We use a Toy Model of chemistry that represents molecules in terms of usual structural formulae to generate large chemical reaction networks. An extremely simplified quantum mechanical energy calculation and a straightforward implementation of reactions as graph rewritings ensure both transparency and closeness to chemical reality, both conditions that are necessary for the analysis of generic properties of large reaction networks. We show that some chemical networks graphs, e.g., repetitive Diels-Alder reactions, have the small-world property and exhibit a scale-free degree distribution. On the other hand, the Formose reaction does not fit well to this paradigm.

Artificial chemistries can be used to explore the generic properties of chemical reaction networks. In order to simulate for instance scenarios of prebiotic evolution the model must be close enough to real chemistry to allow at least semi-quantitative comparisons. One example is a previously described Toy Model that represents molecules as graphs, thereby neglecting 3D space, and employs a highly simplified version of the Extended H¨uckel Theory (EHT) to compute molecular properties. Here we show how the Toy Model can be extended to multiple phases by connecting the EHT calculations with chemical thermodynamics.

A Toy Model of an artificial chemistry that treats molecules as graphs was implemented based on a simple Extended Hückel Theory method. Here we describe an extension of the model that models chemical reactions as the result of “collisions”. In order to avoid a possible bias arising from prescribed generic reaction mechanisms, the reactions are simulated in a way that treats the formation and breakage of individual chemical bonds as elementary operations.

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: This thesis gives a broad overview of what artificial chemistries (ACs) are, a brief review of several ACs and their applications, and an in depth analysis of one speci c AC: the four-bit binary string system. The model designed by Banzhaf [1] for in silico examination was recreated using the Python programming language. The initial motivation was to identify an existing AC that could be used to elucidate the sequence-function relationship, which led to the simultaneous investigation of self-organization in AC systems [7]. The interest in sequence-function relationships stems from their importance for self-production of objects [35]. For self-replication to be possible in larger organizations, the components of the organization must be able to continuously produce themselves [3, 7]. We chose the four-bit binary string system for investigation because of its simple design and implementation, its ability to yield complex results from interactions between a small population of objects, and its analogy to the DNA{RNA{protein organisation. When a population of objects are allowed to continuously interact, self-production and self-organization occur, even in simple arti cial systems [7, 8]. The stability of the emergent organizations depends on the interactions of its components, which must be capable of self-production if they are to maintain the organization [27]. Self-production of objects depends on their sequence-function relationship, which determines their rate of replication when interacting with other objects. / AFRIKAANSE OPSOMMING: Hierdie tesis verskaf `n bree oorsig van die algemene aard van artifisiele chemies (ACs), `n kort opsomming van `n paar ACs en hul toepassings, en `n diepgaande analise van een spesifieke AC: die 4-bis binere stringstelsel. Die model wat Banzhaf [1] ontwerp het vir in silico eksperimentering is hier herskep in die Python programmeringstaal. Die aanvanklike motivering was om `n bestaande AC te identifiseer wat gebruik kon word om die sekwens-funksie verwantskap te ontrafel, en dit het gelei tot die gelyktydige ondersoek van self-organisasie in AC stelsels [7]. Ons belangstelling in sekwens-funksie verwantskappe spruit uit hul belang vir die selfproduksie van objekte [35]. Om selfreplisering in meer omvangryke organisasies moontlik te maak moet die komponente in staat wees om hulself eenstryk te produseer [3, 7]. Ons het `n 4-bis stelsel vir hierdie studie gekies omdat die ontwerp en implementering eenvoudig is, omdat interaksies binne `n klein populasie van objekte komplekse resultate gee, en omdat die stelsel se organisasie analoog aan die DNA-RNA-proteien organisasie is. Wanneer `n populasie van objekte toegelaat word om eenstryk op mekaar te reageer vind self-produksie en self-organisasie vanself plaas, selfs in eenvoudige artifsiele stelsels [7, 8]. Die stabiliteit van die emergente organisasies hang af van die interaksies tussen die komponente, wat self die vermoe tot selfproduksie moet he indien hulle die organisasie in stand wil hou [27]. Selfproduksie van objekte hang af van hul sekwens-funsieverwantskap, wat op hul beurt bepaal hoe vinnig hulle repliseer wanneer in interaksie met ander objekte.