A Toy Model of Chemical Reaction Networks - TBI - UniversitÃ¤t Wien

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10 CHAPTER 2. ARTIFICIAL CHEMISTRIES Educts Intermediates Products Figure 2.2: The Atomoid model. Molecules are built from “atoms” connected by bond handles differingin energy level and energy structure. Initiation −→ Elongation −→ Termination −→ Figure 2.3: Simulation steps of RNA growth by the rewritable graph chemistry of [78]. the system from the start. These simple artificial atomic reaction rules lead to dissipative structures. The model enables one to follow on an atomic level how those dissipative structures lead to the emergence of self-reproductive hypercycles. Fig. 2.2 shows a simple example network. The rewritable graph chemistry of [78], fig. 2.3, is designed to be complementary to the string-oriented analysis of nucleic acid polymers. The string editing is replaced by graph rewriting rules. They are encoded by subgraph graph replacements on labeled graphs called variable graphs, rep-
2.2. ATOMOIDS, GRAPHS, AND MATRICES 11 Mass spectrum calculation Molecular property prediction EROS ODE integration reactors, phases and modes Reaction rules Figure 2.4: Modular organization of the organic chemistry simulation package EROS. resenting chemical reactions. This model is used to simulate DNA and RNA transformations like enzymatic processing or combinatorial networks of catalyzed reactions. The model generates all possible derivation paths. It could be applied also to small organic molecules. The Iterated Graph Model of [83] applies a limited subset of chemical reactions to a soup of molecules. Each chemical reaction, in this case food-browning reaction, is implemented as a separate function working on a molecular graph. The dynamics of the system are simulated by explicit collision. Pairs of molecules are chosen with a frequency proportional to their concentration in the soup and are submitted to a reaction function with a probability equivalent to the reaction rate. The reaction rates are fitted to match the evolution of the concentrations to experimental values. EROS [50] is similar to the Toy Model by its straightforward implementation. Its basic architecture transparently reflects the three components molecules, reactions, and networks. The energy calculation for molecules involves are rule-based efficient generation of 3D coordinates, which makes it possible to accurately calculate many molecular properties. Reactions are hard-coded by two general reaction schemes. They are essentially pseudopericyclic σ and π electron shiftings whereby bonds are broken and formed. The CRN is generated exhaustively. The CRN generation can be combined with a “sifting-out of reactions”, a model reduction based on reaction site properties, reaction enthalpy and reaction rates. EROS also implements phases, see fig. 2.4 for its module-oriented organization. Approaches trying to avoid hard-coding reactions need to use a description of generic reactions [59]. The description used by the Toy Model is presented in sect. 4.1. SMIRKS is a development of SMILES (sect. 3.3) capable of encoding generic reaction transforms as a line notation. However, rewrite rules are graphs and thus do not have the limitations of a line notation representation. Although all graph representations of generic reaction contain the same information [110, ch. 1], they differ by the stage or the part of the reaction
Page 1 and 2: A Toy Model of Chemical Reaction Ne
Page 3: i Dank an alle, die zum Gelingen di
Page 7: v Zusammenfassung Chemische Reaktio
Page 10 and 11: viii CONTENTS B GRW 61 C Organic re
Page 12 and 13: 2 CHAPTER 1. INTRODUCTION ▽ △
Page 14 and 15: 4 CHAPTER 1. INTRODUCTION ¡ ¡ ¡
Page 16 and 17: 6 CHAPTER 1. INTRODUCTION and symme
Page 18 and 19: 8 CHAPTER 2. ARTIFICIAL CHEMISTRIES
Page 22: 12 CHAPTER 2. ARTIFICIAL CHEMISTRIE
Page 25 and 26: 3.1. EXTENDED HÜCKEL THEORY 15 is
Page 27 and 28: 3.2. FURTHER APPROXIMATIONS 17 K. F
Page 29 and 30: 3.2. FURTHER APPROXIMATIONS 19 Figu
Page 31 and 32: 3.2. FURTHER APPROXIMATIONS 21 are
Page 33 and 34: 3.3. CHEMICAL STRUCTURE REPRESENTAT
Page 35 and 36: 3.3. CHEMICAL STRUCTURE REPRESENTAT
Page 37 and 38: 3.4. WAVE FUNCTION ANALYSIS 27 Derw
Page 39 and 40: Table 3.6: Overlap matrix for prope
Page 41 and 42: 3.5. PERFORMANCE 31 3.5 Performance
Page 43 and 44: 3.6. FRONTIER MOLECULAR ORBITAL THE
Page 45 and 46: Chapter 4 Chemical reactions A mole
Page 47 and 48: 4.1. GRAPH REWRITING 37 Graphical t
Page 49 and 50: 4.1. GRAPH REWRITING 39 C C C C C C
Page 51 and 52: 4.2. GRAPH REWRITE ENGINE 41 O O O
Page 53 and 54: Chapter 5 Reaction networks 5.1 Net
Page 55 and 56: 5.3. NETWORK PROPERTIES 45 O 3 NO 3
Page 57 and 58: 5.3. NETWORK PROPERTIES 47 (see ch.
Page 59 and 60: Chapter 6 Computational results Whe
Page 61 and 62: O O O O O O O O O O O O O O O O O O
Page 63 and 64: 6.3. GRAPH-THEORETIC PROPERTIES 53
Page 65 and 66: Chapter 7 Conclusion and Outlook Th
Page 67 and 68: Using the rules of mass action kine
Page 69 and 70: Appendix A Parameters The energy ca
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Appendix B GRW GRW is implemented i
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Appendix C Organic reactions Fromht
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Bibliography [1] R. Albert and A.-L
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BIBLIOGRAPHY 67 [25] O. Diels and K
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BIBLIOGRAPHY 69 [50] J. Gasteiger a
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BIBLIOGRAPHY 71 [76] W. Langenbeck.
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BIBLIOGRAPHY 73 [102] S. Schuster,
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BIBLIOGRAPHY 75 [126] R. Woodward a
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The Wooing of Archibald Modern tren
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