Two Examples of Docking Algorithms

With thanks to Maria Teresa Gil Lucientes

Example: HIV-1 Protease

Active Site(Aspartyl groups)

Docking to find drug candidates

Example: HIV-1 Protease

Docking to find drug candidates

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 other’s structure as they interact

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

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

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

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)

i

j

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

Alpha Shapes: Example

Alpha=infinity

Alpha=3.0 Å

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

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

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.

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/~smithgr/soft.html

DOCK

DOCK works in 5 steps: Step 1 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

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

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.

Docking protocol

Docking protocol: Step 1

RANDOM START POSITIONRANDOM 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

Docking protocol: Step 2

LOW-RESOLUTION MONTE CARLO SEARCHLOW-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

Docking protocol: Step 3

HIGH-RESOLUTION REFINEMENTHIGH-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

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

Docking protocol: Step 3

COMPUTATIONAL EFFICIENCY

1. The packing algorithm usually varies the conformation of one residue at a time; rotamer optimization is performed once every eight cycles

2. Periodically filter to detect and reject inferior decoys without further refinement

Docking protocol: Step 4

CLUSTERING & PREDICTIONSCLUSTERING & 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

Docking protocol: Results

CAPRI Challenge (2002)

• At least one docking partner presented in its unbound form

• Participants permitted 5 attempts for each target

The 7 CAPRI Docking Targets

CAPRI Challenge

Participants & Algorithms

Results: CAPRI Challenge

This were the results for the different predictors and targets:

Conclusions

The computational molecular docking problem is far from being solved.

There are two major bottle-necks:1. The algorithms handle limited flexibility

2. Need selective and efficient scoring functions