A New Model for Approximating RNA Folding Trajectories and Population Kinetics

RNA participates both in functional aspects of the cell and in gene regulation. The interactions of these molecules are mediated by their secondary structure which can be viewed as a planar circle graph with arcs for all the chemical bonds between pairs of bases in the RNA sequence. The problem of predicting RNA secondary structure, specifically the chemically most probable structure, has many useful and efficient algorithms. This leaves RNA folding, the problem of predicting the dynamic behavior of RNA structure over time, as the main open problem. RNA folding is important for functional understanding, because some RNA molecules change secondary structure in response to interactions with the environment. The full RNA folding model on at most O(3n) secondary structures is the gold standard. We present a new subset approximation model for the full model, give methods to analyze its accuracy, and discuss the relative merits of our model as compared with a pre-existing subset approximation. The main advantage of our model is that it generates Monte Carlo folding pathways with the same probabilities with which they are generated under the full model. The pre-existing subset approximation does not have this property. MSC Classification: 62P10, 92B05, 60J27