0.9 Protein-ligand docking, including flexible receptor-flexible  (Page 3/9)

Knowledge-based scoring functions

Knowledge-based scoring functions are derived from a statistical analysis of structures of protein-ligand complexes in the RCSB Protein Databank (PDB). Searches are made for each possible pair of atoms in contact with each other. Interactions found to occur more frequently than would be predicted by random chance are considered attractive (stabilizing), and interactions that occur less frequently are considered repulsive (destabilizing). Examples of knowledge-based scoring functions include Muegge’s Potential of Mean Force function [3] and DrugScore [4] .

Rigid receptor docking

Parameterization of the problem

Many docking algorithms make the simplifying, but potentially quite inaccurate, assumption that the receptor is a rigid object and attempt to dock the ligand to it. The receptor conformation used is generally one from a receptor-ligand complex whose structure has been determined by x-ray crystallography or NMR spectroscopy. Because the receptor cannot move, the degrees of freedom of the problem are those of the ligand: three translational, three global-rotational, and one internal dihedral rotation for each rotatable bond. It is generally assumed that bond lengths and the angles formed by adjacent bonds do not change, and on the scale of most ligands (10 to 40 atoms), this assumption is a reasonable one. Docking to a rigid receptor is thus an optimization problem over a 6 + n dimensional space, where n is the number of rotatable bonds in the ligand.

Examples of rigid-receptor docking programs

Autodock 3.0

Link to The Autodock project home page

Autodock is actually a set of closely related programs and algorithms developed at the Scripps Research Institute and the University of California at San Diego.

Search technique

Autodock can use one of several optimization methods to search for the best placement of the ligand:

• Simulated annealing: At each step of simulated annealing, the position and internal rotational state of the ligand is adjusted and the energy calculated. If the energy decreases, the move is accepted. If not, it may be accepted with some probability that depends on the current temperature of the annealing. As the search goes on, the temperature is decreased, and eventually, the final state of the ligand is returned as the docked conformation. Because simulated annealing is a Monte Carlo (randomized) method, different runs will generally produce different solutions.
• A genetic algorithm: The genetic algorithm represents the states of the degrees of freedom of the ligand as a string of digits, and this string is referred to as a gene. A population of different genes is generated at random, and each is scored using the Autodock energy function. Genes are selected to form the next population based on their score, with better scoring genes more likely to be selected. A gene may be selected more than once, and some may not be selected at all. Pairs of the selected genes are allowed to cross over with each other. In this process, a segment of the gene is selected and the values in this range are exchanged between them. The hope is that by combined two partially good solutions, we will eventually find a better solution.
• a Lamarckian genetic algorithm (LGA): This is the same as the standard genetic algorithm except that, before they are scored, each conformation (gene) is subjected to energy minimization. The next population is then founded by members of this energy-minimized population. The name "Lamarckian" refers to the failed genetic theory of Jean-Baptiste Lamarck, who held that an organism could pass on changed experienced in its lifetime to its offspring. This theory was eventually abandoned in favor of Mendel's now-familiar laws of inheritance. The LGA is faster than both simulated annealing and the standard genetic algorithm, and it allows the docking of ligands with more degrees of freedom.