watermap: mapping solvation free energies of active site waters and using this data to understand...

WaterMap: Mapping Solvation Free Energies of Active Site Waters and Using This Data to Understand Binding AffinitiesRichard A. Friesner

Columbia University

Thermodynamic Decomposition of Ligand/Protein Binding

Solvated LigandSolvated Ligand Solvated Apo Protein

Solvated Apo Protein

Desolvated Ligand

Desolvated Ligand

Solvated Ligand in Bioactive Conformation

Solvated Ligand in Bioactive Conformation

Ligand-Induced Desolvated

Protein Binding Site

Ligand-Induced Desolvated

Protein Binding Site

Solvated Protein in Ligand-Induced

Conformation

Solvated Protein in Ligand-Induced

Conformation

Protein/Ligand Complex

Protein/Ligand Complex

Gbind Gi1

5

i

For lead optimization and comparison between two ligands, ∆∆G(4) is typically largest component of ∆∆Gbind

∆G(5) ∆H reward∆Srot/trans penalty

∆G(1)∆Hconf penalty∆Sconf

penalty

∆G(3)∆H penalty∆S reward

∆G(2) ∆Hconf penalty∆Sconf penalty

∆G(4) ∆H ?∆S ?

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

Naphthyl ring is hydrophobically enclosed in allosteric pocket – huge drop in binding affinity if this group is removed

p38 MAP Kinase

1kv2

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

HIV-1 Protease

1hpx

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

CKD2

1aq1

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 validatedby all atom MD simulations

1stp

1Lazaridis T (1998) J Phys Chem B 102:3531-35412Young T et al. (2007) PNAS 104:808-8133Abel R et al. (2008) J Am Chem Soc 130:2817-2831

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 densityg = correlation function sw = solute-solvent termssww = solute-solvent-solvent terms

Se kbw

gsw r, lngsw r, drd

kbw

2

22gsww r

2, 2 lngsww r2, 2 dr2d 2 ...

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

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

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

Example solvent density distribution and clustering (Streptavidin)

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.)

Hydration Site Thermodynamics

WaterMap Binding Energy Predictions – Factor Xa Inhibitors(no adjustable parameters)

Experimental ∆∆Gbind (kcal/mol)

Cal

cula

ted

∆∆

Gbi

nd (

kcal

/mol

)

-7

R2 = 0.63

-6 -5 -4 -3 -2 -1 0 1

Abel et al. J. Am. Chem. Soc. 2008, 130, 2817

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

FXa – SAR of neutral P1

substituents

2500 nM 2100 nM 470 nM10,000 nM

89 nM 73 nM 3 nM

= stable waters & favorable enthalpy= most unstable water in binding site

Case Study 1: thrombin

Experimental ΔG bind (297 K kcal/mol)Experimental ΔG bind (297 K kcal/mol) Experimental ΔG bind (297 K kcal/mol)

WM

ΔG

bin

d (k

cal/m

ol)

MM

-GB

/SA

ΔG

bin

d (k

cal/m

ol)

WM

/MM

ΔG

bin

d (k

cal/m

ol)

R2 = 0.26P.I. = 0.64

R2 = 0.51P.I. = 0.66

R2 = 0.82P.I. = 0.91

WM MM-GB/SA WM/MM

R2MW

=0.45

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)

The ERBIN PDZ-domain

WaterMap calculations explain origin of high affinity and selectivity of peptides

y = 0.5647x + 19.144R2 = 0.7314

-9

-8

-7

-6

-5

-4

-3

-2

-38 -36 -34 -32 -30 -28 -26 -24 -22

WaterMap ∆G (kcal/mol)

Exp

erim

enta

l ∆G

(kc

al/m

ol)

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 -TS and H larger than 1 kcal/mol (i.e., enthalpically and entropically

unstable waters) are shown

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

Abl/c-Kit selectivity

Bcl-xL WaterMap

ABT-737

All highly unstable (unhappy) waters in binding site (∆G > 2.8 kcal/mol)

High potency ligands displace all highly unstable waters and no stable waters

9 w

aters in

ea

ch bin

S-enantiomers bind much more weakly than R-enatiomers

R

1.5

2.0

1.9

R-enantiomer displaces 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

S-enantiomer does not displace 3 unstable waters

CDK2 inhibitors

1ke6 1ke7 1ke81ke91ke5

∆Gbind (kcal/mo

l)

-11.2 -11.0 -8.5 -8.4 -8.2

∆∆G between tight and weak binders is ~3 kcal/mol

Differences in receptor structures result in different location and energy of key water site

2iw9 – has cyclin A2 bound1ke6 – does not have cyclin A2 bound

∆G = 3.4 kcal/mol

∆G = 2.1 kcal/mol

Shifted 0.5 Å away from R-group

PDB ID

Has Cyclin A2 bound

R2 slope

1oiy yes 0.55 0.60

1oiu yes 0.55 0.41

1oi9 yes 0.74 0.72

2iw9 yes 0.99 0.94

1ke7 no 0.25 0.81

1ke9 no 0.15 0.55

1ke5 no 0.49 0.48

1ke8 no 0.42 -1.14

1ke6 no 0.00 0.07

Correlation between experimental ∆G of binding and WaterMap ∆G

Using the “right” structure when predicting binding affinities

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

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

CDK2: DDG=~-2.5 kcal/mol (Exp.)

2BHH Carbonyl variant

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

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

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

Receptor R2 Ave. Error

# Decoys ≤ -9.0

Jnk3(vrtx) 0.4 0.9 8upa 0.4 1.1 0aur 0.5 0.7 14dpp4 0.3 1.1 7erk2 0.9 0.8 1err 0.5 0.8 7lck 0.9 0.7 12pim 0.1 1.0 30rho 0.2 1.0 38

Receptor R2 Ave. Error

# Decoys ≤ -9.0

abl (dfg-in) 0.5 0.9 20alr2 0.6 1.1 59cdk2 0.5 1.1 16er 0.3 0.8 5fviia 0.7 1.1 0fxa 0.6 1.0 1hivrt 0.3 1.1 24hsp90 0.6 0.5 0Jnk(pdb) 0.3 0.9 8oppa 0.4 1.0 1p38 (dfg-in) 0.8 1.0 1p38(dfg-out) 0.6 1.2 3pde4 0.7 1.6 35pka 0.6 1.3 0ppar 0.2 0.7 3ptp1b 0.6 1.0 3thrombin 0.5 1.4 10

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)

“Bumped” chelated solvent

“Bumped” chelated solvent

“Bumped” C-terminal regulatory region

“Bumped” C-terminal regulatory region

Example of a good native

Coworkers

• Columbia– Bruce Berne, Tom Young, Robert Abel, Lingle Wang

• Schrodinger – Ramy Farid, John Shelley, Woody Sherman, Thijs Beuman, Rob

Murphy