Analysis of Complex Diseases: A Mathematical Perspective

228 Pages·2013·5.117 MB·English

by  Wang, PhD, Guanyu

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CRC Press
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CRC Press
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Version Date: 20131029
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Dedication
To my wife Yanbing Xu
To my parents Jinzhi Pan and Zhuyan Wang
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Contents
Preface..................................................................xiii
AbouttheAuthor........................................................xvii
Prelude:Yin-YangPhilosophy.............................................xix
Abbreviations............................................................xxi
PART I Organismal Level: What Is Required
Chapter1 FoodIntakeandEnergyMetabolism.............................3
1.1 GastrointestinalTract......................................3
1.1.1 Stomach.........................................3
1.1.2 SmallIntestine...................................4
1.1.3 LargeIntestine...................................5
1.2 AccessoryDigestiveOrgans...............................5
1.2.1 Liver............................................5
1.2.2 Pancreas.........................................5
1.3 GlucoseTransportation....................................6
1.4 MetabolicProfileofOrgans................................9
1.4.1 Brain............................................9
1.4.2 SkeletalMuscle.................................10
1.4.3 CardiacMuscle..................................11
1.4.4 SmoothMuscle..................................12
1.4.5 Liver...........................................12
1.4.6 Kidney.........................................13
1.4.7 AdiposeTissue..................................13
1.5 GlucoseMetabolism.....................................14
1.5.1 Glycolysis......................................15
1.5.2 AlcoholicFermentation..........................17
1.5.3 LacticAcidFermentation.........................17
1.5.4 CitricAcidCycle................................17
1.5.5 OxidativePhosphorylation........................19
1.6 GlucoseStorageandGeneration...........................21
1.6.1 Glycogenesis....................................21
1.6.2 Glycogenolysis..................................22
1.6.3 Gluconeogenesis................................23
1.6.4 FatSynthesisFromGlucose......................24
Chapter2 GlucoseHomeostasis..........................................25
2.1 Homeostasis............................................25
2.2 Glucose-InsulinFeedbackSystem.........................26
2.2.1 Glucose.........................................26
2.2.2 Insulin..........................................26
2.2.3 GlucoseandInsulinHomeostasis..................27
2.2.4 AberrantHomeostasis............................28
vii
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viii Contents
2.3 MathematicalModeling..................................29
2.3.1 TheFunctionm(t)...............................30
2.3.2 TheFunction f(G)..............................31
2.3.3 FastingState....................................31
2.3.4 AbsorptiveState.................................32
Chapter3 OptimalGlucoseHomeostasis..................................33
3.1 OptimizationandHomeostasis............................33
3.2 FormulationoftheOptimizationProblem..................35
3.3 DeterminationofOptimalSolutions.......................36
3.4 LocalOptimality........................................36
3.4.1 Pontryagin’sMaximumPrinciple..................37
3.4.2 TheOptimalControlIsNecessarilyAll-or-None....37
3.4.3 TheOptimalu(t)isaSquarePulse................38
3.4.4 DeterminationoftheOptimalControlu(I).........39
3.4.5 TheOptimalControlu(I)IsaBistable(Toggle)
Switch..........................................40
3.4.6 TheThreshold I andItsHeterogeneity...........42
on
3.5 GlobalOptimality.......................................43
3.5.1 AssignmentofParameters........................43
3.5.2 SearchfortheGloballyOptimalControl...........43
3.5.3 InsightsfromtheObtainedGlobalOptima..........46
3.5.4 TheYin-YangInsulin............................49
Chapter4 BistabilityasaFundamentalPhenomenon.......................51
PART II Molecular Level: What Can Be Provided?
Chapter5 MolecularBiology............................................57
5.1 CentralDogmaofMolecularBiology......................57
5.1.1 DNAReplication(DNA→DNA).................57
5.1.2 Transcription(DNA→RNA).....................58
5.1.3 Translation(RNA→Protein).....................58
5.2 PosttranslationalModification.............................58
5.2.1 ProteinStructuralChanges........................58
5.2.2 AminoAcidChemicalChanges...................59
5.2.3 AdditionofOtherProteinsorPeptides.............59
5.2.4 AdditionofFunctionalGroups....................59
5.3 PhosphorylationandDephosphorylation...................60
5.3.1 SitesofProteinPhosphorylation...................60
5.3.2 FunctionsofProteinPhosphorylation..............60
5.3.3 NetworksofPhosphorylation.....................61
5.4 EnzymeKinetics........................................61
5.5 Ultrasensitivity..........................................64
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Contents ix
5.5.1 CooperativeBinding.............................64
5.5.2 Zero-OrderUltrasensitivity.......................65
5.6 Zero-OrderAdaptivity...................................69
Chapter6 BiomolecularNetwork.........................................73
6.1 StructuralProperties.....................................73
6.1.1 Modularity......................................73
6.1.2 RecurringMotifs................................74
6.1.3 RegulatoryMotifs...............................75
6.1.4 Scale-freeProperty..............................77
6.2 DynamicalProperties....................................78
6.2.1 DynamicalChangeandAttractor..................78
6.2.2 Stability........................................79
6.2.3 MonostabilityandMultistability...................80
6.2.4 Sensitivity......................................81
6.3 CentralChallenges.......................................81
Chapter7 PI3K-AKT-TORPathway......................................83
7.1 Phosphoinositide3-kinase(PI3K).........................83
7.1.1 ClassIPI3Ks ...................................84
7.1.2 ClassIIPI3Ks...................................84
7.1.3 ClassIIIPI3K...................................84
7.1.4 PI3KSignalingandInsulinResistance.............85
7.1.5 PI3KSignalingandCellGrowth..................85
7.1.6 PI3KSignalingandCancer.......................85
7.2 ProteinKinaseB(AKT)..................................86
7.2.1 AKTPhosphorylation(Activation)................86
7.2.2 AKTDephosphorylation(Deactivation)............87
7.2.3 AKTSignalingandMetabolism...................88
7.2.4 AKTSignalingandWhole-BodyGlucose
Homeostasis....................................88
7.3 TargetofRapamycin(TOR)..............................89
7.3.1 mTORComplex1...............................89
7.3.2 mTORC1Regulators.............................90
7.3.2.1 Nutrients...............................90
7.3.2.2 GrowthFactors.........................90
7.3.2.3 Energy.................................91
7.3.2.4 Stress..................................91
7.3.3 mTORComplex2...............................91
7.3.4 RapamycinandItsEffectsonmTOR..............92
7.3.5 mTORSignalingandCellGrowth.................92
7.3.5.1 FastingandStarvation...................93
7.3.5.2 OverfeedingandInsulinResistance.......93
7.3.5.3 AdipogenesisandLipogenesis............94
7.3.6 mTORSignalingandCancer......................94
7.4 PathwayDescription.....................................95