Cellular Systems Biology or Biological Network Analysis
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1 Cellular Systems Biology or Biological Network Analysis Joel S. Bader Department of Biomedical Engineering Johns Hopkins University (c) 2012 December 4,
2 Preface Cells are systems. Standard engineering and mathematics texts should provide an excellent introduction to understanding how cells behave, mapping inputs to outputs. Unfortunately, cells are not linear, time-independent systems. Saturation and cooperative response break linearity. Cellular states change with time. Cells are not even deterministic, violating the assumptions of non-linear systems analysis. This book provides a self-contained introduction to cells as non-linear, time-dependent, stochastic, spatial systems. Each major section is motivated by a canonical biological pathway or phenomenon that requires the introduction of new concepts. All the required mathematical techniques are developed from the motivating examples. The book is designed as a text for advanced undergraduate or graduate students. Prerequisites are univariate calculus, linear algebra, basic molecular biology, and rudimentary facility with a programming language for computational experiments. Linear systems and Laplace transforms are helpful, but are also reviewed in the initial chapters. Each chapter is designed to be covered in an hour lecture, and problems are provided in an Appendix. This book is developed from course notes for Systems Bioengineering III: Genes to Cells, taught by me since 2007 as a required course for our B.S. in Biomedical Engineering. Joel S. Bader, Baltimore, MD iii
3 Contents Preface ii I Cells as Linear Systems 1 1 Cellular Signal Transduction 2 2 Linear Systems Analysis 3 3 The Laplace Transform and Complex Variables 4 4 Signal Transduction Cascades and MAPK Signaling 5 5 Generating Functions for Pharmacokinetics and Pharmacodynamics 6 6 Positive Feedback and Caffeine Response 7 II Cells as Non-linear Systems 8 7 Saturation and Cooperative Response 9 8 Joint Models of Transcription and Translation 10 9 Positive and Negative Auto-Regulation Combinatorial Regulation Non-Linear Cascades and Logic Gates 13 iv
4 CONTENTS v III Cells as Stochastic Systems Delta-Notch Signaling Stochastic Dynamics Noise in Gene and Protein Expression Stochastic Simulations and the Gillespie Algorithm Stability Analysis 19 IV Cells as Spatial Systems Morphogen Gradient Patterning Diffusion Solving the Diffusion Equation Patterning and Noise 24 V Cellular Networks Diffusion on a Network Network Topology, Motifs, and Clustering The Giant Component Network Partitioning and Spectral Clustering Metabolic Networks and Flux Balance Analysis 30 A Problems 31
5 Part I Cells as Linear Systems 4
6 Chapter 1 Cellular Signal Transduction 5
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13 Chapter 3 The Laplace Transform and Complex Variables 7
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18 Chapter 4 Signal Transduction Cascades and MAPK Signaling 8
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22 Chapter 5 Generating Functions for Pharmacokinetics and Pharmacodynamics 9
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31 Part II Cells as Non-linear Systems 11
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40 Chapter 9 Positive and Negative Auto-Regulation 14
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46 Chapter 10 Combinatorial Regulation 15
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51 Chapter 11 Non-Linear Cascades and Logic Gates 16
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67 Chapter 14 Noise in Gene and Protein Expression 20
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71 Chapter 15 Stochastic Simulations and the Gillespie Algorithm 21
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86 Chapter 17 Morphogen Gradient Patterning 24
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