Two Examples of Docking Algorithms

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Two Examples of Docking Algorithms

• With thanks to Maria Teresa Gil Lucientes

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Example HIV-1 Protease
Docking to find drug candidates
Active Site (Aspartyl groups)
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Example HIV-1 Protease

• Docking to find drug candidates

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Why is this difficult?

• of possible conformations are astronomical
• thousands of degrees of freedom (DOF)
• Free energy changes are small
• Below the accuracy of our energy functions
• Molecules are flexible
• alter each others structure as they interact

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Some techniques

• Surface representation, that efficiently
  represents the docking surface and identifies the
  regions of interest (cavities and protrusions)
• Connolly surface
• Lenhoff technique
• Kuntz et al. Clustered-Spheres
• Alpha shapes
• Surface matching that matches surfaces to
  optimize a binding score
• Geometric Hashing

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Surface Representation

• Each atomic sphere is given the van der Waals
  radius of the atom
• Rolling a Probe Sphere over the Van der Waals
  Surface leads to the Solvent Reentrant Surface or
  Connolly surface

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Lenhoff technique

• Computes a complementary surface for the
  receptor instead of the Connolly surface, i.e.
  computes possible positions for the atom centers
  of the ligand

Atom centers of the ligand
van der Waals surface
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Kuntz et al. Clustered-Spheres

• Uses clustered-spheres to identify cavities on
  the receptor and protrusions on the ligand
• Compute a sphere for every pair of surface
  points, i and j, with the sphere center on the
  normal from point i
• Regions where many spheres overlap are either
  cavities (on the receptor) or protrusions (on the
  ligand)

j
i
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Alpha Shapes

• Formalizes the idea of shape
• In 2D an edge between two points is
  alpha-exposed if there exists a circle of
  radius alpha such that the two points lie on the
  surface of the circle and the circle contains no
  other points from the point set

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Alpha Shapes Example
Alphainfinity
Alpha3.0 Å
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Surface Matching

• Find the transformation (rotation translation)
  that will maximize the number of matching surface
  points from the receptor and the ligand
• First satisfy steric constraints
• Find the best fit of the receptor and ligand
  using only geometrical constraints
• then use energy calculations to refine the
  docking
• Selet the fit that has the minimum energy

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Geometric Hashing

• Building the Hash Table
• For each triplet of points from the ligand,
  generate a unique system of reference
• Store the position and orientation of all
  remaining points in this coordinate system in the
  Hash Table
• Searching in the Hash Table
• For each triplet of points from the receptor,
  generate a unique system of reference
• Search the coordinates for each remaining point
  in the receptor and find the appropriate hash
  table bin For every entry there, vote for the
  basis

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Geometric Hashing

• Determine those entries that received more than a
  threshold of votes, such entry corresponds to a
  potential match
• For each potential match recover the
  transformation T that results in the best
  least-squares match between all corresponding
  triplets
• Transform the features of the model according to
  the recovered transformation T and verify it. If
  the verification fails, choose a different
  receptor triplet and repeat the searching.

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Example Docking Programs

• DOCK (I. D. Kuntz, UCSF)
• AutoDOCK (A. Olson, Scripps)
• RosettaDOCK (Baker, U Wash., Gray, JHU)
• More information in http//www.bmm.icnet.uk/smit
  hgr/soft.html

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DOCK

• DOCK works in 5 steps
• Step 1 Start with coordinates of target receptor
• Step 2 Generate molecular surface for receptor
• Step 3 Fill active site of receptor with spheres
• potential locations for ligand atoms
• Step 4 Match sphere centers to ligand atoms
• determines possible orientations for the ligand
• Step 5 Find the top scoring orientation

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Other Docking programs

• AutoDock
• designed to dock flexible ligands into receptor
  binding sites
• Has a range of powerful optimization algorithms
• RosettaDOCK
• models physical forces
• Creates a large number of decoys
• degeneracy after clustering is final criterion in
  selection of decoys to output

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A Protein-Protein Docking Algorithm (Gray Baker)

• Goal to predict protein-protein complexes from
  the coordinates of unbound monomer components.
• Two steps A low-resolution Monte Carlo search
  and a final optimization using Monte Carlo
  minimization.
• Up to 105 independent simulations produce
  decoys that are ranked using an energy
  function.
• The top-ranking decoys are clustered for output.

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Docking protocol
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Docking protocol Step 1

• RANDOM START POSITION
• Creation of a decoy begins with a random
  orientation of each partner and a translation of
  one partner along the line of protein centers to
  create a glancing contact between the proteins

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Docking protocol Step 2

• LOW-RESOLUTION MONTE CARLO SEARCH
• Low-resolution representation N, C?, C, O for
  the backbone and a centroid for the side-chain
• One partner is translated and rotated around the
  surface of the other through 500 Monte Carlo move
  attempts
• The score terms A reward for contacting
  residues, a penalty for overlapping residues, an
  alignment score, residue environment and
  residue-residue interactions

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Docking protocol Step 3

• HIGH-RESOLUTION REFINEMENT
• Explicit side-chains are added to the protein
  backbones using a rotamer packing algorithm, thus
  changing the energy surface
• An explicit minimization finds the nearest local
  minimum accessible via rigid body translation and
  rotation
• Start and Finish positions are compared by the
  Metropolis criterion

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Docking protocol Step 3

• Before each cycle, the position of one protein is
  perturbed by random translations and by random
  rotations
• To simultaneously optimize the side-chain
  conformations and the rigid body position, the
  side-chain packing and the minimization
  operations are repeated 50 times

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Docking protocol Step 3

• COMPUTATIONAL EFFICIENCY
• The packing algorithm usually varies the
  conformation of one residue at a time rotamer
  optimization is performed once every eight cycles
• Periodically filter to detect and reject inferior
  decoys without further refinement

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Docking protocol Step 4

• CLUSTERING PREDICTIONS
• Repeat search to create approximately 105 decoys
  per target
• Cluster best 200 decoys by a hierarchical
  clustering algorithm using RMSD
• The clusters with the most members become
  predictions, ranked by cluster size

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Docking protocol Results
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CAPRI Challenge (2002)
The 7 CAPRI Docking Targets

• At least one docking partner presented in its
  unbound form
• Participants permitted 5 attempts for each
  target

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CAPRI Challenge
Participants Algorithms
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Results CAPRI Challenge
This were the results for the different
predictors and targets
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Conclusions

• The computational molecular docking problem is
  far from being solved.
• There are two major bottle-necks
• The algorithms handle limited flexibility
• Need selective and efficient scoring functions