RNA secondary structure prediction is a fundamental problem in structural bioinformatics. The prediction problem is difficult because RNA secondary structures may contain pseudoknots formed by crossing base pairs. We introduce k-partite secondary structures as a simple classification of RNA secondary structures with pseudoknots. An RNA secondary structure is k-partite if it is the union of k ps...

Many different programs have been developed for the prediction of the secondary structure of an RNA sequence. Some of these programs generate an ensemble of structures, all of which have free energy close to that of the optimal structure, making it important to be able to quantify how similar these different structures are. To deal with this problem, we define a new class of metrics, the mounta...

A secondary structure is a planar, labeled graph on the vertex set {1; : : : ; n} having two kind of edges: the segments [i; i+1], for 16 i6 n− 1 and arcs in the upper half-plane connecting some vertices i; j, i6 j, where j− i ¿ l, for some :xed integer l. Any two arcs must be totally disjoint. We enumerate secondary structures with respect to their size n, rank l and order k (number of arcs), ...

A statistical reference for RNA secondary structures with minimum free energies is computed by folding large ensembles of random RNA sequences. Four nucleotide alphabets are used: two binary alphabets, AU and GC, the biophysical AUGC and the synthetic GCXK alphabet. RNA secondary structures are made of structural elements, such as stacks, loops, joints, and free ends. Statistical properties of ...

Secondary structures of polynucleotides can be view as a certain class of planar vertex-labeled graphs. We construct recursion formulae enumerating various sub-classes of these graphs as well as certain structural elements (sub-graphs). First order asymptotics are derived and their dependence on the logic of base pairing is computed and discussed.

We prove two topological theorems in physical chemistry. Namely, we introduce a hybrid of transverse and tangential measures on train tracks to prove sphericity of various simplicial complexes which arise from certain idealized models of physical chemistry. These complexes are at once identified with Thurston’s space of projective geodesic laminations on an ideal polygon and with the analogue o...