APPROACHES FOR UNVEILING THE KINETIC MECHANISMS OF VOLTAGE GATED ION CHANNELS IN NEURONS ______________________________________ A Dissertation Presented to the Faculty of the Graduate School At the University of Missouri-Columbia __________________________________________________________________ In Partial Fulfillment for the Requirements for the Degree of Doctor of Philosophy __________________________________________________ Submitted by MARCO ANTONIO NAVARRO Dr. Lorin Milescu, Dissertation mentor May 2019 © Copyright by Marco Navarro 2019 All Rights Reserved The undersigned, appointed by the dean of the Graduate School, have examined the dissertation entitled APPROACHES FOR UNVEILING THE KINETIC MECHANISMS OF VOLTAGE GATED ION CHANNELS IN NEURONS presented by Marco Navarro, a candidate for the degree of Doctor of Philosophy, and hereby certify that, in their opinion, it is worthy of acceptance. _______________________________________________ Professor Lorin Milescu _______________________________________________ Professor Mirela Milescu _______________________________________________ Professor David Schulz _______________________________________________ Professor Kevin Gillis Thesis Committee Dr. Lorin S Milescu Assistant Professor, Department of Biological Sciences University of Missouri, Columbia, MO Dr. Mirela Milescu Assistant Professor, Department of Biological Sciences University of Missouri, Columbia, MO Dr. David Schulz Professor, Department of Biological Sciences University of Missouri, Columbia, MO Dr. Kevin Gillis Professor, Department of Biological Engineering Professor Medical Pharmacology and Physiology University of Missouri, Columbia, MO ACKNOWLEDGEMENTS For the love of science, may we stand tall on the shoulders of giants. Thank you to all the laboratory animals who have been sacrificed for the sake of this work. Our progress towards understanding of physiology could not be achieved without this sacrifice. I would like to thank those who supported me and kept me alive these many years, all the doctors, nurses, coaches, family, and friends. Most of my inspiration in life stems from my parents. All the rocket launch videos and building model rockets drove my love for science and understanding and was fostered by my father’s love for space and aeronautics. My mother was the best teacher I could ever ask for. She taught me to be a disciplined, well-rounded person that takes life for what it is and make the most of it. Thank you for always being there for love and support. Throughout all my years, my sister Jo and my brother Aaron have always challenged me to be the best person I could be. My family has always helped keep me in check. I’m not sure how one can get through the PhD process without a strong support system like them. They always know how to make me laugh and help find the small light of positivity in the vast darkness of space. I would never have been here without their encouragement and support to bring me to the best of my ability. I would like to especially thank my mentors Lorin and Mirela Milescu. They shared with me their enthusiasm to understand ion channel biophysics. They stood by my side, always challenging me to think differently, explore new areas of science and always exposing me to new science and ideas. Your support through the years has kept me going steady, even when things get tough. They have taught me how to think things through and overall have made me a better person. I swear that I do not always, intentionally try to ignore you, all the time. Well… maybe I did a few times, but not on purpose, I promise. I would like to thank the other strong educators in my life, who taught me to challenge the norms and to learn to solve problems. Each classroom along the way taught me to learn and think ii critically, rather than simple memorization. I would like to particularly mention Patrice Whalen, Jane Johnston, and Cheryl Lenox. As my first science teachers, they filled the classroom with fun and excitement, always pushing their students to ask critical questions in order to build an understanding of life. I also have to thank Dr. Daniel Warren for supporting the start of my scientific career. Through his mentorship, he shared his excitement with physiology and challenged me to pursue a PhD. I also would like to thank Dr. David Schulz and Dr. Kevin Gillis for serving as strong mentors, who challenged me to perform at the best of my ability. I would also like to thank Dr. Andy McClellan, Dr. Troy Zars, Dr. Michael Garcia, Dr. Jeffrey C. Smith, Dr. Richard Defazio and Dr. Analisa Scememi for their help in and guidance whenever I needed it. I would never have been as productive as I have been without the generous support from my funding sources. I would like to particularly thank Dr. Mark Hannick, Dr. John David, and Debbie Allen as they made the transition to graduate school easy and their support throughout the years is priceless. I always thank them for the chance to travel and help give back to the community to recruit new students to Mizzou. I cherish many moments that would not be possible by the strong support and development of graduate students. This dissertation would also never have happened without the strong presence of science throughout American culture. I would especially like to thank the creators/producers of Cosmos, the Magic School Bus, Pinky and the Brain, Bill Nye the Science Guy, Out of the Box, and Zoboomafoo. These TV shows were the backbone of my childhood entertainment and they inspired me to achieve scientific discovery, embrace new technology and most importantly learn to experiment. I would also like to thank the creators and producers of Jeopardy, Trivial Pursuit, and the GameShowNetwork, as these entertainment trivia shows keep our minds fresh. Without many of these platforms, I would not have had the drive and passion for science as I do now. I would like to thank my colleagues and support team at Mizzou especially Autoosa Salari, PhD, who as a wonderful mentor that set the bar high each week to challenge my ability and make me a iii strong scientist. I would also like to thank the Milescu Lab team of undergraduates that helped drive the spirit of science on our projects, mainly Benton Berigan, Jaime Hibbard, Jenna Lin, Michael Miller and Tyler Nivin. I would also like to mention the other undergraduate students who have always been great lab members: Tyler Carron, Ben Vega M.D., Brooklyn White, Paige Martinez, Kaydee Harper, Ben Zars, Megan Saracino, Taylor ‘Gray’ Hallman, Connor Engel, Luke Cowan, and Hamza Iqbal. The following lists members of my Mizzou family that must be named at this time. Thank you all the fun moments we have experienced and I hope to make many more in the future: Jake Burkhart, Vince Baggett, Benton Berigan, Marzie Armishneva, Tim Pale, Ronnie LeCombe, Laura Arnold, Elle Cook, Cindy Kyi, Kawasi Lett, Brian Lane, Nathan Harness, Megan Murphy, Gideon Ney, Eric Villalon, Tom Anderson, Alice Tipton, Mitch Tucker, Maria Jones, Aditi Mishra, Carlos Rivera, Daniel Kick, Joe Santin, Michael Gray, Austin Lynn, and Hedieh Attai. For the countless times we took a moment to relax and enjoy what life brings to us, Cheers! I would also like to thank my other family of friends that were always willing to answer the phone and offer any guidance. Thank you for putting up with me and continuing to offer the valuable third-party advice that I often went to you for help. I would like to particularly mention all the members of the kik thread, Erin Carrol, Katie Montez, Maciej Gonek, and Ryan Paynok. I would also like to thank the support staff that was always there to help: Debbie Allen, Nila Emerich, Alan Marshall, Josh Hartley, Tyeece Little, Sadiya Aswad, and Waleed Atoud. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS ……………………………………....……………………...ii LIST OF FIGURES……………………………………………………………................xi Abstract……………………………………………………………………….................xiii Introduction………………………………………………………………………...…......1 Chapter 1 Modeling the kinetic mechanisms of voltage-gated ion channels…….......3 1.1. Introduction......................................................................................................4 1.2. Ion channel models………………………………………………..................6 1.2.1 Kinetic mechanisms………………………………………………...7 1.2.2 Markov formalism………………………………………………….9 1.2.3 Hodgkin-Huxley-type models……………………………………..11 1.3. Solving ion channel models…………………………………………...........12 1.4. Experimental aspects……………………………………………….............17 1.4.1 Voltage clamp protocol design……………………………………17 1.4.2 Limitations of the recording system………………………………19 1.4.3 Experimental artifacts……………………………………………..21 1.5. Fitting the data………………………………………...………....................25 1.5.1 Goodness of fit…………………………………………………….25 1.5.2 Computing the cost function………………………………………27 1.5.3 Model parameters………………………………………………….29 1.6. Dynamic clamp - testing models in live neurons…………………….....…..30 1.6.1 Solving the model in real-time…………………………………….31 1.6.2 Equipment and software …………………………………………..34 v 1.6.3 Preparing and running a dynamic clamp experiment……………..38 1.7. Conclusions…………………………………………………………………40 1.8. Figures and figure legends………………………………………………….41 Chapter 2. Estimating kinetic mechanisms with prior knowledge: linear and nonlinear parameter constraints……………………………………………………...47 2.1. Introduction...................................................................................................49 2.2. Materials and methods……...……………………………………………...52 2.2.1 Model parameters………………………………………………....52