Deep learning path-like collective variable for enhanced sampling molecular dynamics.

Several enhanced sampling techniques rely on the definition of collective variables to effectively explore free energy landscapes. The existing variables that describe the progression along a reactive pathway offer an elegant solution but face a number of limitations. In this paper, we address these challenges by introducing a new path-like collective variable called the "deep-locally non-linear-embedding," which is inspired by principles of the locally linear embedding technique and is trained on a reactive trajectory. The variable mimics the ideal reaction coordinate by automatically generating a non-linear combination of features through a differentiable generalized autoencoder that combines a neural network with a continuous k-nearest neighbor selection. Among the key advantages of this method is its capability to automatically choose the metric for searching neighbors and to learn the path from state A to state B without the need to handpick landmarks a priori. We demonstrate the effectiveness of DeepLNE by showing that the progression along the path variable closely approximates the ideal reaction coordinate in toy models, such as the Müller-Brown potential and alanine dipeptide. Then, we use it in the molecular dynamics simulations of an RNA tetraloop, where we highlight its capability to accelerate transitions and estimate the free energy of folding.

Boosting Ensemble Refinement with Transferable Force-Field Corrections: Synergistic Optimization for Molecular Simulations.

A novel method combining the force-field fitting approach and ensemble refinement by the maximum entropy principle is presented. Its formulation allows us to continuously interpolate between these two methods, which can thus be interpreted as two limiting cases. A cross-validation procedure enables us to correctly assess the relative weight of both of them, distinguishing scenarios in which the combined approach is meaningful from those in which either ensemble refinement or force-field fitting separately prevails. The efficacy of their combination is examined for a realistic case study of RNA oligomers. Within the new scheme, molecular dynamics simulations are integrated with experimental data provided by nuclear magnetic resonance measures. We show that force-field corrections are in general superior when applied to the appropriate force-field terms but are automatically discarded by the method when applied to inappropriate force-field terms.

Simultaneous refinement of molecular dynamics ensembles and forward models using experimental data.

A novel method combining the maximum entropy principle, the Bayesian-inference of ensembles approach, and the optimization of empirical forward models is presented. Here, we focus on the Karplus parameters for RNA systems, which relate the dihedral angles of γ, ß, and the dihedrals in the sugar ring to the corresponding 3J-coupling signal between coupling protons. Extensive molecular simulations are performed on a set of RNA tetramers and hexamers and combined with available nucleic-magnetic-resonance data. Within the new framework, the sampled structural dynamics can be reweighted to match experimental data while the error arising from inaccuracies in the forward models can be corrected simultaneously and consequently does not leak into the reweighted ensemble. Carefully crafted cross-validation procedure and regularization terms enable obtaining transferable Karplus parameters. Our approach identifies the optimal regularization strength and new sets of Karplus parameters balancing good agreement between simulations and experiments with minimal changes to the original ensemble.

Molecular Simulations Matching Denaturation Experiments for N6-Methyladenosine.

Post-transcriptional modifications are crucial for RNA function and can affect its structure and dynamics. Force-field-based classical molecular dynamics simulations are a fundamental tool to characterize biomolecular dynamics, and their application to RNA is flourishing. Here, we show that the set of force-field parameters for N6-methyladenosine (m6A) developed for the commonly used AMBER force field does not reproduce duplex denaturation experiments and, specifically, cannot be used to describe both paired and unpaired states. Then, we use reweighting techniques to derive new parameters matching available experimental data. The resulting force field can be used to properly describe paired and unpaired m6A in both syn and anti conformation, which thus opens the way to the use of molecular simulations to investigate the effects of N6 methylations on RNA structural dynamics.

Automatic Learning of Hydrogen-Bond Fixes in the AMBER RNA Force Field.

The capability of current force fields to reproduce RNA structural dynamics is limited. Several methods have been developed to take advantage of experimental data in order to enforce agreement with experiments. Here, we extend an existing framework which allows arbitrarily chosen force-field correction terms to be fitted by quantification of the discrepancy between observables back-calculated from simulation and corresponding experiments. We apply a robust regularization protocol to avoid overfitting and additionally introduce and compare a number of different regularization strategies, namely, L1, L2, Kish size, relative Kish size, and relative entropy penalties. The training set includes a GACC tetramer as well as more challenging systems, namely, gcGAGAgc and gcUUCGgc RNA tetraloops. Specific intramolecular hydrogen bonds in the AMBER RNA force field are corrected with automatically determined parameters that we call gHBfixopt. A validation involving a separate simulation of a system present in the training set (gcUUCGgc) and new systems not seen during training (CAAU and UUUU tetramers) displays improvements regarding the native population of the tetraloop as well as good agreement with NMR experiments for tetramers when using the new parameters. Then, we simulate folded RNAs (a kink-turn and L1 stalk rRNA) including hydrogen bond types not sufficiently present in the training set. This allows a final modification of the parameter set which is named gHBfix21 and is suggested to be applicable to a wider range of RNA systems.

Toward Convergence in Folding Simulations of RNA Tetraloops: Comparison of Enhanced Sampling Techniques and Effects of Force Field Modifications.

Atomistic molecular dynamics simulations represent an established technique for investigation of RNA structural dynamics. Despite continuous development, contemporary RNA simulations still suffer from suboptimal accuracy of empirical potentials (force fields, ffs) and sampling limitations. Development of efficient enhanced sampling techniques is important for two reasons. First, they allow us to overcome the sampling limitations, and second, they can be used to quantify ff imbalances provided they reach a sufficient convergence. Here, we study two RNA tetraloops (TLs), namely the GAGA and UUCG motifs. We perform extensive folding simulations and calculate folding free energies (ΔGfold°) with the aim to compare different enhanced sampling techniques and to test several modifications of the nonbonded terms extending the AMBER OL3 RNA ff. We demonstrate that replica-exchange solute tempering (REST2) simulations with 12-16 replicas do not show any sign of convergence even when extended to a timescale of 120 µs per replica. However, the combination of REST2 with well-tempered metadynamics (ST-MetaD) achieves good convergence on a timescale of 5-10 µs per replica, improving the sampling efficiency by at least 2 orders of magnitude. Effects of ff modifications on ΔGfold° energies were initially explored by the reweighting approach and then validated by new simulations. We tested several manually prepared variants of the gHBfix potential which improve stability of the native state of both TLs by ∼2 kcal/mol. This is sufficient to conveniently stabilize the folded GAGA TL while the UUCG TL still remains under-stabilized. Appropriate adjustment of van der Waals parameters for C-H···O5' base-phosphate interaction may further stabilize the native states of both TLs by ∼0.6 kcal/mol.

Toward empirical force fields that match experimental observables.

Biomolecular force fields have been traditionally derived based on a mixture of reference quantum chemistry data and experimental information obtained on small fragments. However, the possibility to run extensive molecular dynamics simulations on larger systems achieving ergodic sampling is paving the way to directly using such simulations along with solution experiments obtained on macromolecular systems. Recently, a number of methods have been introduced to automatize this approach. Here, we review these methods, highlight their relationship with machine learning methods, and discuss the open challenges in the field.