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Complexity in Chemistry下载
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1. ON THE COMPLEXITY OFFULLERENES
AND NANOTUBES 1
′ ˇ ′
MilanRandic, Xiaofeng Guo,DejanPlavsicand Alexandru
T.Balaban
1. Introduction . . .......................... 1
2. On the ComplexityoftheComplexityConcept . . ....... 3
3. Complexity and Branching .................... 4
4. Complexity ofSmaller Molecules ................ 7
5. AugmentedValence asa Complexity Index . . . ....... 16
6. Complexity ofSmaller Fullerenes ................ 20
7. Comparisonof LocalAtomic Environments . . . ....... 25
8. The Roleof Symmetry . ..................... 29
9. ConcludingRemarkson the Complexity ofFullerenes ..... 34
10. On the ComplexityofCarbon Nanotubes ............ 36
10.1. Introductoryremarks . . ................ 36
10.2. Helicityof nanotubes . . ................ 38
Acknowledgement . . . ..................... 43
References . . .......................... 44
2. COMPLEXITYANDSELF-ORGANIZATIONIN
BIOLOGICALDEVELOPMENTANDEVOLUTION 49
Stuart A. NewmanandGabor Forgacs
1. Introduction: ComplexChemicalSystemsinBiological
DevelopmentandEvolution . .................. 49
2. Dynamic,MultistabilityandCellDifferentiation . ....... 51
2.1. Cellstatesanddynamics ................ 53
xv
xvi Contents
2.2. Epigenetic multistability:theKeller autoregulatory
transcriptionfactor network model .......... 55
2.3. Dependence ofdifferentiationon cell-cell
interaction: theKaneko-Yomo“isologous
Ddiversification” model ................ 59
3. BiochemicalOscillationsandSegmentation .......... 65
3.1. Oscillatorydynamicoscillationsandsomitogenesis . . 65
3.2. TheLewis model of the somitogenesis
oscillator . ....................... 66
4. Reaction-Diffusion Mechanismsand Embryonic
Pattern Formation ........................ 70
4.1. Reaction-diffusion systems ............... 71
4.2. Axisformationandleft-right asymmetry........ 71
4.3. Meinhardt’smodelsforaxisformationand
symmetry breaking ................... 72
5. Evolution of DevelopmentalMechanisms . . . ......... 76
5.1. Segmentationin insects ................. 77
5.2. Chemical dynamicsandthe evolutionof
insect segmentation ................... 80
5.3. Evolution ofdevelopmentalrobustness ........ 83
6. Conclusions . ........................... 89
References . ........................... 91
3. THE CIRCLETHAT NEVER ENDS:
CAN COMPLEXITY BE MADE SIMPLE? 97
Donald C.Mikulecky
1. Introduction:TheNatureoftheProblemandWhyit
Has No ClearSolution . . . ................... 97
1.1. Thehumanmind and the external world ........ 99
1.2. Scienceand the mythof objectivity . ......... 100
1.3. Contextdependenceandselfreference ......... 102
2. An IntroductiontoRelational SystemsTheory ......... 103
2.1. Relational blockdiagrams ............... 103
2.2. Informationasaninterrogative.
Theanswerto“why?” . . . .............. 104
2.3. Functionalcomponentsandtheir central role
incomplex systems ................... 106
2.4. Theanswerto“whyisthewholemore
thanthesumof its parts?” . .............. 106
2.5. Reductionismandrelationalsystemstheory
compared . ....................... 107
Contents xvii
2.6. Thefunctional componentisnotcomputable ..... 108
2.7. An example:the [M,R]systemand the
organism/machinedistinction ............. 108
2.8. Relational models ofmechanisms ........... 112
2.9. Newtonian dynamicsisnotunique;thereare
alternativesthat yield equivalentresults ........ 112
2.10. Topology, thermodynamics and
relational modeling . .................. 114
2.11. Themathematicsofscienceorisall
mathematicsscientific? ................. 117
2.12. Theparallelsbetween vectorcalculus and topology . . 118
3. The Structureof Network Thermodynamicsas Formalism . . 118
3.1. Networkthermodynamic modeling is
analogoustomodelingelectric circuits ........ 119
3.2. Thenetworkthermodynamicmodelofasystem . . . 120
3.3. Characterizingthenetworks usingan
abstraction of the network elements . . ........ 120
3.4. Thenatureofthe analogmodelsthat
constitutenetworkthermodynamics .......... 121
3.5. Theconstitutivelawsforallphysicalsystems
are analogoustotheconstitutivelawsforelectrical
networksorcanbeconstructedas themodelsfor
electronicelements .................. 122
3.6. The resistance as a general systems element ...... 123
3.7. The capacitanceas ageneralsystems element ..... 124
3.8. The topologyof a network . . . ............ 126
3.9. The formaldescriptionofanetwork .......... 126
3.10. The formalsolutionofalinearresistivenetwork . . . 128
3.11. The useofmultiportsforcoupledprocesses:
theentryto biological applications .......... 130
3.12. Linearmultiports arebasedon
non-equilibriumthermodynamics . . . ........ 130
4. Simulation ofNon-Linear Networkson Spice . . ....... 133
4.1. Simulationofchemical reactionnetworks ....... 134
4.2. Simulationofmasstransport in
compartamentalsystems and bulkflow ........ 134
4.3. Networkthermodynamicscontributions totheory:
somefundamentals ................... 135
4.4. The canonical representation oflinearnon-equilibrium
systems,the metricstructureofthermodynamics,
andtheenergetic analysis ofcoupledsystems .... 135
xviii Contents
4.5. Tellegen’stheoremandthe onsager
reciprocal relations (ORR) ............... 136
5. RelationalNetworksandBeyond . . . ............. 138
5.1. Amessagefrom network theory . . . ......... 138
5.2. An“emergent”property ofthe2-port
currentdivider . . ................... 139
5.3. Theuse ofrelationalsystems theory in
chemistryandbiology:past,present, and future . . . 141
5.4. Conclusion: thereisnoconclusion . . ......... 144
References . ........................... 148
4. GRAPHSASMODELSOFLARGE-SCALE
BIOCHEMICALORGANIZATION 155
′ ′
Pau Fernandezand Ricard V. Sole
1. Introduction ............................ 155
2. Basic PropertiesofRandom Graphs ............... 157
2.1. Degree distribution . .................. 158
2.2. Components ....................... 159
2.3. Average path length . .................. 159
2.4. Clustering . . ...................... 161
2.5. Small-worlds ....................... 162
3. Protein StructureandContact Graphs . ............. 164
3.1. Proteinsaresmall worlds . . . ............. 165
3.2. Hierarchicalclustering incontactmaps ........ 166
4. Protein Interaction Networks .................. 169
4.1. Assortativenessandcorrelations . . . ......... 171
4.2. Correlationprofiles ................... 172
4.3. Proteomemodel . . . .................. 175
5. Gene Networks .......................... 180
6. Overview . . ........................... 187
Acknowledgements . . ...................... 188
References . ........................... 188
5. QUANTITATIVE MEASURESOF
NETWORK COMPLEXITY 191
Danail Bonchevand GregoryA.Buck
1. Some History ........................... 191
2. Networksas Graphs . ...................... 193
2.1. Basic notions ingraphtheory[36-38] ......... 193
2.2. Adjacency matrixandrelated graph descriptors .... 195
2.3. Clustercoefficient and extendedconnectivity . .... 196
Contents xix
2.4. Graph distances ..................... 198
2.5. Weighted graphs ..................... 201
3. How to MeasureNetworkComplexity . ............ 202
3.1. Careful withsymmetry! . ................ 202
3.2. CanShannon’s informationcontent measure
topologicalcomplexity? . . . ............. 203
3.3. Global,average, andnormalizedcomplexity...... 205
3.4. Thesubgraphcount,SC, anditscomponents ..... 207
3.5. Overall connectivity, OC ................ 210
3.6. Thetotalwalk count,TWC ............... 211
4. Combined ComplexityMeasuresBasedon the
Graph Adjacency and Distance .................213
4.1. The A/D index . ..................... 213
4.2. The complexity index B ................. 215
5. Vertex AccessibilityandComplexity ofDirectedGraphs . . . 218
6. Complexity Estimates of Biological
and EcologicalNetworks . . . ..................221
6.1. Networksof ProteinComplexes ............ 222
6.2. Foodwebs . . . ..................... 226
7. Overview . . . .......................... 230
Acknowledgement . . . ..................... 232
References . . .......................... 232
6. CELLULARAUTOMATAMODELS OFCOMPLEX
BIOCHEMICAL SYSTEMS 237
Lemont B. Kierand Tarynn M. Witten
1. Reality,Systems,andModels .................. 237
1.1. Introduction ....................... 237
1.2. The “what” ofmodelingandsimulation ........ 238
1.3. Back tomodels ..................... 244
1.4. Modelsinchemistryandmolecularbiology ...... 246
2. GeneralPrinciples ofComplexity ................ 248
2.1. Defining complexity:complicatedvs.complex .... 248
2.2. Definingcomplexity:agents,hierarchy,
self-organization,emergence,anddissolvence .... 250
3. ModelingEmergence inComplexBiosystems ......... 257
3.1. Cellularautomata .................... 257
3.2. Thegeneralstructure . . ................ 258
3.3. Cellmovement ..................... 262
3.4. Movement (transition)rules ............... 267
3.5. Collectionofdata .................... 273
xx Contents
4. Examples ofCellularAutomata Models . . . ......... 274
4.1. Introduction ....................... 274
4.2. Waterstructure . . . .................. 275
4.3. Cellularautomatamodels of molecularbond
interactions ....................... 277
4.4. Diffusion inwater . . .................. 280
4.5. Chreodetheoryof diffusioninwater . ......... 283
4.6. Modelingbiochemical networks ............ 289
5. General Summary ........................ 297
References . ........................... 298
7. THE COMPLEXNATUREOFECODYNAMICS 303
Robert E. Ulanowicz
1. Introduction ............................ 303
2. Measuring The EffectsofIncorporatedConstraints . . .... 306
3. Ecosystemsand Contingency .................. 307
4. Autocatalysis andNon-MechanicalBehavior . ......... 311
5. Causality Reconsidered . . . .................. 316
6. Quantifying Constraintin Ecosystems ............. 318
7. New ConstraintstoHelpFocus aNewPerspective ....... 324
Acknowledgements . . ...................... 327
References . ........................... 327
NAME INDEX . . ........................... 331
SUBJECTINDEX ........................... 337
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