Int. J. Mol. Sci. 2011, 12, 226-251; doi:10.3390/ijms12010226
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`OPEN ACCESS
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`International Journal of
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`Molecular Sciences
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`ISSN 1422-0067
`www.mdpi.com/journal/ijms
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`Article
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`Computational Docking of Antibody-Antigen Complexes,
`Opportunities and Pitfalls Illustrated by Influenza
`Hemagglutinin
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`Mattia Pedotti †, Luca Simonelli †, Elsa Livoti and Luca Varani *
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`Institute for Research in Biomedicine, via Vela 6, 6500 Bellinzona, Switzerland;
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`E-Mails: mattia.pedotti@irb.unisi.ch (M.P.); luca.simonelli@irb.unisi.ch (L.S.);
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`elsa.livoti@irb.unisi.ch (E.L.)
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`† These authors contributed equally to this work.
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`* Author to whom correspondence should be addressed; E-Mail: luca.varani@irb.unisi.ch;
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`Tel.: +41-91-820-0321; Fax: +41-91-820-0302.
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`Received: 2 November 2010; in revised form: 22 December 2010 / Accepted: 4 January 2011 /
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`Published: 5 January 2011
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`Abstract: Antibodies play an increasingly important role in both basic research and the
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`pharmaceutical industry. Since their efficiency depends, in ultimate analysis, on their
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`atomic interactions with an antigen, studying such interactions is important to understand
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`how they function and, in the long run, to design new molecules with desired properties.
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`Computational docking, the process of predicting the conformation of a complex from its
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`separated components, is emerging as a fast and affordable technique for the structural
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`characterization of antibody-antigen complexes. In this manuscript, we first describe the
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`different computational strategies for the modeling of antibodies and docking of their
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`complexes, and then predict the binding of two antibodies to the stalk region of influenza
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`hemagglutinin, an important pharmaceutical target. The purpose is two-fold: on a general
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`note, we want to illustrate the advantages and pitfalls of computational docking with a
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`practical example, using different approaches and comparing the results to known
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`experimental structures. On a more specific note, we want to assess if docking can be
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`successful in characterizing the binding to the same influenza epitope of other antibodies
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`with unknown structure, which has practical relevance for pharmaceutical and biological
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`research. The paper clearly shows that some of the computational docking predictions can
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`be very accurate, but the algorithm often fails to discriminate them from inaccurate
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`solutions. It is of paramount importance, therefore, to use rapidly obtained experimental
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`data to validate the computational results.
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`Keywords: antibody modeling; computational docking;
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`influenza; hemagglutinin;
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`antibody-antigen complexes
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`1. Introduction
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`Individuals that recover from the attack of a pathogen have antibodies (Abs) capable of detecting
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`and neutralizing the same pathogen in a future encounter, usually conferring life-long protection from
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`it. Detection and neutralization are initiated by the binding of these antibodies to antigens, often
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`surface proteins, through specific atomic interactions between the antibody and the region of the
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`antigen (Ag) that it recognizes (epitope). A better understanding of these interactions is expected to
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`accelerate vaccine development, since most current vaccines are based on the generation of
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`neutralizing antibody responses. If we understand the structural rules governing Ab-Ag interactions in
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`a given virus, for instance, then we have the molecular basis to attempt to design and synthesize new
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`epitopes to be used as vaccines, optimize the antibodies themselves for passive immunization or design
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`new drugs mimicking the antibodies or their effect.
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`In addition to pharmaceutical development, antibodies play an increasingly relevant role in basic
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`research and industrial processes, where they are starting to be used as recognition elements sensitive
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`to the presence of a given antigen. Designing and synthesizing new antibodies with desired properties
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`would, therefore, have a profound impact, but we are very far away from being able to do that. Despite
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`antibodies having been known and characterized for several decades [1,2], in fact, we still know
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`remarkably little about their interactions. Given an antibody structure, for instance, we cannot even
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`predict whether it can bind a protein, nucleic acid or sugar, let alone the specific antigen or
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`conformational epitope that it recognizes. The study of Ab-Ag complexes should further our
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`understanding of the general principles of recognition and, in the long run, gives us the basis for the
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`successful design of new molecules or the rational optimization of existing ones.
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`The best way to study atomic interaction is to obtain the three-dimensional structure of
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`antibody-antigen complexes. Traditionally, this is achieved by experimental techniques like X-ray
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`crystallography, an often long and laborious process with high failure rate. Thanks to advances in
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`algorithms and processing power, however, we can now use computational techniques for the
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`structural characterization of intermolecular complexes. Computational docking—the process of
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`predicting the conformation of a complex starting from its separated components—provides a fast and
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`inexpensive route to obtain structures, including those which are not suitable for experimental
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`determination. Although computational docking is still in its infancy and marred by several limitations,
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`there is no doubt that it will become more and more accurate, relevant and widespread in the
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`coming years.
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`Here we first illustrate the application of computational docking to the study of antibody-antigen
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`interactions, and then highlight the strengths and weaknesses of the approach by predicting the binding
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`of two different antibodies to hemagglutinin, the surface protein of influenza virus and an important
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`pharmaceutical target. Being able to accurately predict those structures, for which X-ray information is
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`available, would strengthen our belief that computational techniques can be used to characterize the
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`binding of new antibodies against the same epitope.
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`1.1. Computational Docking
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`Computational docking, a relatively new and constantly evolving technique, is the process of
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`predicting the structure of a multi-molecular complex from the structures of its separated components.
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`Its progress has been monitored since 2002 by the ―Critical Assessment of PRediction of Interactions‖
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`project (CAPRI) [3], a comparative evaluation of protein-protein docking algorithms on a set of known
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`targets. Here we focus on docking of antibodies to protein antigens, which presents specific challenges
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`but also has peculiar features exploitable to ease the calculations.
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`In a typical docking protocol, the structures of the antigen and antibody are separated by
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`approximately 25 Å and subsequently brought together by the chosen algorithm. The first necessary
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`step, therefore, is obtaining the structures of the isolated antigen and antibody. The starting structure
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`may be defined as follows:
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`(i) ―Bound‖, if it originates from an experimental structure of the complex that needs to be docked.
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`This is interesting when developing docking procedures but it is generally not biologically
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`attractive, because computational docking is unlikely to add relevant information if an
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`experimental structure is already available.
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`(ii) ―Unbound‖, if it originates from an experimental structure of the molecule not bound to the
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`partner that needs to be docked, i.e., either free or bound to a different partner. This is the most
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`common scenario for antigens, especially since the number of available protein structures is
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`increasing thanks to several structural genomics efforts. Structures of free antibodies, instead, are
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`usually not available, nor they would be particularly useful since Abs are known to drastically
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`change conformation upon binding [4].
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`(iii) ―Modeled‖, if it has been predicted by homology modeling and/or other computational techniques
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`like ab initio predictions or molecular dynamics. A thorough description of homology modeling
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`for protein antigens is beyond the scope of this manuscript. Suffice to say that the results are
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`remarkably accurate if the target protein has sequence similarity to a protein with known structure
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`and that even ab initio predictions are starting to produce accurate results, albeit much less than
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`homology modeling [5–7]. Antibody structures can be predicted with remarkable accuracy and
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`precision as well; the process is relatively different from standard protein modeling and is covered
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`in the next sections.
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`1.2. Antibody Structure, Implications for Modeling
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`Antibodies are large (~150 kDa), y-shaped molecules containing a so-called Fc region (Fragment,
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`Crystallizable, it binds to various cell receptors and mediates a response of the immune system) and
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`two Fab regions (Fragment, Antigen Binding). The latter are composed by one heavy and one light
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`chain, each with a constant and a variable domain called FV (Figure 1). The FV is the only domain
`responsible for antigen binding and, therefore, the only one that needs to be considered for docking. It
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`is further subdivided in a framework region, highly conserved in both sequence and conformation, and
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`six highly variable CDR loops (Complementarity Determining Region), three from each chain and
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`often referred to as L1, L2, L3, H1, H2, and H3.
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`Figure 1. Schematic (a) and cartoon (b) representation of a full antibody structure.
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`Antigens bind to the tip of the VH and VL domains.
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`Despite their high sequence variability, five of the six loops (all except H3) can assume just a small
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`repertoire of main-chain conformations, called ―canonical structures‖ [5–7]. These conformations are
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`determined by the length of the loops and by the presence of key residues at specific positions in the
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`antibody sequence. The specific pattern of residues that determines each canonical structure forms a
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`signature that can be recognized in the sequence of an antibody of unknown structure, allowing
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`successful prediction of the canonical structure itself with high accuracy [8,9]. Uncertainties arise in
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`the relatively rare cases when a loop is particularly long and/or does not follow canonical structures.
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`The H3 loop does not appear to adopt canonical structures, instead, and predicting its conformation
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`requires more sophisticated and less accurate approaches.
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`The framework regions can also be reliably predicted since known structures with high sequence
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`identity are often available. Due to the presence of conserved residues at the interface between the light
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`and heavy chain, the relative geometry of these domains is also well preserved [10]. Correct
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`assembling of the heavy and light chain is nonetheless critical for the accurate orientation of the
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`antigen binding interface and errors may arise in the modeling.
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`It is important to note that the rules and templates used for modeling are based on structures of
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`antibodies bound to their antigen and are therefore accurate in the context of the bound conformation
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`of an antibody.
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`1.3. Antibody Modeling Based on Canonical Structures, the PIGS Server
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`PIGS (Prediction of ImmunoGlobulin Structure [11]) is a web-based server for the automatic
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`prediction of antibody structure [12] based on the canonical structure method [13]. The Web Antibody
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`Modelling server, WAM [14], utilizes the same approach but offers less features and is generally less
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`convenient to utilize.
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`In the canonical structure method, the sequence of each variable domain (VL and VH) of the
`antibody of unknown structure (target) is independently aligned with the corresponding variable
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`domain sequences of all the immunoglobulins of known structure. For this step, standard database
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`searching (e.g., BLAST) [15], and multiple sequence alignment (e.g., Clustalw) [16] programs can be
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`used, but it is important to verify that residues at key structural positions are correctly aligned. The
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`backbone structure of the framework is then modeled using the known structures with highest
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`sequence identity as template. The rationale for this is that, in general, the higher the residue identity in
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`the core of two proteins the more similar the conformation in this region [8] and, hence, the higher the
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`quality of the model. Similarly, the conformation of the CDR loops is predicted using known templates
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`with the same canonical loop conformation and high sequence identity. Different combinations of
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`templates can be used as illustrated below.
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`(i) Best heavy and light chains. Use the chains with highest sequence identity as templates. Since
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`they come from different antibodies, the two chains need to be packed together by a least-squares
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`fit of the residues conserved at the interface. This may introduce errors in the relative orientation
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`of the two chains, with adverse consequences for the accurate modeling of the antigen binding site.
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`(ii) Same canonical structures. Use a template whose CDR loops have the same canonical structures
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`as the target even if a template with higher sequence identity exists for one or both chains. If
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`framework and loops are taken from different templates, then the loops need to be grafted in,
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`possibly introducing errors: the residues adjacent to the loop are superimposed to the framework
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`by a weighted least-square fit of the main chain.
`(iii) Same antibody. Use the same antibody as template for both heavy and light chain, even if
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`templates with higher sequence identity exist. This does not require optimization of the relative
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`orientation of the two chains and thus avoids the errors illustrated earlier.
`(iv) Same antibody and canonical structures. The template is an antibody with the same canonical
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`structures as the target and it is used to model both framework and the CDR loops. This option
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`does not require optimization of framework orientation nor loop grafting and may offer more
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`accurate results even if templates with higher sequence identity are available for one of the chains.
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`The approach tends to fail, however, if the identity is too low.
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`The conformation of five of the six CDR loops can be modeled as described but no canonical
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`structure is known for the H3 loop. However, the so-called ―torso‖ region, i.e., the H3 residues closer
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`to the framework, can still be predicted by similarity to antibodies sharing the same torso
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`conformation [17–19]. The ―head‖ region of H3, instead, follows rules of standard protein hairpins and
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`can be predicted by similarity to protein loops (not just antibodies) with high sequence identity, but the
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`result is usually less accurate than for other CDR loops.
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`The subsequent step consists in the modeling of the side chains conformations. At sites where the
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`parent structure and the model have the same amino acid the conformation of the parent structure is
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`retained. Otherwise, the side chain conformation is copied from antibodies with high sequence
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`similarity or imported from standard rotamer libraries [20]. Finally, the model is refined by a few
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`cycles of energy minimization to improve the stereochemistry, especially in those regions where
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`segments of structures coming from different immunoglobulins have been joined, but not to
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`significantly refine the models.
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`1.4. Antibody Modeling by Rosetta Antibody
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`Rosetta Antibody [21] is a homology modeling program to predict antibody FV structures. It uses a
`simple energy function to simultaneously optimize the CDR loop backbone dihedral angles, the
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`relative orientation of the light and heavy chains and the side chain conformations. The program can be
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`downloaded and run on local computers or modeling requests can be submitted to a web
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`server [22,23]. Rosetta Antibody first identifies the antibody templates with highest sequence identity
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`for each framework and CDR loops; the loop templates are then grafted onto the framework and
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`the full FV is assembled. This crude model is used as input for a second stage: a multi-start,
`Monte-Carlo-plus-minimization algorithm that generates two thousand candidate structures. H3 loop
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`conformations are generated by assembling small peptide fragments [24] and sidechains are finally
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`optimized via rotamer packing and energy minimization [25]. The CDR backbone torsion angles and
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`relative orientation of light and heavy framework are also perturbed and minimized with a
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`pseudo-energy function that includes van der Waals energy, orientation-dependent hydrogen
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`bonding [26],
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`implicit Gaussian salvation [27], side chain rotamer propensities [28] and a
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`low-weighted distance-dependent dielectric electrostatic energy [29]. In the end, a scoring function is
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`used to discriminate the 10 best antibody models that are offered as standard result.
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`1.5. Other Procedures for Antibody Modeling
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`Methods based on canonical structures are generally very effective but somehow limited by the lack
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`of structural templates for a few loop conformations. Other methods model the CDR loops using
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`templates selected by sequence identity (to other Abs or proteins in general) rather than by the
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`presence of key residues as in the canonical structures method [30–32]. Alternative approaches have
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`been used to model CDR loops with ab initio methods based on physicochemical principles [33–38],
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`which have the advantage of not requiring any template and can thus be applied even if no suitable
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`canonical structure is found. Their major limitation is that, due to our poor comprehension of the
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`physicochemical principles governing protein structures, the pseudo-energy functions used to evaluate
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`the different conformations often fail to distinguish a correct prediction. Another limitation is that
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`ab initio methods tend to have higher computational costs than similarity-based approaches. As our
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`understanding of protein structure and energy function increases, the combination of the canonical
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`structure procedure with other more sophisticated computational approaches may offer improvements.
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`1.6. The Docking Calculation
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`Having chosen or generated the starting structures for antibody and antigen, the molecules are then
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`brought together by the preferred algorithm. Computational docking must face two problems [39]:
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`(1) Finding the correct solution, which is usually achieved by changing the relative position of the
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`partners and repeating the calculation thousands of times; (2) discriminating the correct solution from
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`the inaccurate ones by use of a so-called ―scoring function‖. Simply put, the scoring function rewards
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`positive interaction between the docking partners (e.g., the formation of a hydrogen bond) and
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`penalizes negative interactions (e.g., steric clashes). The assumption is that the correct biological
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`structure is energetically favored and has, therefore, the lowest energy. Scoring functions, also referred
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`to as pseudo-energy, try to simulate this energy by accounting for biophysical considerations such as
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`hydrophobic and electrostatic interactions, salt bridges, hydrogen bonds, etc, but also statistical and
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`empirical considerations such as the degree of conserved residues at the interface.
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`When searching for the correct binding orientation, the two (or more) molecules are allowed to
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`move and the score is assessed after each step. Minimization protocols only retain conformations with
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`a lower energy (better score) than the previous; other protocols (e.g., Monte-Carlo) may retain
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`conformations with higher energy in an attempt to overcome local energy minima that do not
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`correspond to the global minimum. The movement is stopped after a predefined number of steps or
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`when the score does not improve further. The conformational parameters changed between each step
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`vary in different docking algorithms, which may be divided in three general classes as described
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`below: (i) only the relative position of the docking partner is changed; (ii) the relative position and
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`the sidechain conformations are changed; (iii) the backbone conformation is altered in addition
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`to the above.
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`In the simplest case, the conformation of the starting structures is not altered at all during the
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`docking process and
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`the scoring function only needs
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`to account for
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`the
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`intermolecular
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`interactions [40,41]. This is called ―rigid body docking‖ and exploits the fact that biological interfaces
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`have highly complementary shapes [42–45]. Needless to say, the approach works best if the starting
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`structures are identical to the bound conformation; although this is not too common in biological
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`complexes, good results can nonetheless be obtained in several cases. Various research groups have
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`used this approach [46–52]; amongst them the program ZDock [53] has achieved good results in the
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`CAPRI experiment [54–57].
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`RosettaDock [58,59] has a first rigid body phase in which sidechains are removed, but in a second
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`phase they are re-introduced and their orientation is optimized [60,61]. Since the sidechain
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`conformation is dictated mainly by a limited number of allowed torsion angles, the task can be
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`completed with reasonable success and limited computational requirements [51].
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`Accurately simulating the backbone movements that often happen upon formation of biological
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`complexes remains a daunting task for docking, which has a very high failure rate when molecules
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`undergo significant conformational changes upon binding. The degrees of freedom available to protein
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`backbone, especially in loop regions, make it extremely difficult to sample and effectively score the
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`sheer amount of possible stable conformations. Among the programs that incorporate backbone
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`flexibility in the docking [62–64], HADDOCK [65,66] uses a rigid body phase followed by sidechain
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`optimization to select the best scoring decoys, and then simulates backbone flexibility on a selected
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`number of decoys (200 with the default options) in a final stage. It is not practical to run the final
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`stage for all the thousands of initial decoys because of the high computational requirements, although
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`this problem will become less significant with increase in computing power. Likewise, a recent
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`update to RosettaDock adds the option of backbone minimization to the standard protocol with
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`moderate success [58].
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`It is not clear which approach should work best when docking antibody-antigen complexes. It is
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`conceivable that in vivo antibodies adapt to and are selected against existing antigen conformations,
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`thus it might be tempting to believe that antigens should not experience drastic changes upon antibody
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`binding. Rigid body docking might be best in this case, but first of all it is doubtful that proteins are
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`not subjected to any conformational motion in solution, not even at the sidechain level, and
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`furthermore, there are examples in which antibodies provoke relatively large allosteric effects on the
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`antigen [67]. The issue is slightly different for the antibody, instead: since antibody modeling uses
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`bound conformations as templates, the conformational rearrangements experienced by the antibody
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`upon binding can be ignored. It should be noted, however, that the canonical structures used for
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`antibody modeling describe the backbone but not the sidechain conformations, which are probably best
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`explored during the docking run. In conclusion, if one believes that the antibody model is accurate and
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`that antigen binding loops are relatively rigid, then it should not be necessary to sample antibody
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`backbone flexibility in the docking run. This assumption appears reasonable for the five CDR loops
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`following canonical structural rules but it might fail for models of the H3 loop, which may be slightly
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`inaccurate and/or might indeed be flexible in the biological context. Conversely, docking methods that
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`vary the CDR loops’ conformation might introduce deviations from the canonical structure and
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`decrease the accuracy.
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`Although it is impossible to draw general rules, using rigid body approaches for the backbone but
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`sampling different sidechain conformations might be a reasonable compromise. It might also prove
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`useful to allow backbone movement for the H3 loop (and others when they do not follow canonical
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`structures) while allowing only sidechain optimization of the remaining antigen binding loops. This
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`behavior can also be approximated by generating multiple antibody models, presumably differing
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`mainly in the H3 conformation, and using all of them as starting structures to be docked without
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`backbone optimization, either as an ensemble [68] or serially. Besides requiring more computational
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`time, this approach exacerbates the problem of providing a reliable scoring function: Errors are
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`generated both by the inability to correctly assess intermolecular interactions and also by
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`intramolecular differences amongst the various starting conformations.
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`1.7. Exploiting the Peculiarities of Antibodies to Simplify the Docking Search
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`Antibodies have a number of features that can be exploited to improve, speed up and simplify the
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`docking search, much like the existence of canonical structures simplifies CDR loop modeling. The
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`recently introduced SNUGDOCK [69,70], for instance, is geared towards antibodies and builds upon
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`the RosettaDock protocol by adding simultaneous optimization of the antibody-antigen position, CDR
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`loops conformation and heavy and light chain relative position.
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`More generally, since we know that Abs interact with antigens through their antigen binding loops,
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`there is no need to search for possible intermolecular contacts in the rest of the molecule. Typically,
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`the antibody is initially positioned with its CDR loops facing the antigen and it is not allowed to
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`deviate from this general orientation for the entire docking process. This not only increases the
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`calculation speed but also generates much fewer possible models of the bound complex (decoys),
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`easing the burden of scoring and analyzing the results. Constraints can also be introduced to reward the
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`CDR residues for being at the interface, penalize them if they are not or penalize contacts between the
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`rest of the antibody and the antigen. However, particular care must be exercised when introducing
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`constraints or bonuses affecting the final score, since it is relatively easy to force an inaccurate solution
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`or discard a valid, albeit slightly inaccurate one. For example, residues close to the CDR loops but not
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`formally belonging to them can be at relatively close distance to the antigen, therefore rejecting any
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`solution involving proximity of non CDR residues to the antigen would be inappropriate. Conversely,
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`in the known experimental structures not every CDR residues interact with the antigen and forcing
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`them to do so during docking would be a mistake.
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`2. Results and Discussion
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`Although an extensive benchmarking of modeling approaches goes beyond the scope of this
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`manuscript, we used computational docking to predict the structures of two antibody-antigen
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`complexes recently determined by X-ray crystallography, with the aim of illustrating the potentials,
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`pitfalls and opportunities of antibody modeling and docking.
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`Most of the antibodies capable of neutralizing influenza virus bind to the highly variable ―globular
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`head‖ region of hemagglutinin, which covers the viral surface. Due to this variability, however, their
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`efficacy is limited to few viral strains and to the narrow timeframe before the virus changes its
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`sequence to prevent antibody binding (anti-flu seasonal vaccines are usually changed every four years
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`for this reason) [71–74]. Two independent research groups have recently described antibodies against
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`the highly conserved ―stalk‖ region of hemagglutinin [75,76]; remarkably, X-ray structures show that
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`they bind to an almost identical epitope utilizing very similar intermolecular contacts, for instance
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`between aromatic residues of the Ab and a conserved hydrophobic patch on the antigen. Antibodies
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`against the stalk have potentially broad reactivity, since the region is conserved in different viral
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`strains, and the virus is not likely to develop resistance against them because of its inability to mutate
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`that part of the molecule. As a consequence, the stalk is pharmaceutically attractive and generating
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`more antibodies targeted against this very region is a worthwhile effort: any computational strategy
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`capable of rapidly and reliably characterizing the binding properties of such new antibodies would be a
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`valuable research tool.
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`2.1. Modeling Antibodies against Influenza Virus Hemagglutinin
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`In this work, we used PIGS and the Rosetta Antibody server to predict the structure of antibody F10
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`(PDB code 3FKU) and CR6261 (PDB code 3GBM) [75,76], results are summarized in Table 1 and
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`cartoon representations of antibodies are shown in Figure 2. The ―same antibody and canonical
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`structure‖ approach (see description in Section 1.3) of the PIGS server is expected to offer the best
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`results, but no viable template with high sequence identity is available. When the ―same antibody‖
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`method is chosen, PIGS returns accurate results: the RMSD to the experimental structure is about 1 Å
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`for CR6261, either for the whole antibody or individual loops, and 1.3 Å for F10. Choosing the
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`individual chains with highest identity as templates (―best heavy and light chains‖ approach described
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`above) brings the RMSD of CR6261 to 1.7 Å, still accurate but somehow less precise than before.
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`Curiously, the most problematic loop is H2 and not H3 as it usually happens. Finally, the ―same
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`canonical structures‖ approach yields the worst model, with RMSD of 2.1 Å (2.4 Å in the least
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`accurate loops). In the case of F10, the last two approaches return models with unacceptable steric
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`clashes and highly unusual features that are consequently discarded, while choosing templates with
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`lower sequence identity gives results worse than the ―same antibody‖ option and not further analyzed.
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`Even if no benchmarking is available, the authors’ recommendation to use the ―same antibody‖
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`approach is in agreement with our general experience and with these particular antibodies.
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`Lassen - Exhibit 1035, p. 9
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`Int. J. Mol. Sci. 2011, 12
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`In contrast to PIGS, Rosetta Antibody does not offer a choice of different modeling methods but,
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`starting from the same templates, returns 10 different models for each target antibody. We refer to
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`them as PIGS or Rosetta1-10 according to the modeling program used and to their relative score,
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`i.e., Rosetta1 is the best scoring model, Rosetta2 the second best scoring and so forth. The best models
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`for CR6261 (e.g., Rosetta2 and Rosetta5 in Table 1) are as accurate as those predicted by PIGS, with
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`RMSD slightly higher but not significantly so; the worst model has RMSD of 1.9 Å (2.5 Å for the H3
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`loop), still an accurate result. Similar considerations are true for F10, with RMSD of 1.7 Å (2.0 Å for
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`H3) for the best model and 2.6 Å (3.4 Å for H3) for the worst one.
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`There is no way to assess which of the 10 Rosetta models is best in a blind experiment, when the
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`antibody structure is not known. The model with the best score, thus preferred by the algorithm, is not
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`the most accurate, neither in this example nor in our general experience but, in a worst-case scenario,
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`even selecting the worst generated model would be acceptable. The issue is not overly important as far
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`as docking is concerned, as it will be shown later, and the ensemble of different models might actually
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`represent a conformational fl