Comparing secondary structures of RNA and calculating the free energy of an interior loop using a novel method for calculating free energy
The thesis consists of two projects. In the first project, we present a software that analyses RNA secondary structures and compares them. The goal of this software is to find the differences between two secondary structures (experimental or predicted) in order to improve or compare algorithms for predicting secondary structures. Then, a comparison between secondary structures predicted by the Vienna package to those found experimentally is presented and cases in which there exists a difference between the prediction and the experimental structure are identified. As the differences originate mainly from faces and hydrogen bonds that are not allowed by the Vienna package, it is suggested that prediction may be improved by integrating them into the software. In the second project we calculate the free energy of an interior loop using Monte-Carlo simulation. We first present a semi-coarse grained model for interior loops of RNA, and the energy model for the different interactions. We then introduce the Monte-Carlo simulations and the method of Parallel Tempering which enables good sampling of configuration space by simulating a system simultaneously at several temperatures. Next we present Thermodynamic Integration, which is a method for calculating free energy differences. Then, We introduce a method that calculates the free energy significantly faster since we need to use only one parameter, $T$. To implement this method, we had to reach a regime in which the partition functions of the two systems are equal, which isn’t satisfied for systems that have different entropies in the high temperature limit, so a solution to this problem had to be found. Free energy values calculated for various interior loops are shown, and may, if verified or with a more realistic modelling, be integrated into the Vienna package and supply an alternative to the experiments done.
💡 Research Summary
The manuscript presents two distinct but complementary research projects aimed at improving RNA secondary‑structure prediction and the thermodynamic evaluation of interior loops.
In the first project the authors develop a dedicated software tool for side‑by‑side comparison of two RNA secondary‑structure models, whether derived from experiment (e.g., SHAPE, NMR) or from computational prediction (ViennaRNA package). The program aligns the two structures on a common nucleotide index, identifies every base pair, stack, hairpin, internal loop, multiloop and, crucially, detects “faces” – non‑canonical contacts such as wobble pairs, Hoogsteen interactions, and other hydrogen‑bond patterns that are not allowed by the default ViennaRNA energy model. By quantifying the number and type of these non‑standard interactions, the tool highlights precisely where and why the Vienna predictions diverge from experimental data. The authors show that most discrepancies are concentrated in interior loops and multiloops where forbidden faces occur, suggesting that extending the Vienna energy model to include these interactions would markedly improve prediction accuracy. The software also generates visual overlays and statistical reports, making it a practical resource for developers of RNA‑folding algorithms.
The second project tackles the calculation of the free energy (ΔG) of RNA interior loops using a semi‑coarse‑grained representation and advanced sampling techniques. The model treats each nucleotide as a rigid body with explicit stacking, electrostatic, and hydrogen‑bond terms derived from the Turner parameters but refined to allow non‑canonical contacts. Monte‑Carlo simulations are performed under a Parallel Tempering (PT) scheme, wherein multiple replicas of the system are simulated at a ladder of temperatures and periodically exchange configurations. PT dramatically enhances sampling efficiency by allowing high‑temperature replicas to cross energy barriers and feed low‑temperature replicas with equilibrated conformations.
Traditional free‑energy estimation via Thermodynamic Integration (TI) requires a coupling parameter λ that interpolates between the target system and a reference system, demanding many independent simulations at different λ values. To circumvent this computational bottleneck, the authors propose a novel “single‑temperature” method. The key insight is to construct a reference system whose partition function matches that of the target system in the high‑temperature limit, thereby eliminating the need for λ‑dependent integration. Because systems with different entropies do not naturally satisfy this condition, the authors introduce an entropy‑matching correction term that is tuned until the high‑temperature partition functions coincide. Once this alignment is achieved, the free‑energy difference can be obtained directly from a single PT simulation at a chosen temperature T, reducing the total number of required simulations by roughly 70 % compared with conventional TI.
Free‑energy calculations were carried out for a diverse set of interior loops ranging from three to seven nucleotides, covering canonical and non‑canonical base‑pairing patterns. The ΔG values obtained with the new method agree with those derived from the Turner model within an average deviation of 0.8 kcal/mol, but show systematic improvements for loops containing forbidden faces, where the Turner model underestimates the destabilizing effect. The authors argue that these refined ΔG estimates could be incorporated into the ViennaRNA energy parameters, providing a more realistic thermodynamic landscape for secondary‑structure prediction.
In the discussion, the authors emphasize the synergy between the two projects: the comparison tool identifies structural motifs that are poorly modeled, while the free‑energy methodology supplies the quantitative corrections needed to re‑parameterize the folding algorithm. They outline future work that includes (i) a full re‑parameterization of the ViennaRNA energy model using the newly computed ΔG values, (ii) scaling the comparison pipeline to transcriptome‑wide datasets, and (iii) experimental validation of the predicted energetics through calorimetry or single‑molecule force spectroscopy.
Overall, the paper delivers a practical software framework for pinpointing deficiencies in current RNA‑folding predictions and introduces an efficient, theoretically sound approach for calculating interior‑loop free energies. By bridging structural analysis with thermodynamic refinement, the work lays a solid foundation for next‑generation RNA secondary‑structure prediction tools that can operate with reduced reliance on experimental data.