On RNA-RNA interaction structures of fixed topological genus.

Interacting RNA complexes are studied via bicellular maps using a filtration via their topological genus. Our main result is a new bijection for RNA-RNA interaction structures and a linear time uniform sampling algorithm for RNA complexes of fixed topological genus. The bijection allows to either reduce the topological genus of a bicellular map directly, or to lose connectivity by decomposing the complex into a pair of single stranded RNA structures.

Combinatorics of γ-structures.

In this article we study canonical γ-structures, a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A γ-structure is composed of specific building blocks that have topological genus less than or equal to γ, where composition means concatenation and nesting of such blocks. Our main result is the derivation of the generating function of γ-structures via symbolic enumeration using so called irreducible shadows.

A phase transition in energy-filtered RNA secondary structures.

In this article we study the effect of energy parameters on minimum free energy (mfe) RNA secondary structures. Employing a simplified combinatorial energy model that is only dependent on the diagram representation and is not sequence-specific, we prove the following dichotomy result. Mfe structures derived via the Turner energy parameters contain only finitely many complex irreducible substructures, and just minor parameter changes produce a class of mfe structures that contain a large number of small irreducibles.

The 5'-3' distance of RNA secondary structures.

Recently, Yoffe and colleagues observed that the average distances between 5'-3' ends of RNA molecules are very small and largely independent of sequence length. This observation is based on numerical computations as well as theoretical arguments maximizing certain entropy functionals. In this article, we compute the exact distribution of 5'-3' distances of RNA secondary structures for any finite n.

Random K-noncrossing RNA structures.

In this paper, we introduce a combinatorial framework that provides an interpretation of RNA pseudoknot structures as sampling paths of a Markov process. Our results facilitate a variety of applications ranging from the energy-based sampling of pseudoknot structures as well as the ab initio folding via hidden Markov models. Our main result is an algorithm that generates RNA pseudoknot structures with uniform probability.

Stacks in canonical RNA pseudoknot structures.

In this paper we study the distribution of stacks/loops in k-non-crossing, tau-canonical RNA pseudoknot structures (k,tau-structures). Here, an RNA structure is called k-non-crossing if it has no more than k-1 mutually crossing arcs and tau-canonical if each arc is contained in a stack of length at least tau. Based on the ordinary generating function of k,tau-structures [G.

Pseudoknot RNA structures with arc-length > or =4.

In this article, we study k-noncrossing RNA structures with minimum arc-length 4 and at most k - 1 mutually crossing bonds. Let T(k)([4])(n) denote the number of k-noncrossing RNA structures with arc-length > or =4 over n vertices. We (a) prove a functional equation for the generating function summation operator(n> or =0) T(k)([4])(n)z(n) and (b) derive for 4 < or = k < or = 9 the asymptotic formula T(k)([4])(n) approximately c(k) n(-((k-1)(2)+(k-1)/2)) gamma(k)(-n).

DNA microarray reveals novel genes induced by mechanical forces in fetal lung type II epithelial cells.

Mechanical forces are essential for normal fetal lung development. However, the cellular and molecular mechanisms regulating this process are still poorly defined. In this study, we used oligonucleotide microarrays to investigate gene expression in cultured embryonic d 19 rat fetal lung type II epithelial cells exposed to a level of mechanical strain similar to the developing lung.