Comparing Protocell and Surface-Based Models of RNA Replicator Systems and Determining Favourable Conditions for Linkage of Functional Strands

Abstract

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.