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Continuum and Atomistic Modeling of Lipid Membranes

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Continuum and Atomistic Modeling of Lipid Membranes CONTINUUM AND ATOMISTIC MODELING OF LIPID MEMBRANES: BIOPHYSICS OF HAIR CELL MECHANOTRANSDUCTION A DISSERTATION SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERISTY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Jichul Kim December 2013 © 2013 by Jichul Kim. All Rights Reserved. Re-distributed by Stanford University under license with the author. This dissertation is online at: http://purl.stanford.edu/yn722bf7253 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Peter Pinsky, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Charles Steele, Co-Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Wei Cai Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost for Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii ABSTRACT A lipid bilayer membrane is not just a simple inert barrier of cells, but a dynamic structure which plays a crucial role in cell functioning. A force conveying role of the lipid membrane for mechanosensitive ion channels is now an accepted phenomenon across various mechanoreceptors. However, such a mechanism has not been established for mechanotransduction in the hair bundle of the auditory sensory hair cell. A major goal of this theoretical study is to investigate the role of the lipid membrane in the hair bundle mechanotransduction in the auditory system, especially in generating the nonlinear bundle force vs. displacement measurements – one of the main features of auditory mechanotransduction. To this end we developed a hair bundle model which reproduces the lipid membrane tented deformation in the stereocilia. To analyze the membrane deformation, the conventional Helfrich theory for the lipid membrane is modified and solved by a novel numerical method using Fourier series. Our hair bundle model, incorporating membrane elasticity with bundle rigid body kinematics and lipid flow components, reproduces nonlinear bundle force measurements and in so doing potentially elucidates aspects of hair cell transduction for which the physical basis has been elusive for three decades. The nonlinear force vs. displacement calculation of the tented membrane, the central goal of this analysis, is further supported by the nonlinear finite element (FE) formulation. This Galerkin finite element method uses the B-spline basis function and Newton’s method to solve the nonlinear equation system. By repeating the tenting problem with the finite element method, the consistency of the nonlinear force vs. displacement calculation compared to our previous approach is demonstrated. The validity of the continuum analysis is also investigated though atomistic modeling of the lipid membrane. The coarse-grained molecular dynamics (MD) simulation of the tented lipid membrane is performed. Time average of the applied force in the equilibrium generates similar nonlinearity with respect to our continuum analysis. iv The results of the MD simulation further support the potential role of the lipid membrane in generating nonlinear hair bundle mechanics. v ACKNOWLEDGEMENT It is an overwhelming moment as I think about the past years at Stanford. There are a great number of individuals to appreciate for supporting me, advising me and also for challenging me. I wish this brief writing can be somewhat my record of deep appreciation for them before a long discussion of my scientific work. First, I cannot thank enough to my adviser, Dr. Peter Pinsky. I am grateful for his generous aids and enthusiastic guidance during my doctoral study. Especially, he has been an adviser who gently and patiently motivated me to learn rather than got after to produce results. For example, since my former studies had been focused on totally different area, theoretical mechanics was somehow a closed book to me when I initiated doctoral study. However, Peter kindly guides me to learn various mechanics theory step by step so that I could develop strong theoretical foundation for the doctoral research. I have been fortunate to share my doctoral study with Dr. Peter Pinsky, a humorous British gentleman, a real researcher and educator, and who always tries to stand for students. Also I deeply thank to Dr. Charles Steele for his support and guidance. He has been a passionate adviser and researcher, who always motivated me to practice intellectual honesty. Working with Charles, an emeritus professor, has been beneficial in many ways by exposing me to a different style of advising. Especially, it has been quite handy to have a meeting with him by knocking his office whenever I have an issue to discuss. As a senior researcher, he was always willing to share his variety of experiences, expertise and insights not only with myself but also with many others in the group. Those have been invaluable in all the works I have accomplished during the doctoral study. Dr. Wei Cai also deserves my great thanks for valuable insights and guidance. Particularly, he has provided me a solid foundation for the atomistic and molecular dynamics study of my research. For this, interactions with him and people in his research group have been truly pleasurable, and their helps and comments over the years are much appreciated. My research was also encouraged by Dr. Anthony Ricci in the otolaryngology department, who supports my theoretical research in terms of real biology. Many discussions and debates with deep sincerity in meeting with him will be missed. vi Likewise, I am thankful for all of the kind concern and the support Dr. Sunil Puria has given for me over the years. I also appreciate Dr. Ellen Kuhl and Dr. Christine Linder for serving committee for my doctoral degree. My doctoral study might not be fun enough without help from many colleagues, senior students and friends who supported me intellectually and mentally. For learning a broad range of mechanics theories in a short time period, it was not possible without help from outstanding teaching assistances (TAs). For this reason, I appreciate Xi Cheng, Seunghwa Ryu, Sohan Dharmaraja, William Cash, Kai Zang and many other TAs for their helps in the courses that I took. I'd also like to thank my other friends in Mechanics and Computation division — Joris, Steven, Shinji, Peter, Ram, Heesun, Adrian, Doreen, Shelley, Maria and many others for the academic discussions, sharing enjoyments and the administrative supports. The presence of good friends has been a true mental support. It was a genuine blessing for sharing my life at Stanford with supportive friends including Caroline, Jungwan, Minkyu, Roy, Jang-hwan, Mi-hye, Sungmin, Jin, Kiwook, and member of Korean Mechanical Engineers (KME) at Stanford. Thanks for all of help in various occasions. I shall affectionately think back how much these people have meant to me and how much precious support and encouragement I have received. Finally, I would like to express the deepest gratitude to my parents Dalsung Kim and Kungsuk Kang. Their unconditional devotion, support and love throughout my life has raised me up, and been the basis of my mental strength. It seems even not possible but I would dearly wish to pay back even an infinitesimal part of their endless grace in the future. My younger sister Kyungmi Kim also deserves my appreciation. She always emits positive energy which makes me happy whenever I chat with her. Her encouragements have been also a great support. Graduate study at Stanford further awakens my intellectual curiosity. I have also realized that I owe many things to people around me. Though I am closing the doctoral study, this is not the end of my academic journey. It is another beginning, and excitingly I expect that many people acknowledged will continue characters in this adventure. Throughout my doctoral study, I believe I have better grown up intellectually and mentally. I shall cherish this valuable experience for a long time. vii TABLE OF CONTENTS 1. Introduction…………………………….…………………………...………...…...……1 1.1 Computational mechanics in predictive life sciences ……….....…..…1 1.2 Background and objective…………………………….…….…………3 1.2.1 Hair cells mechanotransduction……….....……...……....……3 1.2.2 Lipid bilayer membranes ……..………...…...….……....……7 1.3 Scope of the dissertation ……………..…………....………………….8 2. Theory for continuum lipid membranes………………………….…………...………10 2.1 Modification Helfrich theory………............…….………..…………10 2.2 Boundary value problem: point stimuli on lipid membranes..……….18 2.2.1 Formulation……………………….…….....…...……....……19 2.2.2 Numerical method .……………..…...….....…...……....……20 2.2.3 Force vs. displacement responses…..…….………….…....…23 3. Biophysical modeling of hair cell mechanotransduction………...…………..………..27 3.1 Main idea and assumption………………...……………...………….28 3.2. Multi-physical hair bundle model ……………......………...………31 3.2.1 Modeling kinematics of hair bundles …….….......…………31 3.2.2 Modeling lipid membranes tenting ………….......…………34 3.2.3 Modeling lipid transport ………….......……………………35 3.2.4
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