A Kinetic Model for G protein-coupled Signal Transduction in Macrophage Cells Patrick Joseph Flaherty Electrical Engineering and Computer Sciences University of California at Berkeley Technical Report No. UCB/EECS-2007-4 http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-4.html January 6, 2007 Copyright © 2007, by the author(s). All rights reserved. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission. A Kinetic Model for G protein-coupled Signal Transduction in Macrophage Cells by Patrick Joseph Flaherty B.S. (Rochester Institute of Technology) 2000 M.S. (University of California at Berkeley) 2003 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering-Electrical Engineering and Computer Sciences and the Designated Emphasis in Communication, Computation, and Statistics and Computational Biology in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA, BERKELEY Committee in charge: Professor Michael I. Jordan, Chair Professor Adam P. Arkin Professor Richard M. Karp Fall 2006 The dissertation of Patrick Joseph Flaherty is approved: Chair Date Date Date University of California, Berkeley Fall 2006 A Kinetic Model for G protein-coupled Signal Transduction in Macrophage Cells Copyright 2006 by Patrick Joseph Flaherty 1 Abstract A Kinetic Model for G protein-coupled Signal Transduction in Macrophage Cells by Patrick Joseph Flaherty Doctor of Philosophy in Engineering-Electrical Engineering and Computer Sciences and the Designated Emphasis in Communication, Computation, and Statistics and Computational Biology University of California, Berkeley Professor Michael I. Jordan, Chair Macrophage cells that are stimulated by two different ligands which bind to G protein- coupled receptors (GPCRs) usually respond as if the stimulus effects are additive, but for a minority of ligand combinations the response is synergistic. The G protein-coupled receptor system integrates multiple, perhaps conflicting, signaling cues from the environment in order to actuate cell morphology, gene expression, ion homeostasis and other physiological states. We study, in detail, the effects of the two signaling molecules complement factor 5a (C5a) and uridine diphosphate (UDP) on the intracellular second messenger calcium to elucidate 2 principals that govern the mechanism of G protein-coupled signal transduction. We have developed a formal hypothesis, in the form of a kinetic model, for the mechanism of action of this GPCR signal transduction system using data obtained from RAW264.7 macrophage cells. Bayesian statistical methods are employed to formally approach uncertainty and tie the model to experimental data. The model is entertained as a tool in the design of investigative experiments. The model accurately predicts a synergistic region in the calcium peak height dose response that results when cells are simultaneous stimulated by C5a and UDP. Though this model is not a complete representation of the G protein-coupled signal transduction system and contains many approximations, it is consistent with our experimental observations and is a useful substrate for further experimentation. Finally, we address the problem of the design of robust experiments for the G protein-coupled signal transduction model. Classical optimal experiment design methods have not been widely adopted in practice for biological systems, in part because the resulting designs can be very brittle if the nominal parameter estimates for the model are poor, and in part because of computational constraints. We present a method for robust experiment design based on a semidefinite programming relaxation. We present an application of this method to the design of experiments for a complex calcium signal transduction pathway, where we have found that the parameter estimates obtained from the robust design are better than those obtained from an “optimal” design. Professor Michael I. Jordan Dissertation Committee Chair i To my family. ii Acknowledgments Many people have volunteered their aid through my work on projects in graduate school and deserve recognition for their selfless help. Though research involving a combination of statistics, engineering and biology is now common, my advisors Michael Jordan and Adam Arkin took a great risk years ago to mentor such research and should be recognized. They have guided, tutored, questioned, challenged and cheered me throughout my time in graduate school and their direction has helped me find my own place in the academic world. The students in the Jordan group were a constant source of learning. I have Alice Zheng to thank for telling me about the Jordan group and encouraging me to attend the group meetings. Dave Blei spent hours teaching me the details of his research so that I would be able to use it for my own. Guri Giaever believed in me and used my research before I might have even used it myself. Guri’s faith helped me to believe that my work can be useful and must meet the highest standards. My work with the Alliance for Cellular Signaling began with a short meeting with Mel Simon. Even since I have looked to Mel for guidance and advise in all of my work. He’s the most insightful, idealistic and kind scientist I have known. I first joined the Arkin lab after meeting with Denise Wolf and thank her for her inspiration and infectious, but playful thirst for knowledge. Tim Ham and Robin Osterhout were there even after hours of studying for prelim exams in room 214. Matt Onsum intro- duced me to the project of this thesis and deserves much of the credit for making the first, but most important steps that I followed. Leor Weinberger taught many of us in the Arkin lab the real meaning of doing good science and that success comes only after hard work. iii Even as an undergraduate student Richie Koche showed his potential as a great scientist. He knew when to work late and when to drag me out of lab for a break after a full day. I first met Shilpa Shroff in the Arkin Lab when I needed a place to live. Shilpa offered her apartment and years later I’ve found a best friend. Finally and most importantly, my family has always supported me with phone calls, cookies, trips home to the farm and constant reminders of the truly important things in life. iv Contents List of Figures vi List of Tables viii 1 Introduction 1 2 G protein-coupled Receptor Signal Transduction Model 6 2.1 ModelStructure ................................. 9 2.1.1 Background................................ 10 2.1.2 Overview ................................. 12 2.2 ReceptorReactions............................... 14 2.2.1 P2YReceptor............................... 15 2.2.2 C5aReceptor............................... 16 2.3 GProteinReactions ............................... 16 2.3.1 Gαi Activation .............................. 18 2.3.2 Gαq Activation.............................. 19 2.4 Phosphoinositide Cascade Reactions . ...... 19 2.4.1 IP3 synthesis by Gαq activated PLCβ3 ................ 23 2.4.2 IP3 synthesis by Gβγ activated PLCβ3 ................ 24 2.4.3 IP3 synthesis by Gαq activated PLCβ4 ................ 25 2.5 IP3ReceptorReactions . .. .. .. .. .. .. .. .. 26 2.5.1 ATPase Pumps and Na2+/Ca2+ Exchangers.. .. .. .. 30 2.5.2 CalciumBuffers ............................. 32 2.6 FeedbackReactions............................... 34 2.6.1 ProteinKinaseC............................. 35 2.6.2 Calcium and DAG are required for PKC activation . 36 2.6.3 GproteinReceptorKinase . 38 2.6.4 Gβγ and PKC are required for GRK activation . 40 2.6.5 RGS is a GAP for Gαq-GTP and Gαi-GTP.............. 41 2.7 Dephosphorylation and Degradation Reactions . ........ 41 2.7.1 C5aR and PLCβ3/4dephosphorylation . 42 2.7.2 DAG degradation and PIP2 synthesis . 42 CONTENTS v 3 Model and Data Analysis 44 3.1 ExperimentalProtocol . 45 3.2 SimulationMethod................................ 46 3.3 InputModel.................................... 46 3.4 Wild-typeData.................................. 48 3.5 KnockdownData................................. 49 3.5.1 GRK2Knockdown ............................ 50 3.5.2 Gαi Knockdown ............................. 51 3.5.3 Gαq Knockdown ............................. 52 3.5.4 PLCβ3Knockdown ........................... 52 3.5.5 PLCβ4Knockdown ........................... 53 3.6 Toxins....................................... 53 3.7 Synergistic Interaction between C5a and UDP . ....... 56 3.7.1 CrosstalkMechanism........................... 59 4 Statistical Inference 62 4.1 BayesianInference ............................... 63 4.1.1 Parameter Confidence Intervals . 64 4.1.2 Prediction Confidence Intervals . 66 4.2 MarkovChainMonteCarlo . 68 4.2.1 Gauss-HermiteQuadrature . 68 4.2.2 LaplaceApproximation . .. .. .. .. .. .. .. 69 4.2.3 Markov Chain Monte Carlo . 70 4.3 PosteriorDensityAnalysis. 72 5 Experiment Design 76 5.1 Locally Optimal Experiment Design . 79 5.2 RobustExperimentDesign . 80 5.3 Application to G protein-coupled Receptor Model . ......... 83 5.3.1 Michaelis-Menten Reaction Model . 83 5.3.2 Calcium Signal Transduction Model . 85 5.4 Discussion..................................... 88 6 Conclusion 90 A Model Implementation 106 A.1 ModelEquations ................................. 106