Recent computational efforts have shown that the current potential energy models used in molecular dynamics are not accurate enough to describe the conformational ensemble of RNA oligomers and suggest that molecular dynamics should be complemented with experimental data. We here propose a scheme based on the maximum entropy principle to combine simulations with bulk experiments. In the proposed scheme the noise arising from both the measurements and the forward models used to back calculate the experimental observables is explicitly taken into account. The method is tested on RNA nucleosides and is then used to construct chemically consistent corrections to the Amber RNA force field that allow a large set of experimental data on nucleosides and dinucleosides to be correctly reproduced. The transferability of these corrections is assessed against independent data on tetranucleotides and displays a previously unreported agreement with experiments. This procedure can be applied to enforce multiple experimental data on multiple systems in a self-consistent framework thus suggesting a new paradigm for force field refinement.

Molecular dynamics (MD) simulations allow investigating the structural dynamics of biomolecular systems with unrivaled time and space resolution. However, in order to compensate for the inaccuracies of the utilized empirical force fields, it is becoming common to integrate MD simulations with experimental data obtained from ensemble measurements. We here review the approaches that can be used to combine MD and experiment under the guidance of the maximum entropy principle. We mostly focus on methods based on Lagrangian multipliers, either implemented as reweighting of existing simulations or through an on-the-fly optimization. We discuss how errors in the experimental data can be modeled and accounted for. Finally, we use simple model systems to illustrate the typical difficulties arising when applying these methods.

Empirical force fields for biomolecular systems are usually derived from quantum chemistry calculations and validated against experimental data. We here show how it is possible to refine the full dihedral-angle potential of the Amber RNA force field by using solution NMR data as well as stability of known structural motifs. The procedure can be used to mix multiple systems and heterogeneous experimental information and crucially depends on a regularization term chosen with a cross-validation procedure. By fitting corrections to the dihedral angles on the order of less than 1 kJ/mol per angle, it is possible to increase the stability of difficult-to-fold RNA tetraloops by more than 1 order of magnitude.

The conformational fluctuations of proteins can be described by structural ensembles. To address the major challenge of determining these ensembles accurately, a wide range of strategies have recently been proposed to combine molecular dynamics simulations with experimental data. Quite generally, there are two ways of implementing this type of approach, either by applying structural restraints during a simulation, or by reweighting a posteriori the conformations from an a priori ensemble. It is not yet clear, however, whether these two approaches can offer ensembles of equivalent quality. The advantages of the reweighting method are that it can involve any type of starting simulation and that it enables the integration of experimental data after the simulations are run. A disadvantage, however, is that this procedure may be inaccurate when the a priori ensemble is of poor quality. Here, our goal is to systematically compare the restraining and reweighting approaches and to explore the conditions required for the reweighting ensembles to be accurate. Our results indicate that the reweighting approach is computationally efficient and can perform as well as the restraining approach when the a priori sampling is accurate. More generally, to enable an effective use of the reweighting approach by avoiding the pitfalls of poor sampling, we suggest metrics for the quality control of the reweighted ensembles.

conformation, dynamics, kinetics, and adaptation. In this study, we use the combination of helices and the dynamic programming algorithm to selectively sample RNA two-dimensional (2D) structures. By calculating the free energies of each sampled structures with the Vfold-derived loop entropic parameters for secondary and pseudoknotted structures, and an empirical energy model for kissing motifs, we predict most stable and metastable structures from sequences. We use the stability of helices to balance the computational efficiency and prediction accuracy. Benchmark test shows that the model improves the prediction of RNA 2D structures with and without crossing base pairs.