Related papers: Expected degree for RNA secondary structure networ…
An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
It has been well accepted that the RNA secondary structures of most functional non-coding RNAs (ncRNAs) are closely related to their functions and are conserved during evolution. Hence, prediction of conserved secondary structures from…
Recently Yoffe {\it et al.} 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…
Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe…
The Human Genome Project has led to an exponential increase in data related to the sequence, structure, and function of biomolecules. Bioinformatics is an interdisciplinary research field that primarily uses computational methods to analyze…
RNA molecules are known to form complex secondary structures including pseudoknots. A systematic framework for the enumeration, classification and prediction of secondary structures is critical to determine the biological significance of…
RNA secondary structure prediction is widely used to understand RNA function. Recently, there has been a shift away from the classical minimum free energy (MFE) methods to partition function-based methods that account for folding ensembles…
We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree…
Background: One-dimensional protein structures such as secondary structures or contact numbers are useful for three-dimensional structure prediction and helpful for intuitive understanding of the sequence-structure relationship. Accurate…
We numerically investigate the robustness of networks with degree-degree correlations between nodes separated by distance $l=2$ in terms of shortest path length. The degree-degree correlation between the $l$-th nearest neighbors can be…
We show the expected order of RNA saturated secondary structures of size $n$ is $\log_4n(1+O(\frac{\log_2n}{n}))$, if we select the saturated secondary structure uniformly at random. Furthermore, the order of saturated secondary structures…
Let Sn denote the network of all RNA secondary structures of length n, in which undirected edges exist between structures s, t such that t is obtained from s by the addition, removal or shift of a single base pair. Using context-free…
We give a Large Deviation Principle (LDP) with explicit rate function for the distribution of vertex degrees in plane trees, a combinatorial model of RNA secondary structures. We calculate the typical degree distributions based on nearest…
RNA function crucially depends on its structure. Thermodynamic models currently used for secondary structure prediction rely on computing the partition function of folding ensembles, and can thus estimate minimum free-energy structures and…
We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of ${\cal O}(N^6)$ in time and ${\cal O}(N^4)$ in storage. The description of the…
Researchers have repeatedly found that the ends of an RNA sequence are significantly closer than expected for a random linear chain. However, we prove that the ends of a branched structure are almost certainly close. Our results are…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity $r$ has received little attention as a subject of theoretical understanding. We study the expected reciprocity of…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…
Metrics for indirectly predicting the folding rates of RNA sequences are of interest. In this letter, we introduce a simple metric of RNA structural complexity, which accounts for differences in the energetic contributions of RNA base…