Matrix models of RNA folding with external interactions: A review

Abstract

The matrix model of (simplified) RNA folding with an external linear interaction in the action of the partition function is reviewed. The important results for structure combinatorics of the model are discussed and analysed in terms of the already existing models. InstallationThe improved understanding of the role of RNA in biological activities with discoveries and developments in the field of biophysics has highlighted the importance of studying their tertiary (folded 3D) conformations [1]. At the very base of understanding the different levels of structures of these biomolecules, lies the quest for understanding three fundamental problems (given in order): (i) to predict an RNA structure (enumeration), (ii) to find energetically viable structures from the enumerated structures and (iii) to determine kinetics of fold formation [2]. Therefore it is extremely essential to first enumerate and classify all possible types of structures (secondary and tertiary) with a given length, i.e., to know the combinatorics. Secondary structures of RNA have been studied successfully and widely using different statistical and computational models, particularly dynamic programming algorithms [3]. Tertiary structures, owing to their complexity, have been largely unaccessible [4]. Some models have captured the effects of pseudoknotted conformations [5] on the combinatorial and thermodynamic aspects [6]. In particular, a graph theoretic model by Haslinger and Stadler [7] considered bi-secondary structures (secondary structures with non-nested pseudoknots) in addition to the secondary structures and found that the total structures grow asymptotically as β L (where L is the length of RNA chain and β is the constraint-dependent combinatoric factor). Hence, depending upon the different constraining conditions faced by an RNA chain under physiological conditions, the total possible conformations may vary. This very idea springs up the thought of interesting outcomes in the study of the effects of different kinds of perturbations/external interactions/constraints