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WaterMap: Mapping Solvation Free Energies and Understanding Binding Affinities

This paper discusses the use of WaterMap to map out the solvation free energies of water clusters in the active site and how this information can be used to understand binding affinities. The paper also includes case studies and applications of WaterMap.

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WaterMap: Mapping Solvation Free Energies and Understanding Binding Affinities

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  1. WaterMap: Mapping Solvation Free Energies of Active Site Waters and Using This Data to Understand Binding Affinities Richard A. Friesner Columbia University

  2. Thermodynamic Decomposition of Ligand/Protein Binding ∆Hconf penalty ∆Sconfpenalty ∆Hconf penalty ∆Sconf penalty ∆G(2) ∆G(1) ∆H penalty ∆S reward ∆H ? ∆S ? ∆G(4) ∆G(3) ∆H reward ∆Srot/trans penalty ∆G(5) Solvated Ligand Solvated Apo Protein Solvated Ligand in Bioactive Conformation Solvated Protein in Ligand-Induced Conformation Desolvated Ligand Ligand-Induced Desolvated Protein Binding Site Protein/Ligand Complex For lead optimization and comparison between two ligands, ∆∆G(4) is typically largest component of ∆∆Gbind

  3. Water displacement is key step that drives binding affinity • Hydrogen bonds are very important for specificity, but can be made by the ligand either in the protein or in solution • Some gain due to releasing waters into bulk, mostly entropic • A few exceptional cases based on unusual electrostatic configurations in the active site (neuramididase) • Most waters in the active site, particularly those in hydrophobic regions, do not have competitive entropy and/or hydrogen bonding as compared to bulk water • Hence if ligand group complementary to protein can displace these waters, significant free energy gains accrue • There are “special” regions of the active site where waters have particularly poor free energies • Hydrophobic enclosure • Hydrophobic enclosure plus correlated hydrogen bonds

  4. p38 MAP Kinase Naphthyl ring is hydrophobically enclosed in allosteric pocket – huge drop in binding affinity if this group is removed 1kv2

  5. HIV-1 Protease No enclosure, hydrophobic groups are only on one “side” of phenyl group of ligand – some benefit, captured in normal hydrophobic pair term, but not nearly as large as when enclosure is present – lack of enclosure explains why HIV protease ligands must be large to acquire substantial binding affinity 1hpx

  6. CKD2 Staurosporine in 1aq1: special H bond NH CO pair 3 kcal/mol reward and central part of ring gets a 3 kcal/mol hydrophobic packing reward 1aq1

  7. Streptavidin / biotin Classic problem in molecular recognition Enclosure + triple correlated H bond explains huge binding affinity of small ligand – result is within 1.5 kcal/mol of experiment Model has now been validated by all atom MD simulations 1stp

  8. Mapping Solvent Chemical Potential – Overview • Based on inhomogenious solvation theory1 • <E> is taken directly from simulation • Se from a local expansion of orientational and spatial correlation functions • Combines MD simulation and trajectory analysis • ~10 ns simulation with explicit waters and restrained protein • Waters are spatially clustered and analyzed • Chemical potential (entropy and enthalpy) are computed for each hydration site • Energy terms are relative to bulk water • Preliminary applications have been published2,3 • Patent filed Sept 2007 r = position  = orientation  = integral over   = bulk water density g = correlation function sw = solute-solvent terms sww = solute-solvent-solvent terms 1Lazaridis T (1998) J Phys Chem B 102:3531-3541 2Young T et al. (2007) PNAS 104:808-813 3Abel R et al. (2008)J Am Chem Soc 130:2817-2831

  9. WaterMap • A systematic approach using molecular dynamics (MD) methods to map out free energy of water clusters in the active site • Clustering techniques used to analyze MD trajectory and identify regions of high and low density • High density regions are assigned enthalpies and entropies using inhomogeous solvation theory • Protocol is simple and fast; remove the ligand, run the MD simulation (overnight on 8 processors), and WaterMap is created for that receptor conformation – can then be used to identify key areas for growing ligand, and in favorable circumstances to estimate change in binding free energy if a group displacing a new water is added • Can also run with ligand present – some technical issues which have been overcome in latest version (will show a few examples) • Numerous applications will be discussed in presentations that follow

  10. Overview of WaterMap positioning as a theoretical method and as used in practice to date • Accurate “relative” structures are absolutely required and induced fit effects can be critical • Even small changes in structure can alter water network in nontrivial ways • For late stage lead optimization, building structures (vs. free docking) is often best as it promotes cancellation of error • Induced fit calculations are critical for novel structures, and then relative protein reorganization energy must be estimated • Much faster than FEP, can be applied to many ligands after one calculation, for favorable cases more accurate due to noise reduction (more discussion later) • Provides vivid, reasonably accurate pictures, useful for medicinal chemists in design process • Exciting successes already observed in explaining literature data and in drug discovery projects

  11. Test of IHT/watermap on simple test cases; methane in hydrophobic model systems, comparison with FEP

  12. Example solvent density distribution and clustering (Streptavidin)

  13. Factor Xa – initial published watermap results for pharmaceutically interesting target (JACS 2008) • Use inhomogenous solvation theory to calculate binding free energy differences between pairs of factor Xa ligands • Pairs chosen so modification of ligand typically displaces waters near hydrophobic surface • Avoids changes in charge state, hydrogen bonding, etc. upon addition of new group (otherwise other effects must be added, work along these lines is in progress) • Map of water molecules built from single structure, ligands superimposed on this structure – so only one MD simulation is required (works in part because fxa is an unusually rigid protein) • Results explain key features of reverse binders currently in Phase III clinical trials (J&J+Bayer, BMS, etc.)

  14. Hydration Site Thermodynamics

  15. WaterMap Binding Energy Predictions – Factor Xa Inhibitors(no adjustable parameters) 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 R2 = 0.63 Calculated ∆∆Gbind (kcal/mol) -7 -6 -5 -4 -3 -2 -1 0 1 Experimental ∆∆Gbind (kcal/mol) Abel et al. J. Am. Chem. Soc.2008, 130, 2817

  16. FXa – SAR of neutral P1 substituents = stable waters & favorable enthalpy = most unstable water in binding site 10,000 nM 2500 nM 2100 nM 470 nM 89 nM 73 nM 3 nM

  17. Case Study 1: thrombin R2 = 0.82 P.I. = 0.91 R2 = 0.26 P.I. = 0.64 R2 = 0.51 P.I. = 0.66 WM/MM ΔG bind (kcal/mol)‏ MM-GB/SA ΔG bind (kcal/mol)‏ WM ΔG bind (kcal/mol)‏ Experimental ΔG bind (297 K kcal/mol)‏ Experimental ΔG bind (297 K kcal/mol)‏ Experimental ΔG bind (297 K kcal/mol)‏ MM-GB/SA WM/MM WM R2MW=0.45

  18. The ERBIN PDZ-domain Phage Display reveals that WETWV is the optimal Erbin binding motif (Skelton et al., JBC, 2003) Alanine scanning of the peptide suggest that P-0 and P-1 are most important for affinity Mutagenesis of the PDZ domain cannot explain the crucial role of Trp at P-1: “curiously, alanine substitutions of residues that contact Trp -1 did not decrease peptide binding” (Skelton et al., JBC, 2003)

  19. WaterMap calculations explain origin of high affinity and selectivity of peptides Experimental ∆G (kcal/mol) y = 0.5647x + 19.144 R2 = 0.7314 WaterMap ∆G (kcal/mol) Unfavorable water molecules are found in the P-0 and P-1 pockets, consistent with experimental data Peptide affinities correlate very well with WaterMap energies (R2=0.73) Only water molecules with -TS and H larger than 1 kcal/mol (i.e., enthalpically and entropically unstable waters) are shown

  20. Abl/c-Kit selectivity Gleevec does not hit this specific high energy water in Abl (red) or c-Kit (green) A methyl variant of Gleevec binds tighter to c-Kit and only displaces the c-Kit water

  21. Bcl-xL WaterMap ABT-737 All highly unstable (unhappy) waters in binding site (∆G > 2.8 kcal/mol)

  22. High potency ligands displace all highly unstable waters and no stable waters 9 waters in each bin

  23. S-enantiomers bind much more weakly than R-enatiomers

  24. 2.0 1.5 1.9 R R-enantiomer displaces 3 unstable waters

  25. S-enantiomer does not displace 3 unstable waters S WaterMap predicts that R-enantiomer will bind with -pKi 3.5 greater than S-enantiomer Experiment: -pKi difference in binding is 2.5

  26. CDK2 inhibitors 1ke6 1ke7 1ke5 1ke9 1ke8 ∆Gbind (kcal/mol) -11.2 -11.0 -8.5 -8.4 -8.2 ∆∆G between tight and weak binders is ~3 kcal/mol

  27. Differences in receptor structures result in different location and energy of key water site ∆G = 2.1 kcal/mol Shifted 0.5 Å away from R-group 2iw9 – has cyclin A2 bound ∆G = 3.4 kcal/mol 1ke6 – does not have cyclin A2 bound

  28. Using the “right” structure when predicting binding affinities Correlation between experimental ∆G of binding and WaterMap ∆G

  29. Using WaterMap with Ligand Present • Should be more accurate since this takes into account how ligand modifies properties of water molecules surrounding it • However, technical problems arise due to creation of pockets of solvent not in contact with bulk – specialized algorithms are needed to populate and sample these regions (particle insertion methods based on Grand Canonical Monte Carlo) • New release has these algorithms and tests indicate substantial improvement; some examples follow

  30. 2bhh: largest outlier of XP for CDK2 data set, no obvious explanation • Actual binding affinity ~ 6kcal/mole; calculations yield ~9 kcal/mole • Approach: run watermap with ligand present (currently subject of extensive studies,appears necessary in a number of interesting cases) • Analogue of 2bhh ligand is available with binding affinity data from literature • By comparing the results for the analogue and for the compound itself, a useful hypothesis is suggested: a modified group of 2bhh disrupts the water structure around the ligand; this effect can be quantified relative to the comparison compound, and the differential (which is NOT represented in the new XP/WM scoring function) is in reasonable agreement with the error in the XP/WM prediction for 2bhh

  31. CDK2: DDG=~-2.5 kcal/mol (Exp.)‏ 2BHH Carbonyl variant

  32. New version of Glide XP – not yet released • First goal is to rank order highly diverse compounds with different charge states, etc. – these data sets do not work well with methods like MM-PBSA, etc. – and at the same time achieve much higher enrichments than previously • Second goal is to eliminate high scoring decoys; current methods with “enrichment” of ~2-5x have huge numbers of incorrectly scored random compounds • Reasonable rank ordering is a necessary condition for making a large improvement • Systematically investigate errors and try to fix them • First develop scoring function that works with self-docking of PDB crystal structures, correcting for core reorganization energy • Then use induced fit methods to enable similar approach to work in cross docking • Key developments • New terms added to XP • Combination of XP and watermap; use of watermap to analyze remaining outliers • Analysis of reorganization energy

  33. Integration of WaterMap with Glide XP • WaterMap run on a single structure • Waters inserted into all members of test set; process contains some noise due to induced fit effects; current algorithm is quite crude but works acceptably at targeted level of accuracy • Need to avoid double counting • Watermap results treated as a correction to XP hydrophobic packing score • Objective is to pick up large differences which indicate a qualitative error in empirical model –key improvements seen in rejection of false positives • Use WaterMap to identify rotatable bonds which are in bulk-like regions – here the implicit approximation in the pair hydrophobic term is not relevant and entropic penalty is applied

  34. Results of integrating watermap with Glide – tests on PDB data sets (decoy data from docking of 1000 decoys, Schrodinger decoy set)

  35. PDE4 decoys • Two fundamental problems identified; neither has anything to do with the scoring function • Problem 1: coordination of metal sites in PDE4 with water molecules • Modeling of metals in problematic in docking calculations • QM studies suggest Zn in PDE4 should have octahedral coordination, or energy is problematic • Water molecules supply this coordination • About 50% of decoys displace one or more key waters with inappropriate group; this never happens in actives • Problem 2: regulatory region blocks part of active site; only appears in recent PDB crystal structures • Affects many of remaining 50% of decoys • If new structure is used for docking, should eliminate this problem • Combination of two effects may explain virtually entire difficulty with PDE4 decoys (NOT a “failure” of scoring function in the traditional sense)

  36. “Bumped” chelated solvent

  37. “Bumped” chelated solvent

  38. “Bumped” C-terminal regulatory region

  39. “Bumped” C-terminal regulatory region

  40. Example of a good native

  41. Coworkers • Columbia • Bruce Berne, Tom Young, Robert Abel, Lingle Wang • Schrodinger • Ramy Farid, John Shelley, Woody Sherman, Thijs Beuman, Rob Murphy

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