Related papers: Topological classification of RNA structures
Due to the hierarchical organization of RNA structures and their pivotal roles in fulfilling RNA functions, the formation of RNA secondary structure critically influences many biological processes and has thus been a crucial research topic.…
As proteins with similar structures often have similar functions, analysis of protein structures can help predict protein functions and is thus important. We consider the problem of protein structure classification, which computationally…
RNA design aims to find a sequence that folds with highest probability into a designated target structure. However, certain structures are undesignable, meaning no sequence can fold into the target structure under the default (Turner) RNA…
Understanding the base pairing of an RNA sequence provides insight into its molecular structure.By mining suboptimal sampling data, RNAprofiling 1.0 identifies the dominant helices in low-energy secondary structures as features, organizes…
The intricate network of interactions observed in RNA three-dimensional structures is often described in terms of a multitude of geometrical properties, including helical parameters, base pairing/stacking, hydrogen bonding and backbone…
In this paper we study irreducibility in RNA structures. By RNA structure we mean RNA secondary as well as RNA pseudoknot structures. In our analysis we shall contrast random and minimum free energy (mfe) configurations. We compute various…
We analyze the structure of two dimensional disordered cellular systems generated by extensive computer simulations. These cellular structures are studied as topological trees rooted on a central cell or as closed shells arranged…
The statistical mechanics of heteropolymer structure formation is studied in the context of RNA secondary structures. A designed RNA sequence biased energetically towards a particular native structure (a hairpin) is used to study the…
The leaves of angiosperms contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We describe a new phenotypic trait of reticulate vascular networks based on the topology of the nested…
Molecular structures of RNA molecules reconstructed from X-ray crystallography frequently contain errors. Motivated by this problem we examine clustering on a torus since RNA shapes can be described by dihedral angles. A previously…
RNA forms elaborate secondary structures through intramolecular base pairing. These structures perform critical biological functions within each cell. Due to the availability of a polynomial algorithm to calculate the partition function…
Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of…
In this paper we study $k$-noncrossing, canonical RNA pseudoknot structures with minimum arc-length $\ge 4$. Let ${\sf T}_{k,\sigma}^{[4]} (n)$ denote the number of these structures. We derive exact enumeration results by computing the…
This paper proposes a new mathematical approach to characterize native protein structures based on the discrete differential geometry of tetrahedron tiles. In the approach, local structure of proteins is classified into finite types…
In this paper, we study the combinatorial set of RNA secondary structures of length $n$ with $m$ base-pairs. For a compact representation, we encode an RNA secondary structure by the corresponding Motzkin word. For this combinatorial set,…
This contribution focuses on the fascinating RNA molecule, its sequence-dependent folding driven by base-pairing interactions, the interplay between these interactions and natural evolution, and its multiple regulatory roles. The four of us…
We showed in this paper that similarity network can be used as an powerful tools to study the relationship of tRNA genes. We constructed a network of 3719 tRNA gene sequences using simplest alignment and studied its topology, degree…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…
It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while…
In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…