Dynamic Systems Biology Modeling and Simulation

882 Pages·2013·55.644 MB·English

by  Joseph DiStefano III

DYNAMIC
SYSTEMS
BIOLOGY
MODELING
AND
SIMULATION
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DYNAMIC
SYSTEMS
BIOLOGY
MODELING
AND
SIMULATION
Joseph DiStefano III
AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON
NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO
SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO
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“For anyone interested in kinetic modeling of substances in physiological systems, Chapter 8 is a must
read. Itsoelegantly coversthe three important areas the readerislikely toencounter ina widerreading
ofthesubject,namelyphysiologically-basedmodelsoforgansandwhole-bodysystems,multicompartmen-
talmodelsappliedtosuchsystems,andapplication ofnoncompartmentalmodels.Itisrareto findinone
chapter all three elements succinctly explored yet in sufficient depth to allow the reader meaningful
insights into their application, pitfalls and limitations. Throughout the chapter the assumptions of system
linearity and stationarity underpin much of the mathematical development, and the reader is rightfully
cautioned that there are situations encountered, for example in toxicology and pharmacology, where one
or more processes is saturable at the applied dose, rendering the system nonlinear, which can often be
readilyincorporatedinthemodelingprocess.”
MalcolmRowland
ProfessorofPharmacy,
UniversityofManchester,U.K.
“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
agreat new contributiontothetextbook offerings in systems biology.”
AlexHoffman
DirectoroftheSanDiegoCenter
forSystemsBiologyandtheUCSDGraduateProgram
inBioinformaticsandSystemsBiology
“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
masterathletewhodoesimpossibleperformancesandmakesthemseemeasy.
“Your Chapter 9 (cid:1) on oscillations and stability (cid:1) 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
understandingyouofferthereader.Youareagreatexplainerandteacher.”
F.EugeneYates
EmeritusProfessorofMedicine,
ChemicalEngineeringandRalphandMarjorieCrumpProfessor
ofBiomedicalEngineering,UCLA
“Chapter 4 covers many aspects of the notion of compartmentalization in the structural modeling of
biomedicalandbiologicalmodels(cid:1)bothlinearandnonlinear.Developmentsarebiophysicallymotivated
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
beenpresented.
“Chapter 5 looks at many important aspects of multicompartmental modeling, examining in more detail
howoutputdatalimitwhatcanbelearntaboutmodelstructure,evenwhensuchdataareperfect.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 ispossibleto simplifya model. All ofthisisdonewith
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
examplesgivenattheend.”
ProfessorKeithGodfrey
UniversityofWarwick,
Coventry,U.K.
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ONTENTS
Preface .............................................................................................................................................................xv
1 Biosystem Modeling & Simulation: Nomenclature
& Philosophy ..........................................................................................1
Overview ............................................................................................................................................................3
ModelingDefinitions .........................................................................................................................................3
ModelingEssentialSystemFeatures ................................................................................................................7
PrimaryFocus:Dynamic(Dynamical)SystemModels .................................................................................11
MeasurementModels&DynamicSystemModelsCombined:Important! ...................................................15
Stability ............................................................................................................................................................17
Top-Down&Bottom-UpModeling ...............................................................................................................20
Source&SinkSubmodels:OneParadigmforBiomodelingwithSubsystemComponents .........................21
Systems,Integration,Computation&ScaleinBiology .................................................................................22
OverviewoftheModelingProcess&BiomodelingGoals ............................................................................27
LookingAhead:ATop-DownModeloftheChapters ...................................................................................34
References .......................................................................................................................................................36
2 Math Models of Systems: Biomodeling 101 .....................39
SomeBasics&aLittlePhilosophy ................................................................................................................41
AlgebraicorDifferentialEquationModels ....................................................................................................42
Differential&DifferenceEquationModels ...................................................................................................43
DifferentKindsofDifferential&DifferenceEquationModels ....................................................................45
Linear&NonlinearMathematicalModels .....................................................................................................47
Piecewise-LinearizedModels:Mild/SoftNonlinearities ................................................................................52
SolutionofOrdinaryDifferential(ODE)&DifferenceEquation(DE)Models ...........................................53
SpecialInputForcingFunctions(Signals)&TheirModelResponses:Steps&Impulses ...........................58
viii Dynamic Systems Biology Modeling and Simulation
StateVariable ModelsofContinuous-TimeSystems .....................................................................................61
LinearTime-Invariant(TI)Discrete-TimeDifferenceEquations(DEs)&TheirSolution ..........................65
Linearity&Superposition ...............................................................................................................................69
LaplaceTransformSolutionofODEs ............................................................................................................70
TransferFunctionsofLinearTIODEModels ...............................................................................................75
MoreonSystemStability ................................................................................................................................79
LookingAhead ................................................................................................................................................80
Exercises ..........................................................................................................................................................82
References .......................................................................................................................................................83
3 Computer Simulation Methods ...............................................85
Overview ..........................................................................................................................................................88
Initial-ValueProblems ....................................................................................................................................90
GraphicalProgrammingofODEs ...................................................................................................................90
Time-DelaySimulations ..................................................................................................................................96
MultiscaleSimulationandTime-Delays ........................................................................................................99
NormalizationofODEs:Magnitude-&Time-Scaling ................................................................................104
NumericalIntegrationAlgorithms:Overview ..............................................................................................109
TheTaylorSeries ..........................................................................................................................................110
TaylorSeriesAlgorithmsforSolvingOrdinaryDifferentialEquations ......................................................112
Computational/NumericalStability ...............................................................................................................116
Self-StartingODESolutionMethods ............................................................................................................117
AlgorithmsforEstimatingandControllingStepwisePrecision ..................................................................122
TaylorSeries-BasedMethodComparisons ...................................................................................................124
StiffODEProblems .......................................................................................................................................126
HowtoChooseaSolver? ..............................................................................................................................129
SolvingDIFFERENCEEquations(DEs)UsinganODESolver .................................................................131
OtherSimulationLanguages&SoftwarePackages .....................................................................................133
TwoPopulationInteractionDynamicsSimulationModelExamples ..........................................................135
TakingStock&LookingAhead ...................................................................................................................138
Exercises ........................................................................................................................................................139
References .....................................................................................................................................................142
4 Structural Biomodeling from Theory & Data:
Compartmentalizations ..............................................................143
Introduction ...................................................................................................................................................145
Compartmentalization:AFirst-Level FormalismforStructuralBiomodeling ............................................146
Contents ix
MathematicsofMulticompartmentalModelingfromtheBiophysics .........................................................157
NonlinearMulticompartmentalBiomodels:SpecialProperties&Solutions ..............................................170
DynamicSystemNonlinearEpidemiologicalModels ..................................................................................174
CompartmentSizes,Concentrations&theConceptofEquivalentDistributionVolumes .........................177
Generaln-CompartmentModelswithMultipleInputs&Outputs ..............................................................180
Data-DrivenModelingofIndirect&Time-Delayed Inputs .........................................................................191
Pools&PoolModels:AccommodatingInhomogeneities ............................................................................195
Recap&LookingAhead ...............................................................................................................................197
Exercises ........................................................................................................................................................198
References .....................................................................................................................................................202
5 Structural Biomodeling from Theory & Data: Sizing,
Distinguishing & Simplifying Multicompartmental
Models .................................................................................................205
Introduction ...................................................................................................................................................207
OutputData(DynamicalSignatures)Reveal DynamicalStructure .............................................................207
MulticompartmentalModelDimensionality,ModalAnalysis&DynamicalSignatures ............................210
ModelSimplification:HiddenModes&AdditionalInsights ......................................................................224
BiomodelStructureAmbiguities:ModelDiscrimination,Distinguishability&
Input(cid:1)OutputEquivalence ............................................................................................................................227
AlgebraandGeometryofMCModelDistinguishability .............................................................................235
Reducible,Cyclic&OtherMCModelProperties .......................................................................................238
Tracers,Tracees&LinearizingPerturbationExperiments ..........................................................................239
RecapandLookingAhead ............................................................................................................................246
Exercises ........................................................................................................................................................247
References .....................................................................................................................................................251
6 Nonlinear Mass Action & Biochemical
Kinetic Interaction Modeling ...................................................253
Overview ........................................................................................................................................................255
KineticInteractionModels ............................................................................................................................256
LawofMassAction ......................................................................................................................................266
ReactionDynamicsinOpenBiosystems ......................................................................................................268
Enzymes&EnzymeKinetics .......................................................................................................................270
Enzymes&IntroductiontoMetabolicandCellularRegulation ..................................................................283
Exercises ........................................................................................................................................................295