The second group presentation covered the antibody-antigen docking paper by Brenke et al. 2012. Before moving to the methodology and results, one has to provide a bit of motivation and fundamentals.

Why Antibodies?

Antibodies are one of the most basic lines of defense of the vertebrate organism. They consist a class of proteins whose structure allows them to adjust their binding profile (affinity and specificity) to bind virtually any protein. The source of this adjustability are the Complementaruty Determining Regions (CDRs) which typically consist of six hypervariable loops. Owing to this binding malleability they are one of the most important biomarkers and biopharmaceuticals. NB: in most cases when people talk about antibodies they mean the IgG, which is the iconic Y-shaped molecule (other classes of antibodies exist and they are different configurations of several IgG molecules, e.g. IgM is a pentamer thereof).

Why Docking?

The number of protein structures in the Protein Data Bank (PDB) is ever increasing. By analyzing these structures we can gain indispensable insights into the working of a living organism through the proxy of protein-protein interactions. The only caveat is that the number of possible complexes crystallized is far behind the number of complexes that could be formed even using the single-protein structures in the PDB alone. This gave rise to the field of protein-protein docking exemplified by tools like ZDOCK, HADDOCK, RosettaDock, ClusPro, PatchDock and many more. These methods receive two unbound proteins as input and they attempt to generate a complex between them which acts as an approximation of the native complex formed in the organism. The available methods are still far from being able to generate reliable complexes, although it appears that there is progress – as demonstrated by successive rounds of the CAPRI experiment.

Why Docking Antibodies?

There are two main classes of docking problems: enzymes and antibodies. Enzymes are considered an easier target for the algorithm because of their shape complementarity and a suitable hydrophobic pockets. Antibodies on the other hand bind proteins on flat surfaces. Furthermore, enzymes undergo correlated mutations with their binding partners over long periods of time whereas antibodies are adjusted towards their binding partner sometimes in a matter of days. Thus, Brenke at al. developed a docking method tailored specifically to the problem of antibody antigen binding.

ADARS

The algorithm developed by Brenke et al. is the only currently available global rigid-body antibody protein docking algorithm. There is another method that also explicitly addresses antibodies, SnugDock, but it rather contributes high-resolution, local, flexible docking capability. Other methods like ZDOCK or PatchDock identify the binding site on the antibody and mask all the other residues that are unlikely to be interacting (although one has to keep in mind that only about 80% of the binding residues are found in the CDRs as defined by either Kabat, Chothia, Abnum or IMGT).

The ADARS algorithm follows from the earlier method, DARS. The main feature of the method is the novel way to calculate the reference state in the statistical potential equation, which forms a component of the algorithms energy function.

 (1)

The function ε provides a definition of a potential between two atom types I and J (for instancehydroxyl oxygen of tyrosine and one of the phenolic ring carbons of phenylalanine). Negative value of the expression in (1) stands for attraction and positive for repulsion. The constant k stands for the Boltzmann constant whereas T for temperature. The expression p^obs approximates the probability of seeing atoms I and J at an interaction distance (defined as less than 6<Å by Brenke et al.) whereas pref denotes the reference state for the interaction of those two atom types. In general pref approximates the background distribution of seeing two atom types together. Thus if pobs happens to be greater than pref, one can assume that the given pair of atoms appears within contact distance more often than expected, meaning that there is a tendency to pair them up. Calculation of a suitable value for the reference state is crucial for the success of the method.

The main contribution of DARS is the way the reference state is computed. Given a training set of protein-protein complexes, a subset of those is selected, binding partners separated and re-docked. Over a set of decoys returned for each target, the number of times a given atom pair (I,J) was observed at an interaction distance is noted. Those frequencies are denoted νIJ and are used in equation (2) to compute the value of pref for a given pair of atoms.

 (2)

Here pref stands for the same pref as in equation (1) (even though capitalized). In the case of ADARS, the value of pref is calculated using a subset of the training set of antibody-antigen complexes in order to customize the method towards those molecules.

Another feature of the method is the symmetry condition. In the original DARS, it was assumed that atomic potentials are symmetric, as given in (3):

 (3)

Brenke et al. note a considerable disparity in atom pairing preferences for antibodies and antigens, leading them to introduce directionality into the knowledge-based potential function by additionally specifying the molecule class the atom came from (i.e. either antibody or antigen).

Results

Authors have used a subset of the target from the Protein-Protein Docking Benchmark 3.0 to test the performance of their asymmetric potential. They have tested three algorithms on this benchmark:

• DARS: the original version of the potential for protein-protein docking
• aDARS: the potential calculated using the antibody-antigen training set although still with the symmetry condition given in (3)
• aADARS: the potential calculated using the antibody-antigen training set with the symmetry condition in (4) removed.

Authors use the Irmsd metric to assess the quality of docking (for details see the CAPRI criteria). A successful decoy has Irmsd of less than 10Å. According to this metric the decoys returned by aDARS are of better quality than those of the original DARS. Furthermore, the quality of aADARS is better than this of aDARS meaning that the asymmetry condition, which is the only distinguishing factor here, contributes to the predictive power.

Conclusion

Brenke et al. have developed a docking method customized for the problem of antibodies. Their algorithm provides approximate solutions to the global rigid-body docking problem. As such the answers are good enough to be able to use more high-resolution methods like SnugDock which are capable of refining the initial pose provided by ADARS.