DiStefano III Dynamic Systems Biology Modeling and Simulation

1. Auflage 2015
ISBN: 978-0-12-410493-8
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 884 Seiten

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. - 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 - The complete PowerPoint slide package (-25 MB) can be obtained by instructors (or prospective instructors) by emailing the author directly, at: [e-mail]

'Professor Joe” - as he is called by his students - is a Distinguished Professor of Computer Science and Medicine and Chair of the Computational & Systems Biology Interdepartmental Program at UCLA - an undergraduate research-oriented program he nurtured and honed over several decades. As an active full-time member of the UCLA faculty for nearly half a century, he also developed and led innovative graduate PhD programs, including Computational Systems Biology in Computer Science, and Biosystem Science and Engineering in Biomedical Engineering. He has mentored students from these programs since 1968, as Director of the UCLA Biocybernetics Laboratory, and was awarded the prestigious UCLA Distinguished Teaching Award and Eby Award for Creative Teaching in 2003, and the Lockeed-Martin Award for Teaching Excellence in 2004. Professor Joe also is a Fellow of the Biomedical Engineering Society. Visiting professorships included stints at universities in Canada, Italy, Sweden and the UK and he was a Senior Fulbright-Hays Scholar in Italy in 1979. Professor Joe has been very active in the publishing world. As an editor, he founded and was Editor-in-Chief of the Modeling Methodology Forum - a department in seven of the American Journals of Physiology - from 1984 thru 1991. As a writer, he authored or coauthored both editions of Feedback and Control Systems (Schaum-McGraw-Hill 1967 and 1990), more than 200 research articles, and recently published his opus textbook: Dynamic Systems Biology Modeling and Simulation (Academic Press/Elsevier November 2013 and February 2014). Much of his research has been based on integrating experimental neuroendocrine and metabolism studies in mammals and fishes with data-driven mathematical modeling methodology - strongly motivated by his experiences in 'wet-lab”. His seminal contributions to modeling theory and practice are in structural identifiability (parameter ambiguity) analysis, driven by experimental encumbrances. He introduced the notions of interval and quasi-identifiablity of unidentifiable dynamic system models, and his lab has developed symbolic algorithmic approaches and new internet software (web app COMBOS) for computing identifiable parameter combinations. These are the aggregate parts of otherwise unidentifiable models that can be quantified - with broad application in model reduction (simplification) and experiment design. His long-term contributions to quantitative understanding of thyroid hormone production and metabolism in mammals and fishes have recently been crystallized into web app THYROSIM - for internet-based research and teaching about thyroid hormone dynamics in humans. Last but not least, Professor Joe is a passionate straight-ahead jazz saxophone player (alto and tenor), an alternate career begun in the 1950s in NYC at Stuyvesant High School - temporarily suspended when he started undergrad school, and resumed again in middle-age. He recently added flute to his practice schedule and he and his band - Acoustically Speaking -can be found occasionally gigging in Los Angeles or Honolulu haunts.

Autoren/Hrsg.

DiStefano III, Joseph

Inhaltsverzeichnis

1;Front Cover;1
2;Dynamic Systems Biology Modeling and Simulation;4
3;Copyright Page;5
4;Contents;8
5;Preface to the First Edition;18
5.1;Pedagogical Struggles;19
5.2;Crystallizing and Focusing – My Way;20
5.2.1;In Other Words… & Other Didactic Devices;22
5.3;How to Use this Book in the Classroom;24
5.4;Acknowledgements;24
5.5;References;25
6;1 Biosystem Modeling & Simulation: Nomenclature & Philosophy;26
6.1;Overview;28
6.2;Modeling Definitions;28
6.2.1;Modeling Science;31
6.3;Modeling Essential System Features;32
6.4;Primary Focus: Dynamic (Dynamical) System Models;36
6.4.1;Deterministic vs. Stochastic Dynamic System Models;37
6.4.1.1;Markov Models;38
6.5;Measurement Models & Dynamic System Models Combined: Important!;40
6.6;Stability;42
6.6.1;Robustness & Fragility;44
6.7;Top-Down & Bottom-Up Modeling;45
6.8;Source & Sink Submodels: One Paradigm for Biomodeling with Subsystem Components;46
6.9;Systems, Integration, Computation & Scale in Biology;47
6.9.1;Systems Biology;47
6.9.2;Systems Physiology & Pharmacology;47
6.9.3;Multiscale Modeling;49
6.9.4;Bioinformatics;51
6.9.5;Computational Systems Biology & Computational Biology;51
6.10;Overview of the Modeling Process & Biomodeling Goals;52
6.10.1;Data-Driven Biomodeling: Structuring, Quantifying, Analyzing and Restructuring;55
6.10.2;The Biomodeling Process in Toto: A Philosophical Recap;58
6.11;Looking Ahead: A Top-Down Model of the Chapters;59
6.12;References;61
7;2 Math Models of Systems: Biomodeling 101;64
7.1;Some Basics & a Little Philosophy;66
7.2;Algebraic or Differential Equation Models;67
7.3;Differential & Difference Equation Models;68
7.4;Different Kinds of Differential & Difference Equation Models;70
7.5;Linear & Nonlinear Mathematical Models;72
7.6;Piecewise-Linearized Models: Mild/Soft Nonlinearities;77
7.7;Solution of Ordinary Differential (ODE) & Difference Equation (DE) Models;78
7.7.1;The Differential Operator D & Characteristic Equation: Characterizing Modes & Modal Dynamics of Linear ODE Models;78
7.7.2;Solution of Linear Time-Invariant (TI) ODEs;80
7.7.2.1;One Way to View ODE Solutions: Classical Approach;80
7.7.3;Convolution;81
7.7.4;The Transient & Steady State Responses: The Modern Systems Approach;83
7.8;Special Input Forcing Functions (Signals) & Their Model Responses: Steps & Impulses;83
7.8.1;The Unit Impulse Input: An Important Equivalence Property;85
7.9;State Variable Models of Continuous-Time Systems;86
7.9.1;Nonlinear (NL) State Variable Biomodels;89
7.10;Linear Time-Invariant (TI) Discrete-Time Difference Equations (DEs) & Their Solution;90
7.10.1;State Variable Models of Discrete-Time Systems;91
7.11;Linearity & Superposition;94
7.12;Laplace Transform Solution of ODEs;95
7.12.1;Four Key Properties of LT & ILT;96
7.12.2;Partial Fraction Expansions;97
7.13;Transfer Functions of Linear TI ODE Models;100
7.13.1;Transfer Function (TF) Matrix of an ODE;101
7.13.2;The Complex Plane: Pole-Zero Maps of Transfer Functions;102
7.14;More on System Stability;104
7.14.1;Stability of Linear TI Dynamic Systems;104
7.15;Looking Ahead;105
7.16;Exercises;107
7.17;References;108
8;3 Computer Simulation Methods;110
8.1;Overview;113
8.2;Initial-Value Problems;115
8.3;Graphical Programming of ODEs;115
8.3.1;Block Diagram Languages;116
8.3.2;Special Input Function Simulations;118
8.3.2.1;Impulse Inputs;121
8.4;Time-Delay Simulations;121
8.5;Multiscale Simulation and Time-Delays;124
8.5.1;Does Model Size Matter?;128
8.6;Normalization of ODEs: Magnitude- & Time-Scaling;129
8.6.1;Magnitude-Scaling ODEs;130
8.6.2;Time-Scaling ODEs;132
8.7;Numerical Integration Algorithms: Overview;134
8.8;The Taylor Series;135
8.9;Taylor Series Algorithms for Solving Ordinary Differential Equations;137
8.9.1;Computing Derivatives;139
8.9.2;Derivative Approximation Formulas;139
8.9.3;Local vs. Global Truncation Errors;140
8.9.4;Roundoff Errors;140
8.10;Computational/Numerical Stability;141
8.11;Self-Starting ODE Solution Methods;142
8.11.1;Euler Method;142
8.11.2;Runge–Kutta Methods;143
8.11.2.1;Main Features of R–K Methods;143
8.11.2.2;Fourth-Order Runge–Kutta Method;144
8.11.3;Stepwise Errors, Tolerances & Error Control;146
8.12;Algorithms for Estimating and Controlling Stepwise Precision;147
8.12.1;Runge–Kutta–Fehlberg (R–K–F);147
8.12.2;Multistep Predictor–Corrector (P–C) Methods;147
8.12.2.1;Simple Multistep Formulas Based on Taylor Series;149
8.13;Taylor Series-Based Method Comparisons;149
8.14;Stiff ODE Problems;151
8.14.1;Stiff Solvers;154
8.15;How to Choose a Solver?;154
8.16;Solving Difference Equations (DEs) Using an ODE Solver;156
8.17;Other Simulation Languages & Software Packages;158
8.17.1;Math-Based Simulation Languages & Software;158
8.17.2;Special Purpose Simulation Packages in Biochemistry & Cell Biology;159
8.17.3;Stochastic Model Simulators;159
8.18;Two Population Interaction Dynamics Simulation Model Examples;160
8.18.1;Simpler & Linear Transcription/Translation Dynamics;160
8.18.2;Simple Predator–Prey Dynamics;162
8.19;Taking Stock & Looking Ahead;163
8.20;Exercises;164
8.21;References;167
9;4 Structural Biomodeling from Theory & Data: Compartmentalizations;168
9.1;Introduction;170
9.2;Compartmentalization: A First-Level Formalism for Structural Biomodeling;171
9.2.1;Basic Multicompartmental (MC) Model Formulation from Structural & Kinetic Data;171
9.2.1.1;Structural & Kinetic Data Complement Each Other;172
9.2.1.2;Input and Output Compartments First;172
9.2.1.3;More Compartments in More Organs;175
9.2.1.4;Handling Structural & Kinetic Data Mismatches: Caveat #1;176
9.2.2;Compartments, State Variables, Graphs, Pools & Chemical Species Defined;179
9.3;Mathematics of Multicompartmental Modeling from the Biophysics;182
9.3.1;The One-Compartment Model and Its Solution;183
9.3.1.1;Impulse-(Bolus)-Input Response: One-Compartment Model;184
9.3.1.2;Step-Input Response: One-Compartment Model;185
9.3.2;The Two-Compartment Model, its Forms, Properties & Solutions;186
9.3.2.1;Model Dynamics with Mass State Variables qi(t);187
9.3.2.2;Model Dynamics with Concentration State Variables ci(t)=qi(t)/Vi;187
9.3.2.3;Output Measurement Models;188
9.3.2.3.1;Model Outputs with Mass Measurements;188
9.3.2.3.2;Model Outputs with Concentration Measurements;188
9.3.2.4;Biosystem & Experiment Model Combined;189
9.3.2.5;Transfer Function Matrix for the Combined Biosystem & Experiment Model;190
9.3.2.6;Unit-Impulse Response from H(s);191
9.3.2.7;Unit-Step Response: LT Solution;193
9.3.3;Steady State Solutions;193
9.3.3.1;Steady State Solutions for the Linear Two-Compartment Model;194
9.4;Nonlinear Multicompartmental Biomodels: Special Properties & Solutions;195
9.4.1;Nonlinear (NL) Compartment Model Building & Analysis;197
9.5;Dynamic System Nonlinear Epidemiological Models;199
9.5.1;SIS, SIR and SIRS Models;200
9.5.2;Epidemics & Reproduction Number R0;202
9.6;Compartment Sizes, Concentrations & the Concept of Equivalent Distribution Volumes;202
9.7;General n-Compartment Models with Multiple Inputs & Outputs;205
9.7.1;Model Dynamics;205
9.7.2;Output Measurements Model;207
9.7.3;The Constituent Compartmental Equations;208
9.7.4;Mammillary & Catenary Compartment Models;213
9.8;Data-Driven Modeling of Indirect & Time-Delayed Inputs;216
9.8.1;Signal Delay with Attenuation;218
9.9;Pools & Pool Models: Accommodating Inhomogeneities;220
9.9.1;Pool Models;220
9.9.2;Pool vs. Compartmental Model Applications: Flux-Balance & Cut-Set Analysis;221
9.10;Recap & Looking Ahead;222
9.11;Exercises;223
9.12;References;227
10;5 Structural Biomodeling from Theory & Data: Sizing, Distinguishing & Simplifying Multicompartmental Models;230
10.1;Introduction;232
10.2;Output Data (Dynamical Signatures) Reveal Dynamical Structure;232
10.2.1;What’s in the Box?;233
10.3;Multicompartmental Model Dimensionality, Modal Analysis & Dynamical Signatures;235
10.3.1;Multiexponential Impulse-Responses, Modes & Mode Parameters;235
10.3.1.1;Simplest Case: Distinct Eigenvalues (Distinct Exponents);236
10.3.2;Dynamical Dimensionality: Establishing the Number of Compartments;237
10.3.2.1;Modes in Data=Minimum Compartment Number;237
10.3.2.2;SISO Multiexponential Minimal Modeling: Some Answers & Insights;238
10.3.2.3;Composite Compartments: More Ambiguity & Insights;239
10.3.3;The Bigger Picture – Visible & Hidden Modes: Distinguishable & Indistinguishable Compartments (State Variables or Species);241
10.3.3.1;Caveat #2 – Too Dynamically Simple?;241
10.3.3.2;Caveat #3 – Hidden Compartments?;243
10.3.4;Finding Modes (or Compartments) Visible in Output Data by Graphical Inspection;246
10.3.5;Automated Mode Detection Using Graph Theory Algorithms;248
10.4;Model Simplification: Hidden Modes & Additional Insights;249
10.4.1;State Variable Aggregation (Reduction): Transfer Functions Tell All;250
10.5;Biomodel Structure Ambiguities: Model Discrimination, Distinguishability & Input–Output Equivalence;252
10.6;*Algebra and Geometry of MC Model Distinguishability;260
10.6.1;Graph Properties & Geometric Rules;261
10.6.1.1;Automation: DISTING;263
10.7;Reducible, Cyclic & Other MC Model Properties;263
10.8;Tracers, Tracees & Linearizing Perturbation Experiments;264
10.8.1;Linearization of NL ODE Models;268
10.8.1.1;Linearized Output Measurement Model;270
10.8.1.2;The Complete Linearized Model;270
10.9;Recap and Looking Ahead;271
10.10;Exercises;272
10.11;References;276
11;6 Nonlinear Mass Action & Biochemical Kinetic Interaction Modeling;278
11.1;Overview;280
11.2;Kinetic Interaction Models;281
11.2.1;Linear & Monomolecular Interactions;282
11.2.2;Monomolecular Chemical Reactions;283
11.2.2.1;Monomolecular Irreversible;283
11.2.2.2;Monomolecular Reversible Conversion: Protein Folding and Unfolding;285
11.2.3;Nonlinear Bimolecular Reactions & Other Species Interactions;286
11.2.3.1;Molecular & Other Collisions: Combinatorial Product Laws;286
11.2.3.2;Energetics, Reaction Activation & Transformation;287
11.2.3.3;Volume & Temperature Effects;290
11.3;Law of Mass Action;291
11.3.1;Reaction Rate Equations;291
11.3.2;Reversible Reactions & Dynamic Equilibrium;292
11.4;Reaction Dynamics in Open Biosystems;293
11.5;Enzymes & Enzyme Kinetics;295
11.5.1;Substrate–Enzyme Interactions: Michaelis–Menten Theory;296
11.5.2;The Quasi-Steady State Assumption (QSSA) & the M–M Approximate Equations;297
11.5.2.1;M–M QSSA Equation Extremes;300
11.5.2.2;M–M QSSA Equation Representations, Transformations & Quantification;300
11.5.3;Total Quasi-Steady State Assumption (tQSSA): When the QSSA is not Valid;302
11.5.4;Summary Equations & Conditions for the QSSA and First-Order tQSSA;304
11.5.5;Enzymatic Regulation of Biochemical Pathways;307
11.6;Enzymes & Introduction to Metabolic and Cellular Regulation;308
11.6.1;A Simple Competitive Reaction: One Enzyme & Two Substrates;309
11.6.2;Local Regulation by Enzymatic Activation–Deactivation;312
11.6.3;*More Complex Regulation: Cooperativity and Allosterism;313
11.6.3.1;*Allosterism Modeling;316
11.6.3.1.1;Other Allosterism Models & Summary Remarks;319
11.7;Exercises;320
11.8;Extensions: Quasi-Steady State Assumption Theory;321
11.8.1;*Classic Michaelis–Menten Theory;322
11.8.2;*Modern Quasi-Steady State Assumption (QSSA) Analysis & a Scaling Lesson;325
11.9;References;328
12;7 Cellular Systems Biology Modeling: Deterministic & Stochastic;332
12.1;Overview;334
12.2;Enzyme-Kinetics Submodels Extrapolated to Other Biomolecular Systems;334
12.2.1;Simple Models of Production Rate Regulation;334
12.2.2;Hill Function Regulation Models;335
12.2.3;Ligand–Receptor Interactions & Drug Dynamics;338
12.2.4;Pharmacodynamic Stimulus & Inhibitory Approximation Functions;342
12.3;Coupled-Enzymatic Reactions & Protein Interaction Network (PIN) Models;343
12.3.1;When the tQSSA is More Appropriate than the QSSA;343
12.4;Production, Elimination & Regulation Combined: Modeling Source, Sink & Control Components;345
12.5;The Stoichiometric Matrix N;347
12.6;Special Purpose Modeling Packages in Biochemistry, Cell Biology & Related Fields;350
12.7;*Stochastic Dynamic Molecular Biosystem Modeling;355
12.8;When a Stochastic Model is Preferred;355
12.9;*Stochastic Process Models & the Gillespie Algorithm;356
12.9.1;Nomenclature & Equations;357
12.9.2;The Chemical Master Equation;359
12.9.3;*The Gillespie Algorithm & Variants;360
12.9.3.1;Algorithm Properties;361
12.9.4;*Stochastic Model Analysis: Ensemble Statistics;362
12.10;Exercises;365
12.11;References;368
13;8 Physiologically Based, Whole-Organism Kinetics & Noncompartmental Modeling;370
13.1;Overview;373
13.2;Physiologically Based (PB) Modeling;374
13.2.1;Nomenclature;375
13.2.2;Simplified Vascular & Tissue Physiology & Anatomy for PB Modeling;375
13.2.2.1;Blood & Lymph Vessels, their Constituents & Tissue Distributions;376
13.2.3;Structuring & Parameterizing a PB Model;378
13.2.3.1;Diagram Notation;378
13.2.3.2;PBPK (PBPD, PBTK) Model Organs & Compartments;378
13.2.3.3;Plasma vs. Blood Concentrations & Flow Rates;380
13.2.3.4;Distribution Dynamics of Blood Constituents in Tissues;380
13.2.3.5;PBPK Model Parameters;381
13.2.4;Dynamical Equations of PB Models;382
13.2.4.1;Simplest Single-Organ Model;383
13.2.4.2;Permeability-Limited Two-Subcompartment (PLT) Organ Model;384
13.2.4.3;Three-Compartment Organ in a Whole-Body Model;385
13.2.4.4;Two-Region Asymptotically Reduced (TAR) Models;388
13.2.4.5;PB Examples in Toxicology;390
13.2.5;Allometric Scaling in PB Models;395
13.3;Experiment Design Issues in Kinetic Analysis (Caveats);397
13.3.1;Linear vs. Nonlinear (NL);398
13.3.1.1;Time-varying vs. Time-Invariant/Stationary;398
13.4;Whole-Organism Parameters: Kinetic Indices of Overall Production, Distribution & Elimination;400
13.4.1;Measures of Elimination & Production & their Data-Driven Models;400
13.4.1.1;Plasma Clearance Rate (PCR);400
13.4.1.1.1;PCR Experiment Designs;401
13.4.1.2;Other Clearance Rates: UCR & FCR;405
13.4.1.3;Distribution Volume, Partition Coefficient & Pool Size Relationships;405
13.4.2;Residence Times;407
13.4.3;Whole-Organism Parameter Relationships;408
13.4.4;Half-Lives;408
13.5;Noncompartmental (NC) Biomodeling & Analysis (NCA);410
13.5.1;Noncompartmental Analysis Formulas;411
13.5.1.1;Noncompartmental Parameters from Multiexponential Models;411
13.5.2;Bioavailability & Bioequivalence in Pharmacology;412
13.5.3;Noncompartment Model Structure Problems;413
13.5.3.1;The Equivalent Sink Problem: NC Model Structural Constraint #1;414
13.5.3.2;The Equivalent Source Problem: NC Model Structural Constraint #2;414
13.5.4;Exchangeable or Circulating Masses & Volumes as NC Parameter Bounds;415
13.5.5;Summarizing Noncompartmental Analysis (NCA) Applicability;417
13.5.6;Bounds for Whole-Organ System Parameters from NCA;418
13.5.7;NC Model Structure Errors & Some Consequences;418
13.5.8;Very Limited Compartmental Equivalents of Noncompartmental Models;420
13.5.9;NC versus MC Modeling: No Easy Choice;422
13.6;Recap & Looking Ahead;422
13.7;Exercises;423
13.8;References;425
14;9 Biosystem Stability & Oscillations;428
14.1;Overview/Introduction;430
14.1.1;Biosystem Stability;430
14.1.2;Oscillations in Biology;431
14.2;Stability of NL Biosystem Models;432
14.2.1;Phase Space Geometry;432
14.2.2;Stability, Equilibrium Points, Steady State Solutions & Nullclines;433
14.2.3;Stability Classifications;436
14.3;Stability of Linear System Models;437
14.4;Local Nonlinear Stability via Linearization;438
14.5;Bifurcation Analysis;439
14.5.1;Other Bifurcation Types;439
14.6;Oscillations in Biology;441
14.6.1;Harmonic Oscillations;441
14.6.2;Limit Cycle Oscillations;441
14.6.2.1;Oscillations & the Selkov Model of Glycolysis;443
14.6.2.2;Oscillations & the Brusselator Model;444
14.7;Other Complex Dynamical Behaviors;445
14.7.1;Chaos;446
14.7.1.1;Complex Dynamic System Behavior & Chaos for the Discrete-Time Logistic Population Growth Model;447
14.7.1.2;The Lorenz Model & Lorenz Attractor;451
14.7.2;Concluding Remarks About Chaos & Complexity;453
14.8;Nonlinear Modes;453
14.8.1;Nonlinear Modes in Systems Biology;455
14.9;Recap & Looking Ahead;455
14.10;Exercises;456
14.11;References;458
15;10 Structural Identifiability;460
15.1;Introduction;462
15.1.1;Model/Parameter Quantification & Identifiability (SI & NI) Defined;463
15.1.2;Structural Identifiability (SI) in the Large;464
15.1.3;Historical Perspective;465
15.2;Basic Concepts;467
15.2.1;Complete Biosystem Model: Constraints as Well as Inputs & Outputs Included;469
15.2.2;Transfer Functions & SI;469
15.2.2.1;Preliminary Definitions;469
15.2.2.2;Structural Invariants;469
15.2.2.3;Ambiguities;476
15.2.2.4;Multiple Inputs;477
15.3;Formal Definitions: Constrained Structures, Structural Identifiability & Identifiable Combinations;479
15.4;Unidentifiable Models;482
15.4.1;Interval Identifiability & Parameter Interval Analysis;482
15.4.2;Parameter Bounds & Quasiidentifiability Conditions;483
15.4.2.1;Bounds for n-Compartment Models;484
15.4.2.2;Bounds on Equivalent Distribution Volumes;485
15.4.2.3;Quasiidentifiability Conditions;486
15.4.3;Informational Limitations in Unidentifiable Models;488
15.5;SI Under Constraints: Interval Identifiability with Some Parameters Known;489
15.5.1;General Catenary & Mammillary Model Equations;489
15.5.2;Feasible Parameter Ranges (Subspace) for Equality Constraints;491
15.5.3;Models with Infeasible or Redundant Constraints;491
15.5.4;The Constrained Parameter Bounding Algorithms;492
15.5.4.1;Catenary Model;492
15.5.4.2;Mammillary Model;493
15.5.5;Joint Submodel Parameters: Another Approach to Interval Identifiability;494
15.6;SI Analysis of Nonlinear (NL) Biomodels;496
15.6.1;Prolog and Overview;496
15.6.2;SI Analysis by Taylor Series;498
15.6.3;SI Analysis by Symbolic Differential Algebra (DA);503
15.7;What’s Next?;507
15.8;Exercises;508
15.9;References;510
16;11 Parameter Sensitivity Methods;514
16.1;Introduction;516
16.2;Sensitivity to Parameter Variations: The Basics;517
16.2.1;Relative Sensitivity of Outputs & Functions of Outputs to Parameter Variations;517
16.2.1.1;Multiple Outputs & Parameters;520
16.3;State Variable Sensitivities to Parameter Variations;520
16.3.1;Total (Global) & First-Order (Local, Linear) Variations & Sensitivities;521
16.3.2;First-Order (Local, Linear) Variations & Sensitivities;521
16.3.3;Local State Variable Sensitivities;522
16.3.4;Some Notable Features of State Variable Sensitivity Functions;524
16.3.5;*The Canonical Sensitivity System;526
16.4;Output Sensitivities to Parameter Variations;528
16.4.1;Some Notable Features of Output Sensitivity Functions;529
16.4.2;Time-Averaged Relative Output Sensitivity Functions;530
16.4.3;Sensitivity Measures of Model Quantification Results (Robustness);531
16.5;*Output Parameter Sensitivity Matrix & Structural Identifiability;533
16.5.1;Key Output Sensitivity Matrix–SI Relationships;533
16.6;*Global Parameter Sensitivities;542
16.7;Recap & Looking Ahead;543
16.8;Exercises;544
16.9;References;545
17;12 Parameter Estimation & Numerical Identifiability;546
17.1;Biomodel Parameter Estimation (Identification);548
17.1.1;Model Quantification by any Other Name;548
17.1.2;Model Fitting;548
17.1.3;Parameter Estimation, Robustness and Sensitivity;551
17.1.3.1;What/Which Parameters are Estimated?;551
17.1.3.2;Robustness, Sensitivity & Parameter Estimation;551
17.1.4;Different Quantification Approaches;553
17.1.4.1;Direct vs. Indirect Parameter Estimation;553
17.1.5;Indirect Parameter Estimation;554
17.1.5.1;Linear Constant-Coefficient Models: Multiexponential Response Approach;554
17.1.6;Linear & Nonlinear in the Parameters Models;556
17.2;Residual Errors & Parameter Optimization Criteria;556
17.2.1;Residual Output Errors for Discrete-Time Measurements;557
17.2.2;Least-Squares (LS) Criteria;557
17.2.3;Weighted Least-Squares (WLS) or Residual Sum of Squares (WRSS) Criteria;558
17.2.3.1;*WLS for More Than One Output: y(t)=[y1(t) ··· ym(t)]T;559
17.2.4;Extended Weighted Least Squares (EWLS);560
17.2.5;Maximum Likelihood (ML);561
17.3;Parameter Optimization Methods 101: Analytical and Numerical;561
17.3.1;The Calculus of Linear Least Squares;562
17.3.2;The Curve-Peeling (or Stripping) Method for Exponential Curve Fitting;563
17.3.3;Iterative Search Algorithms, Local & Global;564
17.3.3.1;Local Search;565
17.3.3.2;*Global Search;567
17.4;Parameter Estimation Quality Assessments;568
17.4.1;Numerical (a Posteriori, Practical) Identifiability (NI): Distinguishing the Practical from the Possible;568
17.4.2;Output Sensitivity Matrix & Numerical Identifiability;569
17.4.3;Parameter Variances, Covariance/Correlation Matrices & Identifiability Relationships;570
17.4.3.1;Parameter Standard Errors (SEs) & Standard Deviations (SDs);571
17.4.3.2;VAR(pi) & CORR(pipj) for Identifiability Testing;572
17.4.4;COV(p)?H(p) from the Hessian Matrix;572
17.4.5;COV(p)=F-1(p) from the Fisher Information Matrix;573
17.4.5.1;The Cramér–Rao Theorem;573
17.4.6;Residual Mean Square (RMS) Error & COV(p*) for Unweighted Regression;575
17.4.7;Covariance & Fisher Information Matrices for Functions b(p) of p;576
17.4.8;*COV(p) by Stochastic Monte Carlo Simulation;577
17.4.9;Robustness and Sensitivities from COV(p);578
17.5;Other Biomodel Quality Assessments;579
17.5.1;Goodness-of-Fit Criteria & Figures of Merit – Subjective & Statistical;579
17.5.1.1;The “Eyeball” Test: Visual Inspection;579
17.5.1.2;Analysis of Residuals;579
17.5.1.3;Appropriate Weighting of the Data;579
17.5.1.4;Independence of Residual Errors;581
17.5.1.5;Gaussian Distribution & Independence of Residuals;581
17.6;Recap and Looking Ahead;581
17.7;Exercises;582
17.8;References;583
18;13 Parameter Estimation Methods II: Facilitating, Simplifying & Working With Data;584
18.1;Overview;586
18.2;Prospective Simulation Approach to Model Reliability Measures;588
18.2.1;Structurally Identifiable or Not;589
18.2.1.1;Structurally Identifiable NL & Numerically Identifiable (NI) or Not NI;592
18.2.1.2;Variances, Covariances & Correlations;592
18.2.1.3;Input–Output Models;596
18.3;Constraint-Simplified Model Quantification;597
18.4;Model Reparameterization & Quantifying the Identifiable Parameter Combinations;601
18.4.1;Reparameterized Model Statistics with Noisy Data;605
18.4.1.1;Covariance COV(b) in Terms of Identifiable Parameter Combinations c;605
18.4.1.2;Combos, Noisy Data & Parameter Equality Constraint Effects;606
18.5;The Forcing-Function Method;608
18.6;Multiexponential (ME) Models & Use as Forcing Functions;611
18.7;Model Fitting & Refitting With Real Data;613
18.8;Recap and Looking Ahead;617
18.9;Exercises;617
18.10;References;619
19;14 Biocontrol System Modeling, Simulation, and Analysis;620
19.1;Overview;622
19.2;Physiological Control System Modeling;622
19.3;Neuroendocrine Physiological System Models;624
19.3.1;Models in the Literature;626
19.3.2;Anatomy of a Neuroendocrine Model;627
19.3.2.1;Neuroendocrine Regulation of Thyroid Hormones (TH) in the Human: A Feedback Control System (fbcs) Simulation Model;627
19.3.2.2;Overall Block Diagram;628
19.3.2.3;Data;628
19.3.2.4;Equations;628
19.3.2.5;Brain Submodels;630
19.3.2.6;TH Submodels;630
19.3.2.7;T3 & T4 (=TH) Distribution and Elimination (D&E) Submodel;631
19.3.2.8;Gut Absorption Submodel – Needed for Representing Oral Dosing;632
19.3.2.9;Preliminary Quantification;632
19.3.2.10;Closed-Loop Quantification;633
19.4;Structural Modeling & Analysis of Biochemical & Cellular Control Systems;635
19.4.1;Open- vs. Closed-Loop Biochemical Reaction Dynamics;635
19.4.1.1;Open-Loop Model;637
19.4.1.2;Closed-Loop Model;639
19.4.1.3;Approximate QSSA Model Solution is Qualitatively Different (Wrong);641
19.5;Transient and Steady-State Biomolecular Network Modeling;642
19.5.1;Modeling Complete Dynamics;642
19.5.2;Different ODE Model Forms;643
19.5.3;Metabolism and Steady State Flux Balance Analysis (FBA);644
19.5.3.1;Optimizing Steady-State Fluxes;644
19.5.4;Experiment Design for FBA by Cutset Analysis;645
19.5.5;Elementary Mode and Extreme Pathway Analysis;646
19.5.6;Metabolomics;648
19.5.7;Metabolomics in Synthetic and Mammalian Biology;648
19.6;Metabolic Control Analysis (MCA);649
19.6.1;Sensitivity Functions of Metabolic Control Analysis;649
19.6.2;Properties of Metabolic Control and Elasticity Coefficients;651
19.6.2.1;Control Coefficient Constraints;651
19.6.2.2;Control and Elasticity Connectivity Properties;651
19.7;Recap and Looking Ahead;651
19.8;Exercises;652
19.9;References;653
20;15 Data-Driven Modeling and Alternative Hypothesis Testing;658
20.1;Overview;660
20.1.1;Let the Data Speak First;660
20.1.2;Formalizing the Modeling Process Based on the Data;660
20.2;Statistical Criteria for Discriminating Among Alternative Models;661
20.2.1;Multiexponential/Multicompartmental Model Discrimination: How Many Modes?;661
20.2.1.1;F-test of Significance;661
20.2.1.2;Testing Estimates of Exponential Coefficients Ai;662
20.2.1.3;Akaike Information Criterion (AIC);662
20.2.1.4;The Schwarz Criterion (SC or BIC);663
20.3;Macroscale and Mesoscale Models for Elucidating Biomechanisms;663
20.3.1;Minimal Macroscale Disease Dynamics Models: Treatment of Viral Infections;663
20.4;Mesoscale Mechanistic Models of Biochemical/Cellular Control Systems;666
20.4.1;What Signals Control Frog Egg Maturation (Cellular Decision-Making)?;667
20.4.2;Testing Six Alternative Steroid Dynamics Hypotheses Using Biochemistry, PK, PD, and Pharmacogenomic Data;670
20.4.2.1;Pedagogic Perspective on Structural Assumptions;672
20.4.3;Testing Manganese Brain Entry Pathway Hypotheses from Quantified Distribution Dynamics of Multiorgan Rat Data;673
20.4.3.1;Model Structure;673
20.4.3.2;Data, Data-Driven Structural Assumptions and Equations;674
20.4.3.3;Model Quantification;676
20.5;Candidate Models for p53 Regulation;676
20.5.1;What Does p53 Do? – Modeler’s Perspective;677
20.5.2;p53 Multifeedback Regulation;678
20.5.3;Other Regulatory Factors and Variables;679
20.5.4;Different p53 Models are OK;679
20.5.5;p53 Oscillations and Models of How They Arise;680
20.5.5.1;Stochastic p53 Models;682
20.5.6;Different Structures for Different Inputs;686
20.5.7;A 4-State Variable Alternative Model for p53–Mdm2–MdmX Signaling;686
20.5.7.1;Model Input;687
20.5.7.2;Model Output Measurement Equations;687
20.5.7.3;Parameter Relationships from Steady State Constraints;689
20.5.7.4;Structural Parameter Identifiability;690
20.5.7.5;Initial Parameter Estimation and Numerical Identifiability;690
20.5.7.6;Preliminary p53 Signaling Model Stability Analysis;691
20.6;Recap and Looking Ahead;691
20.7;Exercises;693
20.8;References;693
21;16 Experiment Design and Optimization;696
21.1;Overview;698
21.2;A Formal Model for Experiment Design;698
21.2.1;Design-Degrees-of-Freedom;700
21.3;Input–Output Experiment Design from the TF Matrix;701
21.3.1;Experiment Design by Exhaustive SI Analysis of the General 2-Compartment Model;703
21.3.2;Experiment Design by Exhaustive SI Analysis of a 6-Compartment Biomodel;705
21.3.2.1;Feasible Experiments;706
21.3.2.2;Transfer Function Matrix;707
21.3.2.3;Identifiability Analysis for Each Hij;707
21.3.2.4;Identifiability Analysis for Combinations of Hij: SI from Multiple Experiments;707
21.3.2.5;Alternative Combinations of Physiological Experiments;708
21.3.2.6;Aggregated Measurements;709
21.3.2.7;Practical Alternatives via External Monitoring;709
21.4;Graphs and Cutset Analysis for Experiment Design;710
21.4.1;Some Cutset Theory and Applications;712
21.4.1.1;Basics of Cutset Analysis;713
21.4.1.2;Procedural Rules for Experiment Design;713
21.4.1.3;Parameter kji from Two or Three Steady State Experiments;715
21.5;Algorithms for Optimal Experiment Design;718
21.5.1;Scalar Optimization Functions of F;719
21.5.2;Optimal Sampling Schedule Design;720
21.6;Sequential Optimal Experiment Design;722
21.6.1;OSS Design Software;722
21.6.2;OSS Design Applied in Practice;724
21.6.2.1;Sequential Designs;724
21.6.2.2;Optimally Quantified Model;724
21.7;Recap and Looking Ahead;724
21.8;Exercises;727
21.9;References;727
22;17 Model Reduction and Network Inference in Dynamic Systems Biology;730
22.1;Overview;732
22.2;Local and Global Parameter Sensitivities;733
22.3;Model Reduction Methodology;733
22.4;Parameter Ranking;734
22.4.1;Simple RMS Metric for Local Sensitivity-Based Parameter Ranking;735
22.4.2;Geometric Metric for Parameter Ranking;735
22.5;Added Benefits: State Variables to Measure and Parameters to Estimate;735
22.5.1;Reducing a Model of NF.B Signaling Dynamics;736
22.5.2;Parameter Ranking Metrics Based on Optimizing the Fisher Information Matrix F;737
22.5.3;Reducing a Model of Interleukin-6 (IL-6) Signaling Dynamics;738
22.5.4;Reducing an Overparameterized (OPM) Model of p53 Signaling Dynamics;738
22.6;Global Sensitivity Analysis (GSA) Algorithms;741
22.6.1;Weighted-Average of Local Relative Sensitivities (WAR) Spy=(.y/y)/(.p/p);743
22.6.1.1;The WAR Approximate GSA Algorithm;744
22.6.2;Multi-Parametric Sensitivity Analysis (MPSA);745
22.6.2.1;MPSA Algorithm;746
22.7;What’s Next?;746
22.8;Exercises;747
22.9;References;747
23;Appendix A: A Short Course in Laplace Transform Representations & ODE Solutions;750
23.1;Transform Methods;751
23.2;Laplace Transform Representations and Solutions;752
23.2.1;Two-Step Solutions;752
23.3;Key Properties of the Laplace Transform (LT) & its Inverse (ILT);753
23.4;Short Table of Laplace Transform Pairs;756
23.5;Laplace Transform Solution of Ordinary Differential Equations (ODEs);757
23.5.1;Partial Fraction Expansions;761
23.5.1.1;Inverse Transforms Using Partial Fraction Expansions;763
23.6;References;763
24;Appendix B: Linear Algebra for Biosystem Modeling;764
24.1;Overview;765
24.2;Matrices;765
24.3;Vector Spaces (V.S.);768
24.4;Linear Equation Solutions;768
24.4.1;Minimum Norm (MN) & Least Squares Pseudoinverse Solutions of Linear Equations;769
24.5;Measures & Orthogonality;769
24.6;Matrix Analysis;770
24.6.1;Matrix Norms;772
24.6.2;Matrix Calculus;772
24.6.3;Computation of f(A), an Analytic Function of a Matrix;774
24.6.3.1;Special Case (a): A=.;774
24.6.3.2;Special Case (b): Spectral Representation of A;775
24.6.3.3;The Cayley–Hamilton Theorem: An Alternative Method for Computing f(A);777
24.6.3.4;A Combination of the Previous Two Methods for Distinct Eigenvalues;778
24.6.3.5;For Nondistinct (Repeated) Eigenvalues;778
24.7;Matrix Differential Equations;779
24.8;Singular Value Decomposition (SVD) & Principal Component Analysis (PCA);780
24.8.1;Singular Value Decomposition (SVD);780
24.8.1.1;Some Properties of the SVD;781
24.8.2;Principal Component Analysis (PCA);781
24.8.3;PCA from SVD;782
24.8.4;Data Reduction & Geometric Interpretation;782
24.9;References;783
25;Appendix C: Input–Output & State Variable Biosystem Modeling: Going Deeper;784
25.1;Inputs & Outputs;785
25.2;Dynamic Systems, Models & Causality;786
25.3;Input–Output (Black-Box) Models;786
25.4;Time-Invariance (TI);787
25.5;Continuous Linear System Input–Output Models;788
25.5.1;Transfer Function (TF) Matrix for Linear TI Input–Output Models;788
25.6;Structured State Variable Models;789
25.6.1;State of a System S or Model M;789
25.6.2;State Variable Models from Input–Output (I–O) Models;789
25.6.3;Dynamic State Variable ODE Models for Continuous Systems;791
25.6.4;Complete Dynamic System Models: Constrained Structures;792
25.6.5;Linear TI State Variable Models;793
25.6.5.1;Input–Output TF Matrix for a State Variable Model;794
25.7;Discrete-Time Dynamic System Models;794
25.7.1;Discrete-Time Input–Output Models;794
25.7.2;The Sampled or z-Transfer Function;795
25.7.3;Discrete-Time State Variable Models;796
25.7.4;Sampled Input–Output Transfer Function Matrix;796
25.8;Composite Input–Output and State Variable Models;797
25.8.1;Composite Input–Output Models;797
25.8.2;Composite State Variable Models;798
25.9;State Transition Matrix for Linear Dynamic Systems;799
25.9.1;Input–Output Model Solutions;799
25.9.2;State Variable Model Solutions;799
25.9.2.1;Continuous Case;799
25.9.2.2;Intuitive Explanation of F;801
25.9.2.3;Time-Invariant Case;801
25.10;The Adjoint Dynamic System;802
25.11;Equivalent Dynamic Systems: Different Realizations of State Variable Models – Nonuniqueness Exposed;803
25.11.1;Key Properties of Equivalent System Models;803
25.11.1.1;Example C.1;804
25.11.1.1.1;Discrete-Time State Variable Models;804
25.12;Illustrative Example: A 3-Compartment Dynamic System Model & Several Discretized Versions of It;805
25.12.1;Discretization & Sampled-Data Representations of the 3-Compartment Model;806
25.12.1.1;Pulse-Train Inputs;807
25.12.1.2;Impulse-Train Inputs;808
25.12.2;Discretized ARMA Model with Impulse-Train Input;808
25.13;Transforming Input–Output Data Models into State Variable Models: Generalized Model Building;810
25.13.1;Time-Invariant Realizations;810
25.13.2;SISO Models;810
25.14;References;812
26;Appendix D: Controllability, Observability & Reachability;814
26.1;Basic Concepts and Definitions;815
26.1.1;Controllability;816
26.1.2;Observability;816
26.2;Observability and Controllability of Linear State Variable Models;818
26.3;Linear Time-Varying Models;818
26.3.1;Controllability Criterion;820
26.3.2;Observability Criterion;821
26.4;Linear Time-Invariant Models;821
26.4.1;Practical Controllability and Observability Conditions;821
26.5;Output Controllability;823
26.5.1;Time-Invariant (TI) Models;824
26.5.2;TI State Variable Models;824
26.6;Output Function Controllability;825
26.7;Reachability;826
26.8;Constructibility;828
26.9;Controllability and Observability with Constraints;831
26.10;Positive Controllability;831
26.11;Relative Controllability (Reachability);832
26.12;Conditional Controllability;832
26.13;Structural Controllability and Observability;833
26.14;Observability and Identifiability Relationships;833
26.15;Controllability and Observability of Stochastic Models;834
26.16;References;835
27;Appendix E: Decomposition, Equivalence, Minimal & Canonical State Variable Models;836
27.1;Realizations (Modeling Paradigms);837
27.2;The Canonical Decomposition Theorem;838
27.3;How to Decompose a Model;841
27.4;Controllability and Observability Tests Using Equivalent Models;844
27.4.1;SISO Models;845
27.4.1.1;Case 1;845
27.4.1.2;Case 2 (SISO);845
27.4.2;MIMO Models;846
27.4.2.1;Case 1;846
27.4.2.2;Case 2;846
27.4.3;Minimal State Variable (ODE) Models from I–O TFs (Data);848
27.4.3.1;Minimal SISO State Variable Models;848
27.4.3.2;Minimal MIMO State Variable Models;849
27.4.4;Canonical State Variable (ODE) Models from I–O Models (Data);849
27.4.4.1;Companion Canonical Models;849
27.4.4.2;Canonical State Variable Models for More General SISO TFs;851
27.4.4.3;Jordan-Canonical State Variable Models for N(s)/D(s);852
27.4.4.4;Controllable Canonical State Variable Models for N(s)/D(s);853
27.4.4.5;Observable Canonical State Variable (ODE) Models for N(s)/D(s);855
27.5;Observable and Controllable Canonical Forms from Arbitrary State Variable Models Using Equivalence Properties;856
27.6;References;860
28;Appendix F: More on Simulation Algorithms & Model Information Criteria;862
28.1;Additional Predictor-Corrector Algorithms;863
28.1.1;Modified Euler Second-Order Predictor and Corrector Formulas;863
28.1.2;An Iterative-Implicit Predictor–Corrector Algorithm;864
28.1.3;Noniterative, Predictor–Modifier–Corrector (P–M–C) Algorithms;864
28.1.3.1;Truncation Error Estimation;864
28.1.4;A Predictor-Modifier Corrector Algorithm Exemplified;865
28.1.5;The Backward-Euler Algorithm for Stiff ODEs;866
28.2;Derivation of the Akaike Information Criterion (AIC);866
28.2.1;The AIC for Nonlinear Regression;869
28.2.1.1;Case 1 – si2 Known;869
28.2.1.2;Case 2 – The Data Variances si2=ksi2 are Known Up to a Proportionality Constant k;870
28.3;The Stochastic Fisher Information Matrix (FIM): Definitions & Derivations;871
28.3.1;FIM for Multioutput Models;872
29;Index;874

Leseproben

Preface to the First Edition
Pedagogical Struggles
I’ve been learning and teaching mathematical (abbrev: math) modeling and computer simulation of biological systems for more than 47 years. As a control systems engineering graduate student in the 1960s searching for a research area, I found myself quite attracted by biological control systems. This was an esoteric and lonely direction at the time; the primary alternatives for control systems engineering PhD students in southern California were well-funded military control system projects most of my peers were choosing. Worthy, but not my calling. Biological control system modeling otherwise fit neatly into the realm of my major field. For added value, it also provided living examples for another collaborative writing project (DiStefano III et al. 1967). There was little integrated pedagogy or support at the time for the subject of my calling and I realized I faced a multidisciplinary learning task. I had to learn a great deal of new vocabulary (and jargon), and digest no small amount of new scientific knowledge – in biophysics and biochemistry as well as basic biology and physiology; all this before I could begin to develop models for addressing and helping solve real problems in life sciences. Credible math modeling – in any field – requires deep knowledge in the domain of the system being modeled. Multicultural aspects of my quest also became evident, as did the varieties of different approaches to modeling science. The cultures in which each of these disciplines function are quite different, most different between life sciences and math. In the 1960s, biology was largely empirical – still firmly rooted in observation and experiment – with a highly disciplined “wet-laboratory” culture. Quite foreign to my math-systems-engineering “work-anywhere-anytime” culture. Biology remains much that way and, although this is changing, it’s still very much reductionist. The other sciences and engineering rely on more theory, as well as empiricism, in the extreme often functioning successfully as “solo” (research) performances – no need for a culture! I minored in physiology as a PhD student and followed an early path studying physiological systems and mathematical and systems engineering-inspired methods for best modeling them. Biomodeling in those days was done primarily at macroscopic and whole-organism levels. Not any more. As technological breakthroughs in measurement technologies have burgeoned in the last half-century, the spatial and temporal scales over which biological systems knowledge is unfolding has generated a need for deeper understanding of molecular and cellular biology, biochemistry and neurobiology at more granular levels. In lieu of specializing in all these areas, interdisciplinary scientists have typically “picked-up” the needed knowledge along the way, as I did. Modern biomedical engineering programs now include the bio-basics. This means courses with substantive content in molecular and cellular biology as well as physiology and biochemistry. After earning my PhD in 1966, I began teaching modeling and simulation of dynamic biological systems via an ad hoc interdisciplinary major called “biocybernetics.” This developed later into a formal PhD field, as well as the moniker of my laboratory at UCLA. I’ve been wrestling with optimizing my pedagogical path ever since, adjusting it continually along the way, with the goal of communicating it ever-better, and upgrading it as new approaches and discoveries have emerged. Crystallizing and Focusing – My Way
MODELING, as such, can stand alone as a mature discipline, but it is done somewhat differently across the multidisciplinary spectrum of its practitioners, and has a history of being studied and developed on an “as-needed” basis, especially in the life sciences. There is, however, a substantial common core of methodologies for dynamic biosystem modeling widely disseminated in journals and books. Much of it is developed or described for different applications, or for single scales (e.g. molecular-cellular, organ-system, or population levels), using a variety of (and sometimes ambiguous) nomenclature. One of my goals as a teacher has been to help crystallize and unify the substance and language of this core of material – to make it more accessible to a larger audience – at the same time exposing and clarifying the ambiguities in some concepts and tools. I’ve been drawing from and merging aspects of the several classical disciplines involved with math modeling in biology into a unified subject matter, maximally comprehensible to undergraduates (and graduates) in any of these sciences or engineering. This textbook codifies this process. It offers a basics-to-intermediate-level treatment of modeling and simulation of dynamical biological systems, focused on classical and contemporary multiscale methodologies, consolidated and unified for modeling from molecular/cellular, organ-system, on up to population levels. It will undoubtedly be of interest to individuals from a variety of disciplines, probably with widely varying degrees of mathematical as well as life science training. It is intended primarily as an upper division (advanced undergraduate), graduate level or summer program textbook in biomedical engineering (bioengineering), computational biology, biomathematics, pharmacology and related departments in colleges and universities. The text material is written in a maximally tutorial style, also accessible to scientists and engineers in industry – anyone with an interest in math modeling and simulation (computational modeling) of biological systems. One or 2 years of college math are prerequisite and, for those with minimum preparation, the needed math (differential and difference equations, Laplace transforms, linear algebra, probability, statistics and stochastics topics, etc) is included either in methods development sections or in appendices. My approach to biomodeling is drawn in large part from my dynamic systems engineering and control theory viewpoint and training (the theory). But my 30 years of “wet-lab” research (the data) – closely integrated with and guided by biomodeling – plays an equal role. The two have motivated each other, first serendipitously, and then by design. Much of the book pedagogy is a distillation and consolidation of my own and my students’ modeling efforts and publications over half a century, including novel and previously unpublished features particularly relevant to modeling dynamic systems in biology. These include qualitative theory and methodologies for recognizing dynamical signatures in data, using structural (multicompartmental and network) models, and no small amount of algebra and graph theory for structuring models, discovering what they are capable of revealing about themselves – from data – and designing experiments for quantifying them from data. Approaches to biomodel formulation by various practitioners – interdisciplinary scientists with basic training in a diversity of fields – have many common features, for example, as found in references like (Rashevsky 1938/1948; Jacquez 1972; Carson et al. 1983; Murray 1993; Edelstein 2005; Palsson 2006; Alon 2007; Klipp et al. 2009; Voit 2012). I’ve made every effort to maintain the best of these developing features as they morph into our communities’ best traditions – toward developing a culture of its own. Following the practice of most expositions of modeling biological systems, the biology, biochemistry and biophysics needed to comprehend context, goals and biomodeling domain details are included within the chapters. Some of this supporting and complementary material is in the text proper, some is in footnotes – as much as needed and space considerations allow. Abundant citations to supplementary and advanced topics are included throughout.1 The chapters include exercises for students and solutions will be available for teachers on the book website. Ancillary material, including computer code and program files for many examples and exercises (Matlab, Simulink, VisSim, SimBiology, Copasi, SBML, Amigo model code, etc) also are included on the book website. In Other Words… & Other Didactic Devices
The substance and style of my teaching and writing developed from my experience in the classroom – typically populated by students from mixed subject backgrounds. Indubitably,2 interdisciplinary material typically needs more explanation, of one disciplinary sort or another. So, with major emphasis on being tutorial, exposition and development of biomodeling methods and applications in this text range from simple introductory material – understandable by any science student with high school math, some physics or chemistry, and maybe some biology – to fairly complex, requiring intermediate-level math skills. There may be more information than perhaps desired by one target group (e.g. the mathematicians) or the other, and I apologize for this necessity in advance. But that same target group should appreciate extra verbiage, examples or redundancy, when the extras are about what they know little about (e.g. cell biology). (So, maybe I should take back the apology?) In any case, such ‘distractions’ have been minimized, or isolated for purposes of ignoring them as desired – as I explain below. For mathematical exposition...