A Sampling of Molecular Dynamics

A SAMPLING OF MOLECULAR DYNAMICS By DANIEL JON SINDHIKARA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009 1 © 2009 Daniel J. Sindhikara 2 To my family 3 ACKNOWLEDGMENTS Upon completion of my studies at University of Florida, I primarily thank my advisor, Professor Adrian Roitberg. Throughout the years I have learned a tremendous amount from him via our scientific conversations, and especially our lively arguments. He has supported me scientifically, academically, and personally more than could ever be asked. I also thank “my second advisor”, Professor Kenneth Merz Jr. for exceptional scientific and professional guidance. I appreciate participation by all my committee members including Professors Stephen Hagen, Aneta Petkova, and James Dufty. I am also grateful for significant assistance on theoretical topics from my colleagues, especially: Gustavo Seabra, Yilin Meng, Andrew Taube, Josh McClellan, and Prakash Verma. I appreciate all my friends and colleagues at the Quantum Theory Project, and the Departments of Physics and Chemistry. I thank the person who inspired me to become a computational physicist, a professor from my undergraduate institution: Dr. Louis DeChiaro. Finally, I thank my parents. They have given me a tremendous amount of support and encouragement throughout graduate school and everything else. I would like to acknowledge sources of funding by the Japan Society for the Promotion of Science (JSPS), the National Science Foundation (NSF) Eastern Asian and Pacific Summer Institute (EAPSI) program, National Institutes of Health grant # GM 066689. Also I have used more than my share of computational resources from the University of Florida High Performance Computing center (UFHPC), and NSF Large Allocations Resource Committee through Grant Nos. TG-MCA05S010 and UT-NTNL0002. 4 TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................................... 4 LIST OF TABLES................................................................................................................................ 9 LIST OF FIGURES ............................................................................................................................ 10 LIST OF ABBREVIATIONS ............................................................................................................ 13 ABSTRACT ........................................................................................................................................ 15 CHAPTER 1 INTRODUCTION....................................................................................................................... 17 1.1 Biological Macromolecules................................................................................................. 17 1.2 Protein Structure .................................................................................................................. 17 1.3 Simulation vs. Experiment .................................................................................................. 18 1.4 The All-Atom Representation of Proteins .......................................................................... 19 1.5 Obstacles in Simulation ....................................................................................................... 20 1.6 Free Energy and Ergodicity................................................................................................. 21 1.7 Monte Carlo Sampling......................................................................................................... 22 1.8 Molecular Dynamics ............................................................................................................ 23 1.9 Protein Folding and the Levinthal Paradox ........................................................................ 24 1.10 Enhanced Sampling ........................................................................................................... 24 1.11 Algorithmic Parallelization ............................................................................................... 25 2 METHODS .................................................................................................................................. 28 2.1 MD integration ...................................................................................................................... 28 2.2 Solvent Models..................................................................................................................... 30 2.2.1 Solvent Models Introduction ..................................................................................... 30 2.2.2 TIP3P water ................................................................................................................ 30 2.2.3 Generalized-Born Implicit Solvent Model ............................................................... 31 2.3 Thermodynamic Integration ................................................................................................ 31 2.4 Biased Ensembles and the Weighted Histogram Analysis Method .................................. 32 2.5 Replica Exchange Molecular Dynamics ............................................................................ 35 2.5.1 Background ................................................................................................................. 35 2.5.2 Implementation ........................................................................................................... 36 2.6 Multicanonical Algorithm Replica Exchange Method ...................................................... 38 5 3 EXCHANGE ATTEMPT FREQUENCY IN REPLICA EXCHANGE MOLECULAR DYNAMICS ................................................................................................................................ 45 3.1 Introduction .......................................................................................................................... 45 3.2 Methods ................................................................................................................................ 46 3.2.1 Simulation Details ...................................................................................................... 46 3.2.2 Conformation Deviation Between Test and Reference Simulations....................... 47 3.3 Results and Discussion ........................................................................................................ 47 3.3.1 Toy Model................................................................................................................... 48 3.3.2 Replica Exchange Diagnostics at High Exchange Attempt Frequencies................ 51 3.3.2.1 Potential energy and conformational distribution ....................................... 51 3.3.2.2 Sampling time ............................................................................................... 53 3.3.2.3 Acceptance of MC moves ............................................................................ 54 3.3.3 High EAF and Current Program Architecture .......................................................... 55 3.4 Conclusions .......................................................................................................................... 56 4 CONFIRMATION OF HIGH EXCHANGE ATTEMPT FREQUENCY BEHAVIOR OF REPLICA EXCHANGE MOLECULAR DYNAMICS IN EXPLICIT SOLVENT ....... 66 4.1 Introduction .......................................................................................................................... 66 4.2 Methods ................................................................................................................................ 66 4.3 Results and Discussion ........................................................................................................ 67 4.3.1 Thermal Equilibration at High EAF .......................................................................... 67 4.3.2 Effect of EAF on Sampling Efficiency ..................................................................... 67 4.4 Conclusions .......................................................................................................................... 68 5 THE NORMALIZED ERGODIC MEASURE FOR PARALLEL SAMPLING ALGORITHMS ........................................................................................................................... 71 5.1 Introduction .......................................................................................................................... 71 5.1.1 Measuring Convergence ............................................................................................ 71 5.1.2 Metrics Used for Parallel Algorithms ....................................................................... 72 5.2 Theory and Methods ............................................................................................................ 73 5.2.1 The Normalized Ergodic Measure ............................................................................ 73 5.2.2 Simulation Details ...................................................................................................... 74 5.3 Results and Discussion ........................................................................................................ 75 5.4 Conclusions .........................................................................................................................

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