key: cord-0312694-iv5x4o6s
authors: Yin, Yizhou; Romei, Matthew; Sankar, Kannan; Pal, Lipika R.; Hoi, Kam Hon; Yang, Yanli; Leonard, Brandon; De Leon Boenig, Gladys; Kumar, Nikit; Matsumoto, Marissa; Payandeh, Jian; Harris, Seth F.; Moult, John; Lazar, Greg A.
title: Novel Antibody Interfaces Revealed Through Structural Mining
date: 2022-04-11
journal: bioRxiv
DOI: 10.1101/2022.04.06.487381
sha: 51d9546b94b1925403ec14b9a4a51554681da47c
doc_id: 312694
cord_uid: iv5x4o6s

Antibodies are fundamental effectors of humoral immunity, and have become a highly successful class of therapeutics. There is increasing evidence that antibodies utilize transient homotypic interactions to enhance function, and elucidation of such interactions can provide insights into their biology and new opportunities for their optimization as drugs. Yet the transitory nature of weak interactions makes them difficult to investigate. Capitalizing on their rich structural data and high conservation, we have characterized all the ways that antibody Fab regions interact crystallographically. This approach led to the discovery of previously unrealized interfaces between antibodies. While diverse interactions exist, β-sheet dimers and variable-constant elbow dimers are recurrent motifs. Disulfide engineering enabled interactions to be trapped and investigated structurally and functionally, providing experimental validation of the interfaces and illustrating their potential for optimization. This work provides first insight into previously undiscovered oligomeric interactions between antibodies, and enables new opportunities for their biotherapeutic optimization.

Avidity-driven amplification of weak transient protein-protein interactions is a common theme in 16 immunological processes. In some instances, weak interactions are clustered at cell-to-cell synapses, e.g. 17 between T cells and antigen presenting cells or target cells. In other cases, protein-level immune 18 complexation can promote naturally weak monovalent affinities to stronger avidity-driven binding events, 19 such as occurs during B cell receptor (BCR) selection and antibody responses (Lingwood et al., 2012) . 20

While the antibody variable region (Fv) commonly binds target antigen with high affinity, monomeric 21 interaction of the fragment crystallizable (Fc) region with effector receptors typically occurs in the µM 22 range where 1:1 binding events are generally inconsequential. Yet within immune complexes, avidity 23 amplifies these interactions into triggers for positive or negative cellular response. A recent illustration of 24 biological selection for avidity-driven triggers is the discovery of a transient homomeric interface in the IgG 1 Fc region that mediates antibody hexamerization (Diebolder et al., 2014) . Nature's ostensible purpose for 2 this interface is the amplification of antibody-mediated complement pathways, which are initiated by 3 interaction of the IgG Fc with pentameric complement protein C1q. 4 Apart from understanding the contribution of weak antibody interfaces to immunology, their 5 further value is their utility for optimization. Monoclonal antibodies are the most successful class of 6 biotherapeutics, delivering enormous impact for the treatment of cancer, autoimmunity, and other 7 diseases (Carter and Lazar, 2018) . As a consequence, antibodies have become one of the most highly 8 engineered protein families. Beyond Fv affinity maturation for target binding, native IgG interfaces 9 between immunoglobulin (Ig) domains and between antibody and cognate Fc receptors have been 10 successfully optimized for enhanced activities. Examples include engineering of the IgG CH3 domain for 11 heterodimerization (Ridgway et al., 1996) that enables bispecific antibody platforms (Spiess et al., 2015) , 12 enhancement of FcR-and complement-mediated effector functions (Chu et al., 2008; Idusogie et al., 13 2001; Lazar et al., 2006; F. Mimoto et al., 2013; Futa Mimoto et al., 2013; Moore et al., 2010; Niwa et al., 14 2004; Richards et al., 2008; Shields et al., 2002 Shields et al., , 2001 Stavenhagen et al., 2007; Umaña et al., 1999) , 15

and half-life extension through binding optimization to the neonatal Fc receptor FcRn (Dall'Acqua et al., 16 2006; Lee et al., 2019; Zalevsky et al., 2010) . These types of subtle modifications to natural and 17 sometimes weak antibody interfaces have met high success in drug development, with many of these 18 platforms in clinically approved drugs (Gaudinski et al., 2018; Ghazi et al., 2011; Kolbeck et al., 2010; 19 Latour et al., 2020; Nordstrom et al., 2011; Ollila et al., 2019; Robbie et al., 2013; Rugo et al., 2021; 20 Salles et al., 2021; Sheridan et al., 2018; Tobinai et al., 2017; Vijayaraghavan et al., 2020) . A corollary is 21 that the discovery of new antibody interfaces creates new opportunities for biotherapeutic optimization. 22

An intriguing aspect of the Fc hexamer discovery is that initial insights were derived from crystal 23 contacts within an IgG structure that had been deposited in the PDB many years prior (Diebolder et al., 24 2014; Saphire et al., 2001) . Distinguishing true biological assemblies from artifactual crystal contacts is a 25 long-studied problem in structural biology (Capitani et al., 2016) . Additional functionally relevant interfaces 26 have been identified from crystal packing, including a Fab homomeric interface (Tamada et al., 2015) and 27 oligomer interfaces in plastocyanin (Crowley et al., 2008) . These examples illustrate that crystal contacts 28 can provide insights into natural biological interfaces, albeit in an ad-hoc manner. 29

Antibodies offer a unique opportunity to investigate interfaces in crystallographic data in an 30 exhaustive manner. The high degree of structural homology of Ig domains together with the large number 31 of antibody structures in the protein data bank (PDB) provide a rich dataset of interactions. In this study 32 we have comprehensively mined the PDB to search for antibody interactions that may not have been 33 previously realized. This work advances a novel structural informatic approach for the investigation of 34 weak protein-protein interactions, and offers new insights into transient interactions in antibodies that may 35 be relevant to immune biology and enable new capabilities for biotherapeutic optimization. 36

All of the β-sheet dimers position the Fab monomers in an antiparallel orientation, with opposed 24 Fv's. In the context of a full-length antibody, using the most N-terminal hinge disulfide (EU position 25

Cys226 in human IgG1) as the tether point and a random coil residue distance of 3.5 Å, the C-termini of 26 the two Fab arms are constrained to a maximal distance of ~35 Å relative to each other. The calculated 27 distance between the HC C-termini of the two Fabs in all of the β-sheet dimers exceed this value (CH1-28 211: 41 Å, . This analysis 29 suggests that the orientation of the two Fabs precludes intra-IgG binding, forcing inter-IgG interactions 30 that would ostensibly promote higher-order complexation. 31 heterodimer (left) and CL-CL homodimer (right). β-sheet residues at the Fab-Fab dimer interface were 10 superimposed for the structural representatives of clusters CH1-211 and CL-211 (left), or CH1-211 and 11 . 12

Beyond β-sheet dimers, an additional recurring motif observed are interfaces mediated by the 1 elbow regions between variable and constant domains (Figure 2 and Supplementary figure 2) . These 2 interactions involve the elbow regions between either two HCs (CH1-207 and CH1-121) or two LCs . CH1-207 is the second most commonly observed 4 interface, and in total, the eight elbow region interfaces comprise 12.7% of nonredundant PDB entries. 5

The proximity of both the elbow and the β-turns/loops varies among these eight interfaces. In the case of 6 CH1-207, there are roughly balanced contributions from the variable and constant region loops and turns 7 (Supplementary table 2) . While elbow-elbow interaction was the general theme among these clusters, 8 as a collection there was greater overall structural dissimilarity relative to the group of β-sheet dimers 9 (Supplementary figure 2) . 10 11 Intra-cluster members show similarities at interface residues 12

To investigate sequence dependence, interface profiles were generated for the six most prevalent 13 clusters (Figure 4) , as well as the three additional clusters that form β-sheet dimers 14 and CL-205) (Supplementary figure 3) . The profiles describe the compositional distribution of each 15 cluster based on species (human, mouse, other), light chain (LC) type (kappa or lambda), as well as 16 human and mouse VH and VL subgroups. In addition, the profiles provide intra-versus inter-cluster 17 sequence identity for both the entire Fv as well as only those residues at each corresponding interface. 18

For the Fv, these values reflect the mean pairwise identities for all VH and VL sequences within a cluster 19 (intra) versus across the clusters (inter). A similar comparison is made for the interface, where only those 20 residues that participate in the interface for the designated cluster are compared. Finally, sequence logos 21 provide weighted sequence composition for cluster members at interface residues. 22 CH1-211 showed no apparent species dependence, being represented by sequences from 23 diverse species, LC type, and VH and VL subgroups (Figure 4) . The diverse subgroup representation is 24 also captured in the similar Fv intra-vs. inter-cluster identities (~50%). Similar overall results were 25 observed for the other top six clusters, with most demonstrating diverse representation of species, LC, 26 and Fv subgroups (Figure 4) . Notable biases are the Fv subgroup trends of CH1-207 and to lesser extent 27 VL-11. These are the two clusters among the top six where the Fv contributes substantially to the 28 interface, specifically the VH for the former and VL for the latter (Figure 2) . These clusters are comprised 29 principally of human subgroup IGHV3 for CH1-207 and human subgroup IGKV1 for VL-11. The 30 consensus interface residues based on their sequence logos (Figure 4 ) are well-represented in these 31 germlines. 32 profile are not repeated in the other charts for visual simplicity. The %ID plot on the right provides the 7 intra (red) versus inter (black) cluster sequence identity for both the entire variable region (Fv) as well as 8

only those residues at the interface as shown in the sequence logo and Supplementary table 2. For the 9

Fv, these values reflect the mean pairwise identities for all VH and VL sequences within the cluster (intra) 10 versus the mean pairwise identities between each member of the cluster and all other members of all 11 other clusters (inter). A similar comparison is made for each interface, where %ID reflects the mean 12 pairwise identity of the residues at the interface of a given cluster aligned with those same residues for 13 each member of the cluster (intra) versus all other members of all other clusters (inter). The sequence 14 logo at the bottom provides weighted sequence composition at interface residues for members of the 15 designated cluster, with numbering according to Kabat and EU conventions for the Fv and constant 16 regions, respectively. 17

The interface residues of CH1-211 are roughly as similar among members of the cluster (intra 1 identity 68%) as they are to those same residues among members of all other clusters (inter identity 64%) 2 ( Figure 4) . In contrast, three of the top clusters, CH1-209, CL-211, and CH1-212, display high intra-3 cluster interface identity (94%, 94%, and 96% respectively) relative to lower inter-cluster identities (70%, 4 58%, and 72% respectively) (Figure 4) . CL-211 is notable also for its bias towards lambda LCs ( Figure  5   4) . While kappa LCs are overrepresented in the PDB set overall (roughly 85% are kappa, 15% are 6 lambda), nearly all of the members of CL-211 are lambda. Deeper investigation revealed that kappa LCs 7 contain a proline at position 204 that terminates the N-terminus of the last β-strand. In contrast, lambda 8

LCs contain a Thr at 204 that, together with a shorter N-terminal loop, enable an extended β-strand that 9 permits β-sheet heterodimerization with the HC. Consistent with this observation, the CL-CL homodimer 10 interface CL-205 also showed a bias for lambda (Supplementary figure 3) . Overall, the diverse nature of 11 the sequences at a global level yet trends for some clusters at an interface level, suggest determinant 12 motifs that may provide further insight into the interactions as well as serve as guides for design. cysteine scanning analysis to explore all possible residue pairs at each interface for distance and 20 geometry that may be conducive to disulfide bond formation (Materials and Methods). A total of 179 21 residue pairs were identified, spanning 77 HC-HC, 54 LC-LC, and 48 HC-LC pairs. While the range of 22 designed variants per cluster was as high as 14, the median was 2 variants per cluster. Cysteine variants 23 were engineered into the Fab region of the anti-Her2 antibody trastuzumab (Carter et al., 1992) . Variant 24 and WT Fab antibodies were expressed in HEK 293 cells, purified by affinity resin, and analyzed by size 25 exclusion chromatography (SEC) ( Figure 5A ). Analysis of the full set of analytical data revealed that 26 many variants showed discrete dimeric species, in addition to monomeric antibody ( Figure 5B and 27 The presence of discrete dimer species in many of the designed variants supports the 1 computational analysis. Yet many of the cysteine variants were >95% monomeric, which is a common 2 expression profile for Fabs without engineered disulfides, as evidenced by WT (Figure 5A and B) . These 3 monomeric constructs represent internal controls, suggesting that transient non-random contact in 4 solution as well as proper geometry are required to form the stable oligomeric species. A subset of 5 variants with the most prominent dimer formation were selected to explore whether dimers could be 6 assembled in vitro. The monomeric Fab species of this variant subset were reduced in solution followed 7 by gradual re-oxidation with dehydroascorbic acid. Upon re-oxidation, discrete dimer species were 8 formed, similar to and correlated with the results from in vivo expression ( Figure 5C 

A representative set of 26 cys-engineered variants were selected to explore functional application. 18

Cysteines for each variant were introduced into an antibody referred to as 3C8 that is an agonist of the 19 receptor OX40 (CD134), which we have previously shown to provide a sensitive system for detecting 20 antibody-mediated receptor clustering (Yang et al., 2019) . Due to low expression yields or variable 21 monomer/dimer ratios, many of the variants were not characterized further. A subset of 5 variants that 22 expressed well and had a favorable monomer/dimer profile were chosen for further purification and 23 separation of species. Final monomer and dimer samples for each variant had high purity and were stable 24 in solution (i.e, they did not interconvert over time based on analytical SEC). Affinity measurements by 25 Biacore indicated that a subset of dimeric versions did not retain binding (data not shown), possibly due 26 to steric clash of antigen binding in the context of the coupled Fab dimer. However, two variants, 27 VH(S113C)/CH1(G178C) at the VH-16 interface and VH(P14C)/CL(D151C) at the CH1-176 interface, 28 maintained their affinities for OX40 (KD's for variants and WT ~10 nM, Supplementary figure 4) . 29

In an NFκB luciferase reporter assay utilizing OX40+ Jurkat cells, the 3C8 antibody has no 30 activity as a bivalent IgG on its own, but is a strong agonist of OX40 signaling when extrinsically 31 crosslinked with a secondary antibody ( Figure 5E ). An Fc-engineered triple variant (RGY) of this IgG that 32 promotes hexamerization (Diebolder et al., 2014) agonizes receptor without reliance on extrinsic 33 crosslinker. Strikingly, Fab dimer versions of the two cysteine-linked variants were capable of agonizing 34 OX40 in the absence of crosslinking, in contrast to inactive monomer versions of the same variants 35 ( Figure 5E ). The ability of the cys-linked Fab dimers to activate receptor signaling despite their bivalency 36 may be due to their ability to engage receptor with a particular geometry and/or orientation. While the 37 mechanism requires further study, these results illustrate how new interfaces may be used to engineer 1 novel geometries and orientations into antibodies in order to enable activities of therapeutic relevance. 2 3

To validate proper disulfide trapping of the interfaces and further support the results, we solved the x-ray 5 structures at <3 Å resolution for a representative subset of disulfide-trapped Fab dimers containing the 6 trastuzumab Fv. Experimental structures included one representative of the β-sheet dimer class [CL-205 7 ( Figure 6A) , and two representatives of the elbow dimer class CH-207 ( Figure 6B ) and VL-108 ( Figure  8 6C). Electron density maps were consistent with the presence of engineered disulfide bonds at the 9 expected sequence positions (Supplementary figure 5) . Experimentally-determined and informatically-10 mined structures were topologically similar, with good superposition at the interface sites (Figure 6) . The 11 most notable alignment discrepancy across the three can be seen for CH1-207. In this structure, the 12 disulfide bond pulls the HC elbow loops closer together on one end. While this perturbation rotates the left 13

Fab with respect to the right Fab, the interface region remains largely intact, suggesting that this 14 discrepancy may be due to disulfide bond constraints rather than the formation of an altered solution-15 phase configuration. Overall, these results provide strong evidence that the observed solution-phase 16 dimers homogeneously resemble the discovered dimer conformation rather than a mixture of interface-17 independent conformations from non-specific disulfide pairing. 18 colors match those in Figure 2 , with the informatically-mined structure at 0% transparency (left) and the 5 experimentally-determined structure at 30% transparency (right). Sulfur atoms participating in disulfide 6 bonds are shown in yellow. Overlays of the interface (middle) for A and C were configured by aligning the 7 α carbons of the Fab dimers from each structure, whereas the overlay for B used a single Fab for 8 alignment (see Results). 9

Discussion 1 Weak transient protein-protein interactions play fundamental roles in diverse biological processes 2 (Garcia-Seisdedos et al., 2017; Humphris and Kortemme, 2007; Ozbabacan et al., 2011) . While best 3 characterized in the context of intracellular signaling cascades, transient interactions are also relevant 4 extracellularly, including during immunological recognition where they can convert the avidity of a cell 5 synapse or antibody complex into a cooperative trigger for cellular activation or inhibition. While obligate 6

interactions are readily investigated with direct biochemical and structural methods such as 7 crystallography and electron microscopy, transient interactions are low in abundance and harder to 8 identify, requiring sensitive and sometimes indirect techniques such as the yeast two-hybrid system, 9 fluorescence resonance energy transfer, nuclear magnetic resonance spectroscopy, and split protein 10 complementation (Ozbabacan et al., 2011; Romei and Boxer, 2013) . While in rare instances weak 11 interactions have been gleaned from crystallographic structures, it can be difficult to distinguish between 12 true biological interfaces and crystal packing artifacts (Capitani et al., 2016) . 13

We have explored a novel structural informatics approach to search for previously 14 uncharacterized interfaces in antibodies. We selected antibodies for three reasons. First, the avid nature 15 of immune complexation provides a biological rationale for the existence of as yet undescribed interfaces 16 that could tune immune response. Second, the virtual one-to-one residue equivalence of antibodies 17 across a large structural data set enables mining of interaction patterns for commonality. Effectively, 18 prevalence in the current work serves as a signal-to-noise parameter that suggests biological relevance. 19

Finally, we are interested in discovering new antibody interfaces for their potential in biotherapeutic 20 engineering. Monoclonal antibodies are one of the most successful classes of drugs across a myriad of 21 medical needs, with the 100th antibody drug recently approved (Mullard, 2021) . While the most effective 22 antibody drugs have historically been native IgGs, recent years have witnessed an acceleration in 23 development and approval of engineered versions optimized for activity (Carter and Lazar, 2018) . Rather 24 than de novo sites, the most clinically successful enhancements are modest mutational modifications of 25 natural and often weak interactions, either intra-IgG or between antibodies and cognate receptors. The 26 logic flows that innovation of new capabilities in antibody therapeutics is best served by the discovery of 27 new natural antibody interfaces. 28

Our characterization of the crystal packing arrangements of 1,456 antibody Fab regions resulted 29 in a diversity of interfaces, with 42 represented in 5 or more PDB entries of nonredundant sequence. The 30 low frequency of most of these together with the generally weak structural and energetic features suggest 31 that many may be crystal artifacts. Confidence in biological relevance is increased by both high 32 prevalence and the existence of shared motifs across multiple results, namely the recurrence of β-sheet 33 dimers and interaction at Fab elbow regions. β-sheet dimers are by far the most commonly observed 34 motif, making up five of the six most prevalent interfaces and present in 30% of nonredundant PDB 35

entries, yet with a diversity of oligomeric and regional architectures. In all cases, the anti-parallel 36 orientations of the paired Fabs, together with their C-terminal distances that exceed hinge flexibility, 37 would preclude intra-Ig Fab interaction, forcing inter-Ig interactions that would promote immune 1 complexation. This notion is supported by the existence of naturally occurring examples where 2 intermolecular β-sheets associate to form protein heterodimers, homodimers, and larger oligomers 3 (Guharoy and Chakrabarti, 2007) . Homodimeric β-sheets are observed naturally, for example in ParB 4 (Schumacher and Funnell, 2005) , transthyretin (Monaco et al., 1995; Prapunpoj and Leelawatwattana, 5 2009) , and Ras-binding domain of c-Raf1 (Nassar et al., 1995) . β-sheet homodimerization has also been 6 successfully used as a template for de novo protein design (Stranges et al., 2011) , and is the commonly 7 observed arrangement in the structures of macrocyclic β-sheet peptides (Cheng et al., 2013) . The 8 intrinsic preference of exposed β-strands to pair is illustrated most dramatically in the aggregation of 9 amyloid fibrils (Greenwald and Riek, 2010) , and it has been proposed that naturally occurring proteins 10 use negative design to avoid edge-to-edge association (Richardson and Richardson, 2002) . Indeed a 11 "generic hypothesis" advanced by Dobson and Karplus suggests that extended β-sheets in amyloid 12 structure are an inherent characteristic of polypeptide chains rather than unique to a specific sequence or 13 structure (Dobson and Karplus, 1999) . This model is consistent with our observation of intermolecular β-14 sheet dimers across varying domains and orientations of the antibody Fab. It is tempting to speculate that 15 the Ig fold, in addition to providing loops for diversity and stable scaffolding to support that diversity, also 16 offers antibodies the additional and previously unrealized benefit of avid transient self-association through 17 inter-strand interactions. 18

Our disulfide engineering experiments provided further support for the discovered interactions 19 and enabled direct structural investigation. Overall, the experimental results suggest that disulfide-trapped 20 species are a result of predisposed contact in solution that, together with favorable geometry, promote 21 coupling of specific homotypic dimers. To explore the functional potential of these interfaces we 22 leveraged a therapeutically relevant antibody-receptor system that is sensitive to oligomeric interaction. 23

The anti-OX40 results represent a first attempt at exploiting this work for optimization, illustrating that the 24 discovered interfaces can serve as novel engineering sites to enhance biotherapeutic properties. 25

While further biological validation of the discovered interfaces is needed, our results suggest a 26 previously unknown structural feature of antibody Ig domains, and one that would be well-suited for 27 avidity-driven immune response. Transient β-sheet dimers could boost antigen affinity at the BCR level 28 during clonal selection. Transient interfaces could also be relevant at the IgG level for the enhancement 29 of antigen neutralization and Fc-mediated effector functions. The often repetitive and multivalent nature of 30 pathogenic targets, as well as the multiclonal nature of antibody response, have provided evolutionary 31 pressure for the multivalency of isotypes such as IgM and IgA (Kumar et al., 2020; Li et al., 2020) and IgG 32 hexamerization (Diebolder et al., 2014) . Such selective pressure has also resulted in more nuanced 33 valency tricks such as chain swap and Fab-dimerization observed in anti-HIV and -SARS-CoV-2 34 antibodies (Calarese et al., 2003; Williams et al., 2021; Wu et al., 2013) , homotypic interactions involved 35 in antibodies against plasmodium (Kucharska et al., 2020) , as well as in the context of therapeutic 36 antibodies (Rougé et al., 2020; Tamada et al., 2015) . While inter-IgG β-sheet interactions are weak, they 37 could become relevant energetic drivers on the cell surface or in the context of a solution immune 1 complex where the effective concentration of IgG may be high. In this manner, the environment of a cell 2 surface or solution immune complex may be akin to a biomolecular condensate (Feng et al., 2019) . While 3 condensates have typically been characterized in the context of intracellular biology, extracellular 4 examples are known, for example contributing to protein assembly in the extracellular matrix and cell-cell 5 adhesion (Chiu et al., 2020; Reichheld et al., 2017) . From this perspective, the Fab crystal lattice may be 6 a proxy for how antibodies behave in their condensed native biological environments. In this light the 7 results here, derived from holistic analysis of antibody structural packing data, provide fresh mechanistic 8 insight into how condensation of immune complexes, either at the cell surface or in solution, may enable 9 amplification of immune interactions into immunological response. 10 11

All Fab structure coordinates and the corresponding meta-information were downloaded from the 14 SAbDab database (Dunbar et al., 2014) on 01/26/2018. Species and germline information was cross-15 checked with information extracted from IMGT/3Dstructure-DB (http://www.imgt.org/3Dstructure-DB/) 16 (Ehrenmann et al., 2009; Kaas et al., 2004) . Fab PDB structures were then filtered to ensure first that 17 each Fab structure was complete (e.g. both heavy and LCs were longer than 180 residues), and second 18 that the structure was solved by X-ray diffraction with valid symmetry information (e.g "SMTRY" lines in 19 "REMARK 290" section). Numbering (UCN) was created as follows. (1) Germline genes (IGHC, IGKC, and IGLC) representing 1 species that appear in the SAbDab dataset were collected from the IMGT database 2 (http://www.imgt.org/vquest/refseqh.html). They were paired with Fab structures containing the highest 3 sequence similarity. IgE sequences were excluded due to lack of available structures in SAbDab. (2) The 4 seven most conserved β-strands corresponding to the protein core were manually identified based on the 5 multiple sequence alignment and structure alignment (if available) of the germline sequences and their 6 paired structures. Interestingly, structures of these β-strands superimpose well even between CH1 and 7 CL. (3) By using these seven intermittent β-strands as fixed regions and accounting for gaps in-between, 8 the representative germline sequences were manually aligned and numbered. The sequence alignment 9 was stored in .stockholm format. (4) Hidden Markov Model (HMM) profile libraries were compiled for each 10 species and germline gene in the manual sequence alignments using the hmmbuild and hmmpress 11 commands of the HMMER program. (5) All Fab constant domain sequences in the structure dataset were 12 then searched against these pre-computed HMM profile libraries using the hmmscan command of the 13 HMMER program, and were mapped to the corresponding positions in the best hit. 14 15

Identification of interfaces. The asymmetric unit in each Fab PDB structure was expanded into a crystal 16 lattice block by running a PyMOL script that calls the symexp command, which expands around the 17 original asymmetric unit up to 30 Å. For computing efficiency, the expanded crystal lattice block was then 18 trimmed down to at most 20 closest Fab monomer structures around the original asymmetric unit, which 19 was large enough to capture almost all potential symmetric interfaces. 20

To exhaustively identify all interfaces between Fab monomers in each crystal lattice block, all 21 pairs of Fab monomers were examined for all interfaces above 100 Å 2 (two-sides) after stripping away 22

water and other small molecules. An undirected graph was then built using Fab monomers as nodes and 23 interfaces as edges. An oligomer here is presented as a connected sub-graph, in which every node has 24 at least 1 edge to other nodes in the same sub-graph. By doing this, the problem of searching for all 25 existing oligomers is transformed to searching for all connected sub-graphs. An in-house merging 26 algorithm was developed to efficiently solve this problem. 27 28 Rotation angles and axis. A transformation matrix was computed between every possible pair of Fab 29 monomers (regardless of contact or not) by calling align and get_object_matrix PyMOL commands. The 30 rotation angle and axis were mathematically determined from the rotation matrix using the following 31 equations: 32

Where is the rotation axis vector, is the rotation angle, and is the trace of . is between 0, 180°, 1 which is a sufficient range to effectively test the rotational symmetry. Specially, when is 180°, to 2 determine the rotation axis, there are the following different possibilities: 3

Due to the limited computation precision, imperfect PDB structures, and pseudo symmetry, very similar 4 rotations were treated as identical rotations. To identify them, a pair of rotations were first compared by 5 angles with a cutoff of 5°, and then compared by the angle between their rotation axes with a cutoff of 5°. 6

The angle between rotation axes was calculated using the more numerically stable method: 7

Where is the angle between axes, and and are the vectors of the two axes. In two special cases, 0° 8 rotations were all dropped, and 180° inter rotation axes (opposite directions) were considered as the 9 same axes. 10

Determination of symmetric oligomers. The last step in the pipeline used the computed rotation 11 information to determine whether a given Fab oligomer is symmetric and in which types. The approach 12 explored every observed rotation in one oligomer. A symmetric rotation allows an oligomer to 13 superimpose to itself. Because a full-atom RSMD calculation on all symmetric rotations for all Fab 14 oligomers was prohibitively expensive, subunits were first represented as centroids that reflected their 15 position and orientation with minimal coordinates. This allowed a fast calculation with a permissive low-16 resolution RMSD threshold to filter out the vast majority of obvious non-symmetric rotations. A full-atom 17 RMSD calculation was applied to the remaining oligomers. Both centroid and full-atom RMSD were 18 required to be < 5 Å for a given rotation to be considered symmetric. Finally, identical symmetric 19 oligomers were identified and collapsed using the same centroid to full-atom RMSD strategy. 20 21 Clustering analysis 22

An interface was described using the set of interacting residues between them (identified by using a 23 distance cutoff ). Analysis was performed using a distance cutoff of 4 Å and 6 Å. 24 = {( , ) ∀ , such that ( , ) ≤ },

The similarity between two interfaces and is defined as the Jaccard index between the sets of 1 interfaces as follows: 2

A variant of the analysis utilized a weighted Jaccard similarity, in which each of the two contact pair sets 3 is a real number vector V, with its elements derived from the distance of the corresponding contact pair 4 (and value 0 for the non-contact residue pairs) as follows. 5

Then, the weighted Jaccard similarity was calculated as 6 , = ∑ min , ( , ) ∀ = 1,2, … | | ∑ max( , ) ∀ = 1,2, … | | The above similarity values were then used to generate distance matrices (using 1 -J or 1 -W as the 7 values) for distance cutoffs of 4 Å and 6 Å. Hierarchical clustering was then performed using single 8 linkage in R using the 'hclust' function. The resulting dendrograms were cut at different heights and the 9 similarities of various cluster members were compared to decide on the optimal cutoff height. The clusters 10 obtained by cutting the Weighted Jaccard index based dendrogram (and interface distance cutoff of 4 Å) 11 at a height of 0.3 was selected for further analysis. Based on the hierarchical clustering, each interface 12 was assigned to an interface cluster. 13 14

For each member of a cluster, the average of all weighted Jaccard similarity indices to all other members 16 was calculated. The representative member of each cluster was defined as the interface that had the 17 highest average weighted Jaccard index to all other members. 18

The name of a given cluster represents the residue at the structural center of the Fab-Fab 19

interface. The name adopts the format X-#, in which X represents commonly used abbreviations for Fab 20 chains (VH, VL, CH1, CL) and # represents the residue number according to either the Kabat or EU 21 numbering convention for variable or constant regions, respectively. The central residue for each cluster 22 was determined as follows. Relevant interface residues for each cluster's representative member were 23 determined by applying an interface distance cutoff of 5 Å. The xyz coordinates of the α-carbon for each 24 interface residue were averaged to obtain the structural average of the interface. For each residue in the 1 interface, the distance between the given residue's α-carbon and the structural average xyz coordinates 2 was determined. The residue with the shortest distance to the central xyz coordinates was used for the 3 naming convention. Duplication was avoided in a small number of instances by choosing the second 4 closest residue to the structural center. 5 6 Sequence analysis 7

For the antibody Fabs in the dataset, all-against-all pairwise alignments were determined for the different 8

Fab regions listed here: VH-only, VL-only, CH1-only, CL-only, and VH/VL-Fv-only. Dynamic 9 programming, with matching residue score at 1, mismatching score at -1, gap-opening score at -6, and 10 gap-extension score at -3, was used to determine the respective alignments. Referencing the pairwise 11 alignment results, Levenshtein distance was calculated to determine the difference between the pairwise-12 compared regions. Percent-identity was then calculated as the subtraction from 100% by the difference 13 percentage. In the case of Fv percent-identity, the respective VH and VL percent-identities were 14 determined separately; then, the average of the VH-and VL-percent-identities was reported as the 15 identity for the compared Fv regions. In the case of interface percent identity, sequence alignments were 16 performed only at the residue positions of a given interface for each interface (Supplementary table 2) . 17

Structural features of interfaces were analyzed using the 'Protein interfaces, surfaces and assemblies' 20 service PISA at the European Bioinformatics Institute. (http://www.ebi.ac.uk/pdbe/prot_int/pistart.html) 21 (Krissinel and Henrick, 2007) . PISA interfaces were downloaded from the PDBePISA site 22

(https://www.ebi.ac.uk/pdbe/pisa/) and mapped to in-house generated oligomer interfaces. Each such 23 oligomer interface consists of single or multiple disconnected PISA interfaces between different chains, 24 and each PISA interface can be included partly or fully, depending on the overlapping interface residues. 25

Buried surface area, number of H-bonds, and number of salt bridges for each interface were calculated 26 as the summation of its component PISA interfaces. In order to accurately analyze the in-house 27 interfaces, we applied two filtering processes for each oligomer interface: (1) removal of PISA interface 28 patches involving antigens, keeping only antibody-antibody interfaces and (2) removal of PISA interfaces 29 for which there was poor overlap (< 0.5) between PISA interface and in-house interface residues. 30 31

The representative structure of each cluster was used to perform an in silico cysteine scanning simulation 33 using the cysteine scanning module (Salam et al., 2014) in the BioLuminate suite (Schrodinger Inc.). 34

Default parameters were used, with residues within 5 Å allowed to be flexible (flex_dist = 5.0) while 35 performing stability calculations. Potential disulfide pairs were identified as those residue pairs with a Cβ-36

Cβ distance within 5.0 Å, irrespective of whether the calculations yielded favorable energies or not. The 37 list of all potential disulfide residue pairs identified through this analysis is summarized in Supplementary  1 tables 3-5. 2 3 DNA construction and protein production 4

The anti-Her2 and anti-OX40 antibodies used in this work have been described previously (Carter et al., 5 1992; Yang et al., 2019) . Molecular biology to generate the Fab disulfide variants was carried out using 6 gene synthesis (Genewiz). DNAs encoding LCs and Fab HCs in the pRK mammalian expression vector 7 were cotransfected into Expi293 cells for expression. Fabs were purified using CaptureSelect CH1-XL 8 affinity resin (Thermo, 194346201L) followed by SEC using a HiLoad 16/600 Superdex 200 column. Fab 9 monomer and dimer fractions were pooled separately during SEC purification to isolate the desired 10 oligomeric species. Protein quality was assessed by SEC using a Waters xBridge BEH200A SEC 3.5um 11 (7.8 x 300 mm) column (Waters,176003596) . For the characterization of oligomeric species following 12 expression, small aliquots of affinity purified Fabs were loaded onto the Waters column, and relative 13 percentages of oligomers were calculated using the area under the chromatogram for each peak. 14 Molecular weight of all Fabs was confirmed by LC/MS. Fabs were stored in a buffer consisting of 20 mM 15 histidine acetate and 150 mM NaCl at pH 5.5. 16 17

Solution binding was assessed using a Biacore T200 instrument (GE). Fabs were captured using either a 19 Series S Protein L chip (Cytiva, 29205138) or a human Fab capture reagent immobilized on a Series S 20 CM5 chip (Cytiva, 29104988 and 29234601) according to the manufacturer's specifications. A 4-fold 21 serial dilution of OX40 starting at 100 nM (G&P Bioscience, FCL0103) was prepared in HBS-P+ buffer (10 22 mM HEPES, 150 mM NaCl, 0.05% v/v surfactant P20, Cytiva, BR100671) and injected for 5 minutes, 23 followed by a 6 minute dissociation period. Affinity constants were obtained through kinetic fitting using 24 the Biacore Evaluation Software (GE). 25 26

Anti-Her2 Fab disulfide variants were exchanged into a phosphate-buffer saline (PBS) solution at pH 7.4 28 and concentrated to 0.5 mg/ml using Amicon Ultra centrifugal filters with a 10 kDa molecular weight cutoff 29 (Millipore, UFC901096). Dithiothreitol (Thermo, R0861) was added to 5 mM from a 40 mM stock solution 30 in water. Samples were incubated at 37C for 2 hours to fully reduce all cysteines. DTT was removed 31 through buffer exchange into PBS using an Amicon Ultra centrifugal filters with a 10 kDa molecular weight 32 cutoff (Millipore, UFC901096). The temperature of the samples was kept at 4C during the buffer 33 exchange process. A ten-fold molar excess of the oxidizing agent (L)-dehydroascorbic acid (Sigma-34 Aldrich, 261556) was then added to each sample from a 5 mM stock solution in PBS, and samples were 35 incubated for one week at room temperature. The oxidation reactions were stopped and any remaining 36 free sulfurs were capped upon addition of N-ethylmaleimide (Pierce, 23030) to 5 mM from a 100 mM 37 stock solution in water. SDS-PAGE of the re-oxidized samples was performed on a 4-15% Criterion TGX 1 precast midi protein gel (Bio-Rad, 5671085) under non-reducing conditions. Relative percentages of 2 oligomeric species were calculated using ImageJ. 3 4 Activity assay 5

The OX40 agonist assay was performed as previously described (Yang et al., 2019) . Briefly, OX40 6 overexpressing Jurkat cells engineered with an NFκB luciferase reporter were seeded at 80,000 cells/well 7 in 20 µl RPMI containing 1% L-glutamine and 10% HI FBS in a 384-well tissue culture plate (Corning Inc., 8 3985BC) . Anti-OX40 antibody formats were serially diluted three-fold in media starting at 30 μg/ml, and 9 10 µl of the concentrated antibodies were added to each well. For the conditions with crosslinking, 10 µl 10 of AffiniPure goat anti-human IgG Fcγ fragment specific antibody (for IgG samples, Jackson 11

ImmunoResearch Laboratories Inc, 109-005-098) in media was added to yield a 1:1 molar ratio with each 12 antibody dilution. For conditions without crosslinker, 10 µl of media was added to each antibody dilution. 13

The plates were then incubated for 16-18 hrs under 5% CO2 at 37°C. 40 µl of Bright Glo (Promega, 14 E2610) was then added to each well and incubated with shaking at room temperature for 5 min. 15

Luminescence was detected using a Perkin Elmer Envision plate reader. For larger panels of antibodies, 16 automation of this assay was developed using a Tecan Fluent. All activity data from this assay is reported 17 as fold change over control well without antibody. 18

Crystallographic structure solution 20

The purified dimers of the anti-Her2 Fab disulfide variants were concentrated to 10 mg/ml in PBS. contained 15 % w/v PEG 3350 and 100 mM sodium succinate. Crystals of the dimers were preserved for 27 data collection by brief soaking in a cryo-protectant buffer (25% glycerol added to the reservoir solution), 28 followed by rapid immersion into liquid nitrogen. Diffraction data were collected at the Advanced Light 29 Source (ALS) beam line 5.0.2 for CH1-207 and VL-108, while data for CL-205 were collected at the 30 Northeastern Collaborative Access Team (NE-CAT) beamline 24IDC. 31

Data were reduced with Global Phasing's autoProc using XDS (Kabsch, 32 2010) . Datasets for CH1-207 and VL-108 were defined with elliptical anisotropic resolution as 33 implemented in the STARANISO procedure (Tickle et al., 2018) . figure 5) and these were introduced during manual model building in Coot (Emsley and 1 Cowtan, 2004) . Of note, the initial solution for VL-108 was determined in a 6-fold symmetry group, but 2 presented only 1 molecule per asymmetric unit in that context with the neighboring linked protomer 3 positioned by apparent crystal symmetry. However, the inability to adequately model the disulfide bond of 4 interest across the special symmetry position and the potential twinning led us to reduce the space group 5 symmetry to P3121 with two Fab molecules per asymmetric unit and to model twinning in the data that 6 had presented as the higher symmetry. Similarly, the CL-205 dataset initially appeared to be in space 7 group P21 with two Fabs per asymmetric unit but had strong indicators of translational pseudo-symmetry 8 (Phenix xtriage (Adams et al., 2010) analysis) and the Rfree value did not decrease much below 30% in 9 refinement efforts. The data were re-processed in P1 and the molecular replacement search repeated to 10 identify 4 Fab molecules per asymmetric unit, and refinement in this setting with amplitude-based twin 11 estimates in REFMAC (Murshudov et al., 1997) provided approximately 4% reduction in R factors. The 12 CH1-207 data were mercifully more straightforward. Models were refined with cycles of REFMAC 13 (Murshudov et al., 1997) , Phenix (Adams et al., 2010) or Buster to reasonable 14 statistics (Supplementary table 7) . CL-205 has 4 Fab molecules per asymmetric unit in space group P1, 15 the engineered interface between the two Fabs, which are assigned chains H (heavy) and L (light) and 16 the second Fab with chains A (heavy) and B (light) and analogously for the neighboring C/D and E/F 17 chain Fabs. The CH1-207 structure also displays 4 Fab molecules/asu, with engineered interfaces 18 between Fabs HL and AB and Fabs CD and EF. Finally, VL-108 contains 2 Fab molecule/asu in a P3121 19 space group setting, twinned, assigned chains HL and AB. 

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