Dynamic Systems Biology Modeling and Simulation

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Dynamic Systems Biology Modeling and Simulation

Dynamic Systems Biology Modeling and Simulation PDF

By Joseph Distefano

Dynamic Systems Biology Modeling and Simulation PDF 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.

Introductory coverage of core mathematical concepts such as linear and nonlinear differential and difference equations, Laplace transforms, linear algebra, probability, statistics and stochastics topics
The pertinent biology, biochemistry, biophysics or pharmacology for modeling are provided, to support understanding the amalgam of “math modeling” with life sciences
Strong emphasis on quantifying as well as building and analyzing biomodels: includes methodology and computational tools for parameter identifiability and sensitivity analysis; parameter estimation from real data; model distinguishability and simplification; and practical bioexperiment design and optimization
Companion website provides solutions and program code for examples and exercises using Matlab, Simulink, VisSim, SimBiology, SAAMII, AMIGO, Copasi and SBML-coded models
A full set of PowerPoint slides are available from the author for teaching from his textbook. He uses them to teach a 10 week quarter upper division course at UCLA, which meets twice a week, so there are 20 lectures. They can easily be augmented or stretched for a 15 week semester course
Importantly, the slides are editable, so they can be readily adapted to a lecturer’s personal style and course content needs. The lectures are based on excerpts from 12 of the first 13 chapters of DSBMS. They are designed to highlight the key course material, as a study guide and structure for students following the full text content

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

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