In hypothesized RNA-World scenarios, replication of RNA strands is catalyzed by error-prone polymerase ribozymes. Incorrect replication leads to the creation of non-functional, parasitic strands which can invade systems of replicators and lead to their death. Studies have shown two solutions to this problem: spatial clustering of polymerases in models featuring elements to limit diffusion, and group selection in models featuring protocells. Making a quantitative comparison of the methods using results from the literature has proven difficult due to differences in model design. Here we develop computational models of replication of a system of polymerases, polymerase complements and parasites in both spatial models and protocell models with near identical dynamics to make meaningful comparison viable. We compare the models in terms of the maximum mutation rate survivable by the system (the error threshold) as well as the minimum replication rate constant required. We find that protocell models are capable of sustaining much higher maximum mutation rates, and survive under much lower minimum replication rates than equivalent surface models. We then consider cases where parasites are favoured in replication, and show that the advantage of protocell models is increased. Given that a system of RNA strands undergoing catalytic replication by a polymerase is fairly survivable in protocell models, we attempt to determine whether isolated strands can develop into genomes. We extend our protocell model to include additional functional strands varying in length (and thus replication rate) and allow for the linkage of strands to form proto-chromosomes. We determine that linkage is possible over a broad range of lengths, and is stable when considering the joining of short functional strands to the polymerase (and the same for the complementary sequences). Moreover, linkage of short functional strands to the polymerase assures more cells remain viable post division by ensuing a good quantity of polymerase equivalents are present in the parent cell prior to splitting. / Thesis / Master of Science (MSc) / Collections of RNA polymers are good candidates for the origin of life. RNA is able to store genetic information and act as polymerase ribozymes allowing RNA to replicate RNA. Polymerases have been experimentally developed in labs, however none are sufficiently general to work well in an origins of life setting. These polymerases are vulnerable to mistakes during copying, making survival of RNA systems difficult. Such systems have been studied by computer simulations, showing that the strands need to be kept together for survival, either on surfaces or in primitive cells. Differences in the details of the models has made comparing the surfaces to cells difficult. This work creates a unified model base allowing for comparison of these two environments. We find that the existence of primitive cells is very beneficial to systems of RNA polymers and thus it is likely such cells existed at the origin of life.

Replicator equations have been studied for three decades as a generic dynamical system modelling replication processes. Here we show how they arise naturally in models of self-replicating polymers and discuss some of their basic properties. We then concentrate on a minimal dynamic model of a protocell by coupling replicating polymers with a growing membrane.