ADVANCES IN RULE-BASED MODELING: COMPARTMENTS, ENERGY, AND HYBRID SIMULATION, WITH APPLICATION TO SEPSIS AND CELL SIGNALING by Justin S. Hogg B. S. Mathematics, University of Pittsburgh, 2004 Submitted to the Graduate Faculty of the School of Medicine in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2013 UNIVERSITY OF PITTSBURGH SCHOOL OF MEDICINE This dissertation was presented by Justin S. Hogg It was defended on June 27th 2013 and approved by Dr. James R. Faeder, Computational and Systems Biology Dr. Gilles Clermont, Critical Care Medicine Dr. Zoltan Oltvai, Pathology Dr. Robert S. Parker, Chemical and Petroleum Engineering Dr. Christopher J. Langmead, School of Computer Science, Carnegie Mellon University Dissertation Director: Dr. James R. Faeder, Computational and Systems Biology ii ADVANCES IN RULE-BASED MODELING: COMPARTMENTS, ENERGY, AND HYBRID SIMULATION, WITH APPLICATION TO SEPSIS AND CELL SIGNALING Justin S. Hogg, PhD University of Pittsburgh, 2013 Biological systems are commonly modeled as reaction networks, which describe the system at the resolution of biochemical species. Cellular systems, however, are governed by events at a finer scale: local interactions among macromolecular domains. The multi-domain structure of macromolecules, combined with the local nature of interactions, can lead to a combina- torial explosion that pushes reaction network methods to their limits. As an alternative, rule-based models (RBMs) describe the domain-based structure and local interactions found in biological systems. Molecular complexes are represented by graphs: functional domains as vertices, macromolecules as groupings of vertices, and molecular bonding as edges. Reaction rules, which describe classes of reactions, govern local modifications to molecular graphs, such as binding, post-translational modification, and degradation. RBMs can be trans- formed to equivalent reaction networks and simulated by differential or stochastic methods, or simulated directly with a network-free approach that avoids the problem of combinatorial complexity. Although RBMs and network-free methods resolve many problems in systems modeling, challenges remain. I address three challenges here: (i) managing model complexity due to cooperative interactions, (ii) representing biochemical systems in the compartmental setting of cells and organisms, and (iii) reducing the memory burden of large-scale network-free sim- ulations. First, I present a general theory of energy-based modeling within the BioNetGen framework. Free energy is computed under a pattern-based formalism, and contextual vari- iii ations within reaction classes are enumerated automatically. Next, I extend the BioNetGen language to permit description of compartmentalized biochemical systems, with treatment of volumes, surfaces and transport. Finally, a hybrid particle/population method is developed to reduce memory requirements of network-free simulations. All methods are implemented and available as part of BioNetGen. The remainder of this work presents an application to sepsis and inflammation. A multi-organ model of peritoneal infection and systemic inflammation is constructed and calibrated to experiment. Extra-corporeal blood purification, a potential treatment for sep- sis, is explored in silico. Model simulations demonstrate that removal of blood cytokines and chemokines is a sufficient mechanism for improved survival in sepsis. However, differences between model predictions and the latest experimental data suggest directions for further exploration. Keywords: rule-based modeling, biochemical kinetics, cell signaling, sepsis, inflammation, hemoadsorption. iv TABLE OF CONTENTS 1.0 RULE-BASED MODELING OF BIOCHEMICAL SYSTEMS .....1 1.1 SYSTEMS BIOLOGY.............................1 1.2 REACTION NETWORK MODELING...................3 1.2.1 Mass-action kinetics..........................4 1.2.2 Non-elementary kinetics........................6 1.2.3 Formal description of reaction networks...............6 1.2.4 Simulation as a discrete stochastic system..............7 1.2.4.1 Gillespie's Stochastic Simulation Algorithm (SSA)....7 1.2.4.2 Accelerated simulation methods..............9 1.2.5 Simulation as a continuous system.................. 10 1.3 COMBINATORIAL COMPLEXITY..................... 11 1.4 RULE-BASED MODELING......................... 13 1.4.1 Network generation.......................... 14 1.4.2 Network-free Simulation....................... 15 1.4.3 BioNetGen: a rule-based modeling platform............. 19 1.4.4 Macromolecules as structured objects................ 20 1.4.5 Molecular complexes as graphs.................... 20 1.4.6 Molecular motifs as subgraphs.................... 21 1.4.7 Biochemical reaction rules as graph transformations........ 22 1.4.8 Anatomy of a BNGL model file................... 23 1.4.9 A Survey of Rule-based Languages and software.......... 24 1.5 THE LIMITS OF RULE-BASED MODELING............... 25 v 1.5.1 Biochemistry is compartmentalized, RBM 1.0 is not........ 25 1.5.2 The curse of cooperativity...................... 26 1.5.3 Network-free simulation of large systems is expensive....... 27 1.5.4 Other limitations not addressed in this dissertation........ 27 2.0 MODELING ENERGY: A PATTERN-BASED APPROACH ...... 29 2.1 MOTIVATION FOR ENERGY-BASED MODELING........... 29 2.1.1 Contextual complexity: hemoglobin example............ 31 2.2 FREE ENERGY PRINCIPLES FOR BIOCHEMICAL SYSTEMS.... 33 2.2.1 Energy................................. 34 2.2.2 Entropy................................ 35 2.2.3 Free energy............................... 37 2.2.3.1 Free energy example: isomerization............ 38 2.2.3.2 Difference in free energy is all that matters........ 38 2.2.3.3 Free energy of formation.................. 39 2.2.4 Gibbs free energy........................... 40 2.2.4.1 Reaction equilibrium.................... 41 2.2.4.2 Detailed balance....................... 42 2.2.4.3 Detailed balance in the hemoglobin model......... 44 2.2.4.4 Elementary kinetics and its connection to detailed balance 44 2.2.4.5 Methods for satisfying detailed balance.......... 46 2.3 MOTIVATING EXAMPLE.......................... 47 2.4 THE THEORY OF ENERGY-BASED MODELING............ 48 2.4.1 Free energy accounting: a pattern-based approach......... 49 2.4.1.1 Computing species free energy............... 49 2.4.1.2 Computing change in free energy due to reaction..... 52 2.4.1.3 Free energy is conserved around loops in the reaction network 53 2.4.2 Energy-based kinetics......................... 54 2.4.2.1 The limits of linear transition state theory........ 56 2.4.3 Non-equilibrium reactions: adding free energy to the system... 59 2.4.4 Ring closure.............................. 62 vi 2.4.5 Comparison to ANC......................... 65 2.5 CONSTRUCTING ENERGY-BASED MODELS WITH BIONETGEN. 66 2.5.1 Block structure............................ 66 2.5.2 Preliminaries.............................. 67 2.5.3 Model parameters........................... 67 2.5.4 Compartments............................. 67 2.5.5 Molecule types and seed species................... 69 2.5.6 Model outputs: observables...................... 71 2.5.7 Energy patterns............................ 71 2.5.8 Reaction rules............................. 72 2.5.8.1 Catalytic enhancement via functional activation energy. 73 2.5.9 Energy parameters.......................... 74 2.5.10 Simulating energy-based models................... 75 2.6 MODEL SELECTION AND CALIBRATION WITH THE ENERGY LASSO 75 2.6.1 Selecting energy patterns....................... 76 2.6.2 The energy lasso method....................... 78 3.0 MODELING COMPARTMENTAL BIOCHEMICAL SYSTEMS .... 81 3.1 INTRODUCTION............................... 81 3.2 A COMPARTMENTAL MODEL OF THE CELL............. 83 3.3 REPRESENTING COMPARTMENTS IN PLAIN BNGL......... 85 3.4 COMPARTMENTAL BNGL......................... 87 3.4.1 Units.................................. 88 3.4.2 Compartment topology........................ 88 3.4.3 Molecule location........................... 89 3.4.4 Species location............................ 89 3.4.5 Reaction rules............................. 91 3.4.5.1 Universal reaction rules................... 91 3.4.5.2 Scope-restricted rules.................... 93 3.4.5.3 Transport rules....................... 95 3.4.6 Comparison with BNGL....................... 97 vii 3.5 DISCUSSION................................. 98 3.5.1 Related work.............................. 99 3.5.2 Limitations............................... 102 4.0 HYBRID PARTICLE/POPULATION SIMULATION METHOD ... 103 4.1 INTRODUCTION............................... 104 4.1.1 Rule-based modeling......................... 104 4.1.2 Computational complexity...................... 105 4.1.3 Combining network-based and network-free approaches...... 108 4.2 METHODS................................... 108 4.2.1 Example models............................ 108 4.2.1.1 Trivalent-ligand bivalent-receptor............. 109 4.2.1.2 Actin polymerization.................... 110 4.2.1.3 FcRI signaling....................... 110 4.2.1.4 EGFR signaling....................... 111 4.2.2 Performance metrics.......................... 112 4.2.2.1 Peak memory........................ 112 4.2.2.2 CPU run time........................ 112 4.2.2.3 Accuracy........................... 112 4.2.3 Software implementation....................... 113 4.3 RESULTS................................... 113 4.3.1 A hybrid particle/population simulation approach......... 113 4.3.1.1 Population species