7, and inactive mGlu2-7 have been deposited in the RCSB Protein Data Bank (PDB) under accession codes 7EPA, 7EPB, 7EPC, and 7EPD, and the Electron Microscopy Data Bank (EMDB) under accession codes EMD-31235, EMD-31236, EMD-31237, and EMD-31238. Atomic coordinates for the structures of mGlu2-TMD-NAM563 and mGlu2-TMD-NAM597 have been deposited in the RCSB PDB under accession codes 7EPE and 7EPF. The uncropped gels shown in Extended Data Fig. 1r, u, aa are displayed in Supplementary Figure 1.

Author contributions J.D. developed the protein expression and purification procedures of mGlu2, prepared the mGlu2 protein samples for cryo-EM and crystallization, solved the crystal structures of mGlu2-TMD-NAMs, performed IP accumulation assay, and helped with manuscript preparation. D.W. developed the protein expression and purification procedures of mGlu7, prepared the mGlu7 protein sample for cryo-EM, performed model building and structure refinement of the homodimers, and helped with the IP accumulation assay and manuscript preparation. H.F. performed the cryo-EM studies of the mGlu2 homodimers. C.X. performed crosslinking, calcium release, and FRET assays. L.T. performed the cryo-EM studies of the mGlu7 homodimer. S.L. developed the protein expression and purification procedures of the mGlu2-7 heterodimer, prepared the mGlu2-7 protein sample for cryo-EM, and performed model building and structure refinement of the heterodimer. S.H. performed the cryo-EM studies of the mGlu2-7 heterodimer. Q.T. performed BRET assay. X.W. and T.X. helped with protein preparation and functional assays. H.Z. collected the crystal diffraction data. X.C. and C.Y. expressed the proteins. P.L. and Xi.W. helped with crosslinking and calcium release assays. J.-P.P. and P.R. helped with data analysis/interpretation and edited the manuscript. Y.Z. and H.L. provided mGlu2 ligands for structural and functional studies. J.L. oversaw crosslinking, calcium release, and FRET assays, helped with data analysis/interpretation, and edited the manuscript. F.S. oversaw the cryo-EM studies of mGlu2 and mGlu7 homodimers, helped with data analysis/interpretation, and edited the manuscript. B.W. and Q.Z. initiated the project, planned and analyzed experiments, supervised the research, and wrote the manuscript with input from all coauthors.

Competing interests

The authors declare no competing interests.

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