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A novel method combining 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 $\gamma$, $\beta$, 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., Comment: Submitted to journal; added zenodo link; replaced fig. 3 with correct one

Conformational dynamics is crucial for ribonucleic acid (RNA) function. Techniques such as nuclear magnetic resonance, cryo-electron microscopy, small- and wide-angle X-ray scattering, chemical probing, single-molecule F\"orster resonance energy transfer or even thermal or mechanical denaturation experiments probe RNA dynamics at different time and space resolutions. Their combination with accurate atomistic molecular dynamics (MD) simulations paves the way for quantitative and detailed studies of RNA dynamics. First, experiments provide a quantitative validation tool for MD simulations. Second, available data can be used to refine simulated structural ensembles to match experiments. Finally, comparison with experiments allows for improving MD force fields that are transferable to new systems for which data is not available. Here we review the recent literature and provide our perspective on this field., Comment: Submitted to journal

Performing alchemical transformations, in which one molecular system is nonphysically changed to another system, is a popular approach adopted in performing free energy calculations associated with various biophysical processes, such as protein-ligand binding or the transfer of a molecule between environments. While the sampling of alchemical intermediate states in either parallel (e.g. Hamiltonian replica exchange) or serial manner (e.g. expanded ensemble) can bridge the high-probability regions in the configurational space between two end states of interest, alchemical methods can fail in scenarios where the most important slow degrees of freedom in the configurational space are in large part orthogonal to the alchemical variable, or if the system gets trapped in a deep basin extending in both the configurational and alchemical space. To alleviate these issues, we propose to use alchemical variables as an additional dimension in metadynamics, augmenting the ability both to sample collective variables and to enhance sampling in free energy calculations. In this study, we validate our implementation of alchemical metadynamics in PLUMED with test systems and alchemical processes with varying complexities and dimensions of collective variable space, including the interconversion between the torsional metastable states of a toy system and the methylation of a nucleoside both in the isolated form and in a duplex. We show that multi-dimensional alchemical metadynamics can address the challenges mentioned above and further accelerate sampling by introducing configurational collective variables. The method can trivially be combined with other metadynamics-based algorithms implemented in PLUMED. The necessary PLUMED code changes have already been released for general use in PLUMED 2.8.

Post-transcriptional modifications are crucial for RNA function, with roles ranging from the stabilization of functional RNA structures to modulation of RNA--protein interactions. Additionally, artificially modified RNAs have been suggested as optimal oligonucleotides for therapeutic purposes. The impact of chemical modifications on secondary structure has been rationalized for some of the most common modifications. However, the characterization of how the modifications affect the three-dimensional RNA structure and dynamics and its capability to bind proteins is still highly challenging. Molecular dynamics simulations, coupled with enhanced sampling methods and integration of experimental data, provide a direct access to RNA structural dynamics. In the context of RNA chemical modifications, alchemical simulations where a wild type nucleotide is converted to a modified one are particularly common. In this Chapter, we review recent molecular dynamics studies of modified ribonucleotides. We discuss the technical aspects of the reviewed works, including the employed force fields, enhanced sampling methods, and alchemical methods, in a way that is accessible to experimentalists. Finally, we provide our perspective on this quickly growing field of research. The goal of this Chapter is to provide a guide for experimentalists to understand molecular dynamics works and, at the same time, give to molecular dynamics experts a solid review of published articles that will be a useful starting point for new research., Submitted as a chapter for the book "RNA Structure and Function", series "RNA Technologies", published by Springer

Chemical probing experiments such as SHAPE are routinely used to probe RNA molecules. In this work, we use atomistic molecular dynamics simulations to test the hypothesis that binding of RNA with SHAPE reagents is affected by cooperative effects leading to an observed reactivity that is dependent on the reagent concentration. We develop a general technique that enables the calculation of the affinity for arbitrary molecules as a function of their concentration in the grand-canonical ensemble. Our simulations of an RNA structural motif suggest that, at the concentration typically used in SHAPE experiments, cooperative binding would lead to a measurable concentration-dependent reactivity. We also provide a qualitative validation of this statement by analyzing a new set of experiments collected at different reagent concentrations.

This chapter discusses how the PLUMED plugin for molecular dynamics can be used to analyze and bias molecular dynamics trajectories. The chapter begins by introducing the notion of a collective variable and by then explaining how the free energy can be computed as a function of one or more collective variables. A number of practical issues mostly around periodic boundary conditions that arise when these types of calculations are performed using PLUMED are then discussed. Later parts of the chapter discuss how PLUMED can be used to perform enhanced sampling simulations that introduce simulation biases or multiple replicas of the system and Monte Carlo exchanges between these replicas. This section is then followed by a discussion on how free-energy surfaces and associated error bars can be extracted from such simulations by using weighted histogram and block averaging techniques.

The non-resonant tunneling regime for charge transfer across nanojunctions is critically dependent on the so-called \beta{} parameter, governing the exponential decay of the current as the length of the junction increases. For periodic materials, this parameter can be theoretically evaluated by computing the complex band structure (CBS) -- or evanescent states -- of the material forming the tunneling junction. In this work we present the calculation of the CBS for organic polymers using a variety of computational schemes, including standard local, semilocal, and hybrid-exchange density functionals, and many-body perturbation theory within the GW approximation. We compare the description of localization and \beta{} parameters among the adopted methods and with experimental data. We show that local and semilocal density functionals systematically underestimate the \beta{} parameter, while hybrid-exchange schemes partially correct for this discrepancy, resulting in a much better agreement with GW calculations and experiments. Self-consistency effects and self-energy representation issues of the GW corrections are discussed together with the use of Wannier functions to interpolate the electronic band-structure., Comment: Accepted for publication on Physical Review B v2: fixed some typos

Recently, we have shown how a colored-noise Langevin equation can be used in the context of molecular dynamics as a tool to obtain dynamical trajectories whose properties are tailored to display desired sampling features. In the present paper, after having reviewed some analytical results for the stochastic differential equations forming the basis of our approach, we describe in detail the implementation of the generalized Langevin equation thermostat and the fitting procedure used to obtain optimal parameters. We discuss in detail the simulation of nuclear quantum effects, and demonstrate that, by carefully choosing parameters, one can successfully model strongly anharmonic solids such as neon. For the reader's convenience, a library of thermostat parameters and some demonstrative code can be downloaded from an on-line repository.

A new reactive force field to describe proton diffusion within the solid-oxide fuel cell material BaZrO3 has been derived. Using a quantum mechanical potential energy surface, the parameters of an interatomic potential model to describe hydroxyl groups within both pure and yttrium-doped BaZrO3 have been determined. Reactivity is then incorporated through the use of the empirical valence bond model. Molecular dynamics simulations (EVB-MD) have been performed to explore the diffusion of hydrogen using a stochastic thermostat and barostat whose equations are extended to the isostress-isothermal ensemble. In the low concentration limit, the presence of yttrium is found not to significantly influence the diffusivity of hydrogen, despite the proton having a longer residence time at oxygen adjacent to the dopant. This lack of influence is due to the fact that trapping occurs infrequently, even when the proton diffuses through octahedra adjacent to the dopant. The activation energy for diffusion is found to be 0.42 eV, in good agreement with experimental values, though the prefactor is slightly underestimated., Comment: Corrected title

We discuss the possibility of implementing asynchronous replica-exchange (or parallel tempering) molecular dynamics. In our scheme, the exchange attempts are driven by asynchronous messages sent by one of the computing nodes, so that different replicas are allowed to perform a different number of time-steps between subsequent attempts. The implementation is simple and based on the message-passing interface (MPI). We illustrate the advantages of our scheme with respect to the standard synchronous algorithm and we benchmark it for a model Lennard-Jones liquid on an IBM-LS21 blade center cluster., Preprint of Proceeding for CSFI 2008

The process of RNA base fraying (i.e. the transient opening of the termini of a helix) is involved in many aspects of RNA dynamics. We here use molecular dynamics simulations and Markov state models to characterize the kinetics of RNA fraying and its sequence and direction dependence. In particular, we first introduce a method for determining biomolecular dynamics employing core-set Markov state models constructed using an advanced clustering technique. The method is validated on previously reported simulations. We then use the method to analyze extensive trajectories for four different RNA model duplexes. Results obtained using D. E. Shaw research and AMBER force fields are compared and discussed in detail, and show a non-trivial interplay between the stability of intermediate states and the overall fraying kinetics., Comment: Supporting information included in ancillary files