Computational Parameter Selection and Simulation of Complex Sphingolipid Pathway Metabolism A Thesis Presented to The Academic Faculty by Peter A. Henning In Partial Fulfillment of the Requirements for the Degree Master of Science in Biomedical Engineering Department of Biomedical Engineering Georgia Institute of Technology August 2006 Copyright c 2006 by Peter A. Henning To my family, Dale, Christine, and Sara, I couldn’t have made it through these trying times without you. iii ACKNOWLEDGEMENTS I would like to acknowledge Gautam Goel and Eberhard Voit for their useful insights into past, present, and future of Systems Biology. I would like to thank Dr. Al Merrill and his group for not only providing the sphingolipid experimental data but also for providing expertise in both sphingolipids and mass spectometry. I’d like to thank my fellow researchers Jin Young Hong, John Phan, Pushkar Mukewar, David Stiles, and Paul Tan for answering my at times ridiculous questions on software and various other topics. I would like to also thank my fellow BME classmates for making the semesters fulfilling requirements not only tolerable but at times fun. I’d like to extend my gratitude to Bob Lee and Maggie Cam for their insight into what changes were necessary to make myself a successful researcher and inspiring me to take possession of my graduate degree. I would like to extend my thanks to the BME Department, Georgia Tech, Emory, and NIDDK for this opportunity to be part of cutting edge research. Last but certainly not least, I am grateful for the support from all of my friends. iv TABLE OF CONTENTS DEDICATION ...................................... iii ACKNOWLEDGEMENTS .............................. iv LIST OF TABLES ................................... ix LIST OF FIGURES .................................. xi SUMMARY ........................................ xv I INTRODUCTION ................................. 1 1.1 Systems Biology Background and Previous Work . 1 1.1.1 Why the time for Systems Biology is Now? . 1 1.1.2 Previous Studies in Systems Biology . 3 1.2 Sphingolipid Basics . 5 1.3 Mathematical Models of Enzymatic Reactions . 8 1.3.1 Zero Order Kinetics . 8 1.3.2 Mass Action Kinetics . 9 1.3.3 Reversible Mass Action Kinetics . 9 1.3.4 Michaelis-Menten Kinetics . 10 1.3.5 Reversible Michaelis-Menten Kinetics . 11 1.3.6 The Kinetic UniUni Mechanism . 11 1.3.7 Generalized Mass Action (GMA) Kinetics . 12 1.3.8 Reversible Generalized Mass Action Kinetics . 13 1.3.9 Reversible Generalized Mass Action Kinetics . 14 1.4 Optimization Method Background . 14 1.4.1 Monte Carlo Methods . 14 1.4.2 Nonlinear Least Squares using the Gauss-Newton Method . 15 1.4.3 Nonlinear Least Squares using the Marquardt-Levenberg Method . 17 1.4.4 Nelder-Mead Simplex Method for Function Minimization . 19 1.4.5 Simulated Annealing . 21 1.4.6 Genetic Algorithm . 23 v II CONSTRUCTION OF A MODELING FRAMEWORK ......... 26 2.1 General Algorithm Design Phase 1 . 26 2.1.1 Building Nonlinear Rate Functions . 26 2.1.2 Cost Function . 30 2.1.3 Results and Discussion . 31 2.1.4 Critique and Conclusions . 41 2.2 General Algorithm Design Phase 2 . 41 2.2.1 Building the Nonlinear Rate Function . 42 2.2.2 Integrator Module . 44 2.2.3 Cost Function . 45 2.2.4 Critique and Conclusions . 46 2.3 General Algorithm Design Phase 3 . 47 2.3.1 Enzymatic Rate Equation . 47 2.3.2 ODE Constructor . 49 2.3.3 Integrator . 50 2.3.4 Cost Function . 50 2.3.5 Results and Discussion . 50 2.3.6 Critique and Conclusions . 53 III VALIDATION OF THE MODELING FRAMEWORK WITH SIMU- LATED DATA ................................... 54 3.1 Methods . 54 3.1.1 Simulated System Design . 54 3.1.2 Monte Carlo Implementation . 55 3.1.3 Simulated Annealing Implementation . 55 3.1.4 Genetic Algorithm Implementation . 56 3.2 Results and Discussion . 56 IV COMPARISON OF NUMERICAL INTEGRATION METHODS FOR USE IN SYSTEMS BIOLOGY ......................... 64 4.1 Abstract . 64 4.2 Background . 65 4.3 Methods . 67 vi 4.4 Results . 68 4.4.1 Test Problem 1: The Oregonator Model . 68 4.4.2 Test Problem 2: High Irradiance Response Model (HIRES) . 68 4.4.3 Test Problem 3: Transient Molecular Flow through a Tube (CLAUS) 70 4.4.4 Test Problem 4: Nerve Excitation Model of Hodgkin and Huxley (HODGK) . 70 4.4.5 Test Problem 5: Aerobic Oxidation of NADH in Horseradish (PO) 71 4.4.6 Test Problem 6: Physiologically Based Pharmacokinetics Model (PBPK) 72 4.4.7 Test Problem 7: HER2-mediated Endocytosis Model (HER2) . 73 4.4.8 Test Problem 8: Yeast Sphingolipid Metabolism Model (SPHINGO) 74 4.5 Discussion . 75 4.6 Conclusion . 78 V A HIGH PERFORMANCE COMPUTING SOLUTION TO PARAME- TER ESTIMATION IN METABOLIC NETWORKS ........... 80 5.1 Abstract . 80 5.2 Background . 81 5.3 Methods . 82 5.3.1 Integration Method . 82 5.3.2 Monte Carlo . 82 5.3.3 Genetic Algorithm . 83 5.4 Results and Discussion . 84 5.4.1 Integrator Performance . 84 5.4.2 Monte Carlo Trials . 92 5.4.3 Genetic Algorithm Trials . 93 5.5 Conclusion . 94 APPENDIX A — MATLAB CODES USED IN MODELING FRAME- WORK ........................................ 97 APPENDIX B — INTEGRATOR TEST PROBLEMS IN MATLAB . 114 APPENDIX C — HIGH PERFOMANCE COMPUTING MONTE CARLO C SOURCE ..................................... 127 APPENDIX D — HIGH PERFORMANCE COMPUTING GENETIC ALGORITHM C SOURCE ........................... 208 vii REFERENCES ..................................... 220 viii LIST OF TABLES 1 True Kinetic Parameters from Simulated System (TRUE) and Best Fit Pa- rameters for 2 Monte Carlo Trials (MC1 and MC2), 2 Simulated Annealing Trials (SA1 and SA2), and a Genetic Algorithm trial (GA). 62 2 OREGO Results: The Oregonator test problem was simulated from time zero to time 316 seconds. The time column represents the execution time in microseconds. The error column is the percent error of the intergrators result when y(1) reaches the initial condition of 4.0 a second time. The best value for this time is 302.85805 as reported in [30]. 69 3 HIRES Results: The HIRES test problem was simulated from time zero to time 400 seconds. The time column represents the execution time in microseconds. The error column is the percent error of the intergrators result when y(7) reaches the same value of y(8), which is 0.00285. The best value for this time is 321.8122 as reported in [30]. 69 4 CLAUS Results: The CLAUS test problem was simulated from time zero to time 40 seconds. The time column represents the execution time in microsec- onds. The error column is the percent error of the intergrators result when y(10) reaches 90% of its steady state value. The best value for this time is 36.7234 as reported in [30]. 70 5 HODGK Results: The HODGK test problem was simulated from time zero to time 20 seconds. The time column represents the execution time in mi- croseconds. The error column is the percent error of the intergrators result when y(4) reaches zero. The best value for this time is 8.17888 as reported in [30]. 71 6 PO Results: The PO test problem was simulated from time zero to time 200 seconds. The time column represents the execution time in microseconds. The error column is the percent error of the intergrators result when y(1), oxygen, reaches 95% of its steady state value. The best value for this time is 82.4159 as determined by high accuracy numerical solution. 72 7 PBPK Results: The PBPK test problem was simulated from time zero to time 40 minutes. The time column represents the execution time in microsec- onds. The error column is the percent error of the integrators result when y(3), liver concentration, reaches a level corresponding to 70% of the peak concentration. The best value for this time is 32.6682 as determined by high accuracy numerical solution. 73 8 HER2 Results: The HER2 test problem was simulated from time zero to time 20 minutes. The time column represents the execution time in microseconds. The error column is the percent error of the integrators result when y(15), intracellular ligand concentration, first reaches 4.75 nM. The best value for this time is 7.7620 as determined by high accuracy numerical solution. 74 ix 9 SPHINGO Results: The SPHINGO test problem was simulated from time zero to time 50 minutes. The time column represents the execution time in microseconds. The error column is the percent error of the integrators result when y(25), acetyl-CoA concentration, first reaches 1300 mM. The best value for this time is 48.6294 minutes as determined by high accuracy numerical solution. 75 x LIST OF FIGURES 1 Sphingolipid Structure: All sphingolipids contain the following three ba- sic components: one molecule of the long-chain amino alcohol sphingosine (shown in pink), one molecule of long chain fatty acid (shown in yellow) and some version of a polar head group (shown in the blue section). 6 2 Sphingolipid Pathway Map: The sphingolipid de novo synthesis pathway is presented in the above figure [61]. 7 3 High Level Algorithm Design Phase 1: The relationship between the three primary components of the design are shown as well as the information that is passed between each of them. 27 4 Six Node Sphingolipid Metabolism System considered in Phase 1: The chem- ical names in the model are given for each of the metabolites. The modelled metabolic network is composed of six dependent variables. Each of the five reversible fluxes are placed on the map as numbered arrows. 28 5 Linear Regression Fitting Results Phase 1: The blue solid lines represent the time derivative taken from actual data measurements.