Energies and 2'-Hydroxyl Group Orientations of RNA Backbone Conformations. Benchmark CCSD(T)/CBS Database, Electronic Analysis, and Assessment of DFT Methods and MD Simulations

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

A general RNA force field: comprehensive analysis of energy minima of molecular fragments of RNA

Force fields are actively used to study RNA. Development of accurate force fields relies on a knowledge of how the variation of properties of molecules depends on their structure. Detailed scrutiny of RNA's conformational preferences is needed to guide such development. Towards this end, minimum energy structures for each of a set of 16 small RNA-derived molecules were obtained by geometry optimization at the HF/6-31G(d,p), B3LYP/apc-1, and MP2/cc-pVDZ levels of theory. The number of minima computed for a given fragment was found to be related to both its size and flexibility. Atomic electrostatic multipole moments of atoms occurring in the [HO-P(O₃)-CH₂-] fragment of 30 sugar-phosphate-sugar geometries were calculated at the HF/6-31G(d,p) and B3LYP/apc-1 levels of theory, and the transferability of these properties between different conformations was investigated. The atomic multipole moments were found to be highly transferable between different conformations with small standard deviations. These results indicate necessary elements of the development of accurate RNA force fields.

Conformational energies and equilibria of cyclic dinucleotides in vacuo and in solution: computational chemistry vs. NMR experiments

Performance of computational methods in modelling cyclic dinucleotides - an important and challenging class of compounds - has been evaluated by two different benchmarks: (1) gas-phase conformational energies and (2) qualitative agreement with NMR observations of the orientation of the χ-dihedral angle in solvent. In gas-phase benchmarks, where CCSD(T) and DLPNO-CCSD(T) methods have been used as the reference, most of the (dispersion corrected) density functional approximations are accurate enough to justify prioritizing computational cost and compatibility with other modelling options as the criterion of choice. NMR experiments of 3'3'-c-di-AMP, 3'3'-c-GAMP, and 3'3'-c-di-GMP show the overall prevalence of the anti-conformation of purine bases, but some population of syn-conformations is observed for guanines. Implicit solvation models combined with quantum-chemical methods struggle to reproduce this behaviour, probably due to a lack of dynamics and explicitly modelled solvent, leading to structures that are too compact. Molecular dynamics simulations overrepresent the syn-conformation of guanine due to the overestimation of an intramolecular hydrogen bond. Our combination of experimental and computational benchmarks provides "error bars" for modelling cyclic dinucleotides in solvent, where such information is generally difficult to obtain, and should help gauge the interpretability of studies dealing with binding of cyclic dinucleotides to important pharmaceutical targets. At the same time, the presented analysis calls for improvement in both implicit solvation models and force-field parameters.

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.

Deciphering the Self-Cleavage Reaction Mechanism of Hairpin Ribozyme

Hairpin ribozyme catalyzes the reversible self-cleavage of phosphodiester bonds which plays prominent roles in key biological processes involving RNAs. Despite impressive advances on ribozymatic self-cleavage, critical aspects of its molecular reaction mechanism remain controversially debated. Here, we generate and analyze the multidimensional free energy landscape that underlies the reaction using extensive QM/MM metadynamics simulations to investigate in detail the full self-cleavage mechanism. This allows us to answer several pertinent yet controversial questions concerning activation of the 2'-OH group, the mechanistic role of water molecules present in the active site, and the full reaction pathway including the structures of transition states and intermediates. Importantly, we find that a sufficiently unrestricted reaction subspace must be mapped using accelerated sampling methods in order to compute the underlying free energy landscape. It is shown that lower-dimensional sampling where the bond formation and cleavage steps are coupled does not allow the system to sufficiently explore the landscape. On the basis of a three-dimensional free energy surface spanned by flexible generalized coordinates, we find that 2'-OH is indirectly activated by adjacent G8 nucleobase in conjunction with stabilizing H-bonding involving water. This allows the proton of the 2'-OH group to directly migrate toward the 5'-leaving group via a nonbridging oxygen of the phosphodiester link. At variance with similar enzymatic processes where water wires connected to protonable side chains of the protein matrix act as transient proton shuttles, no such de/reprotonation events of water molecules are found to be involved in this ribozymatic transesterification. Overall, our results support an acid-catalyzed reaction mechanism where A38 nucleobase directly acts as an acid whereas G8, in stark contrast, participates only indirectly via stabilizing the nascent nucleophile for subsequent attack. Moreover, we conclude that self-cleavage of hairpin ribozyme follows an A_N + D_N two-step associative pathway where the rate-determining step is the cleavage of the phosphodiester bond. These results provide a major advancement in our understanding of the unique catalytic mechanism of hairpin ribozyme which will fruitfully impact on the design of synthetic ribozymes.

Modeling of canonical and C2′-O-thiophenylmethyl modified hexamers of RNA. Insights into the nature of structural changes and thermal stability

Modification of the C2′-O-position with thiophenylmethyl groups on both strands leads to thermal stabilization of the duplex. Predicting the effects that modifications will have on structure of RNA is of importance in the development of new RNA technologies.

Quantum chemical benchmark study on 46 RNA backbone families using a dinucleotide unit

We have created a benchmark set of quantum chemical structure-energy data denoted as UpU46, which consists of 46 uracil dinucleotides (UpU), representing all known 46 RNA backbone conformational families. Penalty-function-based restrained optimizations with COSMO TPSS-D3/def2-TZVP ensure a balance between keeping the target conformation and geometry relaxation. The backbone geometries are close to the clustering-means of their respective RNA bioinformatics family classification. High-level wave function methods (DLPNO-CCSD(T) as reference) and a wide-range of dispersion-corrected or inclusive DFT methods (DFT-D3, VV10, LC-BOP-LRD, M06-2X, M11, and more) are used to evaluate the conformational energies. The results are compared to the Amber RNA bsc0χOL3 force field. Most dispersion-corrected DFT methods surpass the Amber force field significantly in accuracy and yield mean absolute deviations (MADs) for relative conformational energies of ∼0.4-0.6 kcal/mol. Double-hybrid density functionals represent the most accurate class of density functionals. Low-cost quantum chemical methods such as PM6-D3H+, HF-3c, DFTB3-D3, as well as small basis set calculations corrected for basis set superposition errors (BSSEs) by the gCP procedure are also tested. Unfortunately, the presently available low-cost methods are struggling to describe the UpU conformational energies with satisfactory accuracy. The UpU46 benchmark is an ideal test for benchmarking and development of fast methods to describe nucleic acids, including force fields.

Untemplated nonenzymatic polymerization of 3',5'cGMP: a plausible route to 3',5'-linked oligonucleotides in primordia

The high-energy 3',5' phosphodiester linkages conserved in 3',5' cyclic GMPs offer a genuine solution for monomer activation required by the transphosphorylation reactions that could lead to the emergence of the first simple oligonucleotide sequences on the early Earth. In this work we provide an in-depth characterization of the effect of the reaction conditions on the yield of the polymerization reaction of 3',5' cyclic GMPs both in aqueous environment as well as under dehydrating conditions. We show that the threshold temperature of the polymerization is about 30 °C lower under dehydrating conditions than in solution. In addition, we present a plausible exergonic reaction pathway for the polymerization reaction, which involves transient formation of anionic centers at the O3' positions of the participating riboses. We suggest that excess Na(+) cations inhibit the polymerization reaction because they block the anionic mechanism via neutralizing the negatively charged O3'. Our experimental findings are compatible with a prebiotic scenario, where gradual desiccation of the environment could induce polymerization of 3',5' cyclic GMPs synthesized in liquid.

DNA-protein π-interactions in nature: abundance, structure, composition and strength of contacts between aromatic amino acids and DNA nucleobases or deoxyribose sugar

Four hundred twenty-eight high-resolution DNA-protein complexes were chosen for a bioinformatics study. Although 164 crystal structures (38% of those searched) contained no interactions, 574 discrete π-contacts between the aromatic amino acids and the DNA nucleobases or deoxyribose were identified using strict criteria, including visual inspection. The abundance and structure of the interactions were determined by unequivocally classifying the contacts as either π-π stacking, π-π T-shaped or sugar-π contacts. Three hundred forty-four nucleobase-amino acid π-π contacts (60% of all interactions identified) were identified in 175 of the crystal structures searched. Unprecedented in the literature, 230 DNA-protein sugar-π contacts (40% of all interactions identified) were identified in 137 crystal structures, which involve C-H···π and/or lone-pair···π interactions, contain any amino acid and can be classified according to sugar atoms involved. Both π-π and sugar-π interactions display a range of relative monomer orientations and therefore interaction energies (up to -50 (-70) kJ mol(-1) for neutral (charged) interactions as determined using quantum chemical calculations). In general, DNA-protein π-interactions are more prevalent than perhaps currently accepted and the role of such interactions in many biological processes may yet to be uncovered.

Molecular Dynamics Simulations of Nucleic Acids. From Tetranucleotides to the Ribosome

We present a brief overview of explicit solvent molecular dynamics (MD) simulations of nucleic acids. We explain physical chemistry limitations of the simulations, namely, the molecular mechanics (MM) force field (FF) approximation and limited time scale. Further, we discuss relations and differences between simulations and experiments, compare standard and enhanced sampling simulations, discuss the role of starting structures, comment on different versions of nucleic acid FFs, and relate MM computations with contemporary quantum chemistry. Despite its limitations, we show that MD is a powerful technique for studying the structural dynamics of nucleic acids with a fast growing potential that substantially complements experimental results and aids their interpretation.