Characterization of Mg2+ Distributions around RNA in Solution

Grand canonical Monte Carlo and deep learning assisted enhanced sampling to characterize the distribution of Mg2+ and influence of the Drude polarizable force field on the stability of folded states of the twister ribozyme

Molecular dynamics simulations are crucial for understanding the structural and dynamical behavior of biomolecular systems, including the impact of their environment. However, there is a gap between the time scale of these simulations and that of real-world experiments. To address this problem, various enhanced simulation methods have been developed. In addition, there has been a significant advancement of the force fields used for simulations associated with the explicit treatment of electronic polarizability. In this study, we apply oscillating chemical potential grand canonical Monte Carlo and machine learning methods to determine reaction coordinates combined with metadynamics simulations to explore the role of Mg2+ distribution and electronic polarizability in the context of the classical Drude oscillator polarizable force field on the stability of the twister ribozyme. The introduction of electronic polarizability along with the details of the distribution of Mg2+ significantly stabilizes the simulations with respect to sampling the crystallographic conformation. The introduction of electronic polarizability leads to increased stability over that obtained with the additive CHARMM36 FF reported in a previous study, allowing for a distribution of a wider range of ions to stabilize twister. Specific interactions contributing to stabilization are identified, including both those observed in the crystal structures and additional experimentally unobserved interactions. Interactions of Mg2+ with the bases are indicated to make important contributions to stabilization. Notably, the presence of specific interactions between the Mg2+ ions and bases or the non-bridging phosphate oxygens (NBPOs) leads to enhanced dipole moments of all three moieties. Mg2+-NBPO interactions led to enhanced dipoles of the phosphates but, interestingly, not in all the participating ions. The present results further indicate the importance of electronic polarizability in stabilizing RNA in molecular simulations and the complicated nature of the relationship of Mg2+-RNA interactions with the polarization response of the bases and phosphates.

Metal Ion Sensing by Tetraloop-like RNA Fragment: Role of Compact Intermediates with Non-Native Metal Ion-RNA Inner-Shell Contacts

Divalent metal ions influence the folding and function of ribonucleic acid (RNA) in the cells. The mechanism of how RNA structural elements in riboswitches sense specific metal ions is unclear. RNA interacts with ions through two distinct binding modes: direct interaction between the ion and RNA (inner-shell (IS) coordination) and indirect interaction between the ion and RNA mediated through water molecules (outer-shell (OS) coordination). To understand how RNA senses metal ions such as Mg2+ and Ca2+, we studied the folding of a small RNA segment from the Mg2+ sensing M-Box riboswitch using computer simulations. This RNA segment has the characteristics of a GNRA tetraloop motif and interestingly requires the binding of a single Mg2+ ion. The folding free energy surface of this simple tetraloop system is multidimensional, with a population of multiple intermediates where the tetraloop and cation interact through IS and OS coordination. The partially folded compact tetraloop intermediates form multiple non-native IS contacts with the metal ion. Thermal fluctuations should break these strong non-native IS contacts so that the tetraloop can fold to the native state, resulting in higher folding free energy barriers. Ca2+ undergoes rapid OS to IS transitions and vice versa due to its lower charge density than Mg2+. However, the ability of Ca2+ to stabilize the native tetraloop state is weaker, as it could not hold the loop-closing nucleotides together due to its weaker interactions with the nucleotides. These insights are critical to understanding the specific ion sensing mechanisms in riboswitches, and the predictions are amenable for verification by nuclear magnetic resonance (NMR) experiments.

Influence of ion and hydration atmospheres on RNA structure and dynamics: insights from advanced theoretical and computational methods

RNA, a highly charged biopolymer composed of negatively charged phosphate groups, defies electrostatic repulsion to adopt well-defined, compact structures. Hence, the presence of positively charged metal ions is crucial not only for RNA's charge neutralization, but they also coherently decorate the ion atmosphere of RNA to stabilize its compact fold. This feature article elucidates various modes of close RNA-ion interactions, with a special emphasis on Mg2+ as an outer-sphere and inner-sphere ion. Through examples, we highlight how inner-sphere chelated Mg2+ stabilizes RNA pseudoknots, while outer-sphere ions can also exert long-range electrostatic interactions, inducing groove narrowing, coaxial helical stacking, and RNA ring formation. In addition to investigating the RNA's ion environment, we note that the RNA's hydration environment is relatively underexplored. Our study delves into its profound interplay with the structural dynamics of RNA, employing state-of-the-art atomistic simulation techniques. Through examples, we illustrate how specific ions and water molecules are associated with RNA functions, leveraging atomistic simulations to identify preferential ion binding and hydration sites. However, understanding their impact(s) on the RNA structure remains challenging due to the involvement of large length and long time scales associated with RNA's dynamic nature. Nevertheless, our contributions and recent advances in coarse-grained simulation techniques offer insights into large-scale structural changes dynamically linked to the RNA ion atmosphere. In this connection, we also review how different cutting-edge computational simulation methods provide a microscopic lens into the influence of ions and hydration on RNA structure and dynamics, elucidating distinct ion atmospheric components and specific hydration layers and their individual and collective impacts.

GPU-specific algorithms for improved solute sampling in grand canonical Monte Carlo simulations

The Grand Canonical Monte Carlo (GCMC) ensemble defined by the excess chemical potential, μex , volume, and temperature, in the context of molecular simulations allows for variations in the number of particles in the system. In practice, GCMC simulations have been widely applied for the sampling of rare gasses and water, but limited in the context of larger molecules. To overcome this limitation, the oscillating μex GCMC method was introduced and shown to be of utility for sampling small solutes, such as formamide, propane, and benzene, as well as for ionic species such as monocations, acetate, and methylammonium. However, the acceptance of GCMC insertions is low, and the method is computationally demanding. In the present study, we improved the sampling efficiency of the GCMC method using known cavity-bias and configurational-bias algorithms in the context of GPU architecture. Specifically, for GCMC simulations of aqueous solution systems, the configurational-bias algorithm was extended by applying system partitioning in conjunction with a random interval extraction algorithm, thereby improving the efficiency in a highly parallel computing environment. The method is parallelized on the GPU using CUDA and OpenCL, allowing for the code to run on both Nvidia and AMD GPUs, respectively. Notably, the method is particularly well suited for GPU computing as the large number of threads allows for simultaneous sampling of a large number of configurations during insertion attempts without additional computational overhead. In addition, the partitioning scheme allows for simultaneous insertion attempts for large systems, offering considerable efficiency. Calculations on the BK Channel, a transporter, including a lipid bilayer with over 760,000 atoms, show a speed up of ~53-fold through the use of system partitioning. The improved algorithm is then combined with an enhanced μex oscillation protocol and shown to be of utility in the context of the site-identification by ligand competitive saturation (SILCS) co-solvent sampling approach as illustrated through application to the protein CDK2.

Influence of Mg2+ Distribution on the Stability of Folded States of the Twister Ribozyme Revealed Using Grand Canonical Monte Carlo and Generative Deep Learning Enhanced Sampling

Metal ions, particularly magnesium ions (Mg2+), play a role in stabilizing the tertiary structures of RNA molecules. Theoretical models and experimental techniques show that metal ions can change RNA dynamics and how it transitions through different stages of folding. However, the specific ways in which metal ions contribute to the formation and stabilization of RNA's tertiary structure are not fully understood at the atomic level. Here, we combined oscillating excess chemical potential Grand Canonical Monte Carlo (GCMC) and metadynamics to bias toward the sampling of unfolded states using reaction coordinates generated by machine learning allowing for examination of Mg2+-RNA interactions that contribute to stabilizing folded states of the pseudoknot found in the Twister ribozyme. GCMC is used to sample diverse ion distributions around the RNA with deep learning applied to iteratively generate system-specific reaction coordinates to maximize conformational sampling during metadynamics simulations. Results from 6 μs simulations performed on 9 individual systems indicate that Mg2+ ions play a crucial role in stabilizing the three-dimensional (3D) structure of the RNA by stabilizing specific interactions of phosphate groups or phosphate groups and bases of neighboring nucleotides. While many phosphates are accessible to interactions with Mg2+, it is observed that multiple, specific interactions are required to sample conformations close to the folded state; coordination of Mg2+ at individual specific sites facilitates sampling of folded conformations though unfolding ultimately occurs. It is only when multiple specific interactions occur, including the presence of specific inner-shell cation interactions linking two nucleotides, that conformations close to the folded state are stable. While many of the identified Mg2+ interactions are observed in the X-ray crystal structure of Twister, the present study suggests two new Mg2+ ion sites in the Twister ribozyme that contribute to stabilization. In addition, specific interactions with Mg2+ are observed that destabilize the local RNA structure, a process that may facilitate the folding of RNA into its correct structure.

Dynamic effects of the spine of hydrated magnesium on viral RNA pseudoknot structure

In the cellular environment, a viral RNA Pseudoknot (PK) structure is responsive to its prevailing ion atmosphere created by a mixture of monovalent and divalent cations. We investigate the influence of such a mixed-salt environment on RNA-PK structure at an atomic resolution through three sets of 1.5 μs explicit solvent molecular dynamics (MD) simulations and also by building a dynamic counterion-condensation (DCC) model at varying divalent Mg²⁺ concentrations. The DCC model includes explicit interaction of the ligand and adjacent chelated Mg²⁺ by extending the recently developed generalized Manning condensation model. Its implementation within an all-atom structure-based molecular dynamics framework bolsters its opportunity to explore large-length scale and long-timescale phenomena associated with complex RNA systems immersed in its dynamic ion environment. In the present case of RNA-PK, both explicit MD and DCC simulations reveal a spine of hydrated-Mg²⁺ to induce stem-I and stem-II closure where the minor groove between these stems is akin to breathing. Mg²⁺ mediated minor-groove narrowing is coupled with local base-flipping dynamics of a base triple and quadruple, changing the stem structure of such RNA. Contrary to the conversational view of the indispensable need for Mg²⁺ for the tertiary structure of RNA, the study warns about the plausible detrimental effect of specific Mg²⁺-phosphate interactions on the RNA-PK structure beyond a certain concentration of Mg²⁺.

SILCS-RNA: Toward a Structure-Based Drug Design Approach for Targeting RNAs with Small Molecules

RNA molecules can act as potential drug targets in different diseases, as their dysregulated expression or misfolding can alter various cellular processes. Noncoding RNAs account for ∼70% of the human genome, and these molecules can have complex tertiary structures that present a great opportunity for targeting by small molecules. In the present study, the site identification by ligand competitive saturation (SILCS) computational approach is extended to target RNA, termed SILCS-RNA. Extensions to the method include an enhanced oscillating excess chemical potential protocol for the grand canonical Monte Carlo calculations and individual simulations of the neutral and charged solutes from which the SILCS functional group affinity maps (FragMaps) are calculated for subsequent binding site identification and docking calculations. The method is developed and evaluated against seven RNA targets and their reported small molecule ligands. SILCS-RNA provides a detailed characterization of the functional group affinity pattern in the small molecule binding sites, recapitulating the types of functional groups present in the ligands. The developed method is also shown to be useful for identification of new potential binding sites and identifying ligand moieties that contribute to binding, granular information that can facilitate ligand design. However, limitations in the method are evident including the ability to map the regions of binding sites occupied by ligand phosphate moieties and to fully account for the wide range of conformational heterogeneity in RNA associated with binding of different small molecules, emphasizing inherent challenges associated with applying computer-aided drug design methods to RNA. While limitations are present, the current study indicates how the SILCS-RNA approach may enhance drug discovery efforts targeting RNAs with small molecules.

Petkov P, Milenov TI, Vayssilov GN. Sodium and Magnesium Ion Location at the Backbone and at the Nucleobase of RNA: Ab Initio Molecular Dynamics in Water Solution

The interactions between Na⁺ or Mg²⁺ ions with different parts of single-stranded RNA molecules, namely, the oxygen atoms from the phosphate groups or the guanine base, in water solution have been studied using first-principles molecular dynamics. Sodium ions were found to be much more mobile than Mg²⁺ ions and readily underwent transitions between a state directly bonded to RNA oxygen atoms and a completely solvated state. The inner solvation shell of Na⁺ ions fluctuated stochastically at a femtosecond timescale coordinating on average 5 oxygen atoms for bonded Na⁺ ions and 5.5 oxygen atoms for solvated Na⁺ ions. In contrast, the inner solvation shell of Mg²⁺ ions was stable in both RNA-bonded and completely solvated states. In both cases, Mg²⁺ ions coordinated 6 oxygen atoms from the inner solvation shell. Consistent with their stable solvation shells, Mg²⁺ ions were more effective than Na⁺ ions in stabilizing the RNA backbone conformation. The exclusion zones between the first and second solvation shells, solvation shell widths, and angles for binding to carbonyl oxygen of guanine for solvated Na⁺ or Mg²⁺ ions exhibited a number of quantitative differences when compared with RNA crystallographic data. The presented results support the distinct capacity of Mg²⁺ ions to support the RNA structure not only in the crystal phase but also in the dynamic water environment both on the side of the phosphate moiety and on the side of the nucleobase.

Contributions and competition of Mg2+ and K+ in folding and stabilization of the Twister ribozyme

Native folded and compact intermediate states of RNA typically involve tertiary structures in the presence of divalent ions such as Mg²⁺ in a background of monovalent ions. In a recent study, we have shown how the presence of Mg²⁺ impacts the transition from partially unfolded to folded states through a "push-pull" mechanism where the ion both favors and disfavors the sampling of specific phosphate-phosphate interactions. To further understand the ion atmosphere of RNA in folded and partially folded states results from atomistic umbrella sampling and oscillating chemical potential grand canonical Monte Carlo/molecular dynamics (GCMC/MD) simulations are used to obtain atomic-level details of the distributions of Mg²⁺ and K⁺ ions around Twister RNA. Results show the presence of 100 mM Mg²⁺ to lead to increased charge neutralization over that predicted by counterion condensation theory. Upon going from partially unfolded to folded states, overall charge neutralization increases at all studied ion concentrations that, while associated with an increase in the number of direct ion-phosphate interactions, is fully accounted for by the monovalent K⁺ ions. Furthermore, K⁺ preferentially interacts with purine N7 atoms of helical regions in partially unfolded states, thereby potentially stabilizing the helical regions. Thus, both secondary helical structures and formation of tertiary structures leads to increased counterion condensation, thereby stabilizing those structural features of Twister. Notably, it is shown that K⁺ can act as a surrogate for Mg²⁺ by participating in specific interactions with nonsequential phosphate pairs that occur in the folded state, explaining the ability of Twister to self-cleave at submillimolar Mg²⁺ concentrations.

Balanced polarizable Drude force field parameters for molecular anions: phosphates, sulfates, sulfamates, and oxides

Polarizable force fields are emerging as a more accurate alternative to additive force fields in terms of modeling and simulations of a variety of chemicals including biomolecules. Explicit treatment of induced polarization in charged species such as phosphates and sulfates offers the potential for achieving an improved atomistic understanding of the physical forces driving their interactions with their environments. To help achieve this, in this study we present balanced Drude polarizable force field parameters for molecular ions including phosphates, sulfates, sulfamates, and oxides. Better balance was primarily achieved in the relative values of minimum interaction energies and distances of the anionic model compounds with water at the Drude and quantum mechanical (QM) model chemistries. Parametrization involved reoptimizing available parameters as well as extending the force field to new molecules with the goal of achieving self-consistency with respect to the Lennard-Jones and electrostatic parameters targeting QM and experimental hydration free energies. The resulting force field parameters achieve consistent treatment across the studied anions, facilitating more balanced simulations of biomolecules and small organic molecules in the context of the classical Drude polarizable force field. Graphical abstract.

Charge Density of Cation Determines Inner versus Outer Shell Coordination to Phosphate in RNA

Divalent cations are often required to fold RNA, which is a highly charged polyanion. Condensation of ions, such as Mg²⁺ or Ca²⁺, in the vicinity of RNA renormalizes the effective charges on the phosphate groups, thus minimizing the intra RNA electrostatic repulsion. The prevailing view is that divalent ions bind diffusively in a nonspecific manner. In sharp contrast, we arrive at the exact opposite conclusion using a theory for the interaction of ions with the phosphate groups using RISM theory in conjunction with simulations based on an accurate three-interaction-site RNA model. The divalent ions bind in a nucleotide-specific manner using either the inner (partially dehydrated) or outer (fully hydrated) shell coordination. The high charge density Mg²⁺ ion has a preference to bind to the outer shell, whereas the opposite is the case for Ca²⁺. Surprisingly, we find that bridging interactions, involving ions that are coordinated to two or more phosphate groups, play a crucial role in maintaining the integrity of the folded state. Their importance could become increasingly prominent as the size of the RNA increases. Because the modes of interaction of divalent ions with DNA are likely to be similar, we propose that specific inner and outer shell coordination could play a role in DNA condensation, and perhaps genome organization as well.

Mg2+ Impacts the Twister Ribozyme through Push-Pull Stabilization of Nonsequential Phosphate Pairs

RNA molecules perform a variety of biological functions for which the correct three-dimensional structure is essential, including as ribozymes where they catalyze chemical reactions. Metal ions, especially Mg2+, neutralize these negatively charged nucleic acids and specifically stabilize RNA tertiary structures as well as impact the folding landscape of RNAs as they assume their tertiary structures. Specific binding sites of Mg2+ in folded conformations of RNA have been studied extensively; however, the full range of interactions of the ion with compact intermediates and unfolded states of RNA is challenging to investigate, and the atomic details of the mechanism by which the ion facilitates tertiary structure formation is not fully known. Here, umbrella sampling combined with oscillating chemical potential Grand Canonical Monte Carlo/molecular dynamics simulations are used to capture the energetics and atomic-level details of Mg2+-RNA interactions that occur along an unfolding pathway of the Twister ribozyme. The free energy profiles reveal stabilization of partially unfolded states by Mg2+, as observed in unfolding experiments, with this stabilization being due to increased sampling of simultaneous interactions of Mg2+ with two or more nonsequential phosphate groups. Notably, these results indicate a push-pull mechanism in which the Mg2+-RNA interactions actually lead to destabilization of specific nonsequential phosphate-phosphate interactions (i.e., pushed apart), whereas other interactions are stabilized (i.e., pulled together), a balance that stabilizes unfolded states and facilitates the folding of Twister, including the formation of hydrogen bonds associated with the tertiary structure. This study establishes a better understanding of how Mg2+-ion interactions contribute to RNA structural properties and stability.

Ions Everywhere? Mg2+ in the μ-Opioid GPCR and Atomic Details of Their Impact on Function

Filizola and co-workers have applied a combination of long-time molecular dynamics and oscillating chemical potential grand canonical Monte Carlo/molecular dynamics to investigate the distribution of Mg²⁺ and Na⁺ in the μ-opioid receptor and their impact on its function. Results indicate atomic details of potential mechanisms by which Mg²⁺ leads to increased efficacy of opioid analgesics. The presence of information flow between the extracellular loops and the intracellular region of the G-protein-coupled receptors that interacts with G-proteins in the presence of Mg²⁺ may be a phenomenon occurring in other G-protein-coupled receptors and, therefore, potentially of broad impact.

Mechanism of μ-Opioid Receptor-Magnesium Interaction and Positive Allosteric Modulation

In the era of opioid abuse epidemics, there is an increased demand for understanding how opioid receptors can be allosterically modulated to guide the development of more effective and safer opioid therapies. Among the modulators of the μ-opioid (MOP) receptor, which is the pharmacological target for the majority of clinically used opioid drugs, are monovalent and divalent cations. Specifically, the monovalent sodium cation (Na⁺) has been known for decades to affect MOP receptor signaling by reducing agonist binding, whereas the divalent magnesium cation (Mg²⁺) has been shown to have the opposite effect, notwithstanding the presence of sodium chloride. Although ultra-high-resolution opioid receptor crystal structures have revealed a specific Na⁺ binding site and molecular dynamics (MD) simulation studies have supported the idea that this monovalent ion reduces agonist binding by stabilizing the receptor inactive state, the putative binding site of Mg²⁺ on the MOP receptor, as well as the molecular determinants responsible for its positive allosteric modulation of the receptor, are unknown. In this work, we carried out tens of microseconds of all-atom MD simulations to investigate the simultaneous binding of Mg²⁺ and Na⁺ cations to inactive and active crystal structures of the MOP receptor embedded in an explicit lipid-water environment and confirmed adequate sampling of Mg²⁺ ion binding with a grand canonical Monte Carlo MD method. Analyses of these simulations shed light on 1) the preferred binding sites of Mg²⁺ on the MOP receptor, 2) details of the competition between Mg²⁺ and Na⁺ cations for specific sites, 3) estimates of binding affinities, and 4) testable hypotheses of the molecular mechanism underlying the positive allosteric modulation of the MOP receptor by the Mg²⁺ cation.

Theory and simulations for RNA folding in mixtures of monovalent and divalent cations

RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion-phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

Quantitative Studies of an RNA Duplex Electrostatics by Ion Counting

RNAs are one of the most charged polyelectrolytes in nature, and understanding their electrostatics is fundamental to their structure and biological functions. An effective way to characterize the electrostatic field generated by nucleic acids is to quantify interactions between nucleic acids and ions that surround the molecules. These ions form a loosely associated cloud referred to as an ion atmosphere. Although theoretical and computational studies can describe the ion atmosphere around RNAs, benchmarks are needed to guide the development of these approaches, and experiments to date that read out RNA-ion interactions are limited. Here, we present ion counting studies to quantify the number of ions surrounding well-defined model systems of RNA and DNA duplexes. We observe that the RNA duplex attracts more cations and expels fewer anions compared to the DNA duplex, and the RNA duplex interacts significantly stronger with the divalent cation Mg²⁺, despite their identical total charge. These experimental results suggest that the RNA duplex generates a stronger electrostatic field than DNA, as is predicted based on the structural differences between their helices. Theoretical calculations using a nonlinear Poisson-Boltzmann equation give excellent agreement with experiments for monovalent ions but underestimate Mg²⁺-DNA and Mg²⁺-RNA interactions by 20%. These studies provide needed stringent benchmarks to use against other all-atom theoretical models of RNA-ion interactions, interactions that likely must be accurately accounted for in structural, dynamic, and energetic terms to confidently model RNA structure, interactions, and function.

Optimization and Evaluation of Site-Identification by Ligand Competitive Saturation (SILCS) as a Tool for Target-Based Ligand Optimization

Chemical fragment cosolvent sampling techniques have become a versatile tool in ligand-protein binding prediction. Site-identification by ligand competitive saturation (SILCS) is one such method that maps the distribution of chemical fragments on a protein as free energy fields called FragMaps. Ligands are then simulated via Monte Carlo techniques in the field of the FragMaps (SILCS-MC) to predict their binding conformations and relative affinities for the target protein. Application of SILCS-MC using a number of different scoring schemes and MC sampling protocols against multiple protein targets was undertaken to evaluate and optimize the predictive capability of the method. Seven protein targets and 551 ligands with broad chemical variability were used to evaluate and optimize the model to maximize Pearson's correlation coefficient, Pearlman's predictive index, correct relative binding affinity, and root-mean-square error versus the absolute experimental binding affinities. Across the protein-ligand sets, the relative affinities of the ligands were predicted correctly an average of 69% of the time for the highest overall SILCS protocol. Training the FragMap weighting factors using a Bayesian machine learning (ML) algorithm led to an increase to an average 75% relative correct affinity predictions. Furthermore, once the optimal protocol is identified for a specific protein-ligand system average predictabilities of 76% are achieved. The ML algorithm is successful with small training sets of data (30 or more compounds) due to the use of physically correct FragMap weights as priors. Notably, the 76% correct relative prediction rate is similar to or better than free energy perturbation methods that are significantly computationally more expensive than SILCS. The results further support the utility of SILCS as a powerful and computationally accessible tool to support lead optimization and development in drug discovery.

Hexahydrated Mg2+ Binding and Outer-Shell Dehydration on RNA Surface

The interaction between metal ions, especially Mg²⁺ ions, and RNA plays a critical role in RNA folding. Upon binding to RNA, a metal ion that is fully hydrated in bulk solvent can become dehydrated. Here we use molecular dynamics simulation to investigate the dehydration of bound hexahydrated Mg²⁺ ions. We find that a hydrated Mg²⁺ ion in the RNA groove region can involve significant dehydration in the outer hydration shell. The first or innermost hydration shell of the Mg²⁺ ion, however, is retained during the simulation because of the strong ion-water electrostatic attraction. As a result, water-mediated hydrogen bonding remains an important form for Mg²⁺-RNA interaction. Analysis for ions at different binding sites shows that the most pronounced water deficiency relative to the fully hydrated state occurs at a radial distance of around 11 Å from the center of the ion. Based on the independent 200 ns molecular dynamics simulations for three different RNA structures (Protein Data Bank: 1TRA, 2TPK, and 437D), we find that Mg²⁺ ions overwhelmingly dominate over monovalent ions such as Na⁺ and K⁺ in ion-RNA binding. Furthermore, application of the free energy perturbation method leads to a quantitative relationship between the Mg²⁺ dehydration free energy and the local structural environment. We find that ΔΔG_hyd, the change of the Mg²⁺ hydration free energy upon binding to RNA, varies linearly with the inverse distance between the Mg²⁺ ion and the nearby nonbridging oxygen atoms of the phosphate groups, and ΔΔG_hyd can reach -2.0 kcal/mol and -3.0 kcal/mol for an Mg²⁺ ion bound to the surface and to the groove interior, respectively. In addition, the computation results in an analytical formula for the hydration ratio as a function of the average inverse Mg²⁺-O distance. The results here might be useful for further quantitative investigations of ion-RNA interactions in RNA folding.

Nucleobase carbonyl groups are poor Mg2+ inner-sphere binders but excellent monovalent ion binders-a critical PDB survey

Precise knowledge of Mg²⁺ inner-sphere binding site properties is vital for understanding the structure and function of nucleic acid systems. Unfortunately, the PDB, which represents the main source of Mg²⁺ binding sites, contains a substantial number of assignment issues that blur our understanding of the functions of these ions. Here, following a previous study devoted to Mg²⁺ binding to nucleobase nitrogens, we surveyed nucleic acid X-ray structures from the PDB with resolutions ≤2.9 Å to classify the Mg²⁺ inner-sphere binding patterns to nucleotide carbonyl, ribose hydroxyl, cyclic ether, and phosphodiester oxygen atoms. From this classification, we derived a set of "prior-knowledge" nucleobase Mg²⁺ binding sites. We report that crystallographic examples of trustworthy nucleobase Mg²⁺ binding sites are fewer than expected since many of those are associated with misidentified Na⁺ or K⁺ We also emphasize that binding of Na⁺ and K⁺ to nucleic acids is much more frequent than anticipated. Overall, we provide evidence derived from X-ray structures that nucleobases are poor inner-sphere binders for Mg²⁺ but good binders for monovalent ions. Based on strict stereochemical criteria, we propose an extended set of guidelines designed to help in the assignment and validation of ions directly contacting nucleobase and ribose atoms. These guidelines should help in the interpretation of X-ray and cryo-EM solvent density maps. When borderline Mg²⁺ stereochemistry is observed, alternative placement of Na⁺, K⁺, or Ca²⁺ must be considered. We also critically examine the use of lanthanides (Yb³⁺, Tb³⁺) as Mg²⁺ substitutes in crystallography experiments.

Polarizable force field for RNA based on the classical drude oscillator

RNA molecules are highly dynamic and capable of adopting a wide range of complex, folded structures. The factors driving the folding and dynamics of these structures are dependent on a balance of base pairing, hydration, base stacking, ion interactions, and the conformational sampling of the 2'-hydroxyl group in the ribose sugar. The representation of these features is a challenge for empirical force fields used in molecular dynamics simulations. Toward meeting this challenge, the inclusion of explicit electronic polarization is important in accurately modeling RNA structure. In this work, we present a polarizable force field for RNA based on the classical Drude oscillator model, which represents electronic degrees of freedom via negatively charged particles attached to their parent atoms by harmonic springs. Beginning with parametrization against quantum mechanical base stacking interaction energy and conformational energy data, we have extended the Drude-2017 nucleic acid force field to include RNA. The conformational sampling of a range of RNA sequences were used to validate the force field, including canonical A-form RNA duplexes, stem-loops, and complex tertiary folds that bind multiple Mg2+ ions. Overall, the Drude-2017 RNA force field reproduces important properties of these structures, including the conformational sampling of the 2'-hydroxyl and key interactions with Mg2+ ions. © 2018 Wiley Periodicals, Inc.

Predicting RNA-Metal Ion Binding with Ion Dehydration Effects

Metal ions play essential roles in nucleic acids folding and stability. The interaction between metal ions and nucleic acids can be highly complicated because of the interplay between various effects such as ion correlation, fluctuation, and dehydration. These effects may be particularly important for multivalent ions such as Mg²⁺ ions. Previous efforts to model ion correlation and fluctuation effects led to the development of the Monte Carlo tightly bound ion model. Here, by incorporating ion hydration/dehydration effects into the Monte Carlo tightly bound ion model, we develop a, to our knowledge, new approach to predict ion binding. The new model enables predictions for not only the number of bound ions but also the three-dimensional spatial distribution of the bound ions. Furthermore, the new model reveals several intriguing features for the bound ions such as the mutual enhancement/inhibition in ion binding between the fully hydrated (diffuse) ions, the outer-shell dehydrated ions, and the inner-shell dehydrated ions and novel features for the monovalent-divalent ion interplay due to the hydration effect.

Determination of Ionic Hydration Free Energies with Grand Canonical Monte Carlo/Molecular Dynamics Simulations in Explicit Water

Grand canonical Monte Carlo (GCMC) simulations of ionic solutions with explicit solvent models are known to be challenging. One challenge arises from the treatment of long-range electrostatics and finite-box size in Monte Carlo simulations when periodic boundary condition and Ewald summation methods are used. Another challenge is that constant excess chemical potential GCMC simulations for charged solutes suffer from inadequate insertion and deletion acceptance ratios. In this work, we address those problems by implementing an oscillating excess chemical potential GCMC algorithm with smooth particle mesh Ewald and finite-box-size corrections to treat the long-range electrostatics. The developed GCMC simulation program was combined with GROMACS to perform GCMC/MD simulations of ionic solutions individually containing Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, F^-, Cl^-, Br^-, I^-, Ca²⁺, and Mg²⁺, respectively. Our simulation results show that the combined GCMC/MD approach can approximate the ionic hydration free energies with proper treatment of long-range electrostatics. Our developed simulation approach can open up new avenues for simulating complex chemical and biomolecular systems and for drug discovery.

RNA as a Complex Polymer with Coupled Dynamics of Ions and Water in the Outer Solvation Sphere

We unravel the internal and collective modes of a widely studied 58-nucleotide rRNA fragment in solvent using atomically detailed molecular dynamics simulations. The variation of lifetimes for water hydrogen bonds with nucleotide groups indicates heterogeneity of water dynamics on the RNA surface. The time scales of interactions of the discrete water molecules with RNA nucleotides extend from several hundred picoseconds to a few nanoseconds. We determine all of the association sites and the spatial distribution of residence times for Mg²⁺, K⁺, and water molecules in those sites. We provide insights into the population of Mg²⁺ and K⁺ ions and water molecules in the outer sphere and how their fluctuations are intricately linked with the kinetics of the 58-mer. We find that many of the long-lived Mg²⁺ sites identified from the simulations agree with the locations of ions in the X-ray structure. We determine the excess ion atmosphere around the rRNA and compare it with experimental data. We investigate the collective behavior of RNA, ions, and water, by performing a joint principle component analysis for the Cartesian coordinates of the RNA phosphorus atoms and for the occupation counts of the association sites. Our results indicate that the 58-mer system is a complex polymer, composed of RNA that is encased by a fluctuating network of associated counterions, co-ions, and water.

Influence of Na+ and Mg2+ ions on RNA structures studied with molecular dynamics simulations

The structure of ribonucleic acid (RNA) polymers is strongly dependent on the presence of, in particular Mg2+ cations to stabilize structural features. Only in high-resolution X-ray crystallography structures can ions be identified reliably. Here, we perform molecular dynamics simulations of 24 RNA structures with varying ion concentrations. Twelve of the structures were helical and the others complex folded. The aim of the study is to predict ion positions but also to evaluate the impact of different types of ions (Na+ or Mg2+) and the ionic strength on structural stability and variations of RNA. As a general conclusion Mg2+ is found to conserve the experimental structure better than Na+ and, where experimental ion positions are available, they can be reproduced with reasonable accuracy. If a large surplus of ions is present the added electrostatic screening makes prediction of binding-sites less reproducible. Distinct differences in ion-binding between helical and complex folded structures are found. The strength of binding (ΔG‡ for breaking RNA atom-ion interactions) is found to differ between roughly 10 and 26 kJ/mol for the different RNA atoms. Differences in stability between helical and complex folded structures and of the influence of metal ions on either are discussed.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Exploring RNA structure and dynamics through enhanced sampling simulations

RNA function is intimately related to its structural dynamics. Molecular dynamics simulations are useful for exploring biomolecular flexibility but are severely limited by the accessible timescale. Enhanced sampling methods allow this timescale to be effectively extended in order to probe biologically relevant conformational changes and chemical reactions. Here, we review the role of enhanced sampling techniques in the study of RNA systems. We discuss the challenges and promises associated with the application of these methods to force-field validation, exploration of conformational landscapes and ion/ligand-RNA interactions, as well as catalytic pathways. Important technical aspects of these methods, such as the choice of the biased collective variables and the analysis of multi-replica simulations, are examined in detail. Finally, a perspective on the role of these methods in the characterization of RNA dynamics is provided.

Consequences of Mg2+ binding on the geometry and stability of RNA base pairs

Quantum chemical calculations reveal the role of magnesium in stabilizing the geometries of intrinsically unstable RNA base pairs.

How Does Mg2+ Modulate the RNA Folding Mechanism: A Case Study of the G:C W:W Trans Basepair

Reverse Watson-Crick G:C basepairs (G:C W:W Trans) occur frequently in different functional RNAs. This is one of the few basepairs whose gas-phase-optimized isolated geometry is inconsistent with the corresponding experimental geometry. Several earlier studies indicate that through post-transcriptional modification, direct protonation, or coordination with Mg²⁺, accumulation of positive charge near N7 of guanine can stabilize the experimental geometry. Interestingly, recent studies reveal significant variation in the position of putatively bound Mg²⁺. This, in conjunction with recently raised doubts regarding some of the Mg²⁺ assignments near the imino nitrogen of guanine, is suggestive of the existence of multiple Mg²⁺ binding modes for this basepair. Our detailed investigation of Mg²⁺-bound G:C W:W Trans pairs occurring in high-resolution RNA crystal structures shows that they are found in 14 different contexts, eight of which display Mg²⁺ binding at the Hoogsteen edge of guanine. Further examination of occurrences in these eight contexts led to the characterization of three different Mg²⁺ binding modes: 1) direct binding via N7 coordination, 2) direct binding via O6 coordination, and 3) binding via hydrogen-bonding interaction with the first-shell water molecules. In the crystal structures, the latter two modes are associated with a buckled and propeller-twisted geometry of the basepair. Interestingly, respective optimized geometries of these different Mg²⁺ binding modes (optimized using six different DFT functionals) are consistent with their corresponding experimental geometries. Subsequent interaction energy calculations at the MP2 level, and decomposition of its components, suggest that for G:C W:W Trans , Mg²⁺ binding can fine tune the basepair geometries without compromising with their stability. Our results, therefore, underline the importance of the mode of binding of Mg²⁺ ions in shaping RNA structure, folding and function.

Unraveling Mg2+-RNA binding with atomistic molecular dynamics

Interaction with divalent cations is of paramount importance for RNA structural stability and function. We report here a detailed molecular dynamics study of all the possible binding sites for Mg2+ on an RNA duplex, including both direct (inner sphere) and indirect (outer sphere) binding. In order to tackle sampling issues, we develop a modified version of bias-exchange metadynamics, which allows us to simultaneously compute affinities with previously unreported statistical accuracy. Results correctly reproduce trends observed in crystallographic databases. Based on this, we simulate a carefully chosen set of models that allows us to quantify the effects of competition with monovalent cations, RNA flexibility, and RNA hybridization. Our simulations reproduce the decrease and increase of Mg2+ affinity due to ion competition and hybridization, respectively, and predict that RNA flexibility has a site-dependent effect. This suggests a nontrivial interplay between RNA conformational entropy and divalent cation binding.