MOLECULAR SURFACE ABSTRACTION by Gregory M. Cipriano A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Computer Sciences) at the UNIVERSITY OF WISCONSIN–MADISON 2010 c Copyright by Gregory M. Cipriano 2010 All Rights Reserved i To Ila, for providing infinite inspiration and distraction. ii ACKNOWLEDGMENTS I would like to thank first of all the members of my committee for their advice and support throughout my time at the University of Wisconsin, especially my advisor, Michael Gleicher. With- out you, this work would not have been possible. I thank everyone in the Graphics Lab, past and present, for many lively discussions and for helping me work through a thousand thorny issues. I thank especially Rachel Heck for going above and beyond (and sacrificing a Saturday) in helping finish my first Vis video. I thank my friends and family for never questioning the value of all this education, for encour- aging me along the way, and for providing the many good times that I’ll remember long after I’ve left Madison. I thank my wonderful wife Ila for a thousand acts of generosity: for making me dinner when I didn’t have time to feed myself, for rubbing my neck when I was stressed, and for making me laugh when I needed it most. Also, I thank her for never shying away from telling me when I was being unclear in my prose or when the colors were all wrong. Finally, I thank CIBM and BACTER, for their financial support. DISCARD THIS PAGE iii TABLE OF CONTENTS Page LIST OF TABLES ....................................... vi LIST OF FIGURES ...................................... vii NOMENCLATURE ...................................... ix ABSTRACT .......................................... x 1 Introduction ........................................ 1 1.1 Problem Overview .................................. 4 1.2 Technical Contributions ................................ 7 1.3 Technical Solutions Overview ............................ 9 1.3.1 Molecular Surface Abstraction ........................ 9 1.3.2 Multi-Scale Surface Curvature Estimation . 10 1.3.3 Ligand Binding Prediction .......................... 11 2 Related Work ....................................... 13 2.1 Molecular Visualization ................................ 13 2.2 Curvature Estimation ................................. 14 2.3 Local Shape Descriptors ............................... 16 2.4 Functional Surface Analysis ............................. 18 2.4.1 Identifying Potential Binding Sites ...................... 18 2.4.2 Alignment, Comparison and Classification . 22 3 Background ........................................ 25 3.1 The Geometric Surface ................................ 25 3.1.1 The Van der Waals Surface .......................... 25 3.1.2 Solvent-Excluded Surface .......................... 26 3.2 Electrochemical Properties .............................. 27 3.2.1 Electrostatic Potential ............................ 28 iv Page 3.2.2 Hydropathy .................................. 29 3.2.3 Hydrogen Donors/Acceptors ......................... 29 3.3 The Lock and Key Metaphor ............................. 30 4 Molecular Surface Abstraction .............................. 31 4.1 Abstracted Surfaces .................................. 32 4.1.1 Smoothing Surface Geometry ........................ 34 4.1.2 Abstracting Surface Fields .......................... 36 4.1.3 Removing Mid-Sized Features ........................ 38 4.1.4 Decaling ................................... 40 4.1.5 Results .................................... 45 4.2 The Client Viewer ................................... 48 4.2.1 High Quality Rendering of Abstracted Surfaces . 48 4.2.2 Multiple Surface Display and Comparison . 49 4.2.3 Results .................................... 51 4.3 GRAPE: GRaphical Abstracted Protein Explorer . 52 4.3.1 Project Goals ................................. 52 4.3.2 Server Side Processing ............................ 53 4.3.3 Client Side Viewer .............................. 56 4.3.4 Social Networking .............................. 59 4.4 Discussion ....................................... 60 5 Multi-Scale Surface Shape Descriptors ......................... 63 5.1 Local Shape Descriptors ............................... 63 5.1.1 Contribution ................................. 65 5.2 Multi-Scale Shape Descriptors ............................ 66 5.2.1 Neighborhood Construction ......................... 68 5.2.2 Height Field ................................. 71 5.2.3 Fitting with Quadratics ............................ 73 5.2.4 Moment-Based Surface Description ..................... 74 5.3 Results ......................................... 76 5.3.1 Performance ................................. 76 5.3.2 Evaluation .................................. 77 5.4 Applications ...................................... 80 5.4.1 Multi-scale Lighting ............................. 80 5.4.2 Segmentation ................................. 82 5.4.3 Stylized Rendering .............................. 83 5.4.4 Multi-scale/Anisotropic Curvature Matching . 84 v Appendix Page 6 Binding Prediction .................................... 85 6.1 Introduction ...................................... 85 6.1.1 Contributions ................................. 86 6.1.2 Method Overview .............................. 87 6.2 The Functional Surface Descriptor .......................... 88 6.2.1 Descriptor Scales ............................... 88 6.2.2 Descriptor Features .............................. 89 6.2.3 Normalization ................................ 90 6.3 Per-Atom Training .................................. 90 6.3.1 Building Training Examples ......................... 91 6.3.2 Training an Atom Learner .......................... 93 6.4 Per-Moiety Prediction ................................. 97 6.4.1 Reducing Sample Count ........................... 97 6.4.2 Predicting For an Atom ............................100 6.4.3 Combining Atom Predictions . 100 6.5 Merging Moiety Predictions .............................103 6.6 Evaluation .......................................103 6.6.1 Training ....................................104 6.6.2 Results ....................................106 6.6.3 Run-Time Performance ............................113 6.7 Comparison to Existing Methods . 115 6.7.1 Thornton, Spherical Harmonics . 115 6.7.2 Kihara, Real Time Search . 116 6.8 Discussion .......................................117 7 Discussion .........................................119 7.1 Issues and Limitations ................................120 7.1.1 Visual Abstraction ..............................120 7.1.2 Curvature ...................................122 7.1.3 Binding Prediction ..............................122 7.2 Future Work ......................................125 LIST OF REFERENCES ...................................127 APPENDIX Molecular Surface Feature Vector Denition . 138 DISCARD THIS PAGE vi LIST OF TABLES Table Page 6.1 Moiety matches used as training examples . 105 6.2 Results of a calcium binding test .............................106 6.3 Test cases .........................................109 Appendix Table A.1 A list of each feature contained within our surface descriptor. 140 DISCARD THIS PAGE vii LIST OF FIGURES Figure Page 1.1 An abstraction: ball-and-stick vs. ribbon diagrams ................... 3 3.1 How electrostatics are sampled onto the surface ..................... 28 4.1 Adenylate Kinase (1ANK) drawn in Pymol, Qutemol, stylized and abstracted . 33 4.2 Surface Field Simplification, before and after ...................... 36 4.3 Steps involved in geometric surface abstraction ..................... 38 4.4 Field of view for stickers vs. geometry .......................... 40 4.5 Local environment mapping diagram .......................... 41 4.6 Fixing issues with patch connectivity .......................... 42 4.7 Jagged vs. smooth (abstract) patch boundaries ..................... 43 4.8 Replacing ligands with ligand shadow stickers ..................... 44 4.9 Ribonuclease example .................................. 45 4.10 Abstraction vs. large probe size ............................. 46 4.11 Gallery of abstractions .................................. 47 4.12 Multiple surface display: 6 aligned RRMS ....................... 50 4.13 Demonstration: comparing ribonucleases ........................ 50 4.14 The GRAPE job queue .................................. 53 4.15 The four sticker types displayed in GRAPE ....................... 57 viii Figure Page 4.16 The GRAPE output window ............................... 58 4.17 A GRAPE recommendation gadget ........................... 59 5.1 Steps involved in generating a descriptor for a single neighborhood . 67 5.2 Shape description, represented at multiple scales .................... 68 5.3 Finding a disc: Dijkstra vs. 2-ring improvement ..................... 69 5.4 Comparing curvature results: Dijkstra vs. 2-ring improvement . 69 5.5 Multi-scale descriptors: sensitivity to noise ....................... 78 5.6 Multi-scale descriptors: sensitivity to tessellation .................... 79 5.7 Multi-scale lighting .................................... 81 5.8 Multi-scale segmentation ................................. 82 5.9 Multi-scale stylized rendering .............................. 83 5.10 Multi-scale curvature matching ............................. 84 6.1 Radii used in the functional surface descriptor ...................... 89 6.2 Building a Corpus using Moiety Exemplars ....................... 92 6.3 Atom training overview ................................