Scoring functions for docking

Docking glossary
Receptor or host or lock The "receiving" molecule, most commonly a protein or other biopolymer. Ligand or guest or key The complementary partner molecule which binds to the receptor. Ligands are most often small molecules but could also be another biopolymer. Docking Computational simulation of a candidate ligand binding to a receptor. Binding mode The orientation of the ligand relative to the receptor as well as the conformation of the ligand and receptor when bound to each other. Pose A candidate binding mode. Scoring The process of evaluating a particular pose by counting the number of favorable intermolecular interactions such as hydrogen bonds and hydrophobic contacts. Ranking The process of classifying which ligands are most likely to interact favorably to a particular receptor based on the predicted free-energy of binding. Docking assessment (DA) Procedure to quantify the predictive capability of a docking protocol.

In the fields of computational chemistry and molecular modelling, scoring functions are fast approximate mathematical methods used to predict the strength of the non-covalent interaction (also referred to as binding affinity) between two molecules after they have been docked. Most commonly one of the molecules is a small organic compound such as a drug and the second is the drug's biological target such as a protein receptor.^[1] Scoring functions have also been developed to predict the strength of other types of intermolecular interactions, for example between two proteins^[2] or between protein and DNA.^[3]

Utility

Scoring functions are widely used in drug discovery and other molecular modelling applications. These include:^[4]

• Virtual screening of small molecule databases of candidate ligands to identify novel small molecules that bind to a protein target of interest and therefore are useful starting points for drug discovery^[5]
• De novo design (design "from scratch") of novel small molecules that bind to a protein target^[6]
• Lead optimization of screening hits to optimize their affinity and selectivity^[7]

A potentially more reliable but much more computationally demanding alternative to scoring functions are free energy perturbation calculations.^[8]

Prerequisites

Scoring functions are normally parameterized (or trained) against a data set consisting of experimentally determined binding affinities between molecular species similar to the species that one wishes to predict.

For currently used methods aiming to predict affinities of ligands for proteins the following must first be known or predicted:

• Protein tertiary structure – arrangement of the protein atoms in three-dimensional space. Protein structures may be determined by experimental techniques such as X-ray crystallography or solution phase NMR methods or predicted by homology modelling.
• Ligand active conformation – three-dimensional shape of the ligand when bound to the protein
• Binding-mode – orientation of the two binding partners relative to each other in the complex

The above information yields the three-dimensional structure of the complex. Based on this structure, the scoring function can then estimate the strength of the association between the two molecules in the complex using one of the methods outlined below. Finally the scoring function itself may be used to help predict both the binding mode and the active conformation of the small molecule in the complex, or alternatively a simpler and computationally faster function may be utilised within the docking run.

Classes

There are three general classes of scoring functions:^[9][10]

• Force field – affinities are estimated by summing the strength of intermolecular van der Waals and electrostatic interactions between all atoms of the two molecules in the complex using a force field. The intramolecular energies (also referred to as strain energy) of the two binding partners are also frequently included. Finally since the binding normally takes place in the presence of water, the desolvation energies of the ligand and of the protein are sometimes taken into account using implicit solvation methods such as GBSA or PBSA.^[11]
• Empirical – based on counting the number of various types of interactions between the two binding partners.^[6] Counting may be based on the number of ligand and receptor atoms in contact with each other or by calculating the change in solvent accessible surface area (ΔSASA) in the complex compared to the uncomplexed ligand and protein. The coefficients of the scoring function are usually fit using multiple linear regression methods. These interactions terms of the function may include for example:
  • hydrophobic — hydrophobic contacts (favorable),
  • hydrophobic — hydrophilic contacts (unfavorable) (Accounts for unmet hydrogen bonds, which are an important enthalpic contribution to binding.^[12] One lost hydrogen bond can account for 1–2 orders of magnitude in binding affinity.^[13]),
  • number of hydrogen bonds (favorable contribution to affinity, especially if shielded from solvent, if solvent exposed no contribution),
  • number of rotatable bonds immobilized in complex formation (unfavorable conformational entropy contribution).
• Knowledge-based (also known as statistical potentials) – based on statistical observations of intermolecular close contacts in large 3D databases (such as the Cambridge Structural Database or Protein Data Bank) which are used to derive "potentials of mean force". This method is founded on the assumption that close intermolecular interactions between certain types of atoms or functional groups that occur more frequently than one would expect by a random distribution are likely to be energetically favorable and therefore contribute favorably to binding affinity.^[14]

Finally hybrid scoring functions have also been developed in which the components from two or more of the above scoring functions are combined into one function.

Refinement

Since different scoring functions are relatively co-linear, consensus scoring functions may not improve accuracy significantly.^[15] This claim went somewhat against the prevailing view in the field, since previous studies had suggested that consensus scoring was beneficial.^[16]

A perfect scoring function would be able to predict the binding free energy between the ligand and its target. But in reality both the computational methods and the computational resources put restraints to this goal. So most often methods are selected that minimize the number of false positive and false negative ligands. In cases where an experimental training set of data of binding constants and structures are available a simple method has been developed to refine the scoring function used in molecular docking.^[17]

References

1. Jain AN (Oct 2006). "Scoring functions for protein-ligand docking". Current Protein & Peptide Science 7 (5): 407–20. doi:10.2174/138920306778559395. PMID 17073693.
2. Lensink MF, Méndez R, Wodak SJ (Dec 2007). "Docking and scoring protein complexes: CAPRI 3rd Edition". Proteins 69 (4): 704–18. doi:10.1002/prot.21804. PMID 17918726.
3. Robertson TA, Varani G (Feb 2007). "An all-atom, distance-dependent scoring function for the prediction of protein-DNA interactions from structure". Proteins 66 (2): 359–74. doi:10.1002/prot.21162. PMID 17078093.
4. Rajamani R, Good AC (May 2007). "Ranking poses in structure-based lead discovery and optimization: current trends in scoring function development". Current Opinion in Drug Discovery & Development 10 (3): 308–15. PMID 17554857.
5. Seifert MH, Kraus J, Kramer B (May 2007). "Virtual high-throughput screening of molecular databases". Current Opinion in Drug Discovery & Development 10 (3): 298–307. PMID 17554856.
6. Böhm HJ (Jul 1998). "Prediction of binding constants of protein ligands: a fast method for the prioritization of hits obtained from de novo design or 3D database search programs". Journal of Computer-Aided Molecular Design 12 (4): 309–23. doi:10.1023/A:1007999920146. PMID 9777490.
7. Joseph-McCarthy D, Baber JC, Feyfant E, Thompson DC, Humblet C (May 2007). "Lead optimization via high-throughput molecular docking". Current Opinion in Drug Discovery & Development 10 (3): 264–74. PMID 17554852.
8. Foloppe N, Hubbard R (2006). "Towards predictive ligand design with free-energy based computational methods?". Current Medicinal Chemistry 13 (29): 3583–608. doi:10.2174/092986706779026165. PMID 17168725.
9. Fenu LA, Lewis RA, Good AC, Bodkin M, Essex JW (2007). "Chapter 9: Scoring Functions: From Free-energies of Binding to Enrichment in Virtual Screening". In Dhoti H, Leach AR. Structure-Based Drug Discovery. Dordrecht: Springer. pp. 223–246. ISBN 978-1-4020-4407-6.
10. Sotriffer C, Matter H (2011). "Chapter 7.3: Classes of Scoring Functions". In Sotriffer C. Virtual Screening: Principles, Challenges, and Practical Guidelines 48. John Wiley & Sons, Inc. ISBN 978-3-527-63334-0.
11. Genheden S, Ryde U (2015). "The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities". Expert Opinion on Drug Discovery 10 (5): 449–61. doi:10.1517/17460441.2015.1032936. PMC 4487606. PMID 25835573.
12. Schneider N, Lange G, Hindle S, Klein R, Rarey M (Jan 2013). "A consistent description of HYdrogen bond and DEhydration energies in protein-ligand complexes: methods behind the HYDE scoring function". Journal of Computer-Aided Molecular Design 27 (1): 15–29. doi:10.1007/s10822-012-9626-2. PMID 23269578.
13. Lange G, Lesuisse D, Deprez P, Schoot B, Loenze P, Bénard D, Marquette JP, Broto P, Sarubbi E, Mandine E (Nov 2003). "Requirements for specific binding of low affinity inhibitor fragments to the SH2 domain of (pp60)Src are identical to those for high affinity binding of full length inhibitors". Journal of Medicinal Chemistry 46 (24): 5184–95. doi:10.1021/jm020970s. PMID 14613321.
14. Muegge I (Oct 2006). "PMF scoring revisited". Journal of Medicinal Chemistry 49 (20): 5895–902. doi:10.1021/jm050038s. PMID 17004705.
15. Englebienne P, Moitessier N (Jun 2009). "Docking ligands into flexible and solvated macromolecules. 4. Are popular scoring functions accurate for this class of proteins?". Journal of Chemical Information and Modeling 49 (6): 1568–80. doi:10.1021/ci8004308. PMID 19445499.
16. Oda A, Tsuchida K, Takakura T, Yamaotsu N, Hirono S (2006). "Comparison of consensus scoring strategies for evaluating computational models of protein-ligand complexes". Journal of Chemical Information and Modeling 46 (1): 380–91. doi:10.1021/ci050283k. PMID 16426072.
17. Hellgren M, Carlsson J, Ostberg LJ, Staab CA, Persson B, Höög JO (Sep 2010). "Enrichment of ligands with molecular dockings and subsequent characterization for human alcohol dehydrogenase 3". Cellular and Molecular Life Sciences 67 (17): 3005–15. doi:10.1007/s00018-010-0370-2. PMID 20405162.