Dynamics of RNA-based replicator networks Camille STEPHAN-OTTO ATTOLINI, Christof FLAMM, Peter STADLER Institut for Theoretical Chemistry and Structural Biology, University of Vienna. Tel , fax , mail. www: Replicator equations are used to model a system of interacting species where the individual replicators are implemented as RNA sequences. Their interactions are modeled by the structure of their co-folding complex based on the thermodynamic rules of RNA folding. For each pair of sequences, the concatenated sequence is taken and its secondary structure found. The replication rates for this pair are calculated as a function of the distance between their co-folding complex and a prescribed target structure. The distance between structures is obtained by the hamming or base-pair distance using the structure’s dot-bracket representation. Simulations of this model give information about the number of species in each generation and their concentration, distance of each pair's structure to the target as well as the average distance and fitness of the system. Weighted graphs defined by the interactions between species are studied in order to get an overall view of the system's behavior and self-organization. The dynamical behavior depends strongly on the parameters of the system and ranges from the survival of only one single dominating specie in each generation to the creation of intricate networks. In the latter case the fitness increases in a stepwise manner as the system approaches the target transition state and maintains, in almost every generation, a number of species greater than a certain lower bound. In many cases the model falls in a fixed configuration: existing species are trapped in a fixed point, their concentrations become stable and new species are accepted in the network only if their interactions are stronger than those existent. Moreover, a new mutation will be accepted only if the rates by which it is catalyzed are good, no matter if it is a good catalyst for the rest of the species. It has been found that the minimum distance reached by the system, depends extremely on the sequences taken as initial conditions. To show this, structures formed after a large number of generations are used in a subsequent model as target structures. Even when changing other initial conditions or the random numbers used in the program, the system approaches the target much faster than in the first case. Comparison between this model and the one with single folded species, makes clear that interaction between species changes completely the way evolution to a fixed target occurs. Survival of one specie depends not only on its self- replication rate, but in the way it is catalyzed by the others. It may happen too that one specie is catalyzed by all the rest, making its concentration grow very fast. This specie will then take all the available resources and kill the rest of the species. Concentration of each specie along time: Fitness jumps occur usually when number of species increases. Correlation between specie’s concentrations is clear from the graph above. In order to generate evolution in the model, mutations are allowed with certain rate and introduced to the system creating new co folded structures. Each generation, the interaction matrix is filled with the rates of the new specie, and the equation integrated. Species are removed from the system whenever their concentration drops below a threshold level. Interaction graph: The new specie catalyses all the rest with the best rate achieved in the system so far, but disappears in the nextt generation due to the lack of good self- replication rate and catalysis from the rest. Interaction graph: Pink lines represent catalysis from smaller id’s to larger, blue lines represent the opposite and black mean catalysis in both directions. This pink almost complete graph talks about cycles where older species help to the replication of all the new species. The black lines going to the first specie mean that structures made by these species, are better than the average, no matter in what order cofolded, Bibliography:  Happel, R. & Stadler, P. F. (1997) The Evolution of Diversity in Replicator Networks. This kind of parasites can destroy the whole net loosing the possible achievements made until then.