Topological Constraints and Their Conformational Entropic Penalties on RNA Folds

Abstract

Functional RNAs can fold into intricate structures using a number of different secondary and tertiary structural motifs. Many factors contribute to the overall free energy of the target fold. This study aims at quantifying the entropic costs coming from the loss of conformational freedom when the sugar-phosphate backbone is subjected to constraints imposed by secondary and tertiary contacts. Motivated by insights from topology theory, we design a diagrammatic scheme to represent different types of RNA structures so that constraints associated with a folded structure may be segregated into mutually independent subsets, enabling the total conformational entropy loss to be easily calculated as a sum of independent terms. We used high-throughput Monte Carlo simulations to simulate large ensembles of single-stranded RNA sequences in solution to validate the assumptions behind our diagrammatic scheme, examining the entropic costs for hairpin initiation and formation of many multiway junctions. Our diagrammatic scheme aids in the factorization of secondary/tertiary constraints into distinct topological classes and facilitates the discovery of interrelationships among multiple constraints on RNA folds. This perspective, which to our knowledge is novel, leads to useful insights into the inner workings of some functional RNA sequences, demonstrating how they might operate by transforming their structures among different topological classes.

Quantifying Structural Diversity of CNG Trinucleotide Repeats using Diagrammatic Algorithms

“…To carry out the ensemble calculations describe in the remainder of this paper, parameters for hairpin loop initiations as well as two-, three-and four-ways junctions are also required in addition to the library of data presented above. These have been reported in a previous paper (21), and since there are a number of details involved, these earlier results will not be repeated here (but loop initiation free energies using WC pairs are summarized in Fig. 5 compared to R:Y and G:G Hoogsteen pairs).…”

“…This library can be sourced from experimental data or from computer simulations. In a previous paper (21), we have provided a complete and consistent set of Monte Carlo simulation results for the entropy values of hairpins, two-, three-and four-way functions. These correspond to diagrams in which the vertices are all degree 4 (i.e.…”

Diagrammatic Theory of RNA Structures and Ensembles with Trinucleotide Repeats

“…• ( ), 1 ( ) and 2 ( ), were obtained from the free energies of formation of duplexes, hairpins and 2-way junctions from Monte Carlo data reported in an earlier paper (4). The functional dependence of the loop free energies on the loop lengths were extended beyond the finite-length data available from the simulations by using scaling relationships, yielding the following expressions at = 310 K:…”

“…Ref. 4, we demonstrated that all graphs representing RNA folds are Eulerian and because of this property, the structure of every graph must consist of one or more root vertices connected by bridges, except for the one with just a single edge. Some examples are shown in Fig.…”

Exponentially few RNA structures are designable

“…Indeed, multiple grammars have been shown to capture major pseudoknot classes while, at the same time, allowing for a characterization of generating functions [36]. An enumeration of designable structures would greatly help in the parametrization of free-energy models, a key aspect of pseudoknot prediction programs which has so far greatly hindered the development of predictive methods [33].…”