Complementarity in the Structure and Dynamics of Protein-DNA Search and Recognition: A Multiscale Modeling Study A Dissertation Presented by Kevin Eduard Hauser to The Graduate School in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Chemistry (Chemical Biology) Stony Brook University December 2016 Kevin Eduard Hauser 2016 Stony Brook University The Graduate School Kevin E. Hauser We, the dissertation committee for the above candidate for the Doctor of Philosophy degree, hereby recommend acceptance of this dissertation. Carlos Simmerling – Dissertation Advisor Professor, Department of Chemistry Orlando Schärer – Chairperson of Defense Professor, Department of Chemistry Robert Rizzo – Committee Member Associate Professor, Department of Applied Mathematics & Statistics Miguel Garcia-Diaz – Dissertation Co-Advisor Associate Professor, Department of Pharmacological Sciences Evangelos Coutsias – External Member Professor, Department of Applied Mathematics & Statistics This dissertation is accepted by the Graduate School Charles Taber Dean of the Graduate School ii Dedication Page To Johnny, and any kid who had a bad gene. iii Frontispiece A human transcription factor partners its superhelical geometry with a distorted DNA helix. iv Table of Contents List of Figures ............................................................................................................................. vii List of Tables .............................................................................................................................. xiv List of Abbreviations................................................................................................................... xvi Chapter 1. Introduction ............................................................................................................. 1 1.1. Transcription factors regulate gene expression ..................................................................... 2 1.2. Diffusion of DNA-binding proteins to target DNA: search mode ........................................ 5 1.3. Helix geometry of biomolecules ......................................................................................... 11 1.4. Molecular Dynamics ........................................................................................................... 14 1.4.1. The Calculus of classical mechanics ................................................................................ 15 1.4.2. Molecular mechanics force field ...................................................................................... 15 1.4.2.1. Additional terms used in contemporary molecular dynamics simulations ................... 19 1.4.3. Classical mechanics equation of motion .......................................................................... 19 1.5. Normal mode analysis & anisotropic network model ......................................................... 22 1.5.1. Harmonic potential energy function ................................................................................ 22 1.5.2. Normal modes .................................................................................................................. 25 1.6. Overview of Projects: Chapter Summaries ......................................................................... 30 1.6.1. The two codes of DNA .................................................................................................... 31 1.6.1. Characterization of biomolecular helices and their complementarity using geometric analysis. ......................................................................................................................................... 32 1.6.2. Asymmetrically coupled structure specificity in protein-DNA complexes ..................... 32 1.6.3. A human transcription factor in search mode .................................................................. 33 1.6.4. Asynchronous shifts by asymmetrical modules bias how MTERF1 slides on DNA ...... 34 Chapter 2. The two codes of DNA .......................................................................................... 36 2.1. Introduction ......................................................................................................................... 36 2.2. Direct readout decodes DNA sequence letters .................................................................... 37 2.2.1. The letter representation of a DNA sequence is an information code ............................. 38 2.2.2. Proteins read letters with direct readout .......................................................................... 40 v 2.3. The energy code of DNA .................................................................................................... 44 2.3.1. Helicoidal parameters measure changes in DNA structure ............................................. 45 2.3.2. Proteins bind specific DNA structures ............................................................................. 47 2.4. Quantitative Models of the DNA Energy Code .................................................................. 49 2.4.1. Experimental approaches to characterizing the DNA energy code ................................. 49 2.4.2. Atomistic molecular dynamics simulations fill gaps in the energy code left by experiment ..................................................................................................................................... 51 2.5. The energy code predicts regulatory protein binding sites ................................................. 52 2.5.1. Ground-state DNA energy landscapes are imprinted with protein binding patterns ....... 52 2.5.2. Dynamic readout predicts nucleosome phasing ............................................................... 53 2.6. Methylation acts as a DNA flexibility switch ..................................................................... 56 2.7. Summary of the two codes of DNA .................................................................................... 56 2.8. Conclusion and perspective ................................................................................................ 57 Chapter 3. Characterization of biomolecular helices and their complementarity using geometric analysis ........................................................................................................... 59 3.1. Introduction ......................................................................................................................... 59 3.2. Theory ................................................................................................................................. 61 3.2.1. Rotate a helix in 3D, then project the helix on the x-y plane ........................................... 61 3.2.2. Spherical coordinates are used to rotate the helix frame ................................................. 64 3.2.3. A linear least squares problem is solved for the circle projected by the helix ................. 64 3.2.4. Helix pitch, twist and rise are calculated from the optimal helix frame .......................... 67 3.3. Methods............................................................................................................................... 69 3.3.1. Nievergelt’s helix ............................................................................................................. 69 3.3.2. Generating artificial helices ............................................................................................. 69 3.3.3. Generating biomolecular helices ...................................................................................... 72 3.3.3.1. Generating helical peptide secondary structure elements ............................................. 72 3.3.3.2. Generating nucleic acid helices .................................................................................... 73 3.3.3.3. Analyzing a superhelical protein-DNA complex .......................................................... 74 3.3.3.4. Using the test helices to estimate accuracy of an analysis ............................................ 75 3.4. Results ................................................................................................................................. 75 3.4.1. The method requires fewer points than TLS to achieve the same accuracy .................... 75 vi 3.4.2. Validation tests of ideal artificial helices ........................................................................ 77 3.4.3. Testing helical secondary structure elements .................................................................. 88 3.4.4. Validation of nucleic acid helices: single- and double-stranded DNA and RNA ............ 94 3.4.5. Characterizing superhelix protein tertiary-structure ...................................................... 100 3.5. Conclusion ........................................................................................................................ 102 Chapter 4. Asymmetrically coupled structure specificity in protein-DNA complexes .... 103 4.1. Introduction ....................................................................................................................... 103 4.2. Methods............................................................................................................................. 108 4.2.1. Experimental dataset ...................................................................................................... 108 4.2.2. Helix analysis ................................................................................................................