Scoring functions for docking

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Scoring functions for protein-ligand (small molecules like drugs) and protein-protein interactions can vary significantly. Protein-protein interaction scoring functions take into account many features important for protein structure (like hydrophobicity, van der Waals interactions, short range as well as long-range electrostatics and overall shape complementarity).

Protein-ligand interaction scoring functions require more sophisticated techniques to evaluate the binding, since they involve very specific interactions that need to be additionally represented in the scoring functions.

Although there has been a proliferation of free-energy calculations based on several simulations, these approaches are typically limited in their applicability because of their compute-intensive nature. Scoring functions typically play an important role in both simplifying the potentially vast space of geometric matching criteria as well as identifying what might constitute a favorable versus unfavorable interaction between the protein and ligand. Three kinds of scoring functions are usually available:

  • Force-field based functions,
  • Empirical functions and
  • Knowledge-based functions.

In addition to this, a fourth kind of scoring function based on the consensus of the above three types is also widely used.

Force-field-based scoring functions

A force-field usually quantifies the sum of two energy values; that of the receptor and the ligand in terms of the interaction energy and the internal energy of the ligand/receptor. The receptor-ligand interaction energy is usually a function of the hydrogen bond energy (depending on the number of hydrogen bonds between the two) as well as the van der Waals energy (steric interactions) usually a measure of the hydrophobic contacts. The internal energy is usually a measure of the strain induced due to steric interactions within the ligand. Computing the internal energy of the receptor is usually harder, since the protein may have a number of conformational states in which it may bind the ligand and partly also due to the fact that most of the current programs allow calculation of only single conformers which makes it easy to just disregard the internal receptor energy. Functional forms of these scoring functions are very similar:

Force-field based approaches are more rigorous and have firm ground in physics and chemistry. However, these scoring functions are difficult to evaluate and are usually attached to some standard program like AMBER, CHARMM, Tripos and so on. Also they suffer from the same kind of disadvantages that normal force-fields suffer from; especially since non-bonded interaction parameters (like donor-acceptor distances) are chosen arbitrarily. These long range interactions play an important role in binding and many programs that do use force-field based approaches to score their posings face these problems.

Amongst the popular programs, GOLD and AutoDock implement a force-field based scoring function. However this does not mean that they exclusively use only these scoring functions. As seen in consensus scoring, often one or more scoring functions are used to evaluate a particular pose, and these may yield better prediction confidence.

Empirical scoring functions

Instead of using a molecular mechanics based approach, these scoring functions try to reproduce experimental data by fitting parameters such as binding energy or closely related factors such as IC50 and so on. The co-efficients for such fits are usually available from regression analysis, which is widely used for a number of data-analytic applications. An immediate appeal of these scoring functions is their simplicity in evaluation; given a set of co-efficients, it is easy to evaluate individual interactions between the receptor and the ligand without much complexity as in force-field based approaches. These advantages do come with certain limitations in that, the co-efficients tend to overfit a particular data-set and hence need not be universal. Thus the parameters estimated from the regression analysis that works well with one set of scoring may not be directly recombined for another scoring another set of predictions.

The empirical scoring functions may have different implementations in different methods, however they do share some common features. A functional form of empirical scoring function is shown below:

Non-bonded interactions may be implemented for different scoring functions differently. Usually distinctions are made for salt-bridges and neutral hydrogen bonds, where as for hydrophobic interactions the aliphatic contributions may be weighed in differently than aromatic interactions.

Knowledge-based scoring functions

Instead of reproducing binding energy and other such parameters, knowledge-based scoring functions are usually implemented to reproduce experimental structures. Usually modelled using atom-atom interaction potentials, these functions are usually simplistic enough to implement rather quickly. Knowledge based approaches tend to capture specific binding effects that are difficult to model explicitly, and they can be often easily used to screen efficiently a very large database of compounds. However given the limited sets of molecular structures available, these functions and their derivations are usually questionable. A functional form of the knowledge based function is shown below: