Docking the Ligand

Once the interaction grid is created using the GridDock algorithm described above, PoPP randomly initializes ligand poses on the grid (up to 10,000x). In the current implementation, PoPP allows ligand conformations to remain flexible, with constraints in place to ensure a physically possible conformation, while keeping the receptor rigid. PoPP accepts only the peptide sequence and generates conformations by placing the peptide on the grid one residue at a time. The initial peptide vertex is randomly selected and then randomly placed on any of the possible interaction space grid vertices; if the critical residue grid is used, the initial placement is constrained to a more limited set of grid points. Subsequent placement of ligand residues will begin with either of the sequentially adjacent residues and alternate between extending in both the N- and C-terminal directions until all ligand residues have been placed on the grid. Subsequent ligand vertices are initially constrained to a distance between1.0−1.4×the value of the fit parameter and to a120◦ angle from the previous two peptide vertices; a smaller

grid object is used to define exclusion spheres for each peptide vertex to prevent the peptide from folding back on itself. Subsequent ligand vertices may also be forced to use a critical grid vertex or weighted to prefer a critical residue grid vertex. The resulting conformation mimics a simplified protein backbone and allows for a surprising number of unique conformations; however, the poses a peptide is allowed to sample is directly influenced by thethickness of the grid: A thicker grid allows more flexible conformations while a thinner grid forces the initial peptide conformation tofitmore closely to the receptor surface.

Once PoPP generates the initial peptide poses, the pose may be translated, rotated, or flipped to generate a series of new poses. Both translation and rotation are initially applied to a single peptide vertex, selected at random, and transformed by a random amount. Translation is limited to up to three times the resolutionof the grid. Rotation randomly selects the φandψ angles and one of adjacent peptide vertices to use as the origin of rotation. For both types of perturbations, adjacent residues may undergo similar perturbations to help ensure the structure remains physically feasible. With a rotational perturbations for example, the same rotation is often applied to residues further along the peptide sequence using the same origin; if subsequent residues would end up outside of the interaction grid, further perturbations are performed to ensure the entire peptide remains within the acceptable region. Flipping affects the entire pose without directly affecting the conformation: The residue composition is re- versed so the ends are swapped although the coordinates of the peptide remain the same. The peptide may assume any conformation provided its vertices (a) remain within the interaction grid and (b) do not enter the exclusion sphere of other peptide vertices.

All poses are scored and ranked using a local Delaunay tessellation and the SNAPP- Interface scores outlined in Chapter 2.5.2. To score a pose, PoPP identifies local receptor residues within a distance of six ˚A from any peptide vertex, calculates the local Delaunay tes- sellation of the ligand and receptor vertices, and scores each of the interfacial simplices. For the initial poses, PoPP calculates the SNAPP-Interface score distribution and selects poses based on a Metropolis Monte Carlo algorithm [107], where all poses at the eighty-fifth per-

centile or higher are automatically chosen, and poses below the threshold are chosen based on a probability distribution described by the Metropolis table. Ligands from selected poses undergo perturbation as described above and subsequently scored. Newly generated poses are selected or discarded as before using the ninetieth percentile from the previous set of scores as the new threshold. The scoring-perturbation loop is continued for 1,000 iterations or until the standard deviation of RMSD for poses in the ninetieth percentile has fallen below 0.2 ˚A. PoPP then selects up to 1,000 poses with the highest SNAPP-Interface score across all iterations to continue with pose refinement.

Once PoPP selects the top 1,000 poses, each of the ligands from the selected poses un- dergoes a refinement step where the ligand residues are allowed to deviate from the discrete coordinates given by the interaction grid2_{. Each ligand and nearby receptor vertex is weighted} using the data generated from CRACLe. Ligand vertices are translated to maximize the ex- pected edge distance between each it and every other residue vertex, both ligand and residue, it shares an edge with. At each stage of refinement, PoPP performs a local Delaunay tessella- tion and rescores the pose. Poses are clustered based on pairwise RMSD between other poses, and for each cluster, PoPP calculates a mean consensus pose that is returned to the user.

Unfortunately, the coarse-grained SPPR model used throughout SNAPP, CRACLe, and PoPP does not lend itself to a pretty, high resolution, finalized structure; we must first convert the ligand residues from an SPPR to a full atomic model. This conversion is not a trivial task, and our implementation is not currently available in the current code distribution. Using structural data collected from Dockground, we apply a vector to each peptide vertex with a direction and magnitude to represent the location of theCα relative to the side chain centroid.

Each vector is based on the residue composition of both the peptide vertex and the residue vertices that share a Delaunay edge with it. Once the residue vector has been calculated for each peptide residue, the atomic coordinates of the side chain and peptide backbone are 2_{The refinement algorithm is partially implemented. Only generation of the consensus pose is currently in} use.

filled in. The fine-grained peptide pose is returned to the user and may be submitted to other programs such Molprobity [108, 109] for structure refinement.