A Phase Transition in Energy-Filtered RNA Secondary Structures

A Phase Transition for the Minimum Free Energy of Secondary Structures of a Random RNA

The free energy of a single-stranded RNA can be calculated by adding the free energies of the components: basepairs, bulges, and loops. Basepairs receive negative free energy while the unpaired bases receive positive free energy. The minimum free energy of a random RNA secondary structure with one domain has value Fn where the sequence length is n. Under simplifying assumptions, we show that fo...

Glass transition in secondary structures formed by random RNA sequences

Formation of RNA secondary structures is an example of the sequence-structure problem omnipresent in biopolymers. A theoretical question of recent interest is whether a random RNA sequence undergoes a finite temperature glass transition. We answer this question affirmatively by first establishing the perturbative stability of the high temperature phase via a two replica calculation. Subsequentl...

Neutral Networks of Minimum Free Energy RNA Secondary Structures

RNA Secondary Structures

The central dogma of molecular biology states that the flow of information is from DNA, through RNA, to proteins. What this means is that DNA is the storage medium of genomic information, while proteins are the molecules with functional and structural rôles. In this view, RNA is mostly considered a ‘supporting actor’, being the medium used for transporting information from storage to where it i...

A growth model for RNA secondary structures

A hierarchical model for the growth of planar arch structures for RNA secondary structures is presented, and shown to be equivalent to a tree-growth model. Both models can be solved analytically, giving access to scaling functions for large molecules, and corrections to scaling, checked by numerical simulations of up to 6500 bases. The equivalence of both models should be helpful in understandi...