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Fast Molecular Surfaces, Constant Ph and Accelerated Dynamics, and Rational Drug Design

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Fast Molecular Surfaces, Constant Ph and Accelerated Dynamics, and Rational Drug Design UC San Diego UC San Diego Electronic Theses and Dissertations Title Implicit solvent method development and application : fast molecular surfaces, constant pH and accelerated dynamics, and rational drug design Permalink https://escholarship.org/uc/item/9j38m5xv Author Mongan John, Mongan John Publication Date 2006 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, SAN DIEGO Implicit Solvent Method Development and Application: Fast Molecular Surfaces, Constant pH and Accelerated Dynamics, and Rational Drug Design A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Bioinformatics by John Mongan Committee in charge: Professor J. Andrew McCammon, Co-chair Professor Gary Huber, Co-chair Professor David A. Case Professor Elizabeth Komives Professor Mauricio Montal Professor Peter Wolynes 2006 Copyright John Mongan, 2006 All rights reserved. The dissertation of John Mongan is approved, and it is acceptable in quality and form for publication on microfilm: Co-chair Co-chair University of California, San Diego 2006 iii For Thuy who always tells me whether it makes sense iv TABLE OF CONTENTS Signature Page ................................. iii Dedication .................................... iv Table of Contents ................................ v List of Figures . viii List of Tables .................................. x Acknowledgements ............................... xi Vita, Publications and Fields of Study . xiii Abstract of the Dissertation ........................... xv 1 Introduction ................................... 1 2 Limitations of atom-centered dielectric boundaries .............. 5 Abstract .................................. 5 2.1 Introduction ................................ 5 2.2 Methods ................................. 7 2.3 Results and Discussion .......................... 8 2.4 Conclusion ................................ 12 3 Generalized Born with a simple, robust molecular volume correction . 16 Abstract .................................. 16 3.1 Introduction ................................ 17 3.2 Theory ................................... 21 3.3 Results and Discussion .......................... 25 3.4 Methods .................................. 34 3.5 Conclusion ................................ 36 3.6 Appendix: Neck region integrals ..................... 37 3.7 Appendix: Coordinates of neck integral maxima . 41 4 Biomolecular simulations at constant pH .................... 43 Abstract .................................. 43 4.1 Introduction ................................ 44 4.2 Calculations of individual pKa values in proteins . 44 4.2.1 Thermodynamic integration and other free energy methods . 44 4.2.2 Implicit solvent models using the Poisson-Boltzmann approach 46 v 4.3 Constant pH simulations ......................... 48 4.3.1 Continuous protonation states with explicit solvent . 50 4.3.2 Continuous protonation states with implicit solvent . 51 4.3.3 Discrete protonation states with explicit solvent . 53 4.3.4 Discrete protonation states with explicit and implicit solvent . 54 4.3.5 Discrete protonation states with implicit solvent . 55 5 Constant pH molecular dynamics in generalized Born implicit solvent . 58 Abstract .................................. 58 5.1 Introduction ................................ 59 5.2 Theory and Methods ........................... 60 5.2.1 Algorithm ............................ 60 5.2.2 Molecular dynamics ....................... 61 5.2.3 Protonation state models ..................... 62 5.2.4 Reference compounds ...................... 63 5.2.5 Test system molecular models . 65 5.2.6 pKa prediction calculations .................... 66 5.3 Results and Discussion .......................... 67 5.3.1 Convergence ........................... 67 5.3.2 Simulation stability ........................ 70 5.3.3 pKa predictions .......................... 71 5.3.4 Non-Henderson-Hasselbalch behavior . 78 5.3.5 Conformation-protonation correlation . 78 5.3.6 Summary ............................. 83 5.4 Appendix: Partial charges of titratable groups . 84 5.4.1 Aspartate charges ......................... 84 5.4.2 Glutamate charges ........................ 84 5.4.3 Histidine charges ......................... 85 5.4.4 Tyrosine charges ......................... 86 5.4.5 Lysine charges .......................... 87 6 Accelerated Molecular Dynamics ....................... 88 Abstract .................................. 88 6.1 Introduction ................................ 88 6.2 Theory ................................... 90 6.3 Methods and Applications ........................ 96 6.4 Results and Discussion .......................... 97 6.4.1 Correct Canonical probability distribution . 97 6.4.2 Enhanced Sampling . 102 6.5 Conclusion ................................110 vi 7 Interactive Essential Dynamics . 111 Abstract ..................................111 7.1 Introduction ................................111 7.2 Theory and Methods . 113 7.3 User Interface ...............................115 7.4 Summary .................................117 8 Computational design of pyrone-based inhibitors of stromelysin-1 . 118 Abstract ..................................118 8.1 Introduction ................................118 8.2 Methods ..................................119 8.3 Results and Discussion . 121 9 Evaluation and binding mode prediction of thiopyrone-based inhibitors of an- thrax lethal factor ................................127 Abstract ..................................127 9.1 Introduction ................................127 9.2 Experimental assays ............................128 9.3 Computational methods . 130 9.4 Computational results and discussion . 133 10 Future Directions ................................138 10.1 Implicit solvation and generalized Born models . 138 10.2 Constant pH molecular dynamics . 140 10.3 Accelerated molecular dynamics . 141 10.4 Zinc(II) protease inhibitor design . 142 10.5 Conclusion ................................143 Bibliography ....................................146 vii LIST OF FIGURES 2.1 Dielectric maps of IFABP ......................... 10 2.2 PMF for histidine-histidine hydrogen bond . 12 2.3 PMF for asparagine-asparagine hydrogen bond . 13 2.4 PMF for alternate orientation of asparagine-asparagine hydrogen bond . 13 2.5 PMF for arginine-aspartate salt bridge . 14 2.6 PMF for β-sheet hydrogen bonding model (alanine-alanine). 14 3.1 Geometry of the neck region ....................... 22 3.2 Numerical integration and analytical approximation of neck region . 23 3.3 Comparison of GB effective radii to PB “perfect” radii . 27 3.4 GB and PB solvation energies over protein A denaturation . 28 3.5 PMFs for validation hydrogen bonding and salt bridge systems . 30 3.6 PMFs for objective function hydrogen bonding and salt bridge systems . 31 3.7 α-carbon RMSD for ubiquitin and thioredoxin MD trajectories . 32 3.8 Ubiquitin backbone hydrogen bond length data . 33 3.9 Three cases of neck regions ........................ 38 4.1 Thermodynamic cycle for calculation of protein sidechain pKa values . 45 4.2 Distribution of protonation energies in ASP-26 of thioredoxin . 47 5.1 Aspartate model compound titration curve . 68 5.2 Time evolution of predicted pKa values for HEWL at pH 3.0 . 69 5.3 HEWL GLU-7 titration curves ...................... 69 5.4 Trajectory of α-carbon RMSD from crystal coordinates for HEWL . 71 5.5 pKa prediction error as a function of offset from experimental pKa . 73 5.6 Coupling of conformation and protonation state . 81 5.7 Structures of conformational cluster centroids . 83 6.1 Schematic representation of accelerated MD potential energy surface . 91 6.2 Acelerated potentials with low threshold . 94 6.3 Acelerated potentials with high threshold . 95 6.4 Alanine dipeptide ............................. 98 6.5 Free energy surface from normal and accelerated MD simulations . 99 6.6 Free energy surface from accelerated MD simulations with high ED . 100 6.7 Free energy surface from accelerated MD simulations with low ED . 101 6.8 Free energy surface for ALA-3 of hepta-alanine at 300K and 400K . 103 6.9 Free energy surface for ALA-4 of hepta-alanine at 300K and 400K . 104 6.10 Eigenspectrum for accelerated MD of hepta-alanine . 105 6.11 PCA projections from normal and accelerated MD of hepta-alanine . 106 6.12 k-means clustering of accelerated MD of hepta-alanine . 107 viii 6.13 Torsional angles of ALA-3 and ALA-4 separated by cluster . 108 7.1 Screen shot of Interactive Essential Dynamics. 116 8.1 Crystal structure of maltol bound to (TpPh,Me)Zn . 120 8.2 Predicted binding mode of AM-5 MPI . 122 8.3 Synthetic scheme for MPIs . 123 8.4 Neonatal cardiac fibroblast (CF) invasion assay results . 125 9.1 LF inhibitors ...............................129 9.2 Lowest energy configuration of AM-2S in LF active site . 134 9.3 Lowest energy configurations for alternate ZBG orientation . 135 9.4 Detail view of positioning of biphenyl group for configuration I . 135 ix LIST OF TABLES 2.1 Solute volumes for various surface definitions .............. 9 2.2 Electrostatic solvation energies for various surface definitions . 10 3.1 Optimized scaling parameters ....................... 26 3.2 Distance between atoms at which neck integral has the maximum value 41 3.3 Maximum value of neck integral ..................... 42 5.1 Reference pKa values for titratable side chains . 64 5.2 pKa predictions for acidic residues of HEWL . 74 5.3 pKa predictions for
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