Holger Kruse

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.

Ion Binding to Quadruplex DNA Stems. Comparison of MM and QM Descriptions Reveals Sizable Polarization Effects Not Included in Contemporary Simulations

Molecular mechanical (MM) force fields are commonly employed for biomolecular simulations. Despite their success, the nonpolarizable nature of contemporary additive force fields limits their performance, especially in long simulations and when strong polarization effects are present. Guanine quadruplex D(R)NA molecules have been successfully studied by MM simulations in the past. However, the G-stems are stabilized by a chain of monovalent cations that create sizable polarization effects. Indeed, simulation studies revealed several problems that have been tentatively attributed to the lack of polarization. Here, we provide a detailed comparison between quantum chemical (QM) DFT-D3 and MM potential energy surfaces of ion binding to G-stems and assess differences that may affect MM simulations. We suggest that MM describes binding of a single ion to the G-stem rather well. However, polarization effects become very significant when a second ion is present. We suggest that the MM approximation substantially limits accuracy of description of energy and dynamics of multiple ions inside the G-stems and binding of ions at the stem-loop junctions. The difference between QM and MM descriptions is also explored using symmetry-adapted perturbation theory and quantum theory of atoms in molecules analyses, which reveal a delicate balance of electrostatic and induction effects.

QM Computations on Complete Nucleic Acids Building Blocks: Analysis of the Sarcin–Ricin RNA Motif Using DFT-D3, HF-3c, PM6-D3H, and MM Approaches

A set of conformations obtained from explicit solvent molecular dynamics (MD) simulations of the Sarcin-Ricin internal loop (SRL) RNA motif is investigated using quantum mechanical (QM, TPSS-D3/def2-TZVP DFT-D3) and molecular mechanics (MM, AMBER parm99bsc0+χol3 force field) methods. Solvent effects are approximated using implicit solvent methods (COSMO for DFT-D3; GB and PB for MM). Large-scale DFT-D3 optimizations of the full 11-nucleotide motif are compared to MM results and reveal a higher flexibility of DFT-D3 over the MM in the optimization procedure. Conformational energies of the SRL motif expose significant differences in the DFT-D3 and MM energy descriptions that explain difficulties in MD simulations of the SRL motif. The TPSS-D3 data are in excellent agreement with results obtained by the hybrid functionals PW6B95-D3 and M06-2X. Computationally more efficient methods such as PM6-D3H and HF-3c show promising but partly inconsistent results. It is demonstrated that large-scale DFT-D3 computations on complete nucleic acids building blocks are a viable tool to complement the picture obtained from MD simulations and can be used as benchmarks for faster computational methods. Methodological challenges of large-scale QM computations on nucleic acids such as missing solvent-solute interactions and the truncation of the studied systems are discussed.

Derivation of Reliable Geometries in QM Calculations of DNA Structures: Explicit Solvent QM/MM and Restrained Implicit Solvent QM Optimizations of G-Quadruplexes

Modern dispersion-corrected DFT methods have made it possible to perform reliable QM studies on complete nucleic acid (NA) building blocks having hundreds of atoms. Such calculations, although still limited to investigations of potential energy surfaces, enhance the portfolio of computational methods applicable to NAs and offer considerably more accurate intrinsic descriptions of NAs than standard MM. However, in practice such calculations are hampered by the use of implicit solvent environments and truncation of the systems. Conventional QM optimizations are spoiled by spurious intramolecular interactions and severe structural deformations. Here we compare two approaches designed to suppress such artifacts: partially restrained continuum solvent QM and explicit solvent QM/MM optimizations. We report geometry relaxations of a set of diverse double-quartet guanine quadruplex (GQ) DNA stems. Both methods provide neat structures without major artifacts. However, each one also has distinct weaknesses. In restrained optimizations, all errors in the target geometries (i.e., low-resolution X-ray and NMR structures) are transferred to the optimized geometries. In QM/MM, the initial solvent configuration causes some heterogeneity in the geometries. Nevertheless, both approaches represent a decisive step forward compared to conventional optimizations. We refine earlier computations that revealed sizable differences in the relative energies of GQ stems computed with AMBER MM and QM. We also explore the dependence of the QM/MM results on the applied computational protocol.

Comparative Assessment of Different RNA Tetranucleotides from the DFT-D3 and Force Field Perspective

Classical force field (FF) molecular dynamics (MD) simulations of RNA tetranucleotides have substantial problems in reproducing conformer populations indicated by NMR experiments. To provide more information about the possible sources of errors, we performed quantum mechanical (QM, TPSS-D3/def2-TZVP) and molecular mechanics (MM, AMBER parm99bsc0+χOL3) calculations of different r(CCCC), r(GACC), and r(UUUU) conformers obtained from explicit solvent MD simulations. Solvent effects in the static QM and MM calculations were mimicked using implicit solvent models (COSMO and Poisson-Boltzmann, respectively). The comparison of QM and MM geometries and energies revealed that the two methodologies provide qualitatively consistent results in most of the cases. Even though we found some differences, these were insufficient to indicate any systematic corrections of the RNA FF terms that could improve the performance of classical MD in simulating tetranucleotides. On the basis of these findings, we inferred that the overpopulation of intercalated conformers in the MD simulations of RNA tetramers, which were not observed experimentally, might be predominantly caused by imbalanced water-solvent and water-water interactions. Apart from the large-scale QM calculations performed to assess the performance of the AMBER FF, a representative spectrum of faster QM methods was tested.

An intricate balance of hydrogen bonding, ion atmosphere and dynamics facilitates a seamless uracil to cytosine substitution in the U-turn of the neomycin-sensing riboswitch

Abstract The neomycin sensing riboswitch is the smallest biologically functional RNA riboswitch, forming a hairpin capped with a U-turn loop—a well-known RNA motif containing a conserved uracil. It was shown previously that a U→C substitution of the eponymous conserved uracil does not alter the riboswitch structure due to C protonation at N3. Furthermore, cytosine is evolutionary permitted to replace uracil in other U-turns. Here, we use molecular dynamics simulations to study the molecular basis of this substitution in the neomycin sensing riboswitch and show that a structure-stabilizing monovalent cation-binding site in the wild-type RNA is the main reason for its negligible structural effect. We then use NMR spectroscopy to confirm the existence of this cation-binding site and to demonstrate its effects on RNA stability. Lastly, using quantum chemical calculations, we show that the cation-binding site is altering the electronic environment of the wild-type U-turn so that it is more similar to the cytosine mutant. The study reveals an amazingly complex and delicate interplay between various energy contributions shaping up the 3D structure and evolution of nucleic acids.

MD and QM/MM Study of the Quaternary HutP Homohexamer Complex with mRNA, l-Histidine Ligand, and Mg2+

The HutP protein from B. subtilis regulates histidine metabolism by interacting with an antiterminator mRNA hairpin in response to the binding of l-histidine and Mg2+. We studied the functional ligand-bound HutP hexamer complexed with two mRNAs using all-atom microsecond-scale explicit-solvent MD simulations performed with the Amber force fields. The experimentally observed protein-RNA interface exhibited good structural stability in the simulations with the exception of some fluctuations in an unusual adenine-threonine interaction involving two closely spaced H-bonds. We further investigated this interaction by comparing QM/MM and MM optimizations, using the QM region comprising almost 350 atoms described at the DFT-D3 level. The QM/MM method clearly improved the adenine-threonine interaction compared to MM, especially when the X-H bond lengths were frozen during the MM optimization to mimic the use of SHAKE in the MD simulations. Thus, both the MM approximation and the use of SHAKE can compromise the description of H-bonds at protein-RNA interfaces. The simulations also revealed a notable Mg2+-parameter dependence in the behavior of the ligand-binding pocket (LBP). With the SPC/E water model, the 12-6 Åqvist and Li&Merz parameters provided an entirely stable LBP structure, but the 12-6 Allnér and 12-6-4 Li&Merz parametrizations resulted in a progressive loss of direct nitrogen-Mg2+ LBP coordination. The Allnér and Li&Merz 12-6 parametrizations were also tested with the TIP3P water model; the LBP was destabilized in both cases. This illustrates the difficulty of consistently describing different Mg2+ interactions using nonpolarizable force fields. Overall, the simulations support the hypothesis that HutP protein becomes fully structured upon ligand binding. Subsequent RNA binding does not affect the protein structure, in keeping with the mechanism inferred from experimental structures.

Nonenzymatic Oligomerization of 3′,5′‐Cyclic CMP Induced by Proton and UV Irradiation Hints at a Nonfastidious Origin of RNA

We report that 3′,5′‐cyclic CMP undergoes nonenzymatic di‐ and trimerization at 20 °C under dry conditions upon proton or UV irradiation. The reaction involves stacking of the cyclic monomers and subsequent polymerization through serial transphosphorylations between the stacked monomers. Proton‐ and UV‐induced oligomerization of 3′,5′‐cyclic CMP demonstrates that pyrimidines—similar to purines—might also have taken part in the spontaneous generation of RNA under plausible prebiotic conditions as well as in an extraterrestrial context. The observed polymerization of naturally occurring 3′,5′‐cyclic nucleotides supports the possibility that the extant genetic nucleic acids might have originated by way of a straight Occamian path, starting from simple reactions between plausibly preactivated monomers.

QM/MM Calculations on Protein–RNA Complexes: Understanding Limitations of Classical MD Simulations and Search for Reliable Cost-Effective QM Methods

Although atomistic explicit-solvent Molecular Dynamics (MD) is a popular tool to study protein-RNA recognition, satisfactory MD description of protein-RNA complexes is not always achieved. Unfortunately, it is often difficult to separate MD simulation instabilities primarily caused by the simple point-charge molecular mechanics (MM) force fields from problems related to the notorious uncertainties in the starting structures. Herein, we report a series of large-scale QM/MM calculations on the U1A protein-RNA complex. This experimentally well-characterized system has an intricate protein-RNA interface, which is very unstable in MD simulations. The QM/MM calculations identify several H-bonds poorly described by the MM method and thus indicate the sources of instabilities of the U1A interface in MD simulations. The results suggest that advanced QM/MM computations could be used to indirectly rationalize problems seen in MM-based MD simulations of protein-RNA complexes. As the most accurate QM method, we employ the computationally demanding meta-GGA density functional TPSS-D3(BJ)/def2-TZVP level of theory. Because considerably faster methods would be needed to extend sampling and to study even larger protein-RNA interfaces, a set of low-cost QM/MM methods is compared to the TPSS-D3(BJ)/def2-TZVP data. The PBEh-3c and B97-3c density functional composite methods appear to be suitable for protein-RNA interfaces. In contrast, HF-3c and the tight-binding Hamiltonians DFTB3-D3 and GFN-xTB perform unsatisfactorily and do not provide any advantage over the MM description. These conclusions are supported also by similar analysis of a simple HutP protein-RNA interface, which is well-described by MD with the exception of just one H-bond. Some other methodological aspects of QM/MM calculations on protein-RNA interfaces are discussed.