Sequence matching algorithms and pairing of noncoding RNAs

Abstract

A new statistical method of alignment of two heteropolymers which can form hierarchical cloverleaf-like secondary structures is proposed. This offers a new constructive algorithm for quantitative determination of binding free energy of two noncoding RNAs with arbitrary primary sequences. The alignment of ncRNAs differs from the complete alignment of two RNA sequences: in ncRNA case we align only the sequences of nucleotides which constitute pairs between two different RNAs, while the secondary structure of each RNA comes into play only by the combinatorial factors affecting the entropc contribution of each molecule to the total cost function. The proposed algorithm is based on two observations: i) the standard alignment problem is considered as a zero-temperature limit of a more general statistical problem of binding of two associating heteropolymer chains; ii) this last problem is generalized onto the sequences with hierarchical cloverleaf-like structures (i.e. of RNA-type).Taking zero-temperature limit at the very end we arrive at the desired "cost function" of the system with account for entropy of side cactus-like loops. Moreover, we have demonstrated in detail how our algorithm enables to solve the "structure recovery" problem. Namely, we can predict in zero-temperature limit the cloverleaflike (i.e. secondary) structure of interacting ncRNAs by knowing only their primary sequences. Contents I. IntroductionA. Binding of noncoding RNAs B. Noncoding RNAs as particular class of associating heteropolymers C. Pairing vs alignment 2 S.K. Nechaev, M.V. Tamm, O.V. Valba II. Theoretical background 5 A. Alignment of linear sequences 5 B. Matching vs pairing of two random linear heteropolymers 6 C. Matching vs pairing of two random RNA-type heteropolymers 8 III. Matching algorithm for two noncoding RNAs A. Matching of linear sequences B. Matching of RNA-type sequences IV. Structure recovery A. Finding the Longest Common Subsequence for linear chains B. Finding the secondary structure for interacting RNA-like chains V. Conclusion A. Temperature dependence of the free energy B. Statistical analysis of a pair of random sequences References I. INTRODUCTION A. Binding of noncoding RNAsAccording to a common definition, the noncoding RNA (ncRNA) is an RNA molecule that is not translated into a protein. The ncRNAs either regulate the gene expression directly, for example by occupying the ribosome binding site, or indirectly providing RNA targeting specificity for a protein-based regulatory mechanism [1]. The class of ncRNAs spreads on regulatory and functional RNAs. In modern classification the term "noncoding RNA" is basically attributed to eucariotic RNAs, sometimes called also "small nonmessenger RNAs". In general, regulatory RNAs act in the cell by one of two basic mechanisms: by base-pairing interactions with other nucleic acids, or by binding to proteins [2]. The base pairing with target molecules constitutes the typical mechanism, by which the ncRNA regulates the gene expression. The base pairing is subdivided in two cl...