<p>A key problem in the origin of life is to understand how an autocatalytic, self-replicating biopolymer system may have originated from a non-living chemical system. This thesis presents mathematical and computational models that address this issue. We consider a reaction system in which monomers (nucleotides) and polymers (RNAs) can be formed by chemical reactions at a slow spontaneous rate, and can also be formed at a high rate by catalysis, if polymer catalysts (ribozymes) are present. The system has two steady states: a ‘dead’ state with a low concentration of ribozymes and a ‘living’ state with a high concentration of ribozymes. Using stochastic simulations, we show that if a small number of ribozymes is formed spontaneously, this can drive the system from the dead to the living state. In the well mixed limit, this transition occurs most easily in volumes of intermediate size. In a spatially-extended two-dimensional system with finite diffusion rate, there is an optimal diffusion rate at which the transition to life is very much faster than in the well-mixed case. We therefore argue that the origin of life is a spatially localized stochastic transition. Once life has arisen in one place by a rare stochastic event, the living state spreads deterministically through the rest of the system. We show that similar autocatalytic states can be controlled by nucleotide synthases as well as by polymerase ribozymes, and that the same mechanism can also work with recombinases, if the recombination reaction is not perfectly reversible. Chirality is introduced into the polymerization model by considering simultaneous synthesis and polymerization of left- and right-handed monomers. We show that there is a racemic non-living state and two chiral living states. In this model, the origin of life and the origin of homochirality may occur simultaneously due to the same stochastic transition.</p> / Doctor of Philosophy (PhD)