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MATH Northrop
Introduction to
COMPLEXITY AND COMPLEX SYSTEMS
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The boundaries between simple and complicated, and complicated and complex d
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system designations are fuzzy and debatable, even using quantitative measures
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of complexity. However, if you are a biomedical engineer, a biologist, physiologist, t
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economist, politician, stock market speculator, or politician, you have encountered o
complex systems. Furthermore, your success depends on your ability to successfully n
interact with and manage a variety of complex systems. In order not to be blindsided to
by unexpected results, we need a systematic, comprehensive way of analyzing, C
modeling, and simulating complex systems to predict unanticipated outcomes. O
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In its engaging first chapters, the book introduces complex systems, Campbell's
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Law, and the Law of Unintended Consequences, and the mathematics necessary
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for conversations in complex systems. Subsequent chapters illustrate concepts via E
commonly studied biological mechanisms. The final chapters focus on higher-level X
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complexity problems, and introduce complexity in economic systems.
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Designed as a reference for biologists and biological engineers, Introduction to
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Complexity and Complex Systems lends itself to use in a classroom course to N
introduce advanced students studying biomedical engineering, biophysics, or D
physiology to complex systems. Engaging and illustrative, this book aids scientists
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and decision makers in managing biological complexity and complex systems.
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Composite
Introduction to
COMPLEXITY AND
COMPLEX SYSTEMS
Robert B. Northrop
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
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particular pedagogical approach or particular use of the MATLAB® software.
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Version Date: 20140703
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I dedicate this text to my complex family.
Contents
Preface................................................................................................................xiii
Author.................................................................................................................xix
Chapter 1 Introduction.to.Complexity.and.Complex.Systems..........................1
1.1. Introduction.to.Complexity...................................................1
1.1.1. When.Is.a.System.Complex?....................................2
1.1.2. Examples..................................................................4
1.1.3. Properties.of.Complex.Systems:.Chaos.and.
Tipping.Points..........................................................5
1.1.4. Law.of.Unintended.Consequences...........................7
1.1.5. Complex.Adaptive.Systems....................................12
1.2. Why.Study.Complex.Systems?............................................13
1.3. Human.Responses.to.Complexity.......................................14
1.4. Complex.Systems.Engineering............................................18
1.5. Summary.............................................................................21
Problems.........................................................................................21
Chapter 2 Introduction.to.Large.Linear.Systems............................................23
2.1. Introduction.........................................................................23
2.2. Linearity,.Causality,.and.Stationarity..................................23
2.3. LTI.System.Tools:.Impulse.Response,.Frequency.
Response,.and.Real.Convolution.........................................25
2.3.1. Transient.Response.of.Systems..............................25
2.3.2. Real.Convolution....................................................25
2.3.3. Steady-State.Sinusoidal.Frequency.Response.
of.LTI.Systems.......................................................31
2.4. Systems.Described.by.Large.Sets.of.Linear.ODEs.............36
2.4.1. Introduction............................................................36
2.4.2. Introduction.to.Matrix.Algebra.and.State.
Variables.................................................................37
2.4.2.1. Matrix.Algebra.......................................37
2.4.2.2. Review.of.Some.Matrix.Operations.......38
2.4.2.3. Introduction.to.State.Variables...............42
2.5. Stability.of.Linear.Systems.................................................48
2.6. Signal.Flow.Graphs.and.Mason’s.Rule................................49
2.6.1. Introduction............................................................49
2.6.2. Signal.Flow.Graphs................................................50
v
vi Contents
2.6.3. Examples.of.Linear.SFG.Reduction.......................51
2.6.4. Measures.of.SFG.Complexity................................57
2.7. Summary.............................................................................58
Problems.........................................................................................59
Chapter 3 Introduction.to.Biochemical.Oscillators.and.Complex,.
Nonlinear.Biochemical.Systems....................................................67
3.1. Introduction:.Some.General.Properties.of.
Nonlinear.Systems...............................................................67
3.2. All.Living.Systems.Are.Nonlinear......................................73
3.2.1. Introduction............................................................73
3.2.2. Mass-Action.Kinetics.and.Nonlinearity.in.
Chemical.Systems..................................................74
3.2.3. Examples.of.Mass-Action.Kinetics........................74
3.3. Parametric.Regulation.in.Complex.Biological.Systems......79
3.3.1. Modeling.Parametric.Control.of.Enzyme.
Function..................................................................84
3.4. Stability,.Limit-Cycle.Oscillations,.and.Chaos.in.
Nonlinear.Biological.Systems.............................................85
3.4.1. Introduction............................................................85
3.4.2. Stability.in.Simple.Linear.and.Nonlinear.
Systems:.Introduction.to.Phase-Plane.Analysis.....86
3.4.3. Examples.of.Simple.Nonlinear.ODEs.with.
Oscillatory.Behavior..............................................89
3.4.4. Instability.in.Systems.with.Transport.Lags...........101
3.4.5. Some.Models.for.Complicated.and.Complex.
Biochemical.Oscillators.......................................105
3.4.6. Synchronization.of.Groups.of.Biological.
Oscillators:.Quorum.Sensing...............................121
3.5. Summary...........................................................................125
Problems.......................................................................................125
Chapter 4 Modularity,.Redundancy,.Degeneracy,.Pleiotropy,.and.
Robustness.in.Complex.Biological.Systems.................................135
4.1. Introduction.......................................................................135
4.2. Measures.of.Modularity....................................................136
4.3. Modularity.in.Physiological.Organ.Systems.....................138
4.3.1. Introduction..........................................................138
4.3.2. Modularity.in.Organ.Systems..............................138
4.3.2.1. Pancreas................................................138
4.3.2.2. Modularity.in.the.hIS...........................138
4.3.2.3. Modularity.and.Plasticity.in.the.hCNS....140
Contents vii
4.4. Modularity.in.Gene.Regulation.and.Development............142
4.4.1. Operons.in.Prokaryotes.and.Eukaryotes..............142
4.4.2. Homeobox.and.Hox.Genes...................................146
4.4.3. Dlx.Genes.............................................................149
4.4.4. Msx.Genes............................................................150
4.5. Network.Motifs.and.Modularity........................................150
4.5.1. Introduction..........................................................150
4.5.2. Motifs.in.E. coli.Transcription.Regulation..........150
4.5.3. Role.of.MicroRNAs.in.Regulatory.Motifs...........155
4.5.4. Summary..............................................................156
4.6. Robustness,.Degeneracy,.Pleiotropy,.and.Redundancy.....156
4.6.1. Introduction..........................................................156
4.6.2. Sensitivities...........................................................157
4.6.3. Noise.Sensitivity...................................................158
4.6.4. Temperature.Sensitivity........................................159
4.6.5. Degeneracy,.Pleiotropy,.and.Redundancy............159
4.6.6. Operons.and.Robustness......................................165
4.7. Summary...........................................................................166
Problems.......................................................................................166
Chapter 5 Evolution.of.Biological.Complexity:.
Invertebrate.Immune.Systems......................................................169
5.1. Introduction.......................................................................169
5.2. Darwinian.Evolution:.A.Brief.Summary...........................170
5.2.1. Introduction...........................................................170
5.3. Why.Does.a.Rise.in.Complexity.Accompany.
Biological.Evolution?..........................................................173
5.3.1. Introduction...........................................................173
5.3.2. Speciation..............................................................175
5.3.3. Origins.of.Species.................................................176
5.3.4. Speciation.by.Horizontal.Gene.Transfer.and.
Transposons..........................................................179
5.4. Examples.of.Biological.Complexity.in.Invertebrate.
Immune.Systems................................................................181
5.4.1. Introduction...........................................................181
5.4.2. Some.Examples.of.Invertebrate.Immunity..........183
5.4.2.1. Sea.Urchins...........................................183
5.4.2.2. Drosophila melanogaster.and.
Other.Dipteran.Insects..........................183
5.4.3. Maggot.Therapy...................................................185
5.4.4. Anticipatory.Responses.or.Immune.
Memory?—Inoculation.in.Invertebrates..............187
viii Contents
5.4.5. Bacterial.AMPs....................................................188
5.4.6. Invertebrate.AMPs:.Applications.in.
Biomedicine..........................................................190
5.5. Summary...........................................................................193
Problems.......................................................................................194
Chapter 6 Complex.Adaptive.and.Innate.Human.Immune.Systems............197
6.1. Introduction.......................................................................197
6.2. Overview.of.the.Complex.Adaptive.hIS............................198
6.3. Summary.of.the.Cells.of.the.hIS.......................................200
6.3.1. Introduction..........................................................200
6.3.2. Macrophages........................................................201
6.3.3. Dendritic.Cells.....................................................203
6.3.4. T-Lymphocytes.....................................................205
6.3.5. Suppressor.T-Cells...............................................207
6.3.6. B-Cells.and.Antibodies........................................208
6.3.7. Memory.B-.and.T-Cells........................................211
6.3.8. Trafficking.of.hIS.Cells........................................212
6.4. Mammalian.Innate.Immune.Systems...............................213
6.4.1. Introduction..........................................................213
6.4.2. Natural.Killer.Cells..............................................213
6.4.3. Neutrophils............................................................214
6.4.4. Mast.Cells.and.Platelets........................................214
6.4.5. Human.Complement.System.................................216
6.4.6. Human.AMPs.in.Innate.Immunity:.The.
Urinary.Tract.........................................................219
6.5. Antigen.Presentation.........................................................220
6.6. Autacoids:.Immunocytokines,.Proteins,.and.
Glycoproteins.Secreted.by.hIS.Cells.................................222
6.7. Discussion:.How.the.hIS.Is.Adaptive................................234
6.8. Catalytic.Antibodies.as.Therapeutic.Agents.....................235
6.9. Summary...........................................................................237
Chapter 7 Complexity.in.Quasispecies.and.MicroRNAs.............................239
7.1. Quasispecies:.Viral.and.Bacterial.Evolutionary.Models.....239
7.1.1. Introduction..........................................................239
7.1.2. VQS.Models.........................................................240
7.1.3. BQS.Models.........................................................242
7.2. Role.of.MicroRNAs.in.the.Regulation.of.Gene.
Expression.and.Disease.....................................................243
7.2.1. Introduction..........................................................243
7.2.2. Mechanisms.of.miRNA.Regulation.of.Gene.
Expression............................................................244
Contents ix
7.2.3. Physiological.Functions.of.miRNAs....................245
7.2.4. miRNAs.in.Disease..............................................246
7.2.4.1. Viruses..................................................246
7.2.4.2. Cancer...................................................247
7.2.4.3. Other.Diseases......................................247
7.2.5. Evolution.of.Gene.Regulation.by.miRNAs..........248
7.3. Summary...........................................................................248
Chapter 8 Introduction.to.Physiological.Complexity:.Examples.of.
Models.of.Some.Complex.Physiological.Systems........................251
8.1. Introduction.......................................................................251
8.2. Physiology.Defined............................................................252
8.3. Homeostasis.......................................................................256
8.4. Structure.and.Function:.Some.Examples.of.Complex.
Physiological.Regulatory.Systems.and.Their.
Simplified.Models.............................................................257
8.4.1. Introduction..........................................................257
8.4.2. Glucoregulation....................................................258
8.4.2.1. Introduction..........................................258
8.4.2.2. Molecules.Important.in.Glycemic.
Regulation.............................................259
8.4.2.3. Hormone.Leptin....................................261
8.4.2.4. Neuropeptide.Y.....................................263
8.4.2.5. Normal.Blood.Glucose.Regulation.
System...................................................265
8.4.2.6. Simple,.Compartmental.Model.for.
Normal.Blood.Glucose.Regulation.......268
8.4.3. hIS.vs..HIV...........................................................277
8.4.3.1. Introduction..........................................277
8.4.3.2. Models.of.HIV.Infection.and.AIDS.....281
8.4.3.3. Reibnegger.hIS.Model..........................289
8.4.3.4. hIS.Model.of.Northrop.(2000).............294
8.4.4. Human.Immune.System.vs..Cancer.....................298
8.4.4.1. Introduction..........................................298
8.4.4.2. Cancer.Vaccines.and.Immunotherapy.....300
8.4.4.3. DeBoer’s.Model.of.the.hIS.vs..
Cancer................................................302
8.4.4.4. hIS.vs..Cancer.Model.of.Clapp.et.al..
(1988)....................................................304
8.4.4.5. Discussion.............................................307
8.5. Examples.of.When.Complex.Physiological.
Systems.Fail...................................................................312
8.5.1. Introduction...........................................................312
8.5.2. General.Organ.Failure...........................................312
