Docking (molecular)

Geometric matching/ shape complementarity methods describe the protein and ligand as a set of features that make them dockable.[10] These features may include molecular surface / complementary surface descriptors. In this case, the receptor's molecular surface is described in terms of its solvent-accessible surface area and the ligand's molecular surface is described in terms of its matching surface description. The complementarity between the two surfaces amounts to the shape matching description that may help finding the complementary pose of docking the target and the ligand molecules. Another approach is to describe the hydrophobic features of the protein using turns in the main-chain atoms. Yet another approach is to use a Fourier shape descriptor technique.[11][12][13] Whereas the shape complementarity based approaches are typically fast and robust, they cannot usually model the movements or dynamic changes in the ligand/ protein conformations accurately, although recent developments allow these methods to investigate ligand flexibility. Shape complementarity methods can quickly scan through several thousand ligands in a matter of seconds and actually figure out whether they can bind at the protein's active site, and are usually scalable to even protein-protein interactions. They are also much more amenable to pharmacophore based approaches, since they use geometric descriptions of the ligands to find optimal binding.

Simulating the docking process is much more complicated. In this approach, the protein and the ligand are separated by some physical distance, and the ligand finds its position into the protein's active site after a certain number of “moves” in its conformational space. The moves incorporate rigid body transformations such as translations and rotations, as well as internal changes to the ligand's structure including torsion angle rotations. Each of these moves in the conformation space of the ligand induces a total energetic cost of the system. Hence, the system's total energy is calculated after every move.

The obvious advantage of docking simulation is that ligand flexibility is easily incorporated, whereas shape complementarity techniques must use ingenious methods to incorporate flexibility in ligands. Also, it more accurately models reality, whereas shape complementary techniques are more of an abstraction.

Clearly, simulation is computationally expensive, having to explore a large energy landscape. Grid-based techniques, optimization methods, and increased computer speed have made docking simulation more realistic.

The search space in theory consists of all possible orientations and conformations of the protein paired with the ligand. However, in practice with current computational resources, it is impossible to exhaustively explore the search space—this would involve enumerating all possible distortions of each molecule (molecules are dynamic and exist in an ensemble of conformational states) and all possible rotational and translational orientations of the ligand relative to the protein at a given level of granularity. Most docking programs in use account for the whole conformational space of the ligand (flexible ligand), and several attempt to model a flexible protein receptor. Each "snapshot" of the pair is referred to as a pose.

A variety of conformational search strategies have been applied to the ligand and to the receptor. These include:

• systematic or stochastic torsional searches about rotatable bonds
• molecular dynamics simulations
• genetic algorithms to "evolve" new low energy conformations and where the score of each pose acts as the fitness function used to select individuals for the next iteration.

Conformations of the ligand may be generated in the absence of the receptor and subsequently docked[14] or conformations may be generated on-the-fly in the presence of the receptor binding cavity,[15] or with full rotational flexibility of every dihedral angle using fragment based docking.[16] Force field energy evaluation are most often used to select energetically reasonable conformations,[17] but knowledge-based methods have also been used.[18]

Peptides are both highly flexible and relatively large-sized molecules, which makes modeling their flexibility a challenging task. A number of methods were developed to allow for efficient modeling of flexibility of peptides during protein-peptide docking.[19]

Computational capacity has increased dramatically over the last decade making possible the use of more sophisticated and computationally intensive methods in computer-assisted drug design. However, dealing with receptor flexibility in docking methodologies is still a thorny issue.[20] The main reason behind this difficulty is the large number of degrees of freedom that have to be considered in this kind of calculations. Neglecting it, however, in some of the cases may lead to poor docking results in terms of binding pose prediction.[21]

Multiple static structures experimentally determined for the same protein in different conformations are often used to emulate receptor flexibility.[22] Alternatively rotamer libraries of amino acid side chains that surround the binding cavity may be searched to generate alternate but energetically reasonable protein conformations.[23][24]

Docking programs generate a large number of potential ligand poses, of which some can be immediately rejected due to clashes with the protein. The remainder are evaluated using some scoring function, which takes a pose as input and returns a number indicating the likelihood that the pose represents a favorable binding interaction and ranks one ligand relative to another.

Most scoring functions are physics-based molecular mechanics force fields that estimate the energy of the pose within the binding site. The various contributions to binding can be written as an additive equation:

${\displaystyle \bigtriangleup G_{bind}=\bigtriangleup G_{solvent}+\bigtriangleup G_{conf}+\bigtriangleup G_{int}+\bigtriangleup G_{rot}+\bigtriangleup G_{t/t}+\bigtriangleup G_{vib}}$

The components consist of solvent effects, conformational changes in the protein and ligand, free energy due to protein-ligand interactions, internal rotations, association energy of ligand and receptor to form a single complex and free energy due to changes in vibrational modes.[25] A low (negative) energy indicates a stable system and thus a likely binding interaction.

An alternative approach is to derive a knowledge-based statistical potential for interactions from a large database of protein-ligand complexes, such as the Protein Data Bank, and evaluate the fit of the pose according to this inferred potential.

There are a large number of structures from X-ray crystallography for complexes between proteins and high affinity ligands, but comparatively fewer for low affinity ligands as the later complexes tend to be less stable and therefore more difficult to crystallize. Scoring functions trained with this data can dock high affinity ligands correctly, but they will also give plausible docked conformations for ligands that do not bind. This gives a large number of false positive hits, i.e., ligands predicted to bind to the protein that actually don't when placed together in a test tube.

One way to reduce the number of false positives is to recalculate the energy of the top scoring poses using (potentially) more accurate but computationally more intensive techniques such as Generalized Born or Poisson-Boltzmann methods.[9]

Docking accuracy[27][28] represents one measure to quantify the fitness of a docking program by rationalizing the ability to predict the right pose of a ligand with respect to that experimentally observed.[29]

Docking screens can also be evaluated by the enrichment of annotated ligands of known binders from among a large database of presumed non-binding, “decoy” molecules.[26] In this way, the success of a docking screen is evaluated by its capacity to enrich the small number of known active compounds in the top ranks of a screen from among a much greater number of decoy molecules in the database. The area under the receiver operating characteristic (ROC) curve is widely used to evaluate its performance.

Resulting hits from docking screens are subjected to pharmacological validation (e.g. IC_50, affinity or potency measurements). Only prospective studies constitute conclusive proof of the suitability of a technique for a particular target.[30]

The potential of docking programs to reproduce binding modes as determined by X-ray crystallography can be assessed by a range of docking benchmark sets.

For small molecules, several benchmark data sets for docking and virtual screening exist e.g. Astex Diverse Set consisting of high quality protein−ligand X-ray crystal structures[31] or the Directory of Useful Decoys (DUD) for evaluation of virtual screening performance.[26]

An evaluation of docking programs for their potential to reproduce peptide binding modes can be assessed by Lessons for Efficiency Assessment of Docking and Scoring (LEADS-PEP).[32]