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Reaction-Diffusion Processes in Muscle Metabolism Parametric and Sensitivity Analysis Santosh Kumar Dasika

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Reaction-Diffusion Processes in Muscle Metabolism Parametric and Sensitivity Analysis Santosh Kumar Dasika Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2010 Reaction-Diffusion Processes in Muscle Metabolism Parametric and Sensitivity Analysis Santosh Kumar Dasika Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ENGINEERING REACTION-DIFFUSION PROCESSES IN MUSCLE METABOLISM - PARAMETRIC AND SENSITIVITY ANALYSIS By SANTOSH KUMAR DASIKA A Dissertation submitted to the Department of Chemical and Biomedical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Fall Semester, 2010 Copyright © 2010 Santosh Kumar Dasika All rights reserved. The members of the committee approve the dissertation of Santosh K. Dasika defended on 20th Oct 2010. _______________________________________ Dr. Bruce R. Locke Professor Directing Dissertation _______________________________________ Dr. Bryant Chase University Representative _______________________________________ Dr. Stephen T. Kinsey Committee Member _______________________________________ Dr. Teng Ma Committee Member _______________________________________ Dr. Samuel C. Grant Committee Member Approved: _____________________________________ Bruce R. Locke, Chair, Department of Chemical and Biomedical Engineering _____________________________________ Ching-Jen Chen, Dean, Dean, College of Engineering The Graduate School has verified and approved the above-named committee members. ii Dedicated to Guruji iii ACKNOWLEDGEMENTS I am grateful to have this opportunity to acknowledge all those who have assisted, guided and supported me in my studies leading to this thesis. Firstly, I am grateful to Dr. Bruce Locke for giving me this wonderful opportunity to work on this project and for his constant guidance, support and motivation throughout the contribution of my research work. I would also like to thank Dr. Stephen Kinsey for his valuable comments and insights into the biological aspects of the project. I would also express my sincere thanks to Dr. Bryant Chase, Dr. Teng Ma and Dr. Samuel Grant for serving as the committee members. I would like to thank Dr. Sachin Shanbhag , School of Computational Science, Florida State University, for his valuable help in Monte Carlo simulations, Dr. Mark Sussman, Dept. of Mathematics, Florida State University, for his help in solving the reaction diffusion equations using Finite Difference scheme. Dr. Milen Kostov, Dept. of Chemical and Biomedical Engineering, Florida State University, for sponsoring a general account at the High Performance Computing, Florida State University, and Mr. Dan Voss of High Performance Computing, Florida State University for his support in executing jobs at the HPC clusters. I would also like to thank National Science Foundation grant for financial support. Last, but not the least, I would like to thank my family and friends, specially my mom Ms. Vijaya Lakshmi, dad Mr. Prabhakar Rao, sister and brother in law, and my dearest friend Jaswanth, for their constant support and encouragement throughout my PhD. I would like to take this opportunity to thank my Guruji (whom I consider the almighty) for his blessings. iv TABLE OF CONTENTS LIST OF FIGURES……………………………………………………………………………. viii LIST OF TABLES…………………………………………………………………………….. xiii ABSTRACT…………………………………………………………………………………… xiv Chapter 1 INTRODUCTION ...................................................................................................... 1 1.1 Introduction ...................................................................................................................... 1 1.2. Description of muscle .......................................................................................................... 2 1.3. Muscle physiology ............................................................................................................... 4 1.3.1. Mitochondrial distribution ............................................................................................ 6 1.3.2. Cell mitochondrial distribution during growth ............................................................. 9 1.4. Objective ............................................................................................................................ 10 1.5. Organization of the text ..................................................................................................... 11 Chapter 2 LITERATURE REVIEW ........................................................................................ 12 2.1 Introduction ......................................................................................................................... 12 2.2. Saks group ...................................................................................................................... 13 2.3. Kinsey and Locke‟s group ................................................................................................. 18 2.4. Modeling O2 transport........................................................................................................ 21 Chapter 3 EFFECTS OF VARIOUS PARAMETERS ON INTRA-CELLULAR DIFFUSION LIMITATION OF METABOLITES ................................................................. 24 v 3.1. Introduction ........................................................................................................................ 24 3.2. Mathematical methods ....................................................................................................... 27 3.2.1. Mitochondrial rate law ................................................................................................ 28 3.2.1.1. Rate law for mitochondrial oxidative phosphorylation ........................................... 28 3.2.1.2. Reaction diffusion model ......................................................................................... 29 3.2.1.3. Volume averaging .................................................................................................... 32 3.2.1.3.1. Boundary conditions ............................................................................................. 37 3.2.1.4. Effectiveness factor .................................................................................................. 38 3.3. Solution technique ............................................................................................................. 40 3.4. Results ................................................................................................................................ 43 3.4.1. Mitochondrial rate law ................................................................................................ 43 3.4.2. Concentration Profiles and Effectiveness Factors ...................................................... 46 3.4.2.1. Effects of Km,ATPase and Boundary O2 concentration ............................................... 51 3.5. Discussion .......................................................................................................................... 53 3.5.1. Numerical issues ......................................................................................................... 53 3.5.2. Hill coefficient ............................................................................................................ 56 3.5.3. Comparison of model with experimental data ............................................................ 57 3.6. Conclusions ........................................................................................................................ 59 Chapter 4 EFFECTS OF MB AND CK ON INTRA-CELLULAR METABOLITE DIFFUSION LIMITATION ...................................................................................................... 62 vi 4.1. Introduction .................................................................................................................... 62 4.2. Modeling methods and formulation ............................................................................... 67 4.3. Computational Results and Discussion .......................................................................... 69 4.3.1. Experimental data comparison ................................................................................ 69 4.3.2. Effect of mitochondrial volume fraction and boundary O2 concentration .............. 77 4.4. Conclusions ........................................................................................................................ 80 Chapter 5 SENSITIVITY ANALYSIS ..................................................................................... 82 5.1. Introduction ........................................................................................................................ 82 5.2. Mathematical methods ....................................................................................................... 85 5.3. Results and discussion ....................................................................................................... 88 Chapter 6 : CONCLUSIONS AND FUTURE WORK ......................................................... 102 6.1. Conclusions ...................................................................................................................... 102 6.2. Future work ...................................................................................................................... 103 A. ATP flux vs. O2 for [Pi] = 5 mM ..........................................................................................
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