Topological language for RNA

  title={Topological language for RNA},
  author={Fenix W. D. Huang and Christian M. Reidys},
  journal={Mathematical biosciences},

Fatgraph models of RNA structure

This review paper discusses minimum free energy folding of pk-structures and combines these above results outlining how to obtain an inverse folding algorithm for PK structures.

Statistics of topological RNA structures

A new bivariate generating function is derived whose singular expansion allows for analysis of the distributions of arcs, stacks, hairpin- , interior- and multi-loops and H-type pseudoknots, kissing hairpins and their respective expectation values.

Statistics of topological RNA structures

In this paper we study properties of topological RNA structures, i.e. RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures

Sequence‐structure relations of biopolymers

It is illustrated that there are multiple sequences in the partition function of a fixed structure, each having nearly the same mutual information, that are nevertheless poorly aligned, indicating the possibility of the existence of relevant patterns embedded in the sequences that are not discoverable using alignments.

Structural relation matching: an algorithm to identify structural patterns into RNAs and their interactions

The problem of identifying a given structural pattern into secondary structures or the associated cores or shadow of both RNAs and RNA–RNA interactions, characterized by arbitrary pseudoknots, is faced and these abstractions are mapped into a matrix, whose elements represent the relations among loops.

Topological Classification of RNA Structures via Intersection Graph

An abstract algebraic representation of RNA secondary structures as a composition of hairpins, considered as basic loops, and a novel methodology to classify RNA structures based on two topological invariants, the genus and the crossing number are proposed.

Michael Waterman's Contributions to Computational Biology and Bioinformatics

On the occasion of Dr. Michael Waterman's 80th birthday, a review of his major contributions to the field of computational biology and bioinformatics including the famous Smith-Waterman algorithm for sequence alignment and algorithms for sequence assembly are reviewed.

A reappraisal of the form – function problem. Theory and phenomenology

It is argued that form has an organizing power, hence a causal action, in the sense that it enables to induce functional events during different biological processes, at the supramolecular, cellular, and organismal levels of organization, and clearly topological forms must be matched with specific kinetic and dynamical parameters to have a functional effectiveness in living systems.

Loop homology of bi-secondary structures II

In this paper, we analyze the homology of the simplicial complex induced by a given pair of RNA secondary structures, R=(S,T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}

Input–output maps are strongly biased towards simple outputs

A practical bound is provided on the probability that a randomly generated computer program produces a given output of a given complexity and this upper bound is applied to RNA folding and financial trading algorithms.



The language of RNA: a formal grammar that includes pseudoknots

A one-to-one correspondence is shown between a polynomial time dynamic programming algorithm and a formal transformational grammar for RNA secondary structure with pseudoknots, which encompasses the context-free grammars and goes beyond to generate pseudoknotted structures.

Topology and prediction of RNA pseudoknots

Gfold admits a topology-dependent parametrization of pseudoknot penalties that increases the sensitivity and positive predictive value of predicted base pairs by 10-20% compared with earlier approaches.

Random generation of RNA secondary structures according to native distributions

A new general framework for deriving algorithms for the non-uniform random generation of combinatorial objects according to the encoding and probability distribution implied by a stochastic context-free grammar is presented.

RNA secondary structure prediction using stochastic context-free grammars and evolutionary history

A method which incorporates evolutionary history into RNA secondary structure prediction, based on stochastic context-free grammars to give a prior probability distribution of structures, which performs very well compared to current automated methods.

Pfold: RNA secondary structure prediction using stochastic context-free grammars

This work presents a practical way of predicting RNA secondary structure that is especially useful when related sequences can be obtained, and improves a previous algorithm based on an explicit evolutionary model and a probabilistic model of structures.

Stochastic context-free grammars for tRNA modeling.

Results show that after having been trained on as few as 20 tRNA sequences from only two tRNA subfamilies, the model can discern general tRNA from similar-length RNA sequences of other kinds, can find secondary structure of new t RNA sequences, and can produce multiple alignments of large sets of tRNAs.

Generation of RNA pseudoknot structures with topological genus filtration.

A dynamic programming algorithm for RNA structure prediction including pseudoknots.

This is the first algorithm to be able to fold optimal (minimum energy) pseudoknotted RNAs with the accepted RNA thermodynamic model and a useful graphical representation borrowed from quantum field theory is adopted.

Statistics of RNA secondary structures

A statistical reference for RNA secondary structures with minimum free energies is computed by folding large ensembles of random RNA sequences, using two binary alphabets, AU and GC, the biophysical AUGC and the synthetic GCXK alphabet.