Fitting Corrections to an RNA Force Field Using Experimental Data

On the specificity of the recognition of m6A-RNA by YTH reader domains

Most processes of life are the result of polyvalent interactions between macromolecules, often of heterogeneous types and sizes. Frequently, the times associated with these interactions are prohibitively long for interrogation using atomistic simulations. Here, we study the recognition of N6-methylated adenine (m6A) in RNA by the reader domain YTHDC1, a prototypical, cognate pair that challenges simulations through its composition and required timescales. Simulations of RNA pentanucleotides in water reveal that the unbound state can impact (un)binding kinetics in a manner that is both model- and sequence-dependent. This is important because there are two contributions to the specificity of the recognition of the Gm6AC motif: from the sequence adjacent to the central adenine and from its methylation. Next, we establish a reductionist model consisting of an RNA trinucleotide binding to the isolated reader domain in high salt. An adaptive sampling protocol allows us to quantitatively study the dissociation of this complex. Through joint analysis of a data set including both the cognate and control sequences (GAC, Am6AA, and AAA), we derive that both contributions to specificity, sequence and methylation, are significant and in good agreement with experimental numbers. Analysis of the kinetics suggests that flexibility in both the RNA and the YTHDC1 recognition loop leads to many low-populated unbinding pathways. This multiple-pathway mechanism might be dominant for the binding of unstructured polymers, including RNA and peptides, to proteins when their association is driven by polyvalent, electrostatic interactions.

Third Metal Ion Dictates the Catalytic Activity of the Two-Metal-Ion Pre-Ribosomal RNA-Processing Machinery

Nucleic acid processing enzymes use a two-Mg2+-ion motif to promote the formation and cleavage of phosphodiester bonds. Yet, recent evidence demonstrates the presence of spatially conserved second-shell cations surrounding the catalytic architecture of proteinaceous and RNA-dependent enzymes. The RNase mitochondrial RNA processing (MRP) complex, which cleaves the ribosomal RNA (rRNA) precursor at the A3 cleavage site to yield mature 5'-end of 5.8S rRNA, hosts in the catalytic core one atypically-located Mg2+ ion, in addition to the ions forming the canonical catalytic motif. Here, we employ biased quantum classical molecular dynamics simulations of RNase MRP to discover that the third Mg2+ ion inhibits the catalytic process. Instead, its displacement in favour of a second-shell monovalent K+ ion propels phosphodiester bond cleavage by enabling the formation of a specific hydrogen bonding network that mediates the essential proton transfer step. This study points to a direct involvement of a transient K+ ion in the catalytic cleavage of the phosphodiester bond and implicates cation trafficking as a general mechanism in nucleic acid processing enzymes and ribozymes.

Molecular Simulations to Investigate the Impact of N6-Methylation in RNA Recognition: Improving Accuracy and Precision of Binding Free Energy Prediction

N6-Methyladenosine (m6A) is a prevalent RNA post-transcriptional modification that plays crucial roles in RNA stability, structural dynamics, and interactions with proteins. The YT521-B (YTH) family of proteins, which are notable m6A readers, functions through its highly conserved YTH domain. Recent structural investigations and molecular dynamics (MD) simulations have shed light on the mechanism of recognition of m6A by the YTHDC1 protein. Despite advancements, using MD to predict the stabilization induced by m6A on the free energy of binding between RNA and YTH proteins remains challenging due to inaccuracy of the employed force field and limited sampling. For instance, simulations often fail to sufficiently capture the hydration dynamics of the binding pocket. This study addresses these challenges through an innovative methodology that integrates metadynamics, alchemical simulations, and force-field refinement. Importantly, our research identifies hydration of the binding pocket as giving only a minor contribution to the binding free energy and emphasizes the critical importance of precisely tuning force-field parameters to experimental data. By employing a fitting strategy built on alchemical calculations, we refine the m6A partial charge parameters, thereby enabling the simultaneous reproduction of N6 methylation on both the protein binding free energy and the thermodynamic stability of nine RNA duplexes. Our findings underscore the sensitivity of binding free energies to partial charges, highlighting the necessity for thorough parametrization and validation against experimental observations across a range of structural contexts.

Machine learning-augmented molecular dynamics simulations (MD) reveal insights into the disconnect between affinity and activation of ZTP riboswitch ligands

The challenge of targeting RNA with small molecules necessitates a better understanding of RNA-ligand interaction mechanisms. However, the dynamic nature of nucleic acids, their ligand-induced stabilization, and how conformational changes influence gene expression pose significant difficulties for experimental investigation. This work employs a combination of computational and experimental methods to address these challenges. By integrating structure-informed design, crystallography, and machine learning-augmented all-atom molecular dynamics simulations (MD) we synthesized, biophysically and biochemically characterized, and studied the dissociation of a library of small molecule activators of the ZTP riboswitch, a ligand-binding RNA motif that regulates bacterial gene expression. We uncovered key interaction mechanisms, revealing valuable insights into the role of ligand binding kinetics on riboswitch activation. Further, we established that ligand on-rates determine activation potency as opposed to binding affinity and elucidated RNA structural differences, which provide mechanistic insights into the interplay of RNA structure on riboswitch activation.

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.

Simple Adjustment of Intranucleotide Base-Phosphate Interaction in the OL3 AMBER Force Field Improves RNA Simulations

Molecular dynamics (MD) simulations represent an established tool to study RNA molecules. The outcome of MD studies depends, however, on the quality of the force field (ff). Here we suggest a correction for the widely used AMBER OL3 ff by adding a simple adjustment of the nonbonded parameters. The reparameterization of the Lennard-Jones potential for the -H8···O5'- and -H6···O5'- atom pairs addresses an intranucleotide steric clash occurring in the type 0 base-phosphate interaction (0BPh). The nonbonded fix (NBfix) modification of 0BPh interactions (NBfix0BPh modification) was tuned via a reweighting approach and subsequently tested using an extensive set of standard and enhanced sampling simulations of both unstructured and folded RNA motifs. The modification corrects minor but visible intranucleotide clash for the anti nucleobase conformation. We observed that structural ensembles of small RNA benchmark motifs simulated with the NBfix0BPh modification provide better agreement with experiments. No side effects of the modification were observed in standard simulations of larger structured RNA motifs. We suggest that the combination of OL3 RNA ff and NBfix0BPh modification is a viable option to improve RNA MD simulations.

Advances, Applications, and Perspectives in Small-Angle X-ray Scattering of RNA

RNAs exhibit a plethora of functions far beyond transmitting genetic information. Often, RNA functions are entailed in their structure, be it as a regulatory switch, protein binding site, or providing catalytic activity. Structural information is a prerequisite for a full understanding of RNA-regulatory mechanisms. Owing to the inherent dynamics, size, and instability of RNA, its structure determination remains challenging. Methods such as NMR spectroscopy, X-ray crystallography, and cryo-electron microscopy can provide high-resolution structures; however, their limitations make structure determination, even for small RNAs, cumbersome, if at all possible. Although at a low resolution, small-angle X-ray scattering (SAXS) has proven valuable in advancing structure determination of RNAs as a complementary method, which is also applicable to large-sized RNAs. Here, we review the technological and methodological advancements of RNA SAXS. We provide examples of the powerful inclusion of SAXS in structural biology and discuss possible future applications to large RNAs.

Optimizing molecular potential models by imposing kinetic constraints with path reweighting

Empirical force fields employed in molecular dynamics simulations of complex systems are often optimized to reproduce experimentally determined structural and thermodynamic properties. In contrast, experimental knowledge about the interconversion rates between metastable states in such systems is hardly ever incorporated in a force field due to a lack of an efficient approach. Here, we introduce such a framework based on the relationship between dynamical observables, such as rate constants, and the underlying molecular model parameters using the statistical mechanics of trajectories. Given a prior ensemble of molecular dynamics trajectories produced with imperfect force field parameters, the approach allows for the optimal adaption of these parameters such that the imposed constraint of equally predicted and experimental rate constant is obeyed. To do so, the method combines the continuum path ensemble maximum caliber approach with path reweighting methods for stochastic dynamics. When multiple solutions are found, the method selects automatically the combination that corresponds to the smallest perturbation of the entire path ensemble, as required by the maximum entropy principle. To show the validity of the approach, we illustrate the method on simple test systems undergoing rare event dynamics. Next to simple 2D potentials, we explore particle models representing molecular isomerization reactions and protein-ligand unbinding. Besides optimal interaction parameters, the methodology gives physical insights into what parts of the model are most sensitive to the kinetics. We discuss the generality and broad implications of the methodology.

The development of nucleic acids force fields: From an unchallenged past to a competitive future

Molecular dynamics simulations have strongly matured as a method to study biomolecular processes. Their validity, however, is determined by the accuracy of the underlying force fields that describe the forces between all atoms. In this article, we review the development of nucleic acids force fields. We describe the early attempts in the 1990s and emphasize their strong influence on recent force fields. State-of-the-art force fields still use the same Lennard-Jones parameters derived 25 years ago in spite of the fact that these parameters were in general not fitted for nucleic acids. In addition, electrostatic parameters also are deprecated, which may explain some of the current force field deficiencies. We compare different force fields for various systems and discuss new tests of the recently developed Tumuc1 force field. The OL-force fields and Tumuc1 are arguably the best force fields to describe the DNA double helix. However, no force field is flawless. In particular, the description of sugar-puckering remains a problem for nucleic acids force fields. Future refinements are required, so we review methods for force field refinement and give an outlook to the future of force fields.

RNA-protein complexes and force field polarizability

Molecular dynamic (MD) simulations offer a way to study biomolecular interactions and their dynamics at the atomistic level. There are only a few studies of RNA-protein complexes in MD simulations, and here we wanted to study how force fields differ when simulating RNA-protein complexes: 1) argonaute 2 with bound guide RNA and a target RNA, 2) CasPhi-2 bound to CRISPR RNA and 3) Retinoic acid-inducible gene I C268F variant in complex with double-stranded RNA. We tested three non-polarizable force fields: Amber protein force fields ff14SB and ff19SB with RNA force field OL3, and the all-atom OPLS4 force field. Due to the highly charged and polar nature of RNA, we also tested the polarizable AMOEBA force field and the ff19SB and OL3 force fields with a polarizable water model O3P. Our results show that the non-polarizable force fields lead to compact and stable complexes. The polarizability in the force field or in the water model allows significantly more movement from the complex, but in some cases, this results in the disintegration of the complex structure, especially if the protein contains longer loop regions. Thus, one should be cautious when running long-scale simulations with polarizability. As a conclusion, all the tested force fields can be used to simulate RNA-protein complexes and the choice of the optimal force field depends on the studied system and research question.

Toward Force Fields with Improved Base Stacking Descriptions

Recent DNA force fields indicate good performance in describing flexibility and structural stability of double-stranded B-DNA. However, it is not clear how accurately base stacking interactions are represented that are critical for simulating structure formation processes and conformational changes. Based on the equilibrium nucleoside association and base pair nicking, we find that the recent Tumuc1 force field improves the description of base stacking compared to previous state-of-the-art force fields. Nevertheless, base pair stacking is still overstabilized compared to experiment. We propose a rapid method to reweight calculated free energies of stacking upon force field modifications in order to generate improved parameters. A decrease of the Lennard-Jones attraction between nucleo-bases alone appears insufficient; however, adjustments in the partial charge distribution on base atoms could help to further improve the force field description of base stacking.

Base-specific RNA force field improving the dynamics conformation of nucleotide

RNA plays a key role in numerous biological processes. Traditional experimental methods have difficulties capturing the structure and dynamic conformation of RNA. Thus, Molecular dynamic simulations (MDs) has become an essential complementary for RNA experiment. However, state-of-the-art RNA force fields have two major limitations of overestimation base stacking propensity and generation of a high ratio of intercalated conformations. Therefore, a two-step strategy was used to optimize the parameters of ff99bsc0χOL3 (named BSFF1) to improve these limitations, which as well adjusted the unbonded parameters of nucleobase heavy atoms and added ζ/α grid-based energy correction map energy term with reweighting. MD simulations of tetranucleotides indicate that BSFF1 can significantly decrease the ratio of intercalated conformations. Tests of single-strand RNA and kink-turn show that BSFF1 force field can reproduce more accurate conformers than ff99bsc0χOL3 force field. BSFF1 can also stabilize the conformers of duplex and riboswitch. The successful ab initio folding of tetraloop further supports the performance of BSFF1. These findings confirm that the newly developed force field BSFF1 can improve the conformer sampling of RNA.

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.

Lone Pair…π Contacts and Structure Signatures of r(UNCG) Tetraloops, Z-Turns, and Z-Steps: A WebFR3D Survey

Z-DNA and Z-RNA have long appeared as oddities to nucleic acid scientists. However, their Z-step constituents are recurrently observed in all types of nucleic acid systems including ribosomes. Z-steps are NpN steps that are isostructural to Z-DNA CpG steps. Among their structural features, Z-steps are characterized by the presence of a lone pair…π contact that involves the stacking of the ribose O4′ atom of the first nucleotide with the 3′-face of the second nucleotide. Recently, it has been documented that the CpG step of the ubiquitous r(UNCG) tetraloops is a Z-step. Accordingly, such r(UNCG) conformations were called Z-turns. It has also been recognized that an r(GAAA) tetraloop in appropriate conditions can shapeshift to an unusual Z-turn conformation embedding an ApA Z-step. In this report, we explore the multiplicity of RNA motifs based on Z-steps by using the WebFR3D tool to which we added functionalities to be able to retrieve motifs containing lone pair…π contacts. Many examples that underscore the diversity and universality of these motifs are provided as well as tutorial guidance on using WebFR3D. In addition, this study provides an extensive survey of crystallographic, cryo-EM, NMR, and molecular dynamics studies on r(UNCG) tetraloops with a critical view on how to conduct database searches and exploit their results.

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 gHBfix_opt. 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 (ΔG_fold^°) 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 ΔG_fold^° 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.

RNA-Specific Force Field Optimization with CMAP and Reweighting

RNA plays a key role in a variety of cell activities. However, it is difficult to capture its structure dynamics by the traditional experimental methods because of the inherent limitations. Molecular dynamics simulation has become a valuable complement to the experimental methods. Previous studies have indicated that the current force fields cannot accurately reproduce the conformations and structural dynamics of RNA. Therefore, an RNA-specific force field was developed to improve the conformation sampling of RNA. The distribution of ζ/α dihedrals of tetranucleotides was optimized by a reweighting method, and the grid-based energy correction map (CMAP) term was first introduced into the Amber RNA force field of ff99bsc0χOL3, named ff99OL3_CMAP1. Extensive validations of tetranucleotides and tetraloops show that ff99OL3_CMAP1 can significantly decrease the population of an incorrect structure, increase the consistency between the simulation results and experimental values for tetranucleotides, and improve the stability of tetraloops. ff99OL3_CMAP1 can also precisely reproduce the conformation of a duplex and riboswitches. These findings confirm that the newly developed force field ff99OL3_CMAP1 can improve the conformer sampling of RNA.

A Computational Study of RNA Tetraloop Thermodynamics, Including Misfolded States

An important characteristic of RNA folding is the adoption of alternative configurations of similar stability, often referred to as misfolded configurations. These configurations are considered to compete with correctly folded configurations, although their rigorous thermodynamic and structural characterization remains elusive. Tetraloop motifs found in large ribozymes are ideal systems for an atomistically detailed computational quantification of folding free energy landscapes and the structural characterization of their constituent free energy basins, including nonnative states. In this work, we studied a group of closely related 10-mer tetraloops using a combined parallel tempering and metadynamics technique that allows a reliable sampling of the free energy landscapes, requiring only knowledge that the stem folds into a canonical A-RNA configuration. We isolated and analyzed unfolded, folded, and misfolded populations that correspond to different free energy basins. We identified a distinct misfolded state that has a stability very close to that of the correctly folded state. This misfolded state contains a predominant population that shares the same structural features across all tetraloops studied here and lacks the noncanonical A-G base pair in its loop portion. Further analysis performed with biased trajectories showed that although this competitive misfolded state is not an essential intermediate, it is visited in most of the transitions from unfolded to correctly folded states. Moreover, the tetraloops can transition from this misfolded state to the correctly folded state without requiring extensive unfolding.

Mechanism of RNA recognition by a Musashi RNA-binding protein

The Musashi RNA-binding proteins (RBPs) regulate translation of target mRNAs and maintenance of cell stemness and tumorigenesis. Musashi-1 (MSI1), long considered as an intestinal and neural stem cell marker, has been more recently found to be over expressed in many cancers. It has served as an important drug target for treating acute myeloid leukemia and solid tumors such as ovarian, colorectal and bladder cancer. One of the reported binding targets of MSI1 is Numb, a negative regulator of the Notch signaling. However, the dynamic mechanism of Numb RNA binding to MSI1 remains unknown, largely hindering effective drug design targeting this critical interaction. Here, we have performed extensive all-atom microsecond-timescale simulations using a robust Gaussian accelerated molecular dynamics (GaMD) method, which successfully captured multiple times of spontaneous and highly accurate binding of the Numb RNA from bulk solvent to the MSI1 protein target site. GaMD simulations revealed that Numb RNA binding to MSI1 involved largely induced fit in both the RNA and protein. The simulations also identified important low-energy intermediate conformational states during RNA binding, in which Numb interacted mainly with the β2-β3 loop and C terminus of MSI1. The mechanistic understanding of RNA binding obtained from our GaMD simulations is expected to facilitate rational structure-based drug design targeting MSI1 and other RBPs.

Short-Range Imbalances in the AMBER Lennard-Jones Potential for (Deoxy)Ribose···Nucleobase Lone-Pair···π Contacts in Nucleic Acids

The lone-pair···π (lp···π) (deoxy)ribose···nucleobase stacking is a recurring interaction in Z-DNA and RNAs that is characterized by sub-van der Waals lp···π contacts (<3.0 Å). It is a part of the structural signature of CpG Z-step motifs in Z-DNA and r(UNCG) tetraloops that are known to behave poorly in molecular dynamics (MD) simulations. Although the exact origin of the MD simulation issues remains unclear, a significant part of the problem might be due to an imbalanced description of nonbonded interactions, including the characteristic lp···π stacking. To gain insights into the links between lp···π stacking and MD, we present an in-depth comparison between accurate large-basis-set double-hybrid Kohn-Sham density functional theory calculations DSD-BLYP-D3/ma-def2-QZVPP (DHDF-D3) and data obtained with the nonbonded potential of the AMBER force field (AFF) for NpN Z-steps (N = G, A, C, and U). Among other differences, we found that the AFF overestimates the DHDF-D3 lp···π distances by ∼0.1-0.2 Å, while the deviation between the DHDF-D3 and AFF descriptions sharply increases in the short-range region of the interaction. Based on atom-in-molecule polarizabilities and symmetry-adapted perturbation theory analysis, we inferred that the DHDF-D3 versus AFF differences partly originate in identical nucleobase carbon atom Lennard-Jones (LJ) parameters despite the presence/absence of connected electron-withdrawing groups that lead to different effective volumes or vdW radii. Thus, to precisely model the very short CpG lp···π contact distances, we recommend revision of the nucleobase atom LJ parameters. Additionally, we suggest that the large discrepancy between DHDF-D3 and AFF short-range repulsive part of the interaction energy potential may significantly contribute to the poor performances of MD simulations of nucleic acid systems containing Z-steps. Understanding where, and if possible why, the point-charge-type effective potentials reach their limits is vital for developing next-generation FFs and for addressing specific issues in contemporary MD simulations.

Tumuc1: A New Accurate DNA Force Field Consistent with High-Level Quantum Chemistry

An accurate molecular mechanics force field forms the basis of Molecular Dynamics simulations to obtain a realistic view of the structure and dynamics of biomolecules such as DNA. Although frequently updated to improve agreement with available experimental data, DNA force fields still rely in part on parameters introduced more than 20 years ago. We have developed an entirely new DNA force field, Tumuc1, derived from quantum mechanical calculations to obtain a consistent set of bonded parameters and partial atomic charges. The performance of the force field was extensively tested on a variety of DNA molecules. It excels in accuracy of B-DNA simulations but also performs very well on other types of DNA structures and structure formation processes such as hairpin folding, duplex formation, and dynamics of DNA-protein complexes. It can complement existing force fields in order to provide an increasingly accurate description of the structure and dynamics of DNA during simulation studies.

Accurate model of liquid-liquid phase behavior of intrinsically disordered proteins from optimization of single-chain properties

Many intrinsically disordered proteins (IDPs) may undergo liquid-liquid phase separation (LLPS) and participate in the formation of membraneless organelles in the cell, thereby contributing to the regulation and compartmentalization of intracellular biochemical reactions. The phase behavior of IDPs is sequence dependent, and its investigation through molecular simulations requires protein models that combine computational efficiency with an accurate description of intramolecular and intermolecular interactions. We developed a general coarse-grained model of IDPs, with residue-level detail, based on an extensive set of experimental data on single-chain properties. Ensemble-averaged experimental observables are predicted from molecular simulations, and a data-driven parameter-learning procedure is used to identify the residue-specific model parameters that minimize the discrepancy between predictions and experiments. The model accurately reproduces the experimentally observed conformational propensities of a set of IDPs. Through two-body as well as large-scale molecular simulations, we show that the optimization of the intramolecular interactions results in improved predictions of protein self-association and LLPS.

Accurate model of liquid-liquid phase behavior of intrinsically disordered proteins from optimization of single-chain properties

Many intrinsically disordered proteins (IDPs) may undergo liquid-liquid phase separation (LLPS) and participate in the formation of membraneless organelles in the cell, thereby contributing to the regulation and compartmentalization of intracellular biochemical reactions. The phase behavior of IDPs is sequence dependent, and its investigation through molecular simulations requires protein models that combine computational efficiency with an accurate description of intramolecular and intermolecular interactions. We developed a general coarse-grained model of IDPs, with residue-level detail, based on an extensive set of experimental data on single-chain properties. Ensemble-averaged experimental observables are predicted from molecular simulations, and a data-driven parameter-learning procedure is used to identify the residue-specific model parameters that minimize the discrepancy between predictions and experiments. The model accurately reproduces the experimentally observed conformational propensities of a set of IDPs. Through two-body as well as large-scale molecular simulations, we show that the optimization of the intramolecular interactions results in improved predictions of protein self-association and LLPS.

On the potential of machine learning to examine the relationship between sequence, structure, dynamics and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) constitute a broad set of proteins with few uniting and many diverging properties. IDPs-and intrinsically disordered regions (IDRs) interspersed between folded domains-are generally characterized as having no persistent tertiary structure; instead they interconvert between a large number of different and often expanded structures. IDPs and IDRs are involved in an enormously wide range of biological functions and reveal novel mechanisms of interactions, and while they defy the common structure-function paradigm of folded proteins, their structural preferences and dynamics are important for their function. We here discuss open questions in the field of IDPs and IDRs, focusing on areas where machine learning and other computational methods play a role. We discuss computational methods aimed to predict transiently formed local and long-range structure, including methods for integrative structural biology. We discuss the many different ways in which IDPs and IDRs can bind to other molecules, both via short linear motifs, as well as in the formation of larger dynamic complexes such as biomolecular condensates. We discuss how experiments are providing insight into such complexes and may enable more accurate predictions. Finally, we discuss the role of IDPs in disease and how new methods are needed to interpret the mechanistic effects of genomic variants in IDPs.

Guanidine-II aptamer conformations and ligand binding modes through the lens of molecular simulation

Regulation of gene expression via riboswitches is a widespread mechanism in bacteria. Here, we investigate ligand binding of a member of the guanidine sensing riboswitch family, the guanidine-II riboswitch (Gd-II). It consists of two stem–loops forming a dimer upon ligand binding. Using extensive molecular dynamics simulations we have identified conformational states corresponding to ligand-bound and unbound states in a monomeric stem–loop of Gd-II and studied the selectivity of this binding. To characterize these states and ligand-dependent conformational changes we applied a combination of dimensionality reduction, clustering, and feature selection methods. In absence of a ligand, the shape of the binding pocket alternates between the conformation observed in presence of guanidinium and a collapsed conformation, which is associated with a deformation of the dimerization interface. Furthermore, the structural features responsible for the ability to discriminate against closely related analogs of guanidine are resolved. Based on these insights, we propose a mechanism that couples ligand binding to aptamer dimerization in the Gd-II system, demonstrating the value of computational methods in the field of nucleic acids research.

Developments in solution-state NMR yield broader and deeper views of the dynamic ensembles of nucleic acids

Nucleic acids do not fold into a single conformation, and dynamic ensembles are needed to describe their propensities to cycle between different conformations when performing cellular functions. We review recent advances in solution-state nuclear magnetic resonance (NMR) methods and their integration with computational techniques that are improving the ability to probe the dynamic ensembles of DNA and RNA. These include computational approaches for predicting chemical shifts from structure and generating conformational libraries from sequence, measurements of exact nuclear Overhauser effects, development of new probes to study chemical exchange using relaxation dispersion, faster and more sensitive real-time NMR techniques, and new NMR approaches to tackle large nucleic acid assemblies. We discuss how these advances are leading to new mechanistic insights into gene expression and regulation.

Targeting structural features of viral genomes with a nano-sized supramolecular drug

RNA targeting is an exciting frontier for drug design. Intriguing targets include functional RNA structures in structurally-conserved untranslated regions (UTRs) of many lethal viruses. However, computational docking screens, valuable in protein structure targeting, fail for inherently flexible RNA. Herein we harness MD simulations with Markov state modeling to enable nanosize metallo-supramolecular cylinders to explore the dynamic RNA conformational landscape of HIV-1 TAR untranslated region RNA (representative for many viruses) replicating experimental observations. These cylinders are exciting as they have unprecedented nucleic acid binding and are the first supramolecular helicates shown to have anti-viral activity in cellulo: the approach developed in this study provides additional new insight about how such viral UTR structures might be targeted with the cylinder binding into the heart of an RNA-bulge cavity, how that reduces the conformational flexibility of the RNA and molecular details of the insertion mechanism. The approach and understanding developed represents a new roadmap for design of supramolecular drugs to target RNA structural motifs across biology and nucleic acid nanoscience.

Deciphering nucleotide modification-induced structure and stability changes

Nucleotide modification in RNA controls a bevy of biological processes, including RNA degradation, gene expression, and gene editing. In turn, misregulation of modified nucleotides is associated with a host of chronic diseases and disorders. However, the molecular mechanisms driving these processes remain poorly understood. To partially address this knowledge gap, we used alchemical and temperature replica exchange molecular dynamics (TREMD) simulations on an RNA duplex and an analogous hairpin to probe the structural effects of modified and/or mutant nucleotides. The simulations successfully predict the modification/mutation-induced relative free energy change for complementary duplex formation, and structural analyses highlight mechanisms driving stability changes. Furthermore, TREMD simulations for a hairpin-forming RNA with and without modification provide reliable estimations of the energy landscape. Illuminating the impact of methylated and/or mutated nucleotides on the structure-function relationship and the folding energy landscape, the simulations provide insights into modification-induced alterations to the folding mechanics of the hairpin. The results here may be biologically significant as hairpins are widespread structure motifs that play critical roles in gene expression and regulation. Specifically, the tetraloop of the probed hairpin is phylogenetically abundant, and the stem mirrors a miRNA seed region whose modification has been implicated in epilepsy pathogenesis.

Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation

Computational studies play an increasingly important role in chemistry and biophysics, mainly thanks to improvements in hardware and algorithms. In drug discovery and development, computational studies can reduce the costs and risks of bringing a new medicine to market. Computational simulations are mainly used to optimize promising new compounds by estimating their binding affinity to proteins. This is challenging due to the complexity of the simulated system. To assess the present and future value of simulation for drug discovery, we review key applications of advanced methods for sampling complex free-energy landscapes at near nonergodicity conditions and for estimating the rate coefficients of very slow processes of pharmacological interest. We outline the statistical mechanics and computational background behind this research, including methods such as steered molecular dynamics and metadynamics. We review recent applications to pharmacology and drug discovery and discuss possible guidelines for the practitioner. Recent trends in machine learning are also briefly discussed. Thanks to the rapid development of methods for characterizing and quantifying rare events, simulation's role in drug discovery is likely to expand, making it a valuable complement to experimental and clinical approaches.

UUCG RNA Tetraloop as a Formidable Force-Field Challenge for MD Simulations

Explicit solvent atomistic molecular dynamics (MD) simulations represent an established technique to study structural dynamics of RNA molecules and an important complement for diverse experimental methods. However, performance of molecular mechanical (MM) force fields (ff's) remains far from satisfactory even after decades of development, as apparent from a problematic structural description of some important RNA motifs. Actually, some of the smallest RNA molecules belong to the most challenging systems for MD simulations and, among them, the UUCG tetraloop is saliently difficult. We report a detailed analysis of UUCG MD simulations, depicting the sequence of events leading to the loss of the UUCG native state during MD simulations. The total amount of MD simulation data analyzed in this work is close to 1.3 ms. We identify molecular interactions, backbone conformations, and substates that are involved in the process. Then, we unravel specific ff deficiencies using diverse quantum mechanical/molecular mechanical (QM/MM) and QM calculations. Comparison between the MM and QM methods shows discrepancies in the description of the 5'-flanking phosphate moiety and both signature sugar-base interactions. Our work indicates that poor behavior of the UUCG tetraloop in simulations is a complex issue that cannot be attributed to one dominant and straightforwardly correctable factor. Instead, there is a concerted effect of multiple ff inaccuracies that are coupled and amplifying each other. We attempted to improve the simulation behavior by some carefully tailored interventions, but the results were still far from satisfactory, underlying the difficulties in development of accurate nucleic acid ff's.

Mg2+ Sensing by an RNA Fragment: Role of Mg2+-Coordinated Water Molecules

RNA molecules selectively bind to specific metal ions to populate their functional active states, making it important to understand their source of ion selectivity. In large RNA systems, metal ions interact with the RNA at multiple locations, making it difficult to decipher the precise role of ions in folding. To overcome this complexity, we studied the role of different metal ions (Mg²⁺, Ca²⁺, and K⁺) in the folding of a small RNA hairpin motif (5'-ucCAAAga-3') using unbiased all-atom molecular dynamics simulations. The advantage of studying this system is that it requires specific binding of a single metal ion to fold to its native state. We find that even for this small RNA, the folding free energy surface (FES) is multidimensional as different metal ions present in the solution can simultaneously facilitate folding. The FES shows that specific binding of a metal ion is indispensable for its folding. We further show that in addition to the negatively charged phosphate groups, the spatial organization of electronegative nucleobase atoms drives the site-specific binding of the metal ions. Even though the binding site cannot discriminate between different metal ions, RNA folds efficiently only in a Mg²⁺ solution. We show that the rigid network of Mg²⁺-coordinated water molecules facilitates the formation of important interactions in the transition state. The other metal ions such as K⁺ and Ca²⁺ cannot facilitate the formation of such interactions. These results allow us to hypothesize possible metal-sensing mechanisms in large metalloriboswitches and also provide useful insights into the design of appropriate collective variables for studying large RNA molecules using enhanced sampling methods.

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.

Integrating NMR and simulations reveals motions in the UUCG tetraloop

We provide an atomic-level description of the structure and dynamics of the UUCG RNA stem-loop by combining molecular dynamics simulations with experimental data. The integration of simulations with exact nuclear Overhauser enhancements data allowed us to characterize two distinct states of this molecule. The most stable conformation corresponds to the consensus three-dimensional structure. The second state is characterized by the absence of the peculiar non-Watson-Crick interactions in the loop region. By using machine learning techniques we identify a set of experimental measurements that are most sensitive to the presence of non-native states. We find that although our MD ensemble, as well as the consensus UUCG tetraloop structures, are in good agreement with experiments, there are remaining discrepancies. Together, our results show that (i) the MD simulation overstabilize a non-native loop conformation, (ii) eNOE data support its presence with a population of ≈10% and (iii) the structural interpretation of experimental data for dynamic RNAs is highly complex, even for a simple model system such as the UUCG tetraloop.

Fine-Tuning of the AMBER RNA Force Field with a New Term Adjusting Interactions of Terminal Nucleotides

Determination of RNA structural-dynamic properties is challenging for experimental methods. Thus, atomistic molecular dynamics (MD) simulations represent a helpful technique complementary to experiments. However, contemporary MD methods still suffer from limitations of force fields (ffs), including imbalances in the nonbonded ff terms. We have recently demonstrated that some improvement of state-of-the-art AMBER RNA ff can be achieved by adding a new term for H-bonding called gHBfix, which increases tuning flexibility and reduces risk of side-effects. Still, the first gHBfix version did not fully correct simulations of short RNA tetranucleotides (TNs). TNs are key benchmark systems due to availability of unique NMR data, although giving too much weight on improving TN simulations can easily lead to overfitting to A-form RNA. Here we combine the gHBfix version with another term called tHBfix, which separately treats H-bond interactions formed by terminal nucleotides. This allows to refine simulations of RNA TNs without affecting simulations of other RNAs. The approach is in line with adopted strategy of current RNA ffs, where the terminal nucleotides possess different parameters for terminal atoms than the internal nucleotides. Combination of gHBfix with tHBfix significantly improves the behavior of RNA TNs during well-converged enhanced-sampling simulations using replica exchange with solute tempering. TNs mostly populate canonical A-form like states while spurious intercalated structures are largely suppressed. Still, simulations of r(AAAA) and r(UUUU) TNs show some residual discrepancies with primary NMR data which suggests that future tuning of some other ff terms might be useful. Nevertheless, the tHBfix has a clear potential to improve modeling of key biochemical processes, where interactions of RNA single stranded ends are involved.

Atomistic to continuum model for studying mechanical properties of RNA nanotubes

With rapid advancements in the emerging field of RNA nanotechnology, its current and potential applications, new important problems arise in our quest to better understand properties of RNA nanocomplexes. In this paper, our focus is on the modeling of RNA nanotubes which are important for many biological processes. These RNA complexes are also important for human beings, with their theurapeutical and biomedical applications discussed vigorously in the literature over the recent years. Here, we develop a continuum model of RNA nanotubes, originally obtained from self assembly of RNA building blocks in the molecular dynamics simulation. Based on the finite element method, we calculate the elastic properties of these nanostructures and provide a relationship between stress and strain induced in the RNA nanotube. We also analyze the variations in the displacement vector along the assembly axis for RNA nanotubes of different sizes. In particular, we show that oscillations in the amplitudes of strains and displacements significantly differ for such RNA nanotubes. These findings are discussed in the context of atomistic simulations and experimental results in this field.

Conformational ensembles of an RNA hairpin using molecular dynamics and sparse NMR data

Solution nuclear magnetic resonance (NMR) experiments allow RNA dynamics to be determined in an aqueous environment. However, when a limited number of peaks are assigned, it is difficult to obtain structural information. We here show a protocol based on the combination of experimental data (Nuclear Overhauser Effect, NOE) and molecular dynamics simulations with enhanced sampling methods. This protocol allows to (a) obtain a maximum entropy ensemble compatible with NMR restraints and (b) obtain a minimal set of metastable conformations compatible with the experimental data (maximum parsimony). The method is applied to a hairpin of 29 nt from an inverted SINEB2, which is part of the SINEUP family and has been shown to enhance protein translation. A clustering procedure is introduced where the annotation of base-base interactions and glycosidic bond angles is used as a metric. By reweighting the contributions of the clusters, minimal sets of four conformations could be found which are compatible with the experimental data. A motif search on the structural database showed that some identified low-population states are present in experimental structures of other RNA transcripts. The introduced method can be applied to characterize RNA dynamics in systems where a limited amount of NMR information is available.

How to learn from inconsistencies: Integrating molecular simulations with experimental data

Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.

Zinc-finger protein CNBP alters the 3-D structure of lncRNA Braveheart in solution

Long non-coding RNAs (lncRNAs) constitute a significant fraction of the transcriptome, playing important roles in development and disease. However, our understanding of structure-function relationships for this emerging class of RNAs has been limited to secondary structures. Here, we report the 3-D atomistic structural study of epigenetic lncRNA, Braveheart (Bvht), and its complex with CNBP (Cellular Nucleic acid Binding Protein). Using small angle X-ray scattering (SAXS), we elucidate the ensemble of Bvht RNA conformations in solution, revealing that Bvht lncRNA has a well-defined, albeit flexible 3-D structure that is remodeled upon CNBP binding. Our study suggests that CNBP binding requires multiple domains of Bvht and the RHT/AGIL RNA motif. We show that RHT/AGIL, previously shown to interact with CNBP, contains a highly flexible loop surrounded by more ordered helices. As one of the largest RNA-only 3-D studies, the work lays the foundation for future structural studies of lncRNA-protein complexes.

Bayesian-Maximum-Entropy Reweighting of IDP Ensembles Based on NMR Chemical Shifts

Bayesian and Maximum Entropy approaches allow for a statistically sound and systematic fitting of experimental and computational data. Unfortunately, assessing the relative confidence in these two types of data remains difficult as several steps add unknown error. Here we propose the use of a validation-set method to determine the balance, and thus the amount of fitting. We apply the method to synthetic NMR chemical shift data of an intrinsically disordered protein. We show that the method gives consistent results even when other methods to assess the amount of fitting cannot be applied. Finally, we also describe how the errors in the chemical shift predictor can lead to an incorrect fitting and how using secondary chemical shifts could alleviate this problem.