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Poisson@Boltzmann*Based*Implicit*Solvent*Methods** UC Irvine UC Irvine Electronic Theses and Dissertations Title Adaptation of PBSA and MMPBSA Methodology For Application to Membrane Protein Binding Free Energy Calculations Permalink https://escholarship.org/uc/item/25k316ww Author Botello-Smith, Wesley Michael Publication Date 2015 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California ! ! ! ! UNIVERSITY!OF!CALIFORNIA,! IRVINE! ! ! Adaptation!of!PBSA!and!MMPBSA!Methodology!For!Application!to!Membrane!Protein! Binding!Free!Energy!Calculations! ! DISSERTATION! ! ! submitted!in!partial!satisfaction!of!the!requirements! for!the!degree!of! ! ! DOCTORATE!OF!PHILOSOPHY! ! in!Chemistry! ! ! by! ! ! Wesley!Michael!BotelloKSmith! ! ! ! ! ! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Thesis!Committee:! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Professor!Ray!Luo,!Chair! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Professor!Douglas!Tobias,!CoKChair! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Professor!Ioan!Andrichioaei! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Introduction!©!2014!World!Scientific! Chapter!1!©!2012!Elsevier! Chapter2!©!2015!American!Chemical!Society! All!other!materials!©!Wesley!Michael!BotelloBSmith! DEDICATION) ! ! ! To! ! ! my!parents,!friends!and!family,! ! but!most!of!all,! ! To!my!loving!wife,! ! !!!!!!!in!recognition!of!their!worth,! ! ! !!!!!!!!and!without!whom!I!could!not!have!come!this!far.! ! ! ! ! ! ii! ! TABLE)OF)CONTENTS) ) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Page! ! LIST!OF!FIGURES! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!v! ! LIST!OF!TABLES! !!!!!!!!!!!!!!!!!!!!!!!!!!!!vi! ! ACKNOWLEDGMENTS! !!!!!!!!!!!!!!!!!!!!!!!!!!!vii! ! ABSTRACT!OF!THE!THESIS! !!!!!!!!!!!!!!!!!!!!!!!!!!viii! ! INTRODUCTION:!Biological!Applications!of!Classical!Electrostatics!Methods!! 1! ! Introduction! 1! ! Poisson.Boltzmann!Based!Implicit!Solvent!Methods! 2! ! Extension!of!PB!Solvent!Models!to!Implicit!Membranes! 5! ! Visualization!and!Structural!Analyses!of!Biomolecules! 8! ! Energetics!Analyses!of!Biomolecules! 12! ! Force!Field!Considerations! 15! ! Numerical!Solvers! 20! ! Distributive!and!Parallel!Implementation! 23! ! Conclusion! 26! ! References! 26! ! CHAPTER!1:!! Numerical!PoissonKBoltzmann!Model!for!! ! Continuum!Membrane!Systems! 33! ! Introduction! 33! ! Method! 35! ! Membrane!Setup! 35! ! Adaptation!of!the!Numerical!FD!Solvers!for!Periodic!! ! Boundary!Conditions! 41! ! Computational!Details! 43! ! Results!and!Discussion! 44! ! Conclusions!and!Future!Directions! 52! ! References! 55! ! ! ! CHAPTER!2:!! Applications!of!MMPBSA!to!Membrane!Proteins!I:! ! Efficient!Numerical!Solutions!of!Periodic!! iii! ! ! PoissonKBoltzmann!Equation! 58! ! Introduction! 58! ! Methods! 62! ! Finite!Volume!Discretization!of!the!Poisson.Boltzmann!Equation! 62! ! Matrix!Representation!of!the!Discrete!Operator! 63! ! Treatment!of!Charged!Solutes! 65! ! Adaptation!of!Conjugate!Gradient!Type!Solvers!to!! ! Periodic!Boundary!Condition! 67! ! Adaptation!of!Successive!Over!Relaxation!to!Periodic!! ! Boundary!Condition! 72! ! Adaptation!of!Geometric!Multigrid!to!Periodic!Boundary!Condition! 73! ! MMPBSA!Calculations! 75! ! Computational!Details! 76! ! Results!and!Discussion! 76! ! Validation!of!Periodic!Numerical!Solvers! 76! ! Optimization!of!Conditioning!Coefficients!for!ICCG! 80! ! Efficiency!Analysis!of!Numerical!Solvers! 82! ! Numerical!Stability!in!Simulations!of!Charged!Solutes! 87! ! Effect!of!Implicit!Membrane!in!MMPBSA!Analysis!of!P2Y12R! 89! ! Conclusions!and!Future!Directions! 91! ! AcknoWledgements! 93! ! References! 93! ! CHAPTER!3:!! Applications!of!MMPBSA!to!Membrane!Proteins!II:! ! Design!and!Analysis!of!Protocol!for!ProteinKLigand!Binding! ! Free!Energy!Calculation! 96! ! Introduction! 96! ! Methods! 101! ! Preparation!of!P2Y12R!Complex!Models!from!Crystal!Structure! 101! ! Preparation!of!Lipid!Membrane!System!Models! 103! ! MD!Simulation!Protocol! 104! ! Binding!Energy!Calculations! 106! ! Implicit!Polar!Solvent!Model! 107! ! Implicit!Non.polar!Solvation!Model! 108! ! Protein!Dielectric!Constant! 108! ! Membrane!Dielectric!Constant! 109! ! Multi.trajectory!Methods! 109! ! Assessment!Metrics! 111! ! Additional!Computational!Details! 111! !!!!!!! iv! ! ! Results! 112! ! Non.polar!Solvent!Model! 113! ! Protein!Dielectric!Constant!Comparison! 115! ! Membrane!Dielectric!Constant!Comparison! 117! ! Multi.trajectory!Method! 118! ! Conclusions! 125! ! References! 126! ! ! CHAPTER!4:!!Summary!and!Conclusions! !!!!!!!!!!!!!!!!!!!!!!!!!129! ! ! ! ! ! ! ! ! ! v! ! LIST)OF)FIGURES) ! ! ! ! ! ! ! ! ! ! ! !!!!!!!!!!!!!!!!!!!!!!Page! ! Figure!1.1:!! Construction!of!solute!and!membrane!level!set!densities! 38! ! Figure!1.2:!! Effective!signed!distance!(Å)!and!level!set!density!distribution!! ! cross!sections!for!model!membrane! 41! ! Figure!1.3:!! Electrostatic!potential!distribution!(kcal/molKeK)!of!Aquaporin!! ! in!vacuum.! 45! ! Figure!1.4!:!! Level!set!cross!sections!and!boundary!grid!points!for!quadrapole!! ! system! 46! ! Figure!1.5!:!! Electrostatic!potential!distribution!(kcal/molKeK)!and!boundary!grid!! ! points!for!the!Aquaporin!coil!system! 48! ! Figure!1.6!:!! CrossKsectional!distribution!of!level!set!density!function!and!! ! boundary!grid!points!for!the!Aquaporin!system! 52! ! Figure!1.7!:!! CrossKsectional!distributions!of!electrostatic!potential!(kcal/molKeK)!! ! for!the!Aquaporin!system! 54! ! Figure!2.1.!! Discretized!Laplacian!operator!for!3x4x5!Grid! 65! ! Figure!2.2.!! Differences!between!electrostatic!energies!by!! ! different!boundary!conditions!vs!fill!ratios! 78! ! Figure!2.3.!! Differences!between!electrostatic!energies!by!! ! different!solvers!vs!grid!volumes! 80! ! Figure!2.4.!! Optimization!of!scaling!coefficients!for!PICCG! 82! ! Figure!2.5.!! Solver!iteration!scaling:!log!iteration!required!vs!log!grid!volume! 83! ! Figure!2.6.!! Solver!time!scaling:!log!solver!time!required!vs!log!grid!volume! 85! ! Figure!2.7.!! Total!PB!time!scaling:!!log!computation!time!vs!log!grid!volume! 86! vi! ! ! Figure!2.8.!! Relative!solver!time!scaling:!log!relative!solver!time!vs!! ! log!grid!volume! 87! ! Figure!2.9.!! Charge!neutrality!achieved:!log!unsigned!relative!net!charge!vs!! ! log!absolute!net!solute!charge! 88! ! Figure!2.10.!! Dependence!of!solver!performance!upon!ionic!strength:!! ! log!solver!time!vs!log!ionic!strength! 89! ! Figure!2.11.!! Effect!of!implicit!solvent!modeling!on!binding!affinity!calculation!! ! for!P2Y12R! 90! ! Figure!3.1:!! Binding!energy!difference!(ΔΔG)!correlation!for!P2Y12R!! ! using!optimized!parameters! 114! ! Figure!3.2:!! Binding!energy!(ΔG)!correlation!for!P2Y12R!using!! ! optimized!parameters! 114! ! Figure!3.3:!! Cumulative!PBSA!binding!free!energies! 119! ! Figure!3.4:!! Comparison!of!mulitKframe!overlays!for!P2Y12R!K!4PXZ! 121! ! Figure!3.5:!! Comparison!of!mulitKframe!overlays!for!P2Y12R!K!4NTJ! 122! ! Figure!3.6:!! Structural!RMSD!plots!for!P2Y12R!production!simulations! 124! ! ! ! ! ! ! ! ! ! ! ! ! ! vii! ! ! ! ! ! ! LIST)OF)TABLES! ! ! ! ! ! ! ! ! ! ! !!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!Page! ! Table!1.1:!! Electrostatic!potentials!for!continuum!water!and!! ! water!+!membrane!solvation!for!various!systems! 49! ! Table!3.1:!! Effect!of!nonKpolar!solvation!term!model! 115! ! Table!3.3:!! Effect!of!protein!dielectric!constant! 116! ! Table!3.4:!! Effect!of!membrane!dielectric!constant! 118! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! viii! ! ! ! ! ! ! ! ACKNOWLEDGMENTS! ! I!would!like!to!thank!my!advisor,!Dr.!Luo,!for!his!patience!and!guidance!throughout! my!time!at!UCI.!I!would!also!like!to!acknowledge!my!lab!colleagues,!present!and!former,! and!in!particular!Mengjuei!Hsieh,!a!former!lab!mate!and!the!previous!deKfacto!tech!support! of!the!lab,!who!was!of!great!help!when!I!was!learning!the!ins!and!outs!of!scripting!and! coding!for!the!PBSA!program!around!which!so!much!of!my!research!revolved.!I!would!also! like!to!thank!my!collaborator!Alec!Follmer!for!all!of!his!help!during!the!second!stage!of!the! P2Y12R!project.!!Lastly,!I!would!like!to!acknowledge!the!NIH!for!its!financial!support!as!this! work!was!supported!in!part!by!NIH!(GM093040!&!GM079383).!! ix! ! CURRICULUM)VITAE) ) Wesley)Michael)Botello?Smith) ! 2001K09! Learning!Facilitator,!Tutorial!Learning!Center,!Santa!Ana!Community!College! ! 2004! ! A.S.!in!Mathematics,!Santa!Ana!Community!College! ! 2004! ! A.S.!in!Chemistry,!Santa!Ana!Community!College! ! 2005! ! STARS!Research!Intership,!Yale! ! ! 2005K09! Academic!Excellence!Workshop!Facilitator,!California!State!Polytechnic!! ! ! University!of!Pomona! ! 2009! ! B.S.!in!Chemistry,!California!State!Polytechnic!University!of!Pomona! ! ! 2009K15! Teaching!Assistant,!Chemistry,!University!of!California,!Irvine! ! 2009K15! Research!Assistant,!Luo!Lab,!University!of!California,!Irvine! ! ! 2015! ! PhD!in!Chemistry,!University!of!California,!Irvine! ! ! FIELD!OF!STUDY! ! Chemistry,!emphasis!on!computational!modeling!and!simulation!of!biomolecules! ! ! PUBLICATIONS! ! Smith!WM,!Prediction!of!Alternate!Enzyme!Conformations!Via!Steered!Molecular!Dynamics.! The!SACNAS!Conference,!Denver!(2005)! ! Smith,!WM,!et!al,!Molecular!Dynamics!Simulations!of!Surfactant!Protein!C!Mimic!in! Phospholipid!Bilayers,!American!Chemical!Society!National!Meeting,!New!Orleans,!April! (2008)! ! BotelloKSmith!WM,!Liu!X,!Cai!Q,!Li!Z,!Zhao!H,!Luo!R,!Numerical!PoissonKBoltzmann!Model! for!Continuum!Membrane!Systems.!Chemical!Physics!Letters.!555:274K281!(2013)! ! ! BotelloKSmith!WM,!et!al,!Numerical!Solutions!of!the!Poisson!Boltzmann!Equation!for! Implicit!Membrane,!Oral!Presentation!at!the!American!Chemical!Society!National!Meeting,!
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