Computational Modeling and Validation of Biopathways Koh Yeow Nam, - PDF document

Computational Modeling and Validation of Biopathways Koh Yeow Nam, Geoffrey A dissertation proposal for the degree of Doctor of Philosophy 24th November 2005 NUS Graduate School for Integrative Sciences and Engineering National University of Singapore

ABSTRACT The proposed research centers on the development of a hybrid modeling framework for the representation, simulation and validation of biopathways. It aims to provide not only the functional view of the cell components but also their dynamics. Most studies on cell functions focus only on either signaling pathways, gene regulatory networks or metabolic pathways. The distinguishing feature of this work will then be to allow these different types of pathways to communicate with one another so that they can function as a whole. Our approach will encompass modeling, data interpretation, parameter estimation and model validation. In the modeling of biopathways, we will not restrict ourselves to a single type of representation. Instead, a combination of different computational models may be used, depending on the type of pathway that is to be modeled. Apart from developing the modeling and simulation framework, proper metrics and validation techniques will also be used to assert the correctness of the models. The developed techniques will then be tested for feasibility using examples from biological experiments. As part of our preliminary studies, we model two well-studied pathways - the Wnt and the Akt signaling pathways. Using these two pathways, we will identify the key issues that arise and our strategy for addressing them.

CONTENTS Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2. Background - Concepts in Biology 2.1 The Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 The Central Dogma . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Transcription and Translation . . . . . . . . . . . . . . . . . . . . . . 6 2.1.3 Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Biological Pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Metabolic Pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Signaling Pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.3 Gene Regulatory Network . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3. A Review of Current Techniques 3.1 Quantitative or Qualitative Modeling? . . . . . . . . . . . . . . . . . . . . . 12 3.2 Kinetic Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2.1 Michaelis-Menten Kinetics . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2.2 Canonical Modeling and S-Systems . . . . . . . . . . . . . . . . . . . 15 3.3 Petri Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4 Hybrid Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.5 Process Calculi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.6 XS-System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.7 Piecewise-affine differential equations . . . . . . . . . . . . . . . . . . . . . . 22 3.8 Other Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Contents ii 3.8.1 Bayesian Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.8.2 Boolean Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.8.3 Association Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.9 Standards and Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.9.1 Systems Biology Markup Language . . . . . . . . . . . . . . . . . . . 28 3.9.2 Systems Biology Workbench . . . . . . . . . . . . . . . . . . . . . . . 30 3.9.3 Cell Illustrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4. Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.1 Framework for Cell Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2 Data Collection and Interpretation . . . . . . . . . . . . . . . . . . . . . . . 35 4.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.1 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.2 Methods and Paradigms for Validation . . . . . . . . . . . . . . . . . 37 4.4 Model Representation and Integration . . . . . . . . . . . . . . . . . . . . . 38 4.5 Issues to be addressed by proposed research . . . . . . . . . . . . . . . . . . 39 5. Preliminary Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.1 The Wnt Pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.1.1 The Wnt Canonical Pathway . . . . . . . . . . . . . . . . . . . . . . 40 5.1.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.1.3 Downstream Gene Regulatory Network . . . . . . . . . . . . . . . . 41 5.1.4 Stem Cells and Differentiation . . . . . . . . . . . . . . . . . . . . . 41 5.1.5 Issues and Non canonical pathways . . . . . . . . . . . . . . . . . . . 43 5.2 AKT and ERK Pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.2.1 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.2.2 Pathway Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.2.3 Topological Ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.2.4 Rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.2.5 Evolutionary Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2.6 Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.2.7 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2.8 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6. Future Plans

LIST OF FIGURES 2.1 Complexity spectrum of biological system . . . . . . . . . . . . . . . . . . . 4 2.2 The Central Dogma of Molecular Biology . . . . . . . . . . . . . . . . . . . 5 2.3 The types of biological pathways . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 The glycolysis metabolic pathway . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Signaling pathway example . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.6 A diagram of a gene regulatory network . . . . . . . . . . . . . . . . . . . . 11 3.1 The MAPK pathway scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 The S-System equations for the MAPK pathway . . . . . . . . . . . . . . . 16 3.3 The components of a Hybrid Functional Petri Net . . . . . . . . . . . . . . 17 3.4 CHARON structure of the bacterium Vibrio fischeri . . . . . . . . . . . . . 19 3.5 An example of an enzyme-catalyzed reaction described using π -calculus . . 20 3.6 Obtaining the automaton from the simulation profile . . . . . . . . . . . . . 21 3.7 A simple regulatory network and its PADE representation . . . . . . . . . . 23 3.8 The phase space box for the simple network . . . . . . . . . . . . . . . . . . 24 3.9 Transition system derived from the differential equations . . . . . . . . . . . 24 3.10 A Bayesian network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.11 A Boolean network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.12 Two possible trajectories of a Boolean network . . . . . . . . . . . . . . . . 27 3.13 Inheritance hierarchy of the SBML classes . . . . . . . . . . . . . . . . . . . 29 3.14 The structure of the SBW framework . . . . . . . . . . . . . . . . . . . . . . 31 3.15 SBW Broker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.16 Cell Illustrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.17 Concentration profiles of a simulation run . . . . . . . . . . . . . . . . . . . 33 4.1 The validation paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2 Issues to be addressed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.1 The Hybrid Functional Petri Net model of the Wnt pathway . . . . . . . . 42 5.2 Profiles of β -catenin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.3 Cell lineage of stem cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 The scheme of the Wnt/Ca 2+ pathway . . . . . . . . . . . . . . . . . . . . . 5.4 44 5.5 The Hybrid Functional Petri Net model of the Akt and ERK pathways . . . 46