文件名称：Complexity in Chemistry
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Chemistry
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