Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2007 DNA Knotting: Occurrences, Consequences & Resolution Jennifer Katherine Mann Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS & SCIENCES DNA KNOTTING: OCCURRENCES, CONSEQUENCES & RESOLUTION By JENNIFER KATHERINE MANN A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Spring Semester, 2007 Copyright © 2007 Jennifer K. Mann All Rights Reserved The members of the Committee approve the Dissertation of Jennifer Katherine Mann defended on February 28, 2007. De Witt L. Sumners Professor Co-Directing Dissertation E. Lynn Zechiedrich Professor Co-Directing Dissertation Nancy L. Greenbaum Outside Committee Member Wolfgang Heil Committee Member Jack Quine Committee Member Approved: Philip L. Bowers, Chair, Mathematics Joseph Travis, Dean, Arts & Sciences The Office of Graduate Studies has verified and approved the above named committee members. ii The dissertation is dedicated to Nicholas R. Cozzarelli, Ph.D. (1938 – 2006). iii ACKNOWLEDGEMENTS I sincerely thank my advisor Dr. De Witt L. Sumners for being a motivating, fair, encouraging, honest, challenging, supportive, and involved mentor. Dr. Sumners’ work led me into biomedical mathematics, and he made possible for me many unique educational experiences. I especially thank Dr. Lynn Zechiedrich for allowing a mathematician to move into her lab and do experiments for five years. In Dr. Zechiedrich’s lab I was allowed to continue to be a mathematician as I also became a molecular biologist and biochemist. This unique mentoring relationship, the interdisciplinary biomedical mathematics program, and financial support from the Program in Mathematics and Molecular Biology gave me tremendous opportunities to experience theoretical, experimental, and computational research. I thank Rick Deibler, Ph.D. for mentoring me and tolerating my endless questions in my early lab days of 2002. I appreciate participating in lab group and sub- group meetings and DNA topological discussions with Lynn, postdoctoral associates Jonathan Fogg, Ph.D. and Jamie Catanese, Ph.D., former graduate student Chris Lopez, Ph.D., and graduate student Graham Randall. All Zechiedrich lab members from the summer of 2002 through the spring of 2007 are to be acknowledged for their contributions to the scientific atmosphere of our lab group. I would also like to thank my committee members Dr. Jack Quine, Dr. Wolfgang Heil, and Dr. Nancy Greenbaum for their guidance and service. I thank Drs. Hue Sun Chan and Zhirong Liu for our collaborative statistical mechanical work. I thank Hue Sun for direction and encouragement. I thank Zhirong for sharing code and data. I acknowledge the Program in Mathematics and Molecular Biology and the Burroughs Wellcome Fund Interfaces Program for generous financial support of my doctoral research. My grandparents and my Mom and Dad taught me to love and value both the pursuit and the attainment of knowledge. Mom and Dad encouraged my interests and made sacrifices so that I might live out my dreams. Most importantly, Mom and Dad endued me with both “roots and wings.” I survived graduate school with the love and support of my sisters, Pam and Melissa. My nephews, Aaron, Patrick, and Ches remind me how amazing life and discovery are. My brothers-in-law Paul and Jason are true brothers. There are not words to express my gratitude to my family for all they have given me and all they add to my life. Friends Sarah Riosa, Nomzamo Matyumza, Caroline Boulis, Ph.D., Irma Cruz- White, Ph.D., and Mack Galloway, Ph.D. are truly appreciated. iv TABLE OF CONTENTS List of Tables ............................................................................................................. viii List of Figures............................................................................................................ ix List of Abbreviations.................................................................................................. xii List of Symbols ....................................................................................................... xiv Abstract ..................................................................................................................... xvi 1. Introduction and Background ............................................................................... 1 1.1 Basics of Knot Theory ................................................................................. 1 1.2 Review of Relevant Molecular Biology and Biochemistry............................ 11 1.3 DNA Topology............................................................................................. 16 1.3.1 DNA Supercoiling 1.3.2 DNA Catenanes 1.3.3 DNA Knots 1.3.4 DNA Topoisomerases 1.4 Type II Topoisomerases.............................................................................. 24 1.4.1 Biological Significance 1.4.2 Mechanism, Structure and Proposed Models 1.5 Dissertation Research Objectives ............................................................... 29 2. Biological Consequences of Unresolved DNA Knotting ....................................... 30 2.1 Introduction ................................................................................................. 30 2.2 Materials and Methods................................................................................ 33 2.2.1 Strains and Plasmids 2.2.2 Antibiotic resistance measurements 2.2.3 Antibodies and immunoblotting 2.2.4 Plasmid loss assay 2.2.5 DNA catenane analysis 2.2.6 Isolation of ampicillin resistant colonies and fluctuation analysis 2.3 Results ....................................................................................................... 37 2.3.1 Experimental Strategy 2.3.2 Hin-mediated recombination and knotting of a plasmid alters function of a reporter gene 2.3.3 Hin recombination and knotting alter β-lactamase levels 2.3.4 Molecular analysis of Hin-mediated effects 2.3.5 Hin-mediated recombination/knotting is mutagenic v 2.4 Discussion................................................................................................... 55 2.4.1 Mechanism of the Hin-mediated effect 2.4.2 Implications for cellular physiology and evolution 3. Statistical Mechanics of Unknotting by Type II Topoisomerases.......................... 59 3.1 Introduction ................................................................................................. 59 3.2 Model and Methods..................................................................................... 64 3.2.1 Counting Conformations in Various Knot States 3.3 Results ........................................................................................................ 73 3.3.1 Conformational Counts and Knot Probabilities 3.3.2 Juxtaposition Geometries and Knot/Unknot Discrimination 3.3.3 Segment Passage and Steady-state Distribution of Topoisomers 3.3.4 Juxtaposition-driven Topological Transitions and Knot Reduction 3.3.5 Knot Reduction by Segment Passage Correlates with Juxtaposition Hookedness 3.3.6 Unknotting and Decatenating Effects of a Juxtaposition are Related 3.4 Discussion................................................................................................... 97 4. DNA Unknotting by Human Topoisomerase IIα ................................................... 98 4.1 Introduction ................................................................................................. 98 4.2 Materials and Methods................................................................................ 100 4.2.1 Strains and Plasmids 4.2.2 DNA Knot Generation and Purification 4.2.3 Gel Electrophoresis and Quantification 4.2.4 DNA Analyses 4.2.5 Unknotting Reactions 4.3 Results ........................................................................................................ 104 4.3.1 Experimental Strategy 4.3.2 Resolution of DNA Knots by Human Topoisomerase IIα 4.4 Discussion................................................................................................... 112 5. Summary, Significance and Future Research ...................................................... 113 APPENDICES ........................................................................................................... 117 A. Knot and Link Table..................................................................................... 117 B. Glossary....................................................................................................... 120 C. Fluctuation Analysis ..................................................................................... 123 C.1 MSS Maximum-likelihood Method C.2 Maple Worksheets: Antibiotic Plate Preparation C.2.1 Ampicillin and Spectinomycin C.2.2 Ampicillin, Spectinomycin, and IPTG C.3 Excel Spreadsheets and Maple Worksheets: Mutation Rate Determinations C.3.1 MSS Maximum-likelihood Calculations for pBR-harboring Strain C.3.2 MSS Maximum-likelihood Calculations for pREC-harboring vi Strain C.3.3 MSS Maximum-likelihood Calculations for pKNOT-harboring Strain D. Monte Carlo Methods................................................................................... 133 D.1 MOS Moves D.2 BFACF Move E. Polynomial Knot Invariant ............................................................................ 135 E.1 HOMFLY Polynomial E.2 Maple Worksheets: