Structural and Thermodynamic Properties of RNA Molecules Using a Knowledge-Based Model

Abstract

We present a coarse-grained model that describes the unfolding process and thermodynamics of ribonucleic acid (RNA) molecules. We obtained and analyzed a set of 1944 three-dimensional RNA structures of various molecular weights and under diverse conditions from the Protein Data Bank. We reduced the description of these molecules from an all-atom representation to a single interacting point per nucleotide, located at its center of mass. From this information, we calculated characteristic properties of the RNA chains, such as the bond distribution function and the contour length, which allowed us to estimate the most probable distance between two nucleotides linked by a phosphodiester bond as a = 5.5 ± 0.4 Å. We also calculated the radius of gyration of these chains, through which we obtained an estimate of the Flory exponent, ν = 0.33 ± 0.01, and a fractal dimension, d F = 3.03 ± 0.09. Furthermore, we determined the persistence length to be l p = 9.5 ± 4.1 Å. On the other hand, the different molecular configurations were used to improve the statistics of the pair distribution functions for various degrees of freedom. These were employed to obtain effective interaction potentials in a previous model [Villada-Balbuena, M.; Carbajal-Tinoco, M. D. J. Chem. Phys. 2024, 161, 165104.], which underwent a series of improvements, reducing the number of fitting parameters and enhancing the description of the radial-angular interaction. The fitting parameters of these potentials were optimized through Brownian dynamics (BD) simulations using the iterative Boltzmann inversion algorithm. The optimized potentials were used in steered BD simulations to model the mechanical unfolding at a constant velocity of a series of hairpins and pseudoknots. The results of these simulations are contrasted with experimental data, achieving excellent agreement. During the unfolding process, we monitored the configurational temperature (CT) of the model’s different degrees of freedom as well as the total CT. We used Jarzynski’s equality to calculate the Helmholtz free energy change, ΔA. Through ΔA and the integral of the force–extension curve, we obtained the Gibbs free energy change ΔG, which was successfully compared with the experimental results of RNA molecules unfolding using optical tweezers. Finally, based on the internal energy change values from the simulations, we estimated the entropy change ΔS. These values were compared with entropy changes from theoretical models. Finally, we utilized our model to calculate the changes in the aforementioned thermodynamic functions for molecules associated with viral protein expression.