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Register a new userEnumeration of RNA structures by Matrix Models
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We enumerate the number of RNA contact structures according to their genus, i.e. the topological character of their pseudoknots. By using a recently proposed matrix model formulation for the RNA folding problem, we obtain exact results for the simple case of an RNA molecule with an infinitely flexible backbone, in which any arbitrary pair of bases is allowed. We analyze the distribution of the genus of pseudoknots as a function of the total number of nucleotides along the phosphate-sugar backbone.
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We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number, whose value quantifies the topological complexity of the folded RNA structure. In such a representation, planar diagrams correspond to pure RNA secondary structures and have zero genus, whereas non planar diagrams correspond to pseudoknotted structures and have higher genus. We analyze real RNA structures from the databases wwPDB and Pseudobase, and classify them according to their topological genus. We compare the results of our statistical survey with existing theoretical and numerical models. We also discuss possible applications of this classification and show how it can be used for identifying new RNA structural motifs.
The ongoing effort to detect and characterize physical entanglement in biopolymers has so far established that knots are present in many globular proteins and also abound in viral DNA packaged inside bacteriophages. RNA molecules, on the other hand, have not yet been systematically screened for the occurrence of physical knots. We have accordingly undertaken the systematic profiling of the ~6,000 RNA structures present in the protein data bank. The search identified no more than three deeply-knotted RNA molecules. These are ribosomal RNAs solved by cryo-em and consist of about 3,000 nucleotides. Compared to the case of proteins and viral DNA, the observed incidence of RNA knots is therefore practically negligible. This suggests that either evolutionary selection, or thermodynamic and kinetic folding mechanisms act towards minimizing the entanglement of RNA to an extent that is unparalleled by other types of biomolecules. The properties of the three observed RNA knotting patterns provide valuable clues for designing RNA sequences capable of self-tying in a twist-knot fold.
In this paper we consider the problem of RNA folding with pseudoknots. We use a graphical representation in which the secondary structures are described by planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze the non-planar topologies of RNA structures and propose a classification of RNA pseudoknots according to the minimal genus of the surface on which the RNA structure can be embedded. This classification provides a simple and natural way to tackle the problem of RNA folding prediction in presence of pseudoknots. Based on that approach, we describe a Monte Carlo algorithm for the prediction of pseudoknots in an RNA molecule.
RNA/protein interactions play crucial roles in controlling gene expression. They are becoming important targets for pharmaceutical applications. Due to RNA flexibility and to the strength of electrostatic interactions, standard docking methods are insufficient. We here present a computational method which allows studying the binding of RNA molecules and charged peptides with atomistic, explicit-solvent molecular dynamics. In our method, a suitable estimate of the electrostatic interaction is used as an order parameter (collective variable) which is then accelerated using bi-directional pulling simulations. Since the electrostatic interaction is only used to enhance the sampling, the approximations used to compute it do not affect the final accuracy. The method is employed to characterize the binding of TAR RNA from HIV-1 and a small cyclic peptide. Our simulation protocol allows blindly predicting the binding pocket and pose as well as the binding affinity. The method is general and could be applied to study other electrostatics-driven binding events.
We present a simplified model of the dynamics of translocation of RNA through a nanopore which only allows the passage of unbound nucleotides. In particular, we consider the disorder averaged translocation dynamics of random, two-component, single-stranded nucleotides, by reducing the dynamics to the motion of a random walker on a one-dimensional free energy landscape of translocation. These translocation landscapes are calculated from the folds of the RNA sequences and the voltage bias applied across the nanopore. We compute these landscapes for 1500 randomly drawn two-letter sequences of length 4000. Simulations of the dynamics on these landscapes display anomalous characteristics, similar to random forcing energy landscapes, where the translocation process proceeds slower than linearly in time for sufficiently small voltage biases across the nanopore, but moves linearly in time at large voltage biases. We argue that our simplified model provides an upper bound to the more realistic translocation dynamics, and thus we expect that all RNA translocation models will exhibit anomalous regimes.
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