Fitting Corrections to an RNA Force Field Using Experimental Data

Empirical force fields for biomolecular systems are usually derived from quantum chemistry calculations and validated against experimental data. We here show how it is possible to refine the full dihedral-angle potential of the Amber RNA force field by using solution NMR data as well as stability of known structural motifs. The procedure can be used to mix multiple systems and heterogeneous experimental information and crucially depends on a regularization term chosen with a cross-validation procedure. By fitting corrections to the dihedral angles on the order of less than 1 kJ/mol per angle, it is possible to increase the stability of difficult-to-fold RNA tetraloops by more than 1 order of magnitude

Molecular Dynamics and Quantum Mechanics of RNA: Conformational and Chemical Change We Can Believe In

Structure and dynamics are both critical to RNA’s vital functions in biology. Numerous techniques can elucidate the structural dynamics of RNA, but computational approaches based on experimental data arguably hold the promise of providing the most detail. In this Account, we highlight areas wherein molecular dynamics (MD) and quantum mechanical (QM) techniques are applied to RNA, particularly in relation to complementary experimental studies

Symmetries of Electrostatic Interaction between DNA Molecules

We study a model for pair interaction $U$ of DNA molecules generated by the discrete dipole moments of base-pairs and the charges of phosphate groups, and find noncommutative group of eighth order ${\cal S}$ of symmetries that leave $U$ invariant. We classify the minima using group ${\cal S}$ and employ numerical methods for finding them. The minima may correspond to several cholesteric phases, as well as phases formed by cross-like conformations of molecules at an angle close to $\rm{90}^{o}$, "snowflake phase". The results depend on the effective charge $Q$ of the phosphate group which can be modified by the polycations or the ions of metals. The snowflake phase could exist for $Q$ above the threshold $Q_C$. Below $Q_C$ there could be several cholesteric phases. Close to $Q_C$ the snowflake phase could change into the cholesteric one at constant distance between adjacent molecules.Comment: 13 pages, 4 figure

Extended molecular dynamics of a c-kit promoter quadruplex.

The 22-mer c-kit promoter sequence folds into a parallel-stranded quadruplex with a unique structure, which has been elucidated by crystallographic and NMR methods and shows a high degree of structural conservation. We have carried out a series of extended (up to 10 μs long, ∼50 μs in total) molecular dynamics simulations to explore conformational stability and loop dynamics of this quadruplex. Unfolding no-salt simulations are consistent with a multi-pathway model of quadruplex folding and identify the single-nucleotide propeller loops as the most fragile part of the quadruplex. Thus, formation of propeller loops represents a peculiar atomistic aspect of quadruplex folding. Unbiased simulations reveal μs-scale transitions in the loops, which emphasizes the need for extended simulations in studies of quadruplex loops. We identify ion binding in the loops which may contribute to quadruplex stability. The long lateral-propeller loop is internally very stable but extensively fluctuates as a rigid entity. It creates a size-adaptable cleft between the loop and the stem, which can facilitate ligand binding. The stability gain by forming the internal network of GA base pairs and stacks of this loop may be dictating which of the many possible quadruplex topologies is observed in the ground state by this promoter quadruplex

A multinuclear solid state NMR, density functional theory and X-Ray diffraction study of hydrogen bonding in Group I hydrogen dibenzoates

An NMR crystallographic approach incorporating multinuclear solid state NMR (SSNMR), X-ray structure determinations and density functional theory (DFT) are used to characterise the H bonding arrangements in benzoic acid (BZA) and the corresponding Group I alkali metal hydrogen dibenzoates (HD) systems. Since the XRD data often cannot precisely confirm the proton position within the hydrogen bond, the relationship between the experimental SSNMR parameters and the ability of gauge included plane augmented wave (GIPAW) DFT to predict them becomes a powerful constraint that can assist with further structure refinement. Both the 1H and 13C MAS NMR methods provide primary descriptions of the H bonding via accurate measurements of the 1H and 13C isotropic chemical shifts, and the individual 13C chemical shift tensor elements; these are unequivocally corroborated by DFT calculations, which together accurately describe the trend of the H bonding strength as the size of the monovalent cation changes. In addition, 17O MAS and DOR NMR form a powerful combination to characterise the O environments, with the DOR technique providing highly resolved 17O NMR data which helps verify unequivocally the number of inequivalent O positions for the conventional 17O MAS NMR to process. Further multinuclear MAS and static NMR studies involving the quadrupolar 7Li, 39K, 87Rb and 133Cs nuclei, and the associated DFT calculations, provide trends and a corroboration of the H bond geometry which assist in the understanding of these arrangements. Even though the crystallographic H positions in each H bonding arrangement reported from the single crystal X-ray studies are prone to uncertainty, the good corroboration between the measured and DFT calculated chemical shift and quadrupole tensor parameters for the Group I alkali species suggest that these reported H positions are reliable

π-π stacking tackled with density functional theory

Through comparison with ab initio reference data, we have evaluated the performance of various density functionals for describing π-π interactions as a function of the geometry between two stacked benzenes or benzene analogs, between two stacked DNA bases, and between two stacked Watson–Crick pairs. Our main purpose is to find a robust and computationally efficient density functional to be used specifically and only for describing π-π stacking interactions in DNA and other biological molecules in the framework of our recently developed QM/QM approach "QUILD". In line with previous studies, most standard density functionals recover, at best, only part of the favorable stacking interactions. An exception is the new KT1 functional, which correctly yields bound π-stacked structures. Surprisingly, a similarly good performance is achieved with the computationally very robust and efficient local density approximation (LDA). Furthermore, we show that classical electrostatic interactions determine the shape and depth of the π-π stacking potential energy surface

Effects of Restrained Sampling Space and Nonplanar Amino Groups on Free-Energy Predictions for RNA with Imino and Sheared Tandem GA Base Pairs Flanked by GC, CG, iGiC or iCiG Base Pairs

Guanine-adenine (GA) base pairs play important roles in determining the structure, dynamics, and stability of RNA. In RNA internal loops, GA base pairs often occur in tandem arrangements and their structure is context and sequence dependent. Calculations reported here test the thermodynamic integration (TI) approach with the amber99 force field by comparing computational predictions of free energy differences with the free energy differences expected on the basis of NMR determined structures of the RNA motifs (5′-GCGGACGC-3′)2, (5′-GCiGGAiCGC-3′)2, (5′-GGCGAGCC-3′)2, and (5′-GGiCGAiGCC-3′)2. Here, iG and iC denote isoguanosine and isocytidine, which have amino and carbonyl groups transposed relative to guanosine and cytidine. The NMR structures show that the GA base pairs adopt either imino (cis Watson−Crick/Watson−Crick A-G) or sheared (trans Hoogsteen/Sugar edge A-G) conformations depending on the identity and orientation of the adjacent base pair. A new mixing function for the TI method is developed that allows alchemical transitions in which atoms can disappear in both the initial and final states. Unrestrained calculations gave ΔG° values 2−4 kcal/mol different from expectations based on NMR data. Restraining the structures with hydrogen bond restraints did not improve the predictions. Agreement with NMR data was improved by 0.7 to 1.5 kcal/mol, however, when structures were restrained with weak positional restraints to sample around the experimentally determined NMR structures. The amber99 force field was modified to partially include pyramidalization effects of the unpaired amino group of guanosine in imino GA base pairs. This provided little or no improvement in comparisons with experiment. The marginal improvement is observed when the structure has potential cross-strand out-of-plane hydrogen bonding with the G amino group. The calculations using positional restraints and a nonplanar amino group reproduce the signs of ΔG° from the experimental results and are, thus, capable of providing useful qualitative insights complementing the NMR experiments. Decomposition of the terms in the calculations reveals that the dominant terms are from electrostatic and interstrand interactions other than hydrogen bonds in the base pairs. The results suggest that a better description of the backbone is key to reproducing the experimental free energy results with computational free energy predictions

Quantitative principles of cis-translational control by general mRNA sequence features in eukaryotes.

BackgroundGeneral translational cis-elements are present in the mRNAs of all genes and affect the recruitment, assembly, and progress of preinitiation complexes and the ribosome under many physiological states. These elements include mRNA folding, upstream open reading frames, specific nucleotides flanking the initiating AUG codon, protein coding sequence length, and codon usage. The quantitative contributions of these sequence features and how and why they coordinate to control translation rates are not well understood.ResultsHere, we show that these sequence features specify 42-81% of the variance in translation rates in Saccharomyces cerevisiae, Schizosaccharomyces pombe, Arabidopsis thaliana, Mus musculus, and Homo sapiens. We establish that control by RNA secondary structure is chiefly mediated by highly folded 25-60 nucleotide segments within mRNA 5' regions, that changes in tri-nucleotide frequencies between highly and poorly translated 5' regions are correlated between all species, and that control by distinct biochemical processes is extensively correlated as is regulation by a single process acting in different parts of the same mRNA.ConclusionsOur work shows that general features control a much larger fraction of the variance in translation rates than previously realized. We provide a more detailed and accurate understanding of the aspects of RNA structure that directs translation in diverse eukaryotes. In addition, we note that the strongly correlated regulation between and within cis-control features will cause more even densities of translational complexes along each mRNA and therefore more efficient use of the translation machinery by the cell

Adsorption of mono- and multivalent cat- and anions on DNA molecules

Adsorption of monovalent and multivalent cat- and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modelled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modelled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands, in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major groove cationic charge is independent on the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salt. Simulations for a larger ion radii, which mimic the effect of the ion hydration, indicate an increased adsorbtion of cations in the major groove.Comment: 34 pages with 14 figure