Scoring Functions

The extent of interaction between two molecules is usually expressed quantitatively by an energy value, which is ultimately based on a model of the physical chemistry of atomic interactions. There is often a trade-off between the sophistication of a scoring function and its computational cost. Rapid screening methods use simple geometric or steric criteria to allow very large numbers of ligands to be docked to a given target. However, these often miss potentially important ligands or binding modes, owing to their poor chemical selectivity. In the middle of the spectrum are enthalpic scoring functions, which account for the potential energy of interaction by using pairwise-atomic Lennard-Jones potentials, 12-10 hydrogen bonding terms, and Coulombic electrostatic terms. These resemble the force fields commonly used in molecular mechanics and molecular dynamics codes, like AMBER [6, 7], CHARMm [8] and GROMOS [9, 10], and require moderate computational resources. Perhaps the most complete scoring functions are those which include not only enthalpic terms but also entropic terms, and which estimate free energies of binding. These use a variety of ways of accounting for loss of conformational degrees of freedom and changes in solvation of the ligand upon binding. Examples of programs that use this type of scoring function are LUDI [11-13] and AutoDock 3.0 [14], These free energy functions are often derived empirically using linear regression analysis, and require careful calibration using a large set of structures of protein-inhibitor complexes of known binding affinity. They have shown excellent results, showing a better prediction of experimental binding constants than purely enthalpic force fields.

The computational cost of energy evaluation may be reduced using precalculated grids [15]. The protein is placed within a grid volume, and a probe atom is sequentially placed at each point. The resultant energy of interaction is calculated. The grid may then be used as a look-up table during docking simulations, greatly speeding the process. Note, how ever, that this normally requires that the protein be modeled as rigid, although it is also possible to represent an ensemble of protein conformations using the grid formalism.

The EPDOCK method has been used to explore different energy functions in molecular docking [16] by looking to protein folding theory. It was noted that rough energy landscapes contain many kinetic barriers to docking. For proper docking, there is a thermodynamic requirement that the crystal structure has the global minimum energy, and a kinetic requirement that this global minimum is accessible to the search. In a rough landscape, there will be many competing minima separated by steep barriers that will compete with the proper minimum. Citing a paper on protein folding, Verkhivker et al. [16] posited that improved search methods are not the best solution to this "kinetic barrier" problem; instead, they preferred a smoothing of the energy landscape. They noted that standard molecular mechanics force fields give very rough surfaces, because of the large repulsive energies. They sought to find a less "frustrated" energy surface by softening the repulsive potentials, using a simple piece-wise function in which the repulsive energy barrier is easily modified. A common approach is to soften repulsive barriers early in a simulation, thus smoothing the energy landscape, and then to restore the barriers towards the end, theoretically funneling the docked conformation into the global minimum. In this work, however, Verkhivker et al. looked for one soft potential that gave the best results when used throughout the simulation. One might question this approach: molecular mechanics potentials are parameterized against physical data, so the steep repulsive barriers are based in fact, and cannot be lightly thrown away at the end. In any case, the coarse potential yielded poor results, with docked conformations rarely less than 2 A RMSD from the crystallographic conformation.

Continue reading here: Evolutionary Algorithms for Protein Ligand Docking

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