Dynamic Systems Biology Modeling and Simuation consolidates and unifies classical and contemporary multiscale methodologies for mathematical modeling and computer simulation of dynamic biological systems – from molecular/cellular, organ-system, on up to population levels. The book pedagogy is developed as a well-annotated, systematic tutorial – with clearly spelled-out and unified nomenclature – derived from the author’s own modeling efforts, publications and teaching over half a century. Ambiguities in some concepts and tools are clarified and others are rendered more accessible and practical. The latter include novel qualitative theory and methodologies for recognizing dynamical signatures in data using structural (multicompartmental and network) models and graph theory; and analyzing structural and measurement (data) models for quantification feasibility. The level is basic-to-intermediate, with much emphasis on biomodeling from real biodata, for use in real applications. Table Of Contents Quotes Preface to the First Edition Pedagogical Struggles Crystallizing and Focusing – My Way How to Use this Book in the Classroom Acknowledgements References Chapter 1. Biosystem Modeling & Simulation: Nomenclature & Philosophy Overview Modeling Definitions Modeling Essential System Features Primary Focus: Dynamic (Dynamical) System Models Measurement Models & Dynamic System Models Combined: Important! Stability Top-Down & Bottom-Up Modeling Source & Sink Submodels: One Paradigm for Biomodeling with Subsystem Components Systems, Integration, Computation & Scale in Biology Overview of the Modeling Process & Biomodeling Goals Looking Ahead: A Top-Down Model of the Chapters References Chapter 2. Math Models of Systems: Biomodeling 101 Some Basics & a Little Philosophy Algebraic or Differential Equation Models Differential & Difference Equation Models Different Kinds of Differential & Difference Equation Models Linear & Nonlinear Mathematical Models Piecewise-Linearized Models: Mild/Soft Nonlinearities Solution of Ordinary Differential (ODE) & Difference Equation (DE) Models Special Input Forcing Functions (Signals) & Their Model Responses: Steps & Impulses State Variable Models of Continuous-Time Systems Linear Time-Invariant (TI) Discrete-Time Difference Equations (DEs) & Their Solution Linearity & Superposition Laplace Transform Solution of ODEs Transfer Functions of Linear TI ODE Models More on System Stability Looking Ahead Exercises References Chapter 3. Computer Simulation Methods Overview Initial-Value Problems Graphical Programming of ODEs Time-Delay Simulations Multiscale Simulation and Time-Delays Normalization of ODEs: Magnitude- & Time-Scaling Numerical Integration Algorithms: Overview The Taylor Series Taylor Series Algorithms for Solving Ordinary Differential Equations Computational/Numerical Stability Self-Starting ODE Solution Methods Algorithms for Estimating and Controlling Stepwise Precision Taylor Series-Based Method Comparisons Stiff ODE Problems How to Choose a Solver? Solving Difference Equations (DEs) Using an ODE Solver Other Simulation Languages & Software Packages Two Population Interaction Dynamics Simulation Model Examples Taking Stock & Looking Ahead Exercises References Chapter 4. Structural Biomodeling from Theory & Data: Compartmentalizations Introduction Compartmentalization: A First-Level Formalism for Structural Biomodeling Mathematics of Multicompartmental Modeling from the Biophysics Nonlinear Multicompartmental Biomodels: Special Properties & Solutions Dynamic System Nonlinear Epidemiological Models Compartment Sizes, Concentrations & the Concept of Equivalent Distribution Volumes General n-Compartment Models with Multiple Inputs & Outputs Data-Driven Modeling of Indirect & Time-Delayed Inputs Pools & Pool Models: Accommodating Inhomogeneities Recap & Looking Ahead Exercises References Chapter 5. Structural Biomodeling from Theory & Data: Sizing, Distinguishing & Simplifying Multicompartmental Models Introduction Output Data (Dynamical Signatures) Reveal Dynamical Structure Multicompartmental Model Dimensionality, Modal Analysis & Dynamical Signatures Model Simplification: Hidden Modes & Additional Insights Biomodel Structure Ambiguities: Model Discrimination, Distinguishability & Input–Output Equivalence Algebra and Geometry of MC Model Distinguishability Reducible, Cyclic & Other MC Model Properties Tracers, Tracees & Linearizing Perturbation Experiments Recap and Looking Ahead Exercises References Chapter 6. Nonlinear Mass Action & Biochemical Kinetic Interaction Modeling Overview Kinetic Interaction Models Law of Mass Action Reaction Dynamics in Open Biosystems Enzymes & Enzyme Kinetics Enzymes & Introduction to Metabolic and Cellular Regulation Exercises Extensions: Quasi-Steady State Assumption Theory References Chapter 7. Cellular Systems Biology Modeling: Deterministic & Stochastic Overview Enzyme-Kinetics Submodels Extrapolated to Other Biomolecular Systems Coupled-Enzymatic Reactions & Protein Interaction Network (PIN) Models Production, Elimination & Regulation Combined: Modeling Source, Sink & Control Components The Stoichiometric Matrix N Special Purpose Modeling Packages in Biochemistry, Cell Biology & Related Fields Stochastic Dynamic Molecular Biosystem Modeling When a Stochastic Model is Preferred Stochastic Process Models & the Gillespie Algorithm Exercises References Chapter 8. Physiologically Based, Whole-Organism Kinetics & Noncompartmental Modeling Overview Physiologically Based (PB) Modeling Experiment Design Issues in Kinetic Analysis (Caveats) Whole-Organism Parameters: Kinetic Indices of Overall Production, Distribution & Elimination Noncompartmental (NC) Biomodeling & Analysis (NCA) Recap & Looking Ahead Exercises References Chapter 9. Biosystem Stability & Oscillations Overview/Introduction Stability of NL Biosystem Models Stability of Linear System Models Local Nonlinear Stability via Linearization Bifurcation Analysis Oscillations in Biology Other Complex Dynamical Behaviors Nonlinear Modes Recap & Looking Ahead Exercises References Chapter 10. Structural Identifiability Introduction Basic Concepts Formal Definitions: Constrained Structures, Structural Identifiability & Identifiable Combinations Unidentifiable Models SI Under Constraints: Interval Identifiability with Some Parameters Known SI Analysis of Nonlinear (NL) Biomodels What’s Next? Exercises References Chapter 11. Parameter Sensitivity Methods Introduction Sensitivity to Parameter Variations: The Basics State Variable Sensitivities to Parameter Variations Output Sensitivities to Parameter Variations Output Parameter Sensitivity Matrix & Structural Identifiability *Global Parameter Sensitivities Recap & Looking Ahead Exercises References Chapter 12. Parameter Estimation & Numerical Identifiability Biomodel Parameter Estimation (Identification) Residual Errors & Parameter Optimization Criteria Parameter Optimization Methods 101: Analytical and Numerical Parameter Estimation Quality Assessments Other Biomodel Quality Assessments Recap and Looking Ahead Exercises References Chapter 13. Parameter Estimation Methods II: Facilitating, Simplifying & Working With Data Overview Prospective Simulation Approach to Model Reliability Measures Constraint-Simplified Model Quantification Model Reparameterization & Quantifying the Identifiable Parameter Combinations The Forcing-Function Method Multiexponential (ME) Models & Use as Forcing Functions Model Fitting & Refitting With Real Data Recap and Looking Ahead Exercises References Chapter 14. Biocontrol System Modeling, Simulation, and Analysis Overview Physiological Control System Modeling Neuroendocrine Physiological System Models Structural Modeling & Analysis of Biochemical & Cellular Control Systems Transient and Steady-State Biomolecular Network Modeling Metabolic Control Analysis (MCA) Recap and Looking Ahead Exercises References Chapter 15. Data-Driven Modeling and Alternative Hypothesis Testing Overview Statistical Criteria for Discriminating Among Alternative Models Macroscale and Mesoscale Models for Elucidating Biomechanisms Mesoscale Mechanistic Models of Biochemical/Cellular Control Systems Candidate Models for p53 Regulation Recap and Looking Ahead Exercises References Chapter 16. Experiment Design and Optimization Overview A Formal Model for Experiment Design Input–Output Experiment Design from the TF Matrix Graphs and Cutset Analysis for Experiment Design Algorithms for Optimal Experiment Design Sequential Optimal Experiment Design Recap and Looking Ahead Exercises References Chapter 17. Model Reduction and Network Inference in Dynamic Systems Biology Overview Local and Global Parameter Sensitivities Model Reduction Methodology Parameter Ranking Added Benefits: State Variables to Measure and Parameters to Estimate Global Sensitivity Analysis (GSA) Algorithms What’s Next? Exercises References Appendix A. A Short Course in Laplace Transform Representations & ODE Solutions Transform Methods Laplace Transform Representations and Solutions Key Properties of the Laplace Transform (LT) & its Inverse (ILT) Short Table of Laplace Transform Pairs Laplace Transform Solution of Ordinary Differential Equations (ODEs) Appendix B. Linear Algebra for Biosystem Modeling Overview Matrices Vector Spaces (V.S.) Linear Equation Solutions Measures & Orthogonality Matrix Analysis Matrix Differential Equations Singular Value Decomposition (SVD) & Principal Component Analysis (PCA) Appendix C. Input–Output & State Variable Biosystem Modeling: Going Deeper Inputs & Outputs Dynamic Systems, Models & Causality Input–Output (Black-Box) Models Time-Invariance (TI) Continuous Linear System Input–Output Models Structured State Variable Models Discrete-Time Dynamic System Models Composite Input–Output and State Variable Models State Transition Matrix for Linear Dynamic Systems The Adjoint Dynamic System Equivalent Dynamic Systems: Different Realizations of State Variable Models – Nonuniqueness Exposed Illustrative Example: A 3-Compartment Dynamic System Model & Several Discretized Versions of It Transforming Input–Output Data Models into State Variable Models: Generalized Model Building Appendix D. Controllability, Observability & Reachability Basic Concepts and Definitions Observability and Controllability of Linear State Variable Models Linear Time-Varying Models Linear Time-Invariant Models Output Controllability Output Function Controllability Reachability Constructibility Controllability and Observability with Constraints Positive Controllability Relative Controllability (Reachability) Conditional Controllability Structural Controllability and Observability Observability and Identifiability Relationships Controllability and Observability of Stochastic Models Appendix E. Decomposition, Equivalence, Minimal & Canonical State Variable Models Realizations (Modeling Paradigms) The Canonical Decomposition Theorem How to Decompose a Model Controllability and Observability Tests Using Equivalent Models Observable and Controllable Canonical Forms from Arbitrary State Variable Models Using Equivalence Properties Appendix F. More on Simulation Algorithms & Model Information Criteria Additional Predictor-Corrector Algorithms Derivation of the Akaike Information Criterion (AIC) The Stochastic Fisher Information Matrix (FIM): Definitions & Derivations Index