Model for Folding and Aggregation in RNA Secondary Structures

We study the statistical mechanics of RNA secondary structures designed to have an attraction between two different types of structures as a model system for heteropolymer aggregation. The competition between the branching entropy of the secondary structure and the energy gained by pairing drives the RNA to undergo a `temperature independent' second order phase transition from a molten to an aggregated phase'. The aggregated phase thus obtained has a macroscopically large number of contacts between different RNAs. The partition function scaling exponent for this phase is \theta ~ 1/2 and the crossover exponent of the phase transition is \nu ~ 5/3. The relevance of these calculations to the aggregation of biological molecules is discussed.