Dynamic Systems Biology Modeling and Simulation


  • Joseph DiStefano III, Distinguished Professor Computer Science, Medicine & Biomedical Engineering Chair, Computational & Systems Biology Interdepartmental Program UCLA Los Angeles CA

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.
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upper-division undergraduate, graduate level, and research level students systems biology, computational biology, biomathematics, biomedical engineering (bioengineering), pharmacology and areas using contemporary dynamical biosystem modeling and simulation methodology.


Book information

  • Published: January 2015
  • ISBN: 978-0-12-410411-2


"This very satisfying book has multiple strengths. The text has marvelous clarity, as do the mathematical demonstrations. All are synoptic, while simultaneously explaining the underlying, fine details. The useful organization is enhanced by superb graphics. Although the author has many technical capabilities, with both range and depth, below I’ll give just one illustrative example of the excellent result. Major themes of modern computation and modeling, as applied to biology, include issues of nonlinearities, chaotic dynamics, emergent properties, and instabilities. For example, consider the problems attendant on complex dynamic systems with multiple scales of time and space so typical of living systems.  The scientific literature in this domain is rich and immense. When I looked into DiStefano’s book for entries dealing with these topics, I found as early as Chapter One a heading: ”Multiscale Modeling”. Elsewhere were other treatments of these aspects of complexity and modeling difficulties such as the famous problem of “stiff ODEs”, here brilliantly examined and explained, with remedies. The many authoritative tutorials by DiStefano amazed me for so effectively distilling the technical essences. They confirm that DiStefano is a great teacher and guide through various profound, classical difficulties. This book is a masterwork."--F. Eugene Yates
"This book provides a systematic review of the concepts of mathematical modeling in various fields. With its simple language, varied practical examples, quick references, appendixes, and clear basic concepts, it provides a thorough explanation of the subject. The well-organized chapters, along with the use of different notations and typescripts, make it a user-friendly book." Rating: 5 Stars--
Doody.com, March 7, 2014
"DiStefano presents this interdisciplinary text merging mathematics, modeling, systems science, and biology. The first chapter introduces the philosophy and nomenclature of modeling and simulation. Chapter two covers mathematics including algebraic models, differential equations, linear and nonlinear modeling, and chapter three describes the use of Taylor series and algorithmic treatment of differential equations in computer simulation methods."--ProtoView.com, February 2014
“I am just in awe of your ability to start with simple ideas and use them to explain sophisticated concepts and methodologies in modeling biochemical and cellular systems (Chapters 6 and 7).  This is a great new contribution to the textbook offerings in systems biology.”--Alex Hoffmann, Director of the San Diego Center for Systems Biology and the UCSD Graduate Program in Bioinformatics and Systems Biology
“I found Chapter 1 to be a marvel of heavy-lifting, done so smoothly there was no detectable sweat.  Heavy-lifting because you laid out the big load of essential vocabulary and concepts a reader has to have to enter the world of biomodeling confidently.  In that chapter you generously acknowledge some us who tried to accomplish this earlier but, compared to your Chapter 1, we were clumsy and boring.  For me, now, Chapter 1 was a "page-turner" to be enjoyed straight through.  You have the gift of a master athlete who does impossible performances and makes them seem easy.
“Your Chapter 9 - on oscillations and stability - is a true jewel.  I have a shelf full of books etc on nonlinear mechanics and system analyses and modeling, but nothing to match the clarity and deep understanding you offer the reader. You are a great explainer and teacher.”--F. Eugene Yates, Emeritus Professor of Medicine, Chemical Engineering and Ralph and Marjorie Crump Professor of Biomedical Engineering, UCLA
“Chapter 4 covers many aspects of the notion of compartmentalization in the structural modeling of biomedical and biological models - both linear and nonlinear.  Developments are biophysically motivated throughout; and compartments are taken to represent entities with the same dynamic characteristics (dynamic signatures). A very positive feature of this text is the numerous worked examples in the text, which greatly help readers follow the material.  At the end of the chapter, there are further well thought out analytical and simulation exercises that will help readers check that they have understood what has been presented.
 â€œChapter 5 looks at many important aspects of multicompartmental modeling, examining in more detail how output data limit what can be learnt about model structure, even when such data are perfect. Among the many features explained are how to establish the size and complexity of a model; how to select between several candidate models; and whether it is possible to simplify a model. All of this is done with respect to the dynamic signatures in the model. As in Chapter 4, readers are helped to understand the often challenging material by means of numerous worked examples in the text, and there are further examples given at the end.”--Professor Keith Godfrey, University of Warwick, Coventry, U.K.

Table of Contents

ContentsPreface 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 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 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 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 .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 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 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 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 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 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 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 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 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 14 Biocontrol System Modeling, Simulation & 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 15 Data-Driven Modeling & 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 16 Experiment Design & Optimization 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 17 Model Reduction & 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 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 Two-Step 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) Partial Fraction Expansions References Appendix B: Linear Algebra for Biosystem Modeling Overview Matrices Vector Spaces (V.S.) Linear Equation Solutions Minimum Norm & Least Squares Pseudoinverse Solutions of Linear Equations Measures & Orthogonality Matrix Analysis Matrix Norms Matrix Calculus Computation of f(A), an Analytic Function of a Matrix Matrix Differential Equations Singular Value Decomposition (SVD) & Principal Component Analysis (PCA) Singular Value Decomposition (SVD) Principal Component Analysis (PCA) PCA from SVD Data Reduction & Geometric Interpretation References 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 Transfer Function (TF) Matrix for Linear TI Input-Output Models Structured State Variable Models State of a System S or Model M State Variable Models from Input-Output (I-O) Models Dynamic State Variable ODE Models for Continuous Systems Complete Dynamic System Models: Constrained Structures Linear TI State Variable Models Discrete-Time Dynamic System Models Discrete-Time Input-Output Models The Sampled or z-Transfer Function Discrete-Time State Variable Models Sampled Input-Output Transfer Function Matrix Composite Input-Output and State Variable Models Composite Input-Output Models Composite State Variable Models State Transition Matrix for Linear Dynamic Systems Input-Output Model Solutions State Variable Model Solutions The Adjoint Dynamic System Equivalent Dynamic Systems: Different Realizations of State Variable Models - Nonuniqueness Exposed Key Properties of Equivalent System Models Illustrative Example: A 3-Compartment Dynamic System Model & Several Discretized Versions of It Discretization & Sampled-Data Representations of the 3-Compartment Model Discretized ARMA Model with Impulse-Train Input Transforming Input-Output Data Models into State Variable Models: Generalized Model Building Time-Invariant Realizations SISO Models References Appendix D: Controllability, Observability & Reachability Basic Concepts and Definitions Controllability Observability Observability and Controllability of Linear State Variable Models Linear Time-Varying Models Controllability Criterion Observability Criterion Linear Time-Invariant Models Practical Controllability and Observability Conditions Output Controllability Time-Invariant (TI) Models TI State Variable Models 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 References 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 SISO Models MIMO Models Minimal State Variable (ODE) Models from I-O TFs (Data) Canonical State Variable (ODE) Models from I-O Models (Data) Observable and Controllable Canonical Forms from Arbitrary State Variable Models Using Equivalence Properties References Appendix F: More On Simulation Algorithms & Model Information Criteria Additional Predictor-Corrector Algorithms Modified Euler Second-Order Predictor and Corrector Formulas An Iterative-Implicit Predictor-Corrector Algorithm Noniterative, Predictor-Modifier-Corrector (P-M-C) Algorithms A Predictor-Modifier Corrector Algorithm Exemplified The Backward-Euler Algorithm for Stiff ODEs Derivation of the Akaike Information Criterion (AIC) The AIC for Nonlinear Regression The Stochastic Fisher Information Matrix (FIM): Definitions & Derivations FIM for Multioutput Models Index