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In this thesis we present a mathematical model describing the populationdynamics of molecules in an artificial chemistry where large molecules can beproduced by successive ligation of pairs of smaller molecules. The chemistrycontains a large number of spontaneous reactions of which a small subset couldbe catalyzed by molecules produced in the chemistry with varying catalyticstrengths. We show ACSs, if present in the catalytic network, can focus theresources of the system into a sparse set of molecules. ACSs can produce abistability in the population dynamics and, in particular, steady stateswherein the ACS molecules dominate the population, i.e., have higherconcentrations compared to the rest of molecules in the chemistry (background).In this thesis we attempt to address two main questions: First, under whatcircumstances do molecules belonging to the ACSs dominate over the background,and second, starting from an initial condition that does not contain goodcatalysts, can a sparse set of large molecules (containing several tens or afew hundred monomers) that are good catalysts arise and be maintained in thesystem at concentrations significantly above the background? We show that if anACS catalyzed by large molecules contains within it (or partially overlapswith) a smaller ACS catalyzed by smaller molecules (referred to as a `nestedACS' structure), the catalytic strength required for the large ACS to dominatecomes down significantly. We show that when the network contains a cascade ofnested ACSs with the catalytic strengths of molecules increasing gradually withtheir size, a sparse subset of molecules including some very large moleculescan come to dominate the system.

Modeling pre-biotic self-organization: The chemical dynamics of autocatalytic networks