Improving Rapid Affinity Calculations for Drug-Protein Interactions

182 Pages·2014·29.41 MB·English

by  Gregory Antonio Ross

Improving Rapid Affinity Calculations
for Drug-Protein Interactions
by
Gregory Antonio Ross
St. Anne’s College
and
Department of Biochemistry
Trinity 2013
A thesis submitted in partial fulfillment for the degree of
Doctor of Philosophy at the University of Oxford
Abstract
Improving Rapid Affinity Calculations for Drug-Protein
Interactions
by Gregory Antonio Ross,
St. Anne’s College, Oxford.
Submitted for the degree of Doctor of Philosophy, Trinity 2013
The rationalisation of drug potency using three-dimensional structures of protein-ligand
complexes is a central paradigm in medicinal research. For over two decades, a major
goal has been to find the rules that accurately relate the structure of any protein-ligand
complextoitsaffinity. Addressingthisproblemisofgreatconcerntothepharmaceutical
industry, which uses virtual screens to computationally assay up to many millions of
compounds against a protein target. A fast and trustworthy affinity estimator could
potentially streamline the drug discovery process, reducing reliance on expensive wet
lab experiments, speeding up the discovery of new hits and aiding lead optimization.
Water plays a critical role in drug-protein interactions. To address the often ambiguous
nature of water in binding sites, a water placement method was developed and found to
beingoodagreementwithX-raycrystallography,neutrondiffractiondataandmolecular
dynamics simulations. The method is fast and has facilitated a large scale study of the
statistics of water in ligand binding sites, as well as the creation of models pertaining
to water binding free energies and displacement propensities, which are of particular
interest to medicinal chemistry.
Structure-based scoring functions employing the explicit water models were developed.
Surprisingly, these attempts were no more accurate than the current state of the art,
and the models suffered from the same inadequacies which have plagued all previous
scoring functions. This suggests a unifying cause behind scoring function inaccuracy.
Accordingly, mathematicalanalysesonthefundamentaluncertaintiesinstructure-based
modelling were conducted. Using statistical learning theory and information theory, the
existence of inherent errors in empirical scoring functions was proven. Among other
results, it was found that even the very best generalised structure-based model is signifi-
cantly limited in its accuracy, and protein-specific models are always likely to be better.
The theoretical framework developed herein hints at modelling strategies that operate
at the leading edge of achievable accuracy.
Acknowledgements
I am greatly indebted to my supervisors Philip Biggin and Garrett Morris for all their
advice,suggestions,andtrust,whichguidedmymeanderingpaththroughcomputational
chemistryandbiochemistry. Thisprojectspringsfromtheirthoughtsondeveloping“wet
pharmacophore” models. I am grateful to Phil for always having an open door and ear,
even for my less than bright ideas.
I have been very lucky to have been a part of the Structural Bioinformatics and Com-
putational Biochemistry Unit. For the good times and work times, warm thanks to
past and present members, particularly Amanda Buyan, Sonya Hanson, Joseph Goose,
Heidi Koldsø, Joanna Lee, Craig Lumb, Jerome Ma, Maria Musgaard, Benjamin Mor-
ris,MichelleSahai,DavidShorthouse,PhillipStansfeld,MatthiasSchmidt,LukasStelzl,
Jemma Trick, Ranjit Vijayan and Shabana Vohra. A special mention goes to Lukas and
Sonyaforourthermodynamicforays(LLAS),andDaveandJemmaforlunchtimemirth.
I am proud to have been accepted into the Doctoral Training Centre, and grateful to
have emerged from it an enlightened and confused interdisciplinarian. I was in fact ac-
cepted onto a brand new course I had previously never heard of: “Systems Approaches
to Biomedical Science Industrial Doctorate Centre”, and I am glad that I was. I must
acknowledge my fellow IDCers, especially for our evening scientific meet-ups through-
out my DPhil. Thanks and sorry to Timothy Rooney and Konrad Krawczyk for their
interesting discussions, and for the collaborations that never happened.
I am especially grateful to have met Jessica McGillen early in my DPhil. Thank you
Jess, for your patience and insight when discussing my science-related ramblings, and
for all time you have spent checking over my often poorly written write-ups. Above all
else, you have turned my already happy time in Oxford into something truly special.
Mymum, dadandbrotherhavebeenincrediblysupportiveofmyprolongedstudies, and
I have always counted on their help and endless encouragement. Mum and Dad, this
thesis is for you.
I am thankful to the Doctoral Training Centre and InhibOx for their funding, without
which this research would not exist. I can only hope that their investment in me has
been, and will be, worthwhile to people other than myself.
ii
List of Publications Originating from this
Thesis
Ross, G. A., Morris, G. M., Biggin, P. C., “Rapid and accurate prediction and scoring
of water molecules in protein binding sites.” PLoS ONE 7 (3), e32036+, Mar. 2012.
Ross, G. A., Morris, G. M., Biggin, P. C., “One size does not fit all: The limits of
structure-based models in drug discovery.,” J. Chem. Theory Comput. 9 (9), 4266-
4274, Aug. 2013.
Ross, G. A., Morris, G. M., Biggin, P. C., “Explicit water in scoring functions: a bias-
variance tradeoff.,” In preparation.
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Contents
Abstract i
Acknowledgements ii
List of Publications Originating from this Thesis iii
List of Figures vii
List of Tables viii
Frequently used Abbreviations ix
1 Introduction 1
1.1 Where are we now? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Strategies in Drug Discovery . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Computational approaches to binding affinity prediction . . . . . . . . . . 4
1.4 Water in binding thermodynamics . . . . . . . . . . . . . . . . . . . . . . 8
1.4.1 The hydrophobic effect . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.2 Hydrophobicity in structure-based drug design . . . . . . . . . . . 11
1.4.3 Hydrophobic consequences for modelling . . . . . . . . . . . . . . . 13
1.5 Objectives for this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Background theory 17
2.1 Binding affinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Thermodynamics and statistical mechanics . . . . . . . . . . . . . . . . . 18
2.3 Statistical learning theory and regression . . . . . . . . . . . . . . . . . . . 24
2.4 Information theory and regression . . . . . . . . . . . . . . . . . . . . . . 29
3 Rapid and accurate placement of water in protein binding sites 34
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.1 AutoDock Vina as a water placement tool . . . . . . . . . . . . . . 37
3.2.2 Applicability of Vina’s scoring function . . . . . . . . . . . . . . . 39
3.2.3 Refinement of the water placement method . . . . . . . . . . . . . 41
3.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
iv
Contents v
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4 Predicting the role of water in protein-ligand binding 54
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.1 Establishing a water binding energy score . . . . . . . . . . . . . . 57
4.2.2 Development of hydrophilic and lipophilic scores . . . . . . . . . . 59
4.2.3 Finding displaced water molecules retrospectively with WaterDock 60
4.2.4 Development of a probabilistic water classifier . . . . . . . . . . . . 61
4.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.1 Water energy model from a data mining procedure . . . . . . . . . 62
4.3.2 Classifying the role of water . . . . . . . . . . . . . . . . . . . . . . 63
4.3.3 Ligand water displacement propensities . . . . . . . . . . . . . . . 66
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5 Explicit water in empirical scoring functions 70
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2.1 Interaction terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2.2 Functional form of the model . . . . . . . . . . . . . . . . . . . . . 80
5.2.3 Data sets and preparation of structures . . . . . . . . . . . . . . . 81
5.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3.1 Water importance in affinity predictions . . . . . . . . . . . . . . . 93
5.3.2 Water placement error . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6 The limits of empirical scoring functions 101
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2 Protein-ligand structures have unique probability distributions . . . . . . 103
6.3 Information theoretic approach to scoring function
error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.3.1 The most accurate descriptors for structure-based scoring functions109
6.3.2 Cross entropy and normally distributed errors . . . . . . . . . . . . 110
6.4 The transferability of structure-based models . . . . . . . . . . . . . . . . 112
6.4.1 The errors of generalised structure-based models . . . . . . . . . . 114
6.4.2 The optimisation of scoring functions . . . . . . . . . . . . . . . . 116
6.5 Scoring with missing information . . . . . . . . . . . . . . . . . . . . . . . 119
6.5.1 Regret and discarded data . . . . . . . . . . . . . . . . . . . . . . . 119
6.5.2 Missing information in forcefield-based scoring functions . . . . . . 121
6.6 Verification of analytical results . . . . . . . . . . . . . . . . . . . . . . . . 122
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7 Conclusions 128
7.1 The prediction of protein-ligand binding affinities . . . . . . . . . . . . . . 128
7.2 Scoring water in protein-ligand interactions . . . . . . . . . . . . . . . . . 131
7.3 Strategies and future directions for virtual screening . . . . . . . . . . . . 133
7.4 Closing remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Contents vi
A Details of protocols and numerical results 137
A.1 Molecular dynamics simulation details . . . . . . . . . . . . . . . . . . . . 137
A.2 WaterDock OppA test set . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
A.3 Water docking protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
A.4 Scoring function results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
B Proofs of main analytical results 141
B.1 Proof of Equations 6.8 and 6.15 . . . . . . . . . . . . . . . . . . . . . . . . 141
B.2 Proof of Equation 6.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.3 Proof of Equation 6.13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
B.4 Proof of Equation 6.14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.5 Proof of Equation 6.16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Bibliography 149
List of Figures
1.1 Main phases in drug discovery . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Importance of shape for the inhibitors of factor Xa . . . . . . . . . . . . . 4
1.3 Bridging and displaced water in OppA . . . . . . . . . . . . . . . . . . . . 8
1.4 Targeted displacement of water in HIV-1 protease . . . . . . . . . . . . . 12
3.1 Comparison of AutoDock Vina to random model . . . . . . . . . . . . . . 44
3.2 Examples of WaterDock predictions . . . . . . . . . . . . . . . . . . . . . 46
3.3 WaterDock predictions in OppA tri-peptide complex . . . . . . . . . . . . 49
3.4 Electron density maps indicating possible water positions . . . . . . . . . 52
4.1 Training set predictions of water energy score . . . . . . . . . . . . . . . . 62
4.2 Examples of hypothetical water displacement . . . . . . . . . . . . . . . . 64
4.3 Distributions of water scores. . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4 Water displacement by ligand group . . . . . . . . . . . . . . . . . . . . . 67
5.1 Interaction pairs considered in scoring functions . . . . . . . . . . . . . . . 73
5.2 Comparison of simple scoring function’s accuracy . . . . . . . . . . . . . . 86
5.3 Errors of all scoring models . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4 ROC curve for virtual screens . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.5 Ranking ability and standard deviation of affinities . . . . . . . . . . . . . 92
5.6 Importance and of scoring terms . . . . . . . . . . . . . . . . . . . . . . . 96
5.7 Water uncertainty and model non-linearity . . . . . . . . . . . . . . . . . 98
6.1 Model of dependency between prospective affinity and structure . . . . . . 107
6.2 Toy example of a general scoring function . . . . . . . . . . . . . . . . . . 116
6.3 Schematic of scoring function landscape . . . . . . . . . . . . . . . . . . . 118
6.4 Scoring error and model parameter space . . . . . . . . . . . . . . . . . . 124
6.5 Absolute errors of different training regimes . . . . . . . . . . . . . . . . . 125
7.1 Solvation structure conservation in GluR2 . . . . . . . . . . . . . . . . . . 132
A.1 Scoring error and model parameter space with absolute errors . . . . . . . 140
vii
List of Tables
3.1 Protein-ligand complexes used to validate AutoDock Vina . . . . . . . . . 40
3.2 Protein-ligand complexes used to optimise WaterDock . . . . . . . . . . . 42
3.3 Overall accuracy of WaterDock . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4 WaterDock statistics per protein-ligand complex . . . . . . . . . . . . . . 49
4.1 Re-weighted AutoDock Vina hydrogen bond score . . . . . . . . . . . . . 62
4.2 Water classification accuracy . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1 Interaction terms used in scoring functions . . . . . . . . . . . . . . . . . . 80
5.2 Training and validation sets . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3 Comparison of the simple scoring function to popular models . . . . . . . 85
5.4 Enrichments due to scoring models . . . . . . . . . . . . . . . . . . . . . . 91
5.5 WaterMap and scoring function comparison . . . . . . . . . . . . . . . . . 93
A.1 WaterDock test set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
A.2 List and accuracies of alternate placement methods . . . . . . . . . . . . . 139
A.3 Performance of linear model . . . . . . . . . . . . . . . . . . . . . . . . . . 139
A.4 Performance of non-linear model . . . . . . . . . . . . . . . . . . . . . . . 140
viii
Frequently used Abbreviations
AIC Akaike’s Information Criterion
AUC Area Under Curve
CSAR Community Structure Activity Resource
GBSA Generalised Born Surface Area
GBT Gradient Boosted Tree
HIV Human Immunodeficiency Virus
IFST Inhomogeneous Fluid Solvation Theory
ITC Isothermal Titration Calorimetry
JAWS Just Add WaterS
MAE Mean Absolute Error
MD Molecular Dynamics
MMSE Minimum Mean Squared Error
MSE Mean Squared Error
NMR Nuclear Magnetic Resonance
PBSA Poisson-Boltzmann Surface Area
PDB Protein Data Bank
PDF Probability Distribution Function
PMF Potential of Mean Force
QSAR Quantitative Structure Activity Relationship
RISM Reference Interaction Site Model
RMSD Root Mean Squared Deviation
ROC Reciever Operating Characteristic
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