Holbrook Kohrt

Aurelien Marabelle
email: aurelien.marabelle@gustaveroussy.fr

Roch Houot

A tribute to the life and career of

Holbrook Kohrt, a key inspiring and influential leader in the new field of immuno-oncology, passed away at the height of his professional life on February 24th 2016, aged 38. This devastating news has left many in the immuno-oncology community with a huge sense of loss and sadness.

Until the very end, Holbrook has been entirely dedicated to simultaneously fight against two diseases. The first was hemophilia, which he fought as a patient, and which eventually took him over. The second was cancer, which he fought as a doctor and researcher in hematology and immunology to which he made major contributions.

People who got a chance to know Holbrook quickly realized that he was clearly in a league of his own. Looking at his curriculum shows how amazing he was to have accomplished so many things in such a short amount of time. Holbrook successfully graduated from Stanford University with both an MD and PhD. There he carried out two post-doctoral fellowships in parallel in the renowned laboratories of Prof. Sam Strober & Prof. Ron Levy. Thanks to his talent, productivity and hard work, Holbrook became an assistant professor at Stanford and led an active research group until his last days. Holbrook authored more than a hundred scientific papers, gave hundreds of educational talks and seminars, and took care of many patients with complete dedication. He was the principal investigator of several cancer immunotherapy clinical trials and research projects and worked relentlessly as an expert and advisor for many in both academia and industry. Holbrook was a member of multiple scientific advisory boards in the biotech industry and the co-founder of ovacure.org, a nonprofit organization for ovarian cancer. With a full MD, PhD training and a daily practice of scientific and clinical research, Holbrook was one of those rare individuals with a true medical and scientific profile. His expertise in immuno-oncology made him even more valuable in the current era of cancer immunotherapy.

The initial focus of his work was on allogeneic stem cell transplantation and cancer vaccines (see his last review on the topic in Annals of Oncology; Tan A et al. Ten Challenges to Success: Past and Present of Ten Cancer Vaccines, in press). However, Holbrook quickly identified the therapeutic potential of immune checkpoint targeted antibodies for treating cancers. He chose to focus on one of them, CD137 (also called 4-1BB) [START_REF] Houot | Therapeutic effect of CD137 immunomodulation in lymphoma and its enhancement by Treg depletion[END_REF]. One of his major achievements was to demonstrate how immunomodulatory antibodies can boost NK-cell mediated anti-tumor immunity. He first observed that upon passive immunotherapy with antitumor monoclonal antibodies (mAbs), mouse and human NK cells up-regulate CD137 on their surface upon activation of Fc-gamma receptors through antibody derived cell cytotoxicity (ADCC). He then nicely demonstrated that combining anti-tumor mAbs with agonistic anti-CD137 mAbs could boost NK cell-induced ADCC and synergize in vivo in tumor-bearing mice. He did a tremendous amount of work to demonstrate that the upregulation of CD137 on NK cells and ADCC enhancement by anti-CD137 mAbs was a common phenomenon seen both in mouse and human B-cell lymphoma treated with anti-CD20 mAbs [START_REF] Kohrt | CD137 stimulation enhances the antilymphoma activity of anti-CD20 antibodies[END_REF], in HER-2+ breast cancer treated with anti-HER2 mAbs [START_REF] Kohrt | Stimulation of natural killer cells with a CD137-specific antibody enhances trastuzumab efficacy in xenotransplant models of breast cancer[END_REF] and in head and neck squamous cell carcinomas (HNSCC) treated with anti-EGFR mAbs [START_REF] Kohrt | Targeting CD137 enhances the efficacy of cetuximab[END_REF]. These results brought early and important insights regarding i) new rational combinations with immunomodulatory mAbs, particularly with tumor-directed mAbs, and ii) the capacity of immunomodulatory mAbs to stimulate innate immunity (in addition to adaptive immunity) against cancer. This pre-clinical work gave rise to several clinical trials (NCT01307267 and NCT01775631).

Interestingly, Holbrook demonstrated three major critical aspects of such tumor-targeted and immune-targeted combinations. First, that it takes several hours to upregulate CD137 on NK cells and that timing is critical when combining tumor-targeted mAbs and anti-CD137 mAbs: co-injections of the two antibodies at the same time would have no synergy whereas waiting 24h after the tumor targeted mAb and before injecting the anti-CD137 would provide full synergy. Second, that passive immunotherapy with anti-EGFR antibody therapy (cetuximab) actually elicits an adaptive anti-EGFR CD8+ T-cell immune response in patients with HNSCC. Third, that the combination of anti-EGFR and anti-CD137 antibodies generates a polyclonal anti-tumor CD8+ T-cell immune response in vivo against both EGFR pos and EGFR neg tumors. These observations support the fact that anti-CD137 Abs can enhance the "vaccinal effect" and favor "epitope spreading" of anti-tumor mAbs [START_REF] Houot | CD137 stimulation enhances the vaccinal effect of anti-tumor antibodies[END_REF]. The preliminary results of the ongoing clinical trial combining rituximab and anti-CD137 suggest that such synergistic combinations might well translate into the clinic for patients with rituximab refractory B-cell lymphomas [START_REF] Gopal | Preliminary results of a Phase 1 study of PF-05082566 in combination with rituximab in patients with relapsed or refractory NHL (study B1641001)[END_REF]. Pursuing on innate immune cells immunomodulation and NK cells immune checkpoint targeted mAbs, Holbrook also demonstrated that anti-KIR antibodies synergize efficiently with anti-CD20 antibodies in pre-clinical models of B-cell lymphomas, providing a pre-clinical rationale for a future lirilumab and rituximab combination trial [START_REF] Kohrt | Anti-KIR antibody enhancement of anti-lymphoma activity of natural killer cells as monotherapy and in combination with anti-CD20 antibodies[END_REF].

Besides his major focus on NK cells, Holbrook has been instrumental in moving forward multiple collaborative projects in which he believed the scientific question needed to be addressed. For instance, Holbrook contributed to the development of the in situ immunization strategy and translated the intra-tumoral anti-CTLA-4 approach very quickly to the clinic (NCT01769222 and [START_REF] Kohrt | Intratumoral immunotherapy to unlock systemic T cell and antitumor responses[END_REF] ). He was also involved in demonstrating the synergistic combination of ibrutinib, a BTK inhibitor, with immunotherapy [START_REF] Sagiv-Barfi | Therapeutic antitumor immunity by checkpoint blockade is enhanced by ibrutinib, an inhibitor of both BTK and ITK[END_REF][START_REF] Sagiv-Barfi | Ibrutinib enhances the antitumor immune response induced by intratumoral injection of a TLR9 ligand in syngeneic mouse lymphoma model[END_REF]. His impressive network of collaborators allowed him to contribute to major cancer immunotherapy and tumor immunology projects [START_REF] Herbst | Predictive correlates of response to the anti-PD-L1 antibody MPDL3280A in cancer patients[END_REF][START_REF] Myklebust | High PD-1 expression and suppressed cytokine signaling distinguish T cells infiltrating follicular lymphoma tumors from peripheral T cells[END_REF][START_REF] Chao | Anti-CD47 Antibody Synergizes with Rituximab to Promote Phagocytosis and Eradicate Non-Hodgkin Lymphoma[END_REF][START_REF] Goldstein | Adoptive cell therapy for lymphoma with CD4 T cells depleted of CD137-expressing regulatory T cells[END_REF][START_REF] Pachynski | The chemoattractant chemerin suppresses melanoma by recruiting natural killer cell antitumor defenses[END_REF][START_REF] Müller | Cotransplantation of pure blood stem cells with antigen-specific but not bulk T cells augments functional immunity[END_REF][START_REF] Lee | CD44+ cells in head and neck squamous cell carcinoma suppress T cell-mediated immunity by selective constitutive and inducible expression of PD-L1[END_REF].

We had the immense privilege of becoming colleagues, collaborators and close friends of Holbrook while spending thousands of hours working with him during our post-docs at Stanford. His bright mind, incredible focus and amazing work capacity amazed all of us. His generosity and care for people around him was limitless. Holbrook did not like politics in science, ego-driven investigators, and endless meetings. All these common issues were a waste of time, and he understood early on with his life-threatening disease that time is a scarce resource. Holbrook loved to have discussions on the science around cancer immunology, but these discussions would always finish with a clear definition of what we should do next and what would be the next experiment plan. He was very enthusiastic about opportunities for new projects and collaborations. Such collaborations have been an important part of his career and, indeed, Holbrook was keen to share his knowledge and expertise with everyone and was prone to sharing samples and experimental data for the advancement of a scientific or clinical project. He was modest about his own achievements and was quick to recognize the achievements of others. In 2015, Holbrook became a member of the editorial board of Annals of Oncology. He was a meticulous referee and editor and his work for Annals was much appreciated by the journal staff and authors alike.

In all of his work, Holbrook brought three enduring characteristics: dedication, focus, and strategy. He also exercised crystal clear pedagogy, distilling the most complex immune phenomenon into a series of simple steps. This skill was highly appreciated by his students and colleagues, whether this was for a basic science course or advice for the strategic development of a biotech company. Finally, he always kept a clear sense of purpose, making sure neither he nor his colleagues ever lost sight of the larger goals of advancing medical knowledge and saving lives. Through both his words and actions, he taught us not just about medicine and science, but about life, friendship, dedication, and focus. Beyond his scientific legacy, Holbrook is survived by his family and his numerous friends and colleagues. We extend our deepest condolences to them. Holbrook will be deeply missed by us all.

Picture of Holbrook

Holbrook Edwin Alan KOHRT (1977-2016)


Simon Marillet

Marie-Paule Lefranc

Pierre Boudinot

Frédéric Cazals

Novel structural parameters of Ig -Ag complexes yield a quantitative description of interaction specificity and binding affinity

Keywords: Antibody -antigen complex, interface, affinity Complexe anticorps -antigène, interface, affinité, positions relatives des CDR

Antibody-antigen complexes challenge our understanding, as analyses to date failed to unveil the key determinants of binding affinity and interaction specificity. We partially fill this gap based on novel quantitative analyses using two standardized databases, the IMGT/3Dstructure-DB and the structure affinity benchmark. First, we introduce a statistical analysis of interfaces which enables the classification of ligand types (protein, peptide, chemical; cross-validated classification error of 9.6%), and yield binding affinity predictions of unprecedented accuracy (median absolute error of 0.878 kcal/mol). Second, we exploit the contributions made by CDRs in terms of position at the interface and atomic packing properties to show that in general, VH CDR3 and VL CDR3 make dominant contributions to the binding affinity, a fact also shown to be consistent with the enthalpy -entropy compensation associated with pre-configuration of CDR3. Our work suggests that the affinity prediction problem could be solved from databases of high resolution crystal structures of complexes with known affinity.

Introduction

Immunoglobulins and the immune response. Adaptive immunity is based on antigen (Ag)-specific lymphocyte responses. Upon specific recognition of an antigenic epitope by a given receptor unique to a lymphocyte, this cell gets activated and proliferates, leading to a clonal expansion. B lymphocytes thus recognize antigens through membrane-bound immunoglobulins (Ig) expressed at their surface. Seric Igs can opsonize bacteria and facilitate their uptake by phagocytes, or neutralize viruses thus preventing recognition by their receptor or fusion with the target cell. Immunoglobulins fundamentally consist of two identical heavy (H) chains and two identical light (L) chains, each H chain being bound to an L chain. The antigen-binding site is located at the top of the paired VH and VL, and generally overlaps the two V domains. It mainly consists of three flexible loops on each V domain, called complementarity determining regions (CDR1-3). The diversity of antibodies is concentrated in the CDRs.

From the structural standpoint, the functional relevance of an Ig depends on its binding affinity for the targeted antigen and the specificity of the interactions, which provides the basis of immune memory and vaccination. The affinity sets the strength of the interaction. For the membrane-bound Ig, it determines if enough aggregation of surface Igs and Ig co-receptors occurs, so that a sufficient signal can be sent to the cell to induce activation and proliferation [START_REF] Batista | Affinity dependence of the b cell response to antigen: a threshold, a ceiling, and the importance of off-rate[END_REF]. For secreted Ig, once bound to the target, pathogens or host infected / tumoral cells, the affinity sets the efficiency of Ig-mediated pathogen opsonisation and/or neutralization, or Ig effector properties (antibody-dependent cell-cytotoxicity or ADCC, complement-dependent cytotoxicity or CDC) [START_REF] Lefranc | The immunoglobulin FactsBook[END_REF].

Ig -Ag complexes and underlying genetic mechanisms. The prominent role played in Ag binding by CDRs has prompted the analysis of CDR-specific statistics. Using a handful of crystallographic structures, canonical conformations i.e. commonly occurring backbone CDR conformations were first reported [START_REF] Chothia | Canonical structures for the hypervariable regions of immunoglobulins[END_REF] and subsequently updated [START_REF] Chothia | Conformations of immunoglobulin hypervariable regions[END_REF][START_REF] Al-Lazikani | Standard conformations for the canonical structures of immunoglobulins[END_REF], using 300 non-redundant Ig structures in the latest work [START_REF] North | A new clustering of antibody CDR loop conformations[END_REF]. Moving from individual CDR to all CDRs, correlations between canonical conformations were further studied [START_REF] Vargas-Madrazo | Canonical structure repertoire of the antigen-binding site of immunoglobulins suggests strong geometrical restrictions associated to the mechanism of immune recognition[END_REF], highlighting the fact that some combinations are multi-specific, while others are specific of an antigen type. The VH CDR3 is the most variable and was therefore the focus of several studies [START_REF] Shirai | Structural classification of CDR-H3 in antibodies[END_REF][START_REF] Morea | Conformations of the third hypervariable region in the VH domain of immunoglobulins[END_REF][START_REF] Shirai | H3-rules: identification of CDR-H3 structures in antibodies[END_REF]] which defined and updated sequence-based rules to predict its conformations. More recently, these studies have been refined, based on a larger number of structures (of the order of hundreds instead of tens). For VL CDR3, new canonical conformations were proposed [START_REF] Kuroda | Systematic classification of CDR-L3 in antibodies: Implications of the light chain subtypes and the VL-VH interface[END_REF], and for VH CDR3, previous rules were updated and complemented [START_REF] Koliasnikov | Antibody CDR H3 modeling rules: extension for the case of absence of Arg H94 and Asp H101[END_REF][START_REF] Kuroda | Structural classification of CDR-H3 revisited: A lesson in antibody modeling[END_REF]. Distinguishing lambda versus kappa chains, it has been shown that canonical conformations from the former are more diverse than those from the latter in the human and the mouse [START_REF] Chailyan | Structural repertoire of immunoglobulin λ light chains[END_REF]. However, the relevance of canonical conformations for the prediction of the 3D structures of CDRs was questioned [START_REF] Choi | Predicting antibody complementarity determining region structures without classification[END_REF], since general loop prediction methods matched (or even outperformed) the prediction performances of methods exploiting specific rules associated with canonical conformations of CDRs. In parallel, two related works [START_REF] Almagro | Identification of differences in the specificity-determining residues of antibodies that recognize antigens of different size: implications for the rational design of antibody repertoires[END_REF][START_REF] Raghunathan | Antigen-binding site anatomy and somatic mutations in antibodies that recognize different types of antigens[END_REF] studied the differential CDR lengths and Specificity-Determining Residues Usage (SDRU, proportion of Ig amino-acids at a given CDR position which contact the antigen) between ligand types. However, these analyses do not allow antigen type predictions. To assess the role of individual CDRs, it has also been established that except in the case of bacterial carbohydrates, diversity in VH CDR3 alone can result in primary responses specific to the antigen [START_REF] Xu | Diversity in the CDR3 region of VH is sufficient for most antibody specificities[END_REF]. Structural and genetic aspects of individual CDRs in natural and artificial antibody repertoires are reviewed in [START_REF] Finlay | Natural and man-made v-gene repertoires for antibody discovery[END_REF].

Ig -Ag complexes and thermodynamics. The analysis of Ig -Ag complexes can also be posed from the thermodynamics standpoint. Specifically, the binding affinity is a thermodynamic quantity describing the chemical equilibrium associated with the two partners (Ig and Ag in our case) and the complex (Ig -Ag, denoted IG/Ag in the IMGT nomenclature [START_REF] Ehrenmann | IMGT/3Dstructure-DB and IMGT/Domain-GapAlign: a database and a tool for immunoglobulins or antibodies, T cell receptors, MHC, IgSF and MhcSF[END_REF]). It is generally measured by the dissociation constant K d (= [Ig] • [Ag]/[Ig -Ag]) of this equilibrium. Equivalently, it is expressed by the corresponding dissociation free energy ∆G d = -RT ln K d /c • = ∆H -T ∆S, in the c • = 1M standard state, with T the temperature and R the gas constant. Thus, by nature, the affinity has an enthalpic component (∆H) qualifying the interaction energy, but also an entropic component (T ∆S) qualifying the loss of dynamical properties upon complex formation (intuitively, the formation of the Ig -Ag complex indeed restricts the degrees of freedom of both partners). These two competing interests illustrate the enthalpy -entropy compensation phenomenon [START_REF] Meng | The free-energy landscape of clusters of attractive hard spheres[END_REF][START_REF] Dunitz | Win some, lose some: enthalpy-entropy compensation in weak intermolecular interactions[END_REF], which stipulates that a favorable enthalpic change upon association is accompanied by an entropic penalty. Predicting binding affinities from structural data requires to quantify this compensation, and is therefore a notoriously challenging problem, for protein complexes in general [START_REF] Kastritis | A structure-based benchmark for protein-protein binding affinity[END_REF][START_REF] Marillet | High resolution crystal structures leverage protein binding affinity predictions[END_REF], and for Ig -Ag complexes in particular [START_REF] Lippow | Computational design of antibody-affinity improvement beyond in vivo maturation[END_REF].

To model the enthalpic component, various parameters have been proposed. Most of these parameters, which describe the morphology of the interface (size, shape, packing properties) and its biochemistry (salt bridges, solvation, hydrogen bonds), were estimated from crystal structures of complexes [START_REF] Jones | Principles of protein-protein interactions[END_REF][START_REF] Lo Conte | The atomic structure of protein-protein recognition sites[END_REF][START_REF] Bouvier | Shelling the Voronoi interface of protein-protein complexes reveals patterns of residue conservation, dynamics and composition[END_REF][START_REF] Malod-Dognin | Characterizing the morphology of protein binding patches[END_REF]. More recently, it has also been shown that non-interacting atoms play an important role, intuitively related to solvent interactions [START_REF] Kastritis | Proteins feel more than they see: Fine-tuning of binding affinity by properties of the noninteracting surface[END_REF]. Such approaches have been applied to Ig -Ag complexes [START_REF] Sundberg | Molecular recognition in antibody-antigen complexes[END_REF], stressing in particular the role of interfacial solvent [START_REF] Bhat | Bound water molecules and conformational stabilization help mediate an antigen-antibody association[END_REF], biochemical properties of Igs as a function of epitopes [START_REF] Deepak T Nair | Epitope recognition by diverse antibodies suggests conformational convergence in an antibody response[END_REF], or the correlation between interface curvature and ligand size [START_REF] Maccallum | Antibody-antigen interactions: contact analysis and binding site topography[END_REF].

To model the entropic component, the conformational and vibrational properties of the partners must be captured. It has indeed been shown that the preconfiguration of the binding site may yield a decreased entropic loss, hence an enhanced binding affinity [START_REF] Manivel | Maturation of an antibody response is governed by modulations in flexibility of the antigen-combining site[END_REF][START_REF] Rajamani | Anchor residues in protein-protein interactions[END_REF][START_REF] Chia-En | Ligand configurational entropy and protein binding[END_REF][START_REF] Schmidt | Preconfiguration of the antigen-binding site during affinity maturation of a broadly neutralizing influenza virus antibody[END_REF]. It has also been shown that a preconfiguration of the variable domains can be induced by the constant domain 1 (CH1) of the heavy chain [START_REF] Pritsch | Can immunoglobulin CH1 constant region domain modulate antigen binding affinity of antibodies[END_REF][START_REF] Torres | The immunoglobulin heavy chain constant region affects kinetic and thermodynamic parameters of antibody variable region interactions with antigen[END_REF], suggesting that the isotype switching commonly occurring during B cell differentiation may affect the affinity through changes in the dynamic properties of the Ig. Parallel to binding affinity, the notion of functional affinity or avidity which takes into account the (possibly negative) cooperativity between monomers of an antibody is highly relevant in-vivo. In that context, constant regions have been shown to influence the avidity [START_REF] Cooper | Role of heavy chain constant domains in antibody-antigen interaction. apparent specificity differences among streptococcal IgG antibodies expressing identical variable domains[END_REF][START_REF] Cooper | Variable domain-identical antibodies exhibit IgG subclass-related differences in affinity and kinetic constants as determined by surface plasmon resonance[END_REF][START_REF] Mccloskey | Human constant regions influence the antibody binding characteristics of mouse-human chimeric IgG subclasses[END_REF][START_REF] Pritsch | Can isotype switch modulate antigen-binding affinity and influence clonal selection[END_REF]. Likewise, an intact ball-and-socket joint between VH and CH1 domains has been shown to affect antibody neutralizing activity [START_REF] Landolfi | The integrity of the ball-and-socket joint between V and C domains is essential for complete activity of a humanized antibody[END_REF].

Contributions. The difficulty of understanding molecular recognition between proteins in general and antibody -antigens in particular is well known [START_REF] Sundberg | Molecular recognition in antibody-antigen complexes[END_REF]. In this work, we present novel quantitative analyses for interfaces of Ig -Ag complexes. Using the annotated IMGT/3Dstructure-DB [START_REF] Ehrenmann | IMGT/3Dstructure-DB and IMGT/Domain-GapAlign: a database and a tool for immunoglobulins or antibodies, T cell receptors, MHC, IgSF and MhcSF[END_REF], the interface between the Ig chains and the Ag is determined using a Voronoi based model for each complex, and decomposed into contributions from CDR, framework (FR) and atoms outside the V-region. This interface allows dissecting the interface into contributions made by CDRs, in terms of position of their atoms at the interface, and of packing properties of these atoms. Using these parameters, we show how to unambiguously distinguish ligand types and predict binding affinity with unprecedented accuracy. We also develop quantitative models for the contribution of VH CDR3 to binding affinity and interaction specificity, bridging the gap between various observations (canonical backbone conformations, mutagenesis data, affinity measurements), and explaining the emergence of function from a combination of structural and dynamical properties.

Inria 2 Material and methods

Voronoi interface models

Given a macro-molecular complex, an interface model is a structural model of the atoms accounting for the interactions, ideally encompassing its enthalpic (i.e. interaction energy) and entropic (i.e., dynamic) dimensions. In the sequel, we model complexes and their interfaces using solvent accessible models [START_REF] Bahadur | A dissection of specific and non-specific protein-protein interfaces[END_REF] and the associated Voronoi based interface model (Figure S3 and [START_REF] Loriot | Modeling macro-molecular interfaces with Intervor[END_REF]).

Solvent accessible models and Voronoi interfaces. The solvent accessible model (SAM) of a set of atoms is a model where each atom is represented by a ball whose radius is the van der Waals radius expanded by the radius r w = 1.4Å of a water probe accounting for a continuous solvation layer [START_REF] Gerstein | Protein geometry: volumes, areas, and distances[END_REF][START_REF] Bahadur | A dissection of specific and non-specific protein-protein interfaces[END_REF]. A convenient construction to study SAM is the Voronoi (power) diagram defined by the atoms [START_REF] Gerstein | Protein geometry: volumes, areas, and distances[END_REF]. In particular, the Voronoi diagram induces a partition of the molecular volume, obtained by computing for each atom its Voronoi restriction, namely the intersection between its atomic ball and its Voronoi region. The volume of this restriction, also called atomic volume, is a direct measure of the atomic packing [START_REF] Gerstein | Protein geometry: volumes, areas, and distances[END_REF].

The exposed surface of a SAM consists of the boundary of the union of balls defining the SAM. This surface consists of spherical polygons, delimited by circle arcs (every such arc is located on the intersection circle of two atoms), themselves delimited by points (each such point is found at the intersection of three atoms). When two molecules assemble to form a complex, the buried surface area (BSA) is the portion of the exposed surface of both partners which gets buried [START_REF] Lo Conte | The atomic structure of protein-protein recognition sites[END_REF]. BSA has been shown to exhibit remarkable correlations with various biophysical quantities [START_REF] Janin | Protein-protein interaction and quaternary structure[END_REF], and notably dissociation free energies for complexes involving moderate flexibility [START_REF] Malod-Dognin | Characterizing the morphology of protein binding patches[END_REF].

Consider the SAM of a complex whose partners are denoted A and B, and also involving interfacial water molecules W. Two atoms are in contact provided that their Voronoi restrictions are neighbors. Pairs of type (A,B) define the AB interface, namely direct contacts between the partners. Focusing on water molecules W sandwiched between the partners, pairs (A,W) and (B,W) correspond to water mediated interactions. It can be shown that all atoms from the partners identified this way form a superset of atoms loosing solvent accessibility [START_REF] Cazals | Revisiting the Voronoi description of protein-protein interfaces[END_REF]. The binding patch of a partner consists of its interface atoms. The atoms of the binding patch can be assigned an integer called its shelling order, which is a measure of the distance of this atom to the boundary of the patch it belongs to [START_REF] Bouvier | Shelling the Voronoi interface of protein-protein complexes reveals patterns of residue conservation, dynamics and composition[END_REF]. This information generalizes the core-rim model [START_REF] Lo Conte | The atomic structure of protein-protein recognition sites[END_REF], and has been shown to provide state-of-the-art correlations with solvent dynamics, conservation of amino acids [START_REF] Bouvier | Shelling the Voronoi interface of protein-protein complexes reveals patterns of residue conservation, dynamics and composition[END_REF], and dissociation free energies [START_REF] Malod-Dognin | Characterizing the morphology of protein binding patches[END_REF]. All tools to compute the parameters just discussed are available within the Structural Bioinformatics Library at http://sbl.inria.fr > Applications > Space Filling Models.

Application to Ig -Ag complexes. For an Ig -Ag complex, we partition the set I of interface atoms just defined into the atoms I Ig contributed by the Ig, and the atoms I Ag contributed by the Ag, so that I = I Ig ∪I Ag . It follows that the number of interface atoms |I| is the sum of those contributed by the Ig and the Ag respectively, namely |I| = |I Ig | + |I Ag |. Similarly, we charge the Buried Surface Area (BSA) to the Ig and Ag respectively, so that BSA = BSA Ig + BSA Ag . These quantities yield the average BSA per interface atom on Ig and Ag side:

bsa Ig = BSA Ig |I Ig | , (1)
bsa

Ag = BSA Ag |I Ag | . (2)
The previous analysis can be generalized to accommodate the structure of Fabs, by decomposing the variable domains of each chain (VH and VL) into to three complementarity determining regions (CDRs) and four framework regions (FRs), resulting in 14 Voronoi interfaces. Practically, we focus on contacts made by the six CDRs, those made by framework regions being negligible (Table SV). (Details of the method used at http://sbl.inria.fr/doc/Space_filling_ model_interface-user-manual.html.) In doing so, a buried surface area is defined for each CDR.

The dataset and data curation: the IMGT/3Dstructure-DB

We use the Ig -Ag complexes from the IMGT/3Dstructure-DB (http://www.imgt.org/3Dstructure-DB/ [START_REF] Ehrenmann | IMGT/3Dstructure-DB and IMGT/Domain-GapAlign: a database and a tool for immunoglobulins or antibodies, T cell receptors, MHC, IgSF and MhcSF[END_REF]), corresponding to the category IG/Ag for IMGT complex type. Each such complex is processed in order to identify canonical complexes involving one heavy chain, one light chain, and one ligand. Upon inspecting such cases, two decisions are made. First, on the antigen side, we retain three types only (peptide, protein, chemical), due to the scarcity of cases involving other types. Moreover, we also remove complexes involving multiple ligands types. For the same reason, regarding species, complexes are assigned to three classes: human, mouse and other. In total, 489 complexes are retained after filtering for missing data, inconsistencies, redundancy, ligand type and speciess. The detailed processing methodology is described in the supplemental section 6.1. The main features of the complexes used are also summarized in the Supplemental file dataset-IMGT-details.csv.

CDR and FR limits of the VH and VL domains are according to the IMGT unique numbering [START_REF] Lefranc | IMGT unique numbering for immunoglobulin and T cell receptor variable domains and Ig superfamily V-like domains[END_REF] (Table SII). Practically, we use the following notations: CDR1-IMGT of VH is written VH CDR1 and FR3-IMGT of VL is written VL FR3. Other CDRs and FRs follow the same scheme.

The binding affinity benchmark

Our affinity predictions exploit the structure affinity benchmark (SAB) [START_REF] Kastritis | A structure-based benchmark for protein-protein binding affinity[END_REF], a manually curated dataset containing 144 cases, each described by three crystal structures (of the unbound partners and of the complex) and the experimentally measured binding affinity in controlled conditions. In this work, we split the SAB into two sets: 14 Ig -Ag cases defining the test set (Table SIII), and 125 non-Ig -Ag cases defining the training set. Five complexes (among which 3 Ig -Ag) were removed from the SAB because only an upper bound on their K d was provided, or had too many missing atoms. Having learned a statistical model from the latter, we predict affinities for Ig -Ag complexes of the former. See details in the Supplemental section.

Predicting ligand types

Antigens in the dataset are categorized as chemical, peptide and protein. Predicting the ligand type therefore requires to build a 3-class predictor.

Relevant variables. In order to predict ligand types , we represent each complex by two variables: bsa Ig and bsa Ag which are the average BSA per atom for atoms on the Ig and the Ag side respectively. These variables define the two-dimensional space displayed in Fig. 1 where each point represents a complex. A classifier i.e. a method predicting the antigen type from the parameters bsa Ag and bsa Ig is then trained on this data. Practically, we use a decision tree partitioning the space into rectangular regions, each corresponding to a ligand type.

Inria

Statistical methodology. Since the performance of classifiers tested on the training data is overestimated and leads to classifiers with poor generalization abilities (overfitting), various schemes have been devised to obtain an estimate of the generalization error.

We use the k-fold cross-validation where the dataset is randomly divided in k subsets of equal size, and k -1 subsets are alternatively used to classify the remaining one. At the end of this procedure, each sample has been predicted and the proportion of misclassified samples can be computed. Here k is set to 5. Since the partition into training and test data used during this procedure is inherently random and may lead to non-representative results for a single run, we report median errors over 1000 cross-validation runs.

In order to size the expected performance of a random classifier, we use a simple permutation test. Basically, complexes are randomly predicted by permuting the ligand types in the original data set and assigning the result of the permutation to each complex. This procedure maintains the number of complexes per ligand type. Median errors over 10000 random permutations are reported.

Ligand redundancy. In total, there are 465 distinct ligands out of 489 complexes, with the most represented ones appearing at most 3 times. Overfitting due to Ag redundancy in the dataset is therefore not an issue.

Predicting binding affinities

Relevant variables. The affinity prediction problem was recently revisited and posed as a sparse linear model estimation problem [START_REF] Marillet | High resolution crystal structures leverage protein binding affinity predictions[END_REF], stressing the importance of two variables. These two variables turn out to be the most informative ones when estimating binding affinities, in the sense where they get selected most often amidst a pool of variables modeling relevant biophysical properties [START_REF] Marillet | High resolution crystal structures leverage protein binding affinity predictions[END_REF].

The first one, the inverse volume-weighted internal path length (IVW-IPL), encodes the size and morphology of the interface and takes atomic packing into account. Let I be the set of interface atoms in a complex. Let SO(a) and Vol(a) be the shelling order and Vol_bound the volume of atom a in the complex (see section 2.1). The, IVW-IPL is defined as follows:

IVW-IPL = a∈I SO(a) Vol_bound(a) (3)
On the one hand, the shelling order refines so-called core-rim models [START_REF] Lo Conte | The atomic structure of protein-protein recognition sites[END_REF]. Borrowing to the notion of cooperative effects involving non-bonded weak interactions, an isotropic or disk-like interface is indeed expected to be more stable than an elongated one-even if their surface areas match.

On the other hand, the atomic packing encodes the local density of neighbors of a given atom, and thus provides a measure for local interactions (hydrogen bonds, van der Waals interactions). Note that packing is a subtle quantity related to the enthalpy -entropy compensation discussed in Introduction, as its properties strike a balance between enthalpy (a large number of neighbors favors interactions) and entropy (too small of a packing is detrimental for dynamics yielding an entropic penalty).

The second variable (NIS charged ) is the fraction of charged residues on the non-interacting surface (NIS, i.e. the exposed surface of the Ig and of the Ag not involved in the interface). The NIS is meant to encode electrostatic properties and solvent interactions [START_REF] Kastritis | Proteins feel more than they see: Fine-tuning of binding affinity by properties of the noninteracting surface[END_REF].

Statistical methodology. We estimate binding affinities using k nearest neighbors regression (knn) [START_REF] Györfi | A distribution-free theory of nonparametric regression[END_REF][START_REF] Biau | Lectures on the nearest neighbor method[END_REF], a non-parametric regression strategy which does not require any a priori on the mathematical model for the response variable estimated -as opposed to linear regression for instance. This strategy is a two step strategy. As a pre-processing step, we compute the parameters IVW-IPL and NIS charged for the training set (125 cases), yielding a point cloud P in the two dimensional space defined by IVW-IPL and NIS charged . (Fig. 2a). To estimate the affinity of a complex q (an Ig -Ag case), we proceed in two steps. First, the k nearest neighbors of q in P are sought, with k a predefined number. Second, the affinity of q is estimated by averaging those of its k nearest neighbors. (Practically, the scikit-learn library [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF] was used, namely the neighbors package for knn regression.)

We assess the quality of our predictions by varying the value k. From a theoretical standpoint [START_REF] Györfi | A distribution-free theory of nonparametric regression[END_REF], it is known that k must be super-logarithmic and sub-linear in the number of cases processed. Since log(144) ∼ 5, we explore the range k ∈ 5, . . . , 25 (Fig. 2b and Figure S9). The results discussed in the main text correspond to k = 10.

In order to assess the impact of the distance to nearest neighbors and of the consistency of their affinity values on the accuracy of the predictions, we compute the average distance d i between each Ig -Ag complex i and its k = 10 nearest neighbors in the training set (i.e. those used to estimate its binding affinity using k-nearest neighbor regression). We also compute the standard deviation of the affinity values σ i of these 10 nearest neighbors. These are compared to the absolute error |e i | (= |experimental_affinity i -predicted_affinity i |) of the prediction on complex i.

Comparing the energetic contribution of interface atoms between CDRs

To assess the respective energetic contributions of CDRs to binding affinity, we dissect the IVW-IPL (Eq. ( 3)) into the contributions of CDR1 + CDR2 and CDR3. We also compute the average normalized shelling order (or ANSO for short) for each CDR

ANSO = 1 |A| a∈A SO(a) Vol_bound(a) , (4)
with A is the set of interface atoms of the CDR and the size of this set is |A|. The distribution of IVW-IPL and ANSO between CDR1 + 2 and CDR3 within the same chain are then compared using a Wilcoxon signed-rank test.

Results

Characteristics of the binding patch predict the ligand type

Atomic solvent accessibility asymmetry is a signature for the ligand type. A classical and informative variable describing a protein -protein interface is the buried surface area (BSA), which is known to correlate to the number of interface atoms [START_REF] Janin | Protein-protein interaction and quaternary structure[END_REF]. In our case, a Pearson coefficient equal to 0.99 is obtained. However, this value drops down to 0.82 and 0.89 respectively for the Ig and the Ag sides, a fact owing to the shape complementarity between the binding patches on the Ig and Ag sides (Figure S4). To further investigate this observation, we compute the average BSA per interface atom for both the Ig and Ag (Eqs. ( 1) and ( 2)). Strikingly, the ligand type has a strong impact on these quantities: complexes involving a chemical ligand have a higher average BSA per atom at the Ag side of the interface (bsa Ag ) than those involving a peptide ligand which in turn have a higher bsa Ag than those involving a protein ligand (Fig. 1).

Inria

Note that bsa Ag and bsa Ig can be seen as proxies for curvature of the Ag and Ig binding patches, hence their strong inverse correlation due to the complementarity between binding patches on the Ig and Ag sides (Figure S3(D,E,F)). This inverse correlation is rather intuitive for small ligands, but may not be trivial for bigger antigens. Our contribution corroborates this fact for a whole set of structures.

To further exploit the ability of the parameters bsa Ag and bsa Ig to characterize interfaces as a function of the ligand type, we build a decision tree classifier (section 2.4, Fig. 1 and Figure S5).

The median cross-validated error over all classes is 9.6% over 1000 repetitions whereas the permutation test resulted in a median error of 56%. More precisely, the median cross-validated error rates per class are 5%, 19% and 7% for chemical, peptides and proteins. The higher error rate for peptides is mostly due to the classifier predicting proteins instead of peptides (Table SIV), which is not unexpected as the criterion to classify polypeptides as peptides or proteins is not standardized. For comparison, the permutation test resulted in error rates of 84% for chemicals, 75% for peptides, and 41% for proteins; clearly showing the influence of the number of complexes per class on the accuracy of the prediction. Overall, our classifier is able to accurately predicts ligand types, despite the fact that the data is unbalanced.

Binding affinity predictions

Our k-nearest neighbors based model predicts 8 (57.14%), 13 (92.86 %) and 13 of the dissociation constants K d within one, two and three orders of magnitude respectively, with a median absolute error of 0.878 kcal/mol, which corresponds in a ratio for K d equal to 4.4 (Fig. 2c). In terms of correlation coefficients, one gets 0.488 (Pearson) and 0.291 (Spearman). These results are very good, as predicting K d within one order of magnitude is essentially the best one can hope for without modeling subtle effects such as the pH in particular [START_REF] Janin | A minimal model of protein-protein binding affinities[END_REF]. They are also informative from a biological standpoint, as an affinity enhancement of two orders of magnitude is typically observed during affinity maturation. In order to compare these results to what could be expected from a null model, we take the average binding affinity of the training dataset (10.78 kcal/mol ±2.84) as prediction for all complexes. This results in a median absolute error of 1.03 kcal/mol, or equivalently, in a ratio for K d equal to 5.7. The previous conclusions must therefore be mitigated, since a simple null model can show good, albeit less so, performances as well.

In order to rationalize the varying accuracy of predictions depending on the complex, we compute the average distance d i between each Ig -Ag complex i and its 10 nearest neighbors in the training set. We also compute the standard deviation of the affinity values of these 10 nearest neighbors σ i (Figure S12). Both d i and σ i are weakly correlated to the absolute prediction error |e i | with Pearson's correlation coefficients of 0.57 and -0.57 respectively. Both coefficients are (weakly) significantly different from zero with p-values of 0.0312 and 0.03316 respectively. The correlation between |e i | and d i /σ i is higher however with a Pearson correlation coefficient equal to 0.72 and a p-value of 0.00363. This suggests that good binding affinity prediction can be obtained provided that sufficiently similar complexes are in the training set and that their affinity values are consistent with each other. Interestingly, this property also accounts for the good performances of the null model.

The success of the affinity prediction owes to two important properties of the learning set (non-Ig -Ag complexes) and the training set (Ig -Ag complexes). First, Ig -Ag complexes fall in a reduced region of the space defined by the two parameters IVW-IPL and NIS charged of the model, i.e. they are similar from the point of view of the model. Second, the Ig -Ag complexes fall in a region which is well represented in the training set (i.e., the rest of the SAB). This means that in the space of the two parameters of the model, Ig -Ag complexes are similar to the other protein -protein complexes of the SAB. In order to predict the binding affinity of Ig -Ag complexes with protein ligands, our model therefore takes advantage of the fact that they are similar both to each other and similar to other protein -protein complexes.

Comparison with the PRODIGY server. In order to see how our approach fares against the state of the art, we compare our results against the PRODIGY server. The PRODIGY server is one of the most recent tools for affinity prediction [START_REF] Li C Xue | Prodigy: a web server for predicting the binding affinity of protein-protein complexes[END_REF], and is based on the work from Vangone et al [START_REF] Vangone | Contacts-based prediction of binding affinity in protein-protein complexes[END_REF].

The accuracy of PRODIGY is lower than that of the current study with median absolute errors of 1.4 versus 0.878 kcal/mol respectively. For reference, we also provide the root mean squared errors (2.226 versus 1.676 kcal/mol), Pearson's correlation coefficients (0.149 versus 0.488) and Spearman's correlation coefficients (0.238 versus 0.291). Interestingly, our method is successful at predicting similar affinities (Fig. 11) for five complexes (1AHW, 1DQJ, 1VFB, 2JEL, 1BJ1) for which PRODIGY predicts widely varying values.

CDRs: lengths and BSA. It has been observed that CDR lengths differ between different antigen types [START_REF] Collis | Analysis of the antigen combining site: correlations between length and sequence composition of the hypervariable loops and the nature of the antigen[END_REF][START_REF] Raghunathan | Antigen-binding site anatomy and somatic mutations in antibodies that recognize different types of antigens[END_REF], a finding suggesting that CDR lengths influence the binding site to accommodate the ligand. We therefore undertook the characterization of this relationship in the IMGT/3Dstructure-DB. Since all the atoms of a CDR may not contribute to the interface, we investigate the correlation between the length of a CDR and its contribution to the BSA. As CDR1 and CDR2 are both encoded by V genes we study them together and subsequently investigate the relationship between [CDR1 . CDR2] pairs and BSA on the one hand, and CDR3 and BSA on the other hand. We observe that CDRs of a given length can display widely varying levels of BSA (Figure S6 and Figure S7). These results indicate that CDR lengths must be complemented to fully describe the involvement of a CDR in the interaction with the Ag. This is backed up by the very limited ability of neural networks trained on sequence data only to predict the ligand type bound by an Ig in [START_REF] Collis | Analysis of the antigen combining site: correlations between length and sequence composition of the hypervariable loops and the nature of the antigen[END_REF]. An error rate of 54% is indeed observed, to be compared to a baseline of 75% for a random predictor on four classes (protein, hapten, nucleotide and viral protein) [START_REF] Collis | Analysis of the antigen combining site: correlations between length and sequence composition of the hypervariable loops and the nature of the antigen[END_REF].

Respective contributions of the CDRs to the interface, for VH and VL domains. In an Ig -Ag complex, it is generally believed that VH contributes more to the recognition than VL. With a BSA of VH strictly larger than that of VL for 430/489 complexes (∼86%) (Fig. 3a), our analyses support this idea. To refine this view, we split the BSA into contributions by the CDRs within a V-domain, observing a great deal of variation across the dataset, independent from the ligand type (Figs. 3b and3c). A general observation is that the sum of contributions of CDR1 and CDR2 essentially matches that of CDR3 for both VH and VL. Consider the sum of the BSA of CDR1 and CDR2 on one hand, and the BSA of CDR3 on the other hand. The first quantity is larger than the second one for ∼46% of the complexes for VH, and for ∼40% of the complexes for VL. Moreover, a Wilcoxon signed-rank test does not find a significant difference between them for VH (two-sided p-value = 0.1460), but does for VL (two-sided p-value = 0.0001), indicating that the contribution of CDR3 in terms of BSA and relative to other CDRs from the same chain is higher for the light chain than for the heavy chain.

To assess the contributions of CDRs to binding energy, we compute both their IVW-IPL and ANSO (Eq. ( 3) and ( 4)) for all complexes (Fig. 4a and4b). We then compare the distributions of these two quantities for CDR1 + 2 and CDR3 in the same chain, using a Wilcoxon signed-rank test at significance level α = 0.01. Consider the sum of the IVW-IPL of CDR1 and CDR2 on one hand, and the IVW-IPL of CDR3 on the other hand. The first quantity is larger than the Inria second one for ∼41% of the complexes for VH, and for ∼27% of the complexes VL (Figure S8). Wilcoxon signed-rank tests find significant differences between them for both VH (two-sided pvalue = 6.404 • 10 -7 ), and VL (two-sided p-value = 7.217 • 10 -30 ). Removing the dependence on the number of atoms, i.e. comparing the ANSO distribution computed on both CDR1 and CDR2 on the one hand and CDR3 on the other hand, leads to significant differences as well for VH (two-sided p-value = 6.221 • 10 -30 ), and VL (two-sided p-value = 2.480 • 10 -37 ).

Thus, as opposed to the results obtained when considering the BSA, the sum of contributions to the binding affinity of CDR1 and CDR2 is significantly lower than that of CDR3 for both VH and VL.

For both chains, the difference in ANSO can be imputed to two facts. First the average shelling order (Section 2.1) for atoms of the CDR3 is higher than those of CDR 1 and 2 (Fig. 4c). Second, their average atomic volume is lower (Fig. 4d). Both are related since the shelling order and the atomic volume are negatively correlated (Figure S8c).

Discussion

In this work, we provide a precise quantitative description of Ig -Ag interfaces, leading to an accurate classification of ligand types and to accurate binding affinity predictions. We also quantify the contributions made by CDRs at interface both in terms of surface area and binding energy, and we show that VH CDR3 is the main factor determining binding affinity and interaction specificity. While these facts were previously known from a qualitative standpoint, the task of designing quantitative models supporting them had remained elusive, with insights focused on specific conformations. Instead, our models provide quantitative estimates illustrating the relationship between structure, dynamics and affinity of Ig -Ag complexes.

Enhanced specificity and affinity descriptions from global interface statistics. The buried surface area (BSA) of a protein complex has long been known to be a simple and informative descriptor of interfaces [START_REF] Bahadur | A dissection of specific and non-specific protein-protein interfaces[END_REF]. We refine this statistic by computing the average BSA contributed by interfacial atoms from the Ig (statistic bsa Ig ) and the Ag (statistic bsa Ag ). These quantities turn out to be clear a signature of the ligand type, a property which can further be exploited for classification purposes. While the classification of Ig -Ag interfaces into classes depending on structural features has already been addressed [START_REF] Chailyan | The association of heavy and light chain variable domains in antibodies: implications for antigen specificity[END_REF][START_REF] Lee | Shapes of antibody binding sites: qualitative and quantitative analyses based on a geomorphic classification scheme[END_REF], our parameters are the first ones yielding such a clear separation between specific antigen types.

To complement this analysis, we perform binding affinity predictions for 14 Ig -Ag complexes, based on structural parameters encoding enthalpic and entropic quantities [START_REF] Marillet | High resolution crystal structures leverage protein binding affinity predictions[END_REF]. Our predictions of K d are accurate within two orders of magnitude for all but one complex and within one order of magnitude for 8 of them. Interestingly, these results stress the relevance of the overall approach, which exploits structural and functional similarities between the test set (the Ig -Ag complexes) and the training set (the SAB deprived from the Ig -Ag complexes). In fact, the high accuracy of our predictions shows that the binding affinity prediction problem could be partially solved using large databases of Ig -Ag complexes with binding affinity measurements.

Our results on specificity analysis and affinity predictions are of immediate practical relevance in the context of Ig design and Ig -Ag docking. Docking is the problem of predicting the pose (i.e., the static structure) and the affinity of a complex from the unbound partners [START_REF] Lensink | Docking, scoring, and affinity prediction in CAPRI[END_REF]. The latter problem is harder than the former, another embodiment of the role of dynamics in the emergence of function. Our parameters are of high interest for both problems. At the pose prediction stage, they provide filters to check that putative Ig -Ag complexes proposed by docking algorithms comply with our classification rules, as a function of the ligand type. In a similar spirit, these parameters are of direct relevance to predict the ligand type from the structure of the Ig VH+VL domains. At the affinity prediction stage, assuming a good quality (i.e., resolution) putative structure for the complex, reliable affinity predictions can be made.

These results also call for extensions, in particular to handle different ligand types (peptides, haptens). Since the quality of predictions owes in particular to a good coverage of the region of the model space targeted by predictions, this extension is likely to be successful assuming a database-identical in spirit to the SAB, providing sufficiently many cases to learn from. From a formal standpoint, we also envision progress on the analysis of the correctness of affinity predictions, based on two ingredients. The first one is the accuracy of estimators for thermodynamic quantities, using parameters such as those used in this work. The second one is the mathematical convergence of regressors, in particular those based on nearest neighbors, as used in this work.

Bridging the gap between structure, dynamics and function. Our findings show that global structural parameters perform remarkably well to predict affinity and specificity, which are notions formally defined in the realm of thermodynamics. It is therefore instrumental to understand which features of CDRs explain the relevance of our parameters. In other words, it appears important to consider at once the role of the six CDRs for most antibody specificities.

If the molecules studied were perfectly rigid, local interactions (hydrogen bonds and van der Waals interactions) would play a prominent role in the formation of the Ig -Ag complex, and the comparable BSA contributed by CDR1+2 vs CDR3 would hint at commensurable contributions from all CDRs. This purely enthalpic view is however insufficient, as preconfiguration/prerigidification of the binding site may yield a decreased entropic loss upon complex formation, hence a enhanced binding affinity [START_REF] Manivel | Maturation of an antibody response is governed by modulations in flexibility of the antigen-combining site[END_REF][START_REF] Rajamani | Anchor residues in protein-protein interactions[END_REF][START_REF] Chia-En | Ligand configurational entropy and protein binding[END_REF][START_REF] Schmidt | Preconfiguration of the antigen-binding site during affinity maturation of a broadly neutralizing influenza virus antibody[END_REF]. A useful proxy for dynamics is the length of VH CDR3, and difficulties were observed to define canonical conformations for VH CDR3 [START_REF] Chothia | Canonical structures for the hypervariable regions of immunoglobulins[END_REF][START_REF] Al-Lazikani | Standard conformations for the canonical structures of immunoglobulins[END_REF][START_REF] Shirai | Structural classification of CDR-H3 in antibodies[END_REF][START_REF] Shirai | H3-rules: identification of CDR-H3 structures in antibodies[END_REF][START_REF] Kuroda | Structural classification of CDR-H3 revisited: A lesson in antibody modeling[END_REF][START_REF] North | A new clustering of antibody CDR loop conformations[END_REF] as opposed to the other CDRs. Indeed, accurate sequence-based conformation predictions are limited to the base or torso of the VH CDR3. In this work, we code the enthalpy -entropy compensation (see discussion in section 2.5) using packing properties via our parameters IVW-IPL and ANSO. This leads to two important observations: first, independently of the number of interface atoms, VH CDR3 contributes significantly more to the binding energy than VH CDR1 and VH CDR2 combined; second, interface atoms in VH CDR3 are more closely packed than in other CDRs in the heavy chain. The latter point implies that it is important to minimize the entropic penalty entailed upon binding, which can be achieved by preformation i.e. the CDR is in bound conformation prior to the binding event. Interestingly the authors of [START_REF] Xu | Diversity in the CDR3 region of VH is sufficient for most antibody specificities[END_REF] come to the conclusion that VH CDR3 is responsible for the specificity of the interaction whereas the other CDRs account for its stability. We provide a quantitative view on this property, based on our parameters IVW-IPL and ANSO.

Summarizing, the genetic variability of VH CDR3 is complemented structurally by its dynamic nature to make it the main factor involved in the determination of the specificity and increase of affinity of an Ig for an Ag. It should be stressed that, although this observation can be used as a guide during the design of Ig, it is by no means necessary, as tight binders can be designed de novo without any CDR -see [START_REF] Fleishman | Computational design of proteins targeting the conserved stem region of influenza hemagglutinin[END_REF] for an example involving the stem of influenza virus hemagglutinin.

Naturally, one should also expand our analysis at the whole Ig level, as various structural features of Igs influence their efficacy in the immune response. These include the ball-and-socket joint relating VL and VH, the CL and CH1 constant domains [START_REF] Lesk | Elbow motion in the immunoglobulins involves a molecular balland-socket joint[END_REF][START_REF] Stanfield | Antibody elbow angles are influenced by their light chain class[END_REF], and more generally the constant regions which have been shown to influence the avidity [START_REF] Cooper | Role of heavy chain constant domains in antibody-antigen interaction. apparent specificity differences among streptococcal IgG antibodies expressing identical variable domains[END_REF][START_REF] Cooper | Variable domain-identical antibodies exhibit IgG subclass-related differences in affinity and kinetic constants as determined by surface plasmon resonance[END_REF][START_REF] Mccloskey | Human constant regions influence the antibody binding characteristics of mouse-human chimeric IgG subclasses[END_REF][START_REF] Pritsch | Can isotype switch modulate antigen-binding affinity and influence clonal selection[END_REF], and are involved in Ig effector properties, such as ADCC or CDC [START_REF] Guddat | Intramolecular signaling upon complexation[END_REF]. A quantitative assessment of the role of these features requires going beyond the Ig -Ag interface level, with a clear focus on the dynamics Inria of the whole Ig protein. Again, the identification of the most relevant degrees of freedom in such regions may pave the way to efficient simulation and design strategies. q q q q q q q q q q q q q q 20 40 60 80 Average shelling order The points labeled 2O5X, 2HKF and 4OGY correspond to complexes displayed in Figure S3. 6 Supplementary information 6.1 The IMGT dataset

Figures

H _ C D R 1 H _ C D R 2 H _ C D R 3 L _ C D R 1 L _ C D R 2 L _ C D R 3
(c) H _ C D R 1 H _ C D R 2 H _ C D R 3 L _ C D R 1 L _ C D R 2 L _ C D R 3

Ig -Ag complexes

We use the Ig -Ag complexes from the IMGT/3Dstructure-DB (http://www.imgt.org/3Dstructure-DB/ [START_REF] Ehrenmann | IMGT/3Dstructure-DB and IMGT/Domain-GapAlign: a database and a tool for immunoglobulins or antibodies, T cell receptors, MHC, IgSF and MhcSF[END_REF]), corresponding to the category IG/Ag for IMGT complex type. Only IMGT-PDB files are kept.

This dataset features 1602 files. Each such complex is processed in order to identify canonical complexes involving one heavy chain, one light chain, and one ligand (Section S6.1.2). A total of 1275 canonical complexes are thus extracted, of which 554 non-redundant complexes. After further filtering on the ligand types (keeping only complexes with a single ligand type among protein, peptide and chemical), 489 complexes remain. • The asymmetric unit of the crystal structure contains two or more Fabs.

• Several molecules have co-cristallized with the Ig -Ag complex.

• Two Ig chains, H and L, and one Ag chain are found but the Ig chains are not annotated as forming a receptor in the IMGT 410 section.

• An Ig receptor is annotated as containing more than two chains.

• The ligand is a multi-chain protein

The following issues are faced:

• A file may not be canonical i.e. there might be several complexes in a single file.

• There might be some issues with the numbering of the chains.

• There might be missing data (residues, chains information, labels)

• Several complexes might be similar and bias the results.

• Some molecules annotated as ligand may actually be buffer molecules (e.g. glycerol)

• Some purification proteins remain (e.g. protein L, A or G) and do not engage in specific contacts with the Ig

Inria

Using the executable sbl-intervor-ABW-atomic.exe from the structural bioinformatics library (SBL, sbl.inria.fr), which implements the Voronoi interface model presented in section 2.1, we proceed in two steps. First, we infer the chains pairings in every file which does not contain a canonical complex. For this, we compute the interfaces between all pairs of chains. We then group L and H chains in pairs for which the number of atoms at the interface is the highest. We then assign the ligand(s) chains to the HL pairs if they make contacts with either chain.

Note that in the case where an Ag is in contact with several Ig, it will be assigned to both Ig. Finally, all buffer molecules and Ig purification proteins (namely protein L, A and G) whose annotated name satisfy the regexp "immunoglobulin g-binding

| protein[ ]+[gl]($|\s|\') | glycerol | 2-Amino-2-Hydroxymethyl-Propane-1,3-Diol | tris | 2-(N-Morpholino)-Ethanesulfonic
Acid" are removed from the files because they are not representative of Ig -Ag interactions.

Crystal contacts. The previous automatic detection raises the problem of crystal contacts, since complexes reported might be false positives.

They could potentially be ruled out by using a cutoff such as the minimal number of atoms at an interface to be considered significant, however, there might also be few contacts between a Fab and a small ligand. It would therefore be necessary to study the distribution of the number of atoms at the interface for different classes of ligands to set a specific cutoff.

To circumvent this issue, we currently exclude from the analysis complexes in which the ligand does not make at least one contact with the variable domain (CDR or FR).

Removing redundancies from IMGT/3Dstructure-DB

Redundant complexes may come from two sources: the same complex may be found in the same asymmetric crystal unit, or it may be found in two different IMGT-PDB files.

We therefore need to remove the redundancy of the dataset to avoid biasing the statistics. For this, we need to consider similarities at the interface level. Once all complexes are extracted from the database, we need to compare the interfaces of all pairs of complexes, group complexes having a similar interface, and keep one representative complex for each group.

We rely on a quick method based upon IMGT labels. Consider triplets formed by the IMGT labels of both Ig chains and the Ag chain (e.g. (VH-CH1, L-KAPPA, Capsid protein C)). We record triplets which have already been included in the analysis and exclude complexes which have the same triplet.

The binding affinity benchmark dataset

Test set. The SAB contains 17 Ig -Ag cases (PDB IDs: 1AHW, 1BJ1, 1BVK, 1DQJ, 1E6J, 1FSK, 1IQD, 1JPS, 1MLC, 1NCA, 1NSN, 1P2C, 1VFB, 1WEJ, 2JEL, 2VIR and 2VIS). Their K d was determined at temperatures ranging between 20 and 25 • C or reported as ambient/room temperature. The temperature was not reported in one case. The pH during measurements ranged between 7 and 7.5 except in one case where it was 4.8 (1BJ1). It was not reported in five cases, and for two it is likely to have been 7.4 (BIAcore standard). All the Igs are either murine or humanized monoclonal Igs raised against their antigen in vivo or in vitro, with K d ranging from 4 • 10 -6 to 10 -10 kcal/mol (or equivalently, ∆G d ranging from 7.36 to 13.64 kcal/mol). Out of these 17 cases, 1IQD and 1NSN are discarded as only an upper bound on their K d is provided in the SAB. Furthermore, 1E6J is also discarded because too many atoms could not be matched between the bound and unbound structures. The 14 remaining cases only involve protein ligands. Among them, five are hen egg lysozymes (HEL), two are a tissue factors(TF), two are hemagglutinins (HA), and the remaining ones are birch pollen allergen (Bet v 1), cytochrome c (Cytc), HPr protein, neuraminidase (NA) and vascular endothelial growth factor (VEGF). We note that the iRMSD and the total RMSD between the bound and unbound form of the Igs are always smaller than 1.24Å and 0.95Å respectively. That is, the 14 cases are essentially rigid cases.

Training set. The rest of the SAB is used to train the model and is called training set in the sequel. 1ZLI is removed from the training set because too many atoms could not be matched between the bound and unbound structures and 1UUG is also removed because only an upper bound on its K d is provided.

Inria

Hierarchical Voronoi interface models

Consider a complex where partner A is an Ig, and partner B an antigen. We wish to accommodate the hierarchical structure of the Fab [START_REF] Lefranc | The immunoglobulin FactsBook[END_REF]. We focus on the variable domains of the heavy and light chains, denoted VH and VL respectively, and decompose each of them into seven regions, namely three Complementarity Determining Regions (CDRs), and the four Framework Regions (FRs) flanking them [START_REF] Lefranc | IMGT unique numbering for immunoglobulin and T cell receptor variable domains and Ig superfamily V-like domains[END_REF] (Table SII). For example, a V domain is decomposed as FR1+CDR1+FR2+CDR2+FR3+CDR3+FR4.

Consider the partition of the variable domains VH and VL induced by the previous 14 labels. For the sake of conciseness and since we focus on interfaces involving the variable domains only, the domains VH and VL are plainly denoted H and L. Using these notations, we partition the IGAg interface as follows:

• Hierarchical bicolor interface (no water): IGAg = (L ∪ H)Ag = LAg ∪ HAg • Hierarchical mediated interface (water mediated only): IGW -AgW = (LW -AgW ) ∪ (HW -AgW )

• Hierarchical tricolor interface (both):

IGAgW = IGAg ∪ (IGW -AgW )
Analogously, the partition of the H (or L) V-domain into seven CDR and FR regions induces a partition of the HAg (or LAg) interface (Figure S2).

The Voronoi facets associated to pairs of type (A, B) define the bicolor interface A-B (bicolor since there are two partners); those associated to pairs of type (A, W ) and (B, W ) define the mediated interface AW -BW , since interactions between A and B are mediated by W (ater) molecules; finally, the union of the bicolor and mediated interface define the tricolor interface ABW . Geometrically, this interface is a polyhedron separating the partners. The curvature of this polyhedron is easily computed [START_REF] Cazals | Revisiting the Voronoi description of protein-protein interfaces: Algorithms[END_REF], and has been shown to provide information on binding modes [START_REF] Cazals | Revisiting the Voronoi description of protein-protein interfaces[END_REF].

IG Ag

IG-Ag complex IG -Ag complex decomposition Solvent accessibility properties of binding patches exhibit a broken symmetry between the Ig and Ag side. In Figure S4, there is a strong correlation between BSA and |I|, a very-well known fact. However,this is less obvious when considering only Ig atoms or Ag atoms. This shows how the shape complementarity between binding patches results in an overall balance between the BSA and the number of atoms at interface. Solvent accessibility asymmetry is a signature for the ligand type. We feed two descriptors (bsa Ag and bsa Ig ) to a classifier in order predict the ligand type of a complex. These descriptors are computed using the sbl-intervor-ABW-atomic.exe binary from the structural bioinformatics library (SBL, sbl.inria.fr). The classifier is a decision tree from the R package rpart.

W IG W Ag H L L V H V L V H V L Interfacial water molecules CDR1 CDR2 CDR3 F R1 F R2 F R3 F R4 Fab F R CDR CDR1 CDR2 CDR3 F R1 F R2 F R3 F R4 F R CDR
We first compute the in-sample classification error. This error is obtained by classifying the training set and results in optimistic error rates. We therefore compute a cross-validated error rate. To this end, we randomly divide the dataset in five subsets of equal size and alternatively use four subsets to classify the fifth. At the end of this procedure, each sample has been predicted and the proportion of misclassified samples can be computed. Since the data is partitioned randomly, we repeat the above procedure 1000 times and compute the average confusion matrix(Table SIV) and both the overall and per class error rates.

The resulting median and average error rates per ligand type are the following: chemical: 5%, 6%; peptide: 19%, 19% ; protein: 7%, 7%. The overall median and average error rates are 9.6% and 9.7% respectively. Since the data is not balanced, i.e. some ligand types are over-represented compared to others we check whether keeping a balanced proportion of classes in each fold would yield differing results. The resulting median and average error rates per ligand type are the following: chemical: 5%, 6%; peptide: 20%, 20% ; protein: 7%, 6%; and the overall median and average error rates are 9.6% and 9.7% respectively, which is essentially similar to the non-balanced cross-validation.

The classification rules resulting from the decision tree run on the whole dataset (i.e. no-crossvalidation) are the following (Figure S5) : bsa Ag ≥ 14.3 ⇒ chemical ligand; 10.7 ≤ bsa Ag < 14.3 ⇒ peptide ligand; bsa Ag < 10.7 AND bsa Ig < 5.75 ⇒ peptide ligand; bsa Ag < 10.7 AND bsa Ig ≥ 5.75 ⇒ protein ligand. Complexes with free VH CDR1 or VH CDR2 are not uncommon since they occur for 45/489 (∼9%) and 50/489 (∼10%) complexes, respectively (3b). In contrast, this is rare for VH CDR3 (6/489 occurrences, ∼1%).

On the other hand, 242/489 (∼49%) complexes involve a free VL CDR2 (3c), a fact to be interpreted in the context of a lesser length variability and, as we shall see, a location on the side of the domain. 70/489 (∼14%) complexes have an free VL CDR1 and 34/489 (∼7%) complexes have an free VL CDR3 which is more than five time as much as VH CDR3. Variation of the atomic volume as a function of the shelling order. Atoms with a higher shelling order tend to be more packed. The rise after shelling order 4 is likely due to a much smaller number of atoms since 1) interfaces with deeply buried atoms are rare, 2) only a limited number of atoms can be deeply buried in an interface. Volume ratio of atom (c)

Binding affinity predictions

Ig -Ag complexes. The structure affinity benchmark (SAB) [START_REF] Kastritis | A structure-based benchmark for protein-protein binding affinity[END_REF] contains 17 Ig -Ag cases (PDB IDs: 1AHW, 1BJ1, 1BVK, 1DQJ, 1E6J, 1FSK, 1IQD, 1JPS, 1MLC, 1NCA, 1NSN, 1P2C, 1VFB, 1WEJ, 2JEL, 2VIR and 2VIS). However, 1IQD and 1NSN are discarded as only an upper bound on their K d is provided in the SAB. Furthermore, 1E6J is also discarded because too many atoms could not be matched between the bound and unbound structures. Finally 1ZLI is removed from the training set because too many atoms could not be matched between the bound and unbound structures and 1UUG is also removed from the training set because of only an upper bound on its K d is provided. q q q q q q q q q q q q q q q q q q q q q 5 10 15 # neighbors q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q Median absolute error (kcal/mol) proportion of predictions within 1 order of magnitude proportion of predictions within 2 order of magnitude proportion of predictions within 3 order of magnitude Experimental ∆G (kcal / mol) Predicted ∆G (kcal / mol) q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q Prodigy Our work

2

 2

  Figure 2

  Figure 3

Figure 4 H

 4 Figure 4

Figure 1 .

 1 Figure 1. Interaction specificity for Ig -Ag complexes: analysis and predictions. Both analyses are based upon the average buried surface areas per atom (Equations (1) (2)): bsa Ig versus bsa Ag . Scatter plot as a function of the ligand type. The three lines (L1, L2 and L3) show the partition defined by the decision tree, separating the ligand types (see main text).

Figure 2 .

 2 Figure 2. Binding affinity analysis and predictions for Ig -Ag complexes. (2a) Complexes in the two-parameter space of the model. The model uses two variables (see main text): IVWIPL: Inverse volume weighted internal path length; NIS_CHARGED: proportion of charged residue on the non-interacting solvent-accessible surface. (2b) Stability of affinity prediction. Performance of the k nearest neighbors estimates when varying the number of neighbors k. Solid line: median absolute error (kcal/mol); dashed, dot-dashed, dotted lines: proportion of predictions with error below 1, 2 and 3 orders of magnitude respectively. (2c) Predicted versus experimental affinities for Ig -Ag complexes. Dashed, dashdotted and dotted lines respectively show errors of ±1.4, ±2.8, ±4.2 kcal/mol, corresponding to K d approximated within one, two and three orders of magnitude.

Figure 3

 3 Figure 3 Buried Surface Area (A 2 ) of the VH and VL domains, and their respective CDRs.

Figure 4 .

 4 Figure 4. Comparison of CDRs in terms of (a) inverse volume-weighted internal path length (IVW-IPL), (b) average normalized shelling order (ANSO), (c) average shelling order, and (d) average atomic volumes. Acknowledgments. Patrice Duroux is acknowledged for his help with the IMGT/3Dstructure-DB database.

Fig. S 1

 1 Fig. S 1 Size of the antigens (number of atoms) Two large peptides (IMGT-PDB file 3W11 chain E, 2301 atoms, and IMGT-PDB file 4R4N chain I, 5172 atoms) are not displayed for readability. See section 2.2 for the data curation methods.

Inria

Fig. S 2

 2 Fig. S 2 Decomposition of anIg -Ag complex. The Ig (or the Fab fragment) is decomposed into heavy (H) and light (L) chains (one H and one L per Fab) whose variable domains only (VH and VL) are of interest in this study. These domains are further decomposed into three complementarity determining regions (CDRs) and four framework regions (FRs). The Voronoi interface of FigureS3is partitioned into contributions from these 14 regions.

Fig. S 3 Inria 6 . 4

 364 Fig. S 3 Voronoi interface model of an Immunoglobulin -Antigen (Ig -Ag) complex, defined from the solvent accessible model of the crystallographic complex. The Ig consists of H and L chains, with here the VH and VL domains shown in grey (cartoon representation), while the Ag consists of the chain in blue (CPK representation). (A) Ig -Ag complex, with the six complementarity determining regions (CDRs) colored using the IMGT conventions (VH CDR1: red, VH CDR2: orange, VH CDR3: purple, VL CDR1: blue, VL CDR2: green, VL CDR3: green-blue). (B) The Voronoi interface is a polyedral model separating the partners, whose parameters (area, curvature) convey information about the binding modes. (C) Each face of the Voronoi interface involves two interacting atoms, either from the partners or the interfacial water molecules sandwiched between them. The buried surface area (BSA) on each partner (by the second partner and interfacial water) is of prime interest to describe the interface. For the Ig, the BSA can be charged to the CDRs and framework regions (FRs). (C, inset) The interface atoms of a partner define its binding patch, which can be shelled into concentric shells (from the outside to the core), defining a distance to the patch boundary. The binding patch on the Ig side is shown from above (inset) where purple, blue and cyan identify atoms with shelling order 1, 2 and 3 respectively. (D, E, F) Voronoi interface of three complexes in (a) to illustrate different types: convex on the Ig side (small chemical ligand), saddle-like (peptide ligand), concave on the Ig side (protein ligand).

Fig. S 4

 4 Fig. S 4 Buried Surface Area versus number of interface atoms: whole interface, Ig side, Ag side. The well-known strong correlation between BSA() and |I| (panel (a)) gets weaker when considering the Ig (panel (b)) and the Ag sides (panel (c)) separately. The Pearson coefficients obtained are equal to 0.99, 0.82 and 0.89 in cases (a,b,c).

Fig. S 5

 5 Fig. S 5 Classification rules characterizing the binding patch depending on the ligand types. See supplemental text for details. The classification rules are: bsa Ag ≥ 14.3 ⇒ chemical ligand; 10.7 ≤ bsa Ag < 14.3 ⇒ peptide ligand; bsa Ag < 10.7 AND bsa Ig < 5.75 ⇒ peptide ligand; bsa Ag < 10.7 AND bsa Ig ≥ 5.75 ⇒ protein ligand. The three lines of a box read as follows: tow row: majority ligand type (chemical, peptide, protein); middle row: fraction for the three classes; bottom row: percentage of the whole dataset.

Fig. S 6

 6 Fig. S 6 Human and mouse VH CDR length versus BSA. The [CDR1. CDR2] length are characteristic of the different Homo sapiens and Mus musculus VH subgroups.There are highly varying levels of BSA for CDR of the same length. The information given by the length of a CDR is therefore not sufficient to infer its contribution to the interface.

Fig. S 7

 7 Fig. S 7 Human and mouse VL CDR length versus BSA. The human [CDR1.CDR2] lengths[6.3] characterize both V-kappa and V-lambda. The other lengths characterize either Vkappa ([7.3],[11.3] and[12.3]) or V-lambda ([8.3] and[9.3]). The mouse [CDR1.CDR2] lengths[7.7] and[9.3] characterize V-lambda. The other lengths characterize V-kappa. There are highly varying levels of BSA for CDR of the same length. The information given by the length of a CDR is therefore not sufficient to infer its contribution to the interface.

  VL CDR3, Mouse.

Inria

Fig. S 8

 8 Fig. S 8 a) and b): IVW-IPL of the CDR of VH and VL respectively. c): Variation of the atomic volume as a function of the shelling order. Atoms with a higher shelling order tend to be more packed. The rise after shelling order 4 is likely due to a much smaller number of atoms since 1) interfaces with deeply buried atoms are rare, 2) only a limited number of atoms can be deeply buried in an interface.

Fig. S 9

 9 Fig. S 9 Stability of affinity prediction using k nearest neighbors estimates, when varying the number of neighbors k.

Fig. S 10 Fig. S 11

 1011 Fig. S 10Binding affinity analysis and predictions for Ig -Ag complexes. Predictions performed by the linear model from[START_REF] Marillet | High resolution crystal structures leverage protein binding affinity predictions[END_REF]. Dashed, dash-dotted and dotted lines respectively show errors of ±1.4, ±2.8, ±4.2 kcal/mol, corresponding to K d approximated within one, two and three orders of magnitude.

Fig. S 12 1 2 . 2 2 . 3 2 . 4 2 . 5 2 . 6 3 8 3 . 1

 1212223242526331 Fig. S 12 Prediction error versus average distance of the 10 nearest-neighbors and the standard deviation of their affinity values.

Table S I

 S Summary of the number of Ig -Ag complexes in each class of species / ligand type. The dataset includes VH (V-domains of heavy chains)and VL comprising V-KAPPA (V domains of kappa chains) and V-LAMBDA (V domains of lambda chains. See section 2.2 for the data curation methods.Canonical complexes.A canonical configuration for a IMGT/3Dstructure-DB IMGT-PDB file is as follows: one H chain, one L chain, one ligand. A non canonical configuration may occur for different reasons:

				Mouse Human Other total
			Peptide	80	32	11	123
			Protein	168	91	30	289
			Chemical	65	7	5	77
			total	313	130	46	489
	Table S II Amino acid positions associated with each IMGT label defining the decom-
	position of a V-domain into seven regions Positions of the complementarity determining
	regions (CDRs) using the IMGT numbering scheme [37]. See section 2.2 for the data curation
	methods.
	Region	FR1	CDR1	FR2	CDR2	FR3	CDR3	FR4
	start-stop 1 -26 27 -38 39 -55 56 -65 66 -104 105 -117 118 -128
	6.1.2 Inferring canonical complexes

Table S III

 S Main features of the Ig -Ag complexes found in the structure affinity benchmark. CDR bounds correspond to the first and last residue numbers in IMGT renumbered PDB files.

	PDB ID	Ig H chain	Ig L chain	Ag chain(s)	Ag type	Species		VH V and J gene	VL V and J gene
	1AHW	B	A	C		Protein	Mus musculus (house mouse)	IGHV14-1*02 IGHJ2*01	IGKV14-111*01 IGKJ2*01
	1BJ1	H	L	WV		Protein	Humanized (humanized)	IGHV7-4-1*02 IGHJ2*01	IGKV1-33*01 IGKJ1*01
	1BVK	E	D	F		Protein	Humanized (humanized)	IGHV4-59*01 IGHJ4*03	IGKV1-27*01 IGKJ1*01
	1DQJ	B	A	C		Protein	Mus musculus (house mouse)	IGHV3-8*02 IGHJ6*03	IGKV5-43*01 IGKJ1*02
	1FSK	C	B	A		Protein	Mus musculus (house mouse)	IGHV1-61*01 IGHJ3*01	IGKV6-20*01 IGKJ1*02
	1JPS	H	L	T		Protein	Homo sapiens (human)	IGHV3-66*04 IGHJ4*03	IGKV1-39*01 IGKJ1*01
	1MLC	B	A	E		Protein	Mus musculus (house mouse)	IGHV1-9*01 IGHJ2*01	IGKV5-43*01 IGKJ2*01
	1NCA	H	L	N		Protein	Mus musculus (house mouse)	IGHV9-3*03 IGHJ2*01	IGKV6-25*01 IGKJ1*01
	1P2C	B	A	C		Protein	Mus musculus (house mouse)	IGHV1-9*01 IGHJ4*01	IGKV5-43*01 IGKJ1*01
	1VFB	B	A	C		Protein	Mus musculus (house mouse)	IGHV2-6-7*01 IGHJ2*01	IGKV12-41*02 IGKJ2*01
	1WEJ	H	L	F		Protein	Mus musculus (house mouse)	IGHV14-3*02 IGHJ2*01	IGKV12-41*02 IGKJ1*01
	2JEL	H	L	P		Protein	Mus musculus (house mouse)	IGHV1-67*01 IGHJ1*01	IGKV1-117*01 IGKJ1*02
	2VIR	B	A	C		Protein	Mus musculus (house mouse)	IGHV2-9*02 IGHJ4*01	IGLV1*01 IGLJ1*01
	2VIS	B	A	C		Protein	Mus musculus (house mouse)	IGHV2-9*02 IGHJ4*01	IGLV1*01 IGLJ1*01
	PDB ID	VH CDR lengths (1, 2, 3)	VL CDR lengths (1, 2, 3)	Ag size (number of atoms)	Ag name
	1AHW	8 8 10		6 3 9				1612		Thromboplastin (synonym: tissue factor, TF, coagulation factor
	1BJ1	8 8 16		6 3 9				1522		VEGF (Vascular endothelial growth factor A)
	1BVK	8 7 10		6 3 9				1001		Lysozyme C [hen egg white] (HEL) EC:3.2.1.17
	1DQJ	8 7 7		6 3 9				1007		Lysozyme C [hen egg white] (HEL) EC:3.2.1.17
	1FSK	8 8 11		6 3 9				1230		Major birch pollen allergen Bet v1
	1JPS	8 8 10		6 3 9				1611		Tissue Factor
	1MLC	8 8 9		6 3 9				1001		Lysozyme C [hen egg white] (HEL) EC:3.2.1.17
	1NCA	8 8 13		6 3 9				3075		Neuraminidase [influenza virus, A/Tern strain, N9 subtype]
	1P2C	8 8 9		6 3 9				1001		Lysozyme C [hen egg white] (HEL) EC:3.2.1.17
	1VFB	8 7 10		6 3 9				1265		Lysozyme C [hen egg white] (HEL) EC:3.2.1.17
	1WEJ	8 8 10		6 3 9				826		Cytochrome c [horse]
	2JEL	8 8 11		11 3 9			640		Histidine-containing protein of the phosphoenolpyruvate: sugar
	2VIR	8 7 16		9 3 9				2075		Hemagglutinin HA1 [influenza virus]; residues: 28-328
	2VIS	8 7 16		9 3 9				2076		Hemagglutinin HA1 [influenza virus] T131I (escape mutant);
	PDB ID	Ig name		Resolution	VH CDR1 bounds	VH CDR2 bounds	VH CDR3 bounds	VL CDR1 bounds	VL CDR2 bounds	VL CDR3 bounds
	1AHW	AB-GAMMA-1_KAPPA	3.0		27 38			56 65	105 117	27 38	56 65	105 117
	1BJ1	AB-GAMMA-1_KAPPA	2.4		27 38			56 65	105 117	27 38	56 65	105 117
	1BVK	V-HEAVY_KAPPA	2.7		27 38			56 65	105 117	27 38	56 65	105 117
	1DQJ	AB-GAMMA-2A_KAPPA	2.0		27 38			56 65	105 117	27 38	56 65	105 117
	1FSK	AB-GAMMA-1_KAPPA	2.9		27 38			56 65	105 117	27 38	56 65	105 117
	1JPS	AB-GAMMA-1_KAPPA	1.85		27 38			56 65	105 117	27 38	56 65	105 117
	1MLC	FAB-GAMMA-1_KAPPA	2.5		27 38			56 65	105 117	27 38	56 65	105 117
	1NCA	AB-GAMMA-2A_KAPPA	2.5		27 38			56 65	105 117	27 38	56 65	105 117
	1P2C	FAB-GAMMA-1_KAPPA	2.0		27 38			56 65	105 117	27 38	56 65	105 117
	1VFB	FV-HEAVY_KAPPA	1.8		27 38			56 65	105 117	27 38	56 65	105 117
	1WEJ	AB-GAMMA-1_KAPPA	1.8		27 38			56 65	105 117	27 38	56 65	105 117
	2JEL	AB-GAMMA-1_KAPPA	2.5		27 38			56 65	105 117	27 38	56 65	105 117
	2VIR	AB-GAMMA-1_LAMBDA	3.25		27 38			56 65	105 117	27 38	56 65	105 117
	2VIS	AB-GAMMA-1_LAMBDA	3.25		27 38			56 65	105 117	27 38	56 65	105 117
	PDB ID 1AHW	K d (M) 3.40 • 10 -9	∆G (kcal/mol) -11.55	iRMSD (Å) 0.69	Method Competitive Inhibition assay	pH not stated
	1BJ1	3.40 • 10 -9	-11.55		0.5		SPR			4.8
	1BVK	1.40 • 10 -8	-10.53		1.24		Stopped-flow inhibition	7
	1DQJ	2.80 • 10 -9	-11.67		0.75		SPR			7.5
	1FSK	2.40 • 10 -10	-13.12		0.45		SPR			7.4
	1JPS	1.00 • 10 -10	-13.64		0.51		SPR			7.2
	1MLC	9.10 • 10 -8	-9.61		0.6		SPR			7.4
	1NCA	8.30 • 10 -9	-11.02		0.24		Fluorescence inhibition assay	7.2
	1P2C	1.02 • 10 -10	-13.63		0.46		SPR			not stated
	1VFB	3.70 • 10 -9	-11.46		1.02		ITC			7.1
	1WEJ	7.14 • 10 -10	-12.48		0.31		Spectroscopic inhibition assay	not stated
	2JEL	2.80 • 10 -9	-11.59		0.17		Fluorescence inhibition assay	7.2
	2VIR	1.00 • 10 -9	-12.28		0.8		SPR			not stated (BIAcore standard:7.4)
	2VIS	4.00 • 10 -6	-7.36		0.8		SPR			not stated (BIAcore standard: 7.4)
	RR n°8963

Avg_Atm_BSA_Ag >= 10.7

	Chemical Peptide Protein	Protein .157 .251 .592 100.0%
			< 10.7
	Peptide .423 .528 .049 37.1%	Protein .000 .087 .913 62.9%
	Avg_Atm_BSA_Ag >= 14.3	Avg_Atm_BSA_IG < 5.75
		< 14.3		>= 5.75
	Chemical .944 .042 .014 16.2%	Peptide .022 .902 .076 21.0%	Peptide .000 .688 .312 3.6%	Protein .000 .050 .950 59.2%
				Inria

Table S IV

 S Average confusion matrix for ligand type prediction. Results obtained by running 5-fold cross-validation 1000 times. Each repetition results in a confusion matrix which is averaged-e.g. on average 4.6 chemicals out of 77 are predicted as peptides.

	X Predicted X X X X Chemical	X X Actual Chemical Peptide Protein X X X 72.4 3.0 1.0
	Peptide	4.6	99.1	17.9
	Protein	0.0	20.9	270.1

Table S V

 S Median BSA and median of BSA/BSA Ig per species and per ligand type. Median BSA contributed to the interface by different parts of the Ig, for various ligand types and species. Percentages relative to the BSA of the whole Ig are included in parentheses.

	Other	Peptide Protein	546.6 (100.0%) 767.4 (100.0%)	462.8 (63.7%) 307.5 (54.0%)	420.0 (58.9%) 241.3 (50.1%)	54.5 (8.0%) 37.6 (8.2%)	148.9 (20.5%) 55.9 (13.8%)	193.2 (26.1%) 108.5 (20.7%)	48.7 (7.6%) 38.2 (7.1%)	0.0 (0.0%) 0.0 (0.0%)	0.1 (0.0%) 15.5 (2.9%)	29.2 (3.5%) 11.5 (2.1%)	0.0 (0.0%) 0.0 (0.0%)	0.0 (0.0%) 0.0 (0.0%)	292.9 (36.3%) 203.7 (46.0%)	247.2 (32.6%) 196.4 (37.5%)	86.1 (12.8%) 49.5 (11.7%)	8.7 (0.9%) 0.0 (0.0%)	111.4 (14.5%) 124.6 (23.2%)	16.8 (2.8%)
		Chemical	275.0 (100.0%)	141.1 (54.4%)	116.2 (42.3%)	23.6 (7.7%)	0.0 (0.0%)	97.3 (35.4%)	15.0 (6.9%)	0.0 (0.0%)	11.3 (3.7%)	0.0 (0.0%)	0.0 (0.0%)	0.0 (0.0%)	132.8 (45.6%)	113.6 (41.3%)	13.5 (4.9%)	0.0 (0.0%)	94.4 (34.2%)	3.7 (1.2%)
	Mouse	Chemical Peptide Protein	254.6 (100.0%) 486.6 (100.0%) 703.9 (100.0%)	154.8 (59.9%) 287.0 (58.4%) 471.1 (64.3%)	128.3 (46.6%) 236.8 (49.5%) 434.9 (57.4%)	19.0 (8.5%) 46.5 (10.0%) 101.7 (14.7%)	13.0 (5.0%) 61.4 (13.2%) 99.8 (14.4%)	76.9 (29.4%) 117.4 (24.1%) 208.7 (29.1%)	24.0 (7.8%) 42.6 (8.4%) 28.8 (4.3%)	0.0 (0.0%) 0.0 (0.0%) 0.0 (0.0%)	11.9 (3.8%) 22.5 (4.4%) 6.6 (0.9%)	0.0 (0.0%) 10.8 (2.3%) 15.7 (2.4%)	0.0 (0.0%) 0.0 (0.0%) 0.0 (0.0%)	0.0 (0.0%) 0.0 (0.0%) 0.0 (0.0%)	104.2 (40.1%) 190.6 (41.6%) 276.3 (35.7%)	92.5 (37.4%) 175.3 (38.2%) 224.5 (30.4%)	32.4 (13.3%) 76.6 (15.7%) 52.5 (7.9%)	0.0 (0.0%) 0.0 (0.0%) 10.0 (1.5%)	52.9 (22.4%) 101.7 (20.6%) 103.3 (16.0%)	0.0 (0.0%) 0.0 (0.0%) 6.8 (0.9%)
	Human	Chemical Peptide Protein	143.7 (100.0%) 645.7 (100.0%) 812.0 (100.0%)	89.8 (57.0%) 418.3 (66.2%) 569.9 (67.7%)	49.4 (39.6%) 381.3 (56.9%) 510.7 (62.1%)	10.3 (7.5%) 63.0 (11.1%) 86.2 (9.5%)	0.0 (0.0%) 76.3 (12.6%) 139.0 (17.4%)	44.0 (26.9%) 180.3 (29.3%) 233.9 (30.4%)	25.8 (11.7%) 24.5 (4.7%) 30.6 (3.4%)	0.0 (0.0%) 0.0 (0.0%) 0.0 (0.0%)	8.1 (5.3%) 6.8 (1.6%) 0.0 (0.0%)	0.0 (0.0%) 15.5 (2.1%) 18.1 (2.5%)	0.1 (0.1%) 0.0 (0.0%) 0.0 (0.0%)	0.0 (0.0%) 0.0 (0.0%) 0.0 (0.0%)	71.2 (43.0%) 185.6 (33.8%) 261.6 (32.3%)	46.3 (30.2%) 162.9 (33.4%) 211.1 (26.9%)	0.0 (0.0%) 46.5 (9.2%) 74.7 (8.3%)	0.0 (0.0%) 0.0 (0.0%) 3.9 (0.5%)	45.0 (23.7%) 114.9 (17.9%) 98.1 (12.1%)	25.0 (16.3%) 0.0 (0.0%) 11.1 (1.3%)
			Ig	VH	VH CDR	VH CDR1	VH CDR2	VH CDR3	VH FR	VH FR1	VH FR2	VH FR3	VH FR4	VH OTHER	VL	VL CDR	VL CDR1	VL CDR2	VL CDR3	VL FR

Table S VI

 S Binding affinities: experimental values against those obtained with two regression methods. KNN predictions: obtained using the k-nearest neighbors regressor, as explained in the text; linear model predictions: obtained with the linear model introduced in[START_REF] Marillet | High resolution crystal structures leverage protein binding affinity predictions[END_REF].

RR n°8963

Acknowledgments. Patrice Duroux is acknowledged for his help with the IMGT/3Dstructure-DB database.

Note that this leaves 14 Ig -Ag cases to predict, using a learning set involving 144-2-3-14 = 125 complexes.

Affinity estimation as a regression problem. In this work, we estimate binding affinities using k nearest neighbors regression (knn) [START_REF] Györfi | A distribution-free theory of nonparametric regression[END_REF][START_REF] Biau | Lectures on the nearest neighbor method[END_REF], a non parametric strategy which does not require any a priori on the mathematical model for the response variable estimated -as opposed to say linear regression.

To describe knn regression, which is a two step strategy, recall that we model complexes using two parameters denoted IVW-IPL and NIS charged (see main text); these variables define a parameter space denoted C. As a pre-processing step, we compute the parameters IVW-IPL and NIS charged for the training set (125 cases), yielding a point cloud P in C (Fig. 2, right panel). To estimate the affinity a complex q, we proceed in two steps. First, the k nearest neighbors of q in P are sought, with k a predefined number. Second, the affinity of q is estimated by averaging those of its k nearest neighbors.

We assess the quality of our predictions in two ways:

• First, by varying the value k. From a theoretical standpoint [START_REF] Györfi | A distribution-free theory of nonparametric regression[END_REF], it is known that k must be super-logarithmic and sub-linear in the number of cases processed. Since log(144) ∼ 5, we explore the range k ∈ 5, . . . , 25 (Fig. 2, right panel). Practically, the results discussed in the main text correspond to k = 10.

• Second, by comparing the estimates against those yielded by the linear model using the same variables. This model corresponds to the one defined in [START_REF] Marillet | High resolution crystal structures leverage protein binding affinity predictions[END_REF]. See Table SVI for this comparison.

Practically, we compute the variables used by the regression method using the binding affinity prediction package from the structural bioinformatics library (SBL, sbl.inria.fr).

For the fitting, we use the scikit-learn library [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF], namely the neighbors package for knn regression, and the linear_model package for the least-squares linear regression.

Results. The median absolute error does not vary much between 8 and 12 neighbors (from 1.008 to 0.898, Figure S9). Moreover, the error for 10 neighbors is close to the median error for the total range considered (0.878 compared to 0.910 kcal/mol).

Statistics for the KNN predictions: Pearson's correlation coefficient: 0.488 (p-value = 0.077). Median absolute error: 0.878. Number of complexes with errors below 1, 2, and 3 orders of magnitude respectively: 8, 13, 3.

Statistics for predictions: obtained with the linear model from [START_REF] Marillet | High resolution crystal structures leverage protein binding affinity predictions[END_REF]: Pearson's correlation coefficient: 0.326 (p-value = 0.255). Median absolute error: 1.017. Number of complexes with errors below 1, 2, and 3 orders of magnitude respectively: 9, 13, 14.

Inria