Vfold: A Web Server for RNA Structure and Folding Thermodynamics Prediction

Background

The ever increasing discovery of non-coding RNAs leads to unprecedented demand for the accurate modeling of RNA folding, including the predictions of two-dimensional (base pair) and three-dimensional all-atom structures and folding stabilities. Accurate modeling of RNA structure and stability has far-reaching impact on our understanding of RNA functions in human health and our ability to design RNA-based therapeutic strategies.

Results

The Vfold server offers a web interface to predict (a) RNA two-dimensional structure from the nucleotide sequence, (b) three-dimensional structure from the two-dimensional structure and the sequence, and (c) folding thermodynamics (heat capacity melting curve) from the sequence. To predict the two-dimensional structure (base pairs), the server generates an ensemble of structures, including loop structures with the different intra-loop mismatches, and evaluates the free energies using the experimental parameters for the base stacks and the loop entropy parameters given by a coarse-grained RNA folding model (the Vfold model) for the loops. To predict the three-dimensional structure, the server assembles the motif scaffolds using structure templates extracted from the known PDB structures and refines the structure using all-atom energy minimization.

Conclusions

The Vfold-based web server provides a user friendly tool for the prediction of RNA structure and stability. The web server and the source codes are freely accessible for public use at “http://rna.physics.missouri.edu”.     

Conformational Entropy of the RNA Phosphate Backbone and Its Contribution to the Folding Free Energy

While major contributors to the free energy of RNA tertiary structures such as basepairing, base-stacking, and charge and counterion interactions have been studied extensively, little is known about the intrinsic free energy of the backbone. To assess the magnitude of the entropic strains along the phosphate backbone and their impact on the folding free energy, we have formulated a mathematical treatment for computing the volume of the main-chain torsion-angle conformation space between every pair of nucleobases along any sequence to compute the corresponding backbone entropy. To validate this method, we have compared the computed conformational entropies against a statistical free energy analysis of structures in the crystallographic database from several-thousand backbone conformations between nearest-neighbor nucleobases as well as against extensive computer simulations. Using this calculation, we analyzed the backbone entropy of several ribozymes and riboswitches and found that their entropic strains are highly localized along their sequences. The total entropic penalty due to steric congestions in the backbone for the native fold can be as high as 2.4 cal/K/mol per nucleotide for these medium and large RNAs, producing a contribution to the overall free energy of up to 0.72 kcal/mol per nucleotide. For these RNAs, we found that low-entropy high-strain residues are predominantly located at loops with tight turns and at tertiary interaction platforms with unusual structural motifs.     

Conformational Entropy of the RNA Phosphate Backbone and Its Contribution to the Folding Free Energy

While major contributors to the free energy of RNA tertiary structures such as basepairing, base-stacking, and charge and counterion interactions have been studied extensively, little is known about the intrinsic free energy of the backbone. To assess the magnitude of the entropic strains along the phosphate backbone and their impact on the folding free energy, we have formulated a mathematical treatment for computing the volume of the main-chain torsion-angle conformation space between every pair of nucleobases along any sequence to compute the corresponding backbone entropy. To validate this method, we have compared the computed conformational entropies against a statistical free energy analysis of structures in the crystallographic database from several-thousand backbone conformations between nearest-neighbor nucleobases as well as against extensive computer simulations. Using this calculation, we analyzed the backbone entropy of several ribozymes and riboswitches and found that their entropic strains are highly localized along their sequences. The total entropic penalty due to steric congestions in the backbone for the native fold can be as high as 2.4 cal/K/mol per nucleotide for these medium and large RNAs, producing a contribution to the overall free energy of up to 0.72 kcal/mol per nucleotide. For these RNAs, we found that low-entropy high-strain residues are predominantly located at loops with tight turns and at tertiary interaction platforms with unusual structural motifs.     

Predicting RNA pseudoknot folding thermodynamics

Based on the experimentally determined atomic coordinates for RNA helices and the self-avoiding walks of the P (phosphate) and C₄ (carbon) atoms in the diamond lattice for the polynucleotide loop conformations, we derive a set of conformational entropy parameters for RNA pseudoknots. Based on the entropy parameters, we develop a folding thermodynamics model that enables us to compute the sequence-specific RNA pseudoknot folding free energy landscape and thermodynamics. The model is validated through extensive experimental tests both for the native structures and for the folding thermodynamics. The model predicts strong sequence-dependent helix-loop competitions in the pseudoknot stability and the resultant conformational switches between different hairpin and pseudoknot structures. For instance, for the pseudoknot domain of human telomerase RNA, a native-like and a misfolded hairpin intermediates are found to coexist on the (equilibrium) folding pathways, and the interplay between the stabilities of these intermediates causes the conformational switch that may underlie a human telomerase disease.     

Electrostatic interactions in a peptide--RNA complex

Parallel experimental measurements and theoretical calculations have been used to investigate the energetics of electrostatic interactions in the complex formed between a 22 residue, alpha-helical peptide from the N protein of phage lambda and its cognate 19 nucleotide box B RNA hairpin. Salt-dependent free energies were measured for both peptide folding from coil to helix and peptide binding to RNA, and from these the salt-dependence of binding pre-folded, helical peptide to RNA was determined ( partial differential (DeltaG degrees (dock))/ partial differential log[KCl]=5.98(+/-0.21)kcal/mol). (A folding transition taking place in the RNA hairpin loop was shown to have a negligible dependence on salt concentration.) The non-linear Poisson-Boltzmann equation was used to calculate the same salt dependence of the binding free energy as 5.87(+/-0.22)kcal/mol, in excellent agreement with the measured value. Close agreement between experimental measurements and calculations was also obtained for two variant peptides in which either a basic or acidic residue was replaced with an uncharged residue, and for an RNA variant with a deletion of a single loop nucleotide. The calculations suggest that the strength of electrostatic interactions between a peptide residue and RNA varies considerably with environment, but that all 12 positive and negative N peptide charges contribute significantly to the electrostatic free energy of RNA binding, even at distances up to 11A from backbone phosphate groups. Calculations also show that the net release of ions that accompanies complex formation originates from rearrangements of both peptide and RNA ion atmospheres, and includes accumulation of ions in some regions of the complex as well as displacement of cations and anions from the ion atmospheres of the RNA and peptide, respectively.     

TBI Server: A Web Server for Predicting Ion Effects in RNA Folding

Background

Metal ions play a critical role in the stabilization of RNA structures. Therefore, accurate prediction of the ion effects in RNA folding can have a far-reaching impact on our understanding of RNA structure and function. Multivalent ions, especially Mg²⁺, are essential for RNA tertiary structure formation. These ions can possibly become strongly correlated in the close vicinity of RNA surface. Most of the currently available software packages, which have widespread success in predicting ion effects in biomolecular systems, however, do not explicitly account for the ion correlation effect. Therefore, it is important to develop a software package/web server for the prediction of ion electrostatics in RNA folding by including ion correlation effects.

Results

The TBI web server http://rna.physics.missouri.edu/tbi_index.html provides predictions for the total electrostatic free energy, the different free energy components, and the mean number and the most probable distributions of the bound ions. A novel feature of the TBI server is its ability to account for ion correlation and ion distribution fluctuation effects.

Conclusions

By accounting for the ion correlation and fluctuation effects, the TBI server is a unique online tool for computing ion-mediated electrostatic properties for given RNA structures. The results can provide important data for in-depth analysis for ion effects in RNA folding including the ion-dependence of folding stability, ion uptake in the folding process, and the interplay between the different energetic components.     

On the application of statistical physics to evolutionary biology

There is a close analogy between statistical thermodynamics and the evolution of allele frequencies under mutation, selection and random drift. Wright's formula for the stationary distribution of allele frequencies is analogous to the Boltzmann distribution in statistical physics. Population size, 2N, plays the role of the inverse temperature, 1/kT, and determines the magnitude of random fluctuations. Log mean fitness, , tends to increase under selection, and is analogous to a (negative) energy; a potential function, U, increases under mutation in a similar way. An entropy, S_H, can be defined which measures the deviation from the distribution of allele frequencies expected under random drift alone; the sum gives a free fitness that increases as the population evolves towards its stationary distribution. Usually, we observe the distribution of a few quantitative traits that depend on the frequencies of very many alleles. The mean and variance of such traits are analogous to observable quantities in statistical thermodynamics. Thus, we can define an entropy, S_Ω, which measures the volume of allele frequency space that is consistent with the observed trait distribution. The stationary distribution of the traits is ; this applies with arbitrary epistasis and dominance. The entropies S_Ω, S_H are distinct, but converge when there are so many alleles that traits fluctuate close to their expectations. Populations tend to evolve towards states that can be realised in many ways (i.e., large S_Ω), which may lead to a substantial drop below the adaptive peak; we illustrate this point with a simple model of genetic redundancy. This analogy with statistical thermodynamics brings together previous ideas in a general framework, and justifies a maximum entropy approximation to the dynamics of quantitative traits.     

Consistency in structural energetics of protein folding and peptide recognition.

We report a new free energy decomposition that includes structure-derived atomic contact energies for the desolvation component, and show that it applies equally well to the analysis of single-domain protein folding and to the binding of flexible peptides to proteins. Specifically, we selected the 17 single-domain proteins for which the three-dimensional structures and thermodynamic unfolding free energies are available. By calculating all terms except the backbone conformational entropy change and comparing the result to the experimentally measured free energy, we estimated that the mean entropy gain by the backbone chain upon unfolding (delta Sbb) is 5.3 cal/K per mole of residue, and that the average backbone entropy for glycine is 6.7 cal/K. Both numbers are in close agreement with recent estimates made by entirely different methods, suggesting a promising degree of consistency between data obtained from disparate sources. In addition, a quantitative analysis of the folding free energy indicates that the unfavorable backbone entropy for each of the proteins is balanced predominantly by favorable backbone interactions. Finally, because the binding of flexible peptides to receptors is physically similar to folding, the free energy function should, in principle, be equally applicable to flexible docking. By combining atomic contact energies, electrostatics, and sequence-dependent backbone entropy, we calculated a priori the free energy changes associated with the binding of four different peptides to HLA-A2, 1 MHC molecule and found agreement with experiment to within 10% without parameter adjustment.     

Structure and stability of RNA/RNA kissing complex: with application to HIV dimerization initiation signal

We develop a statistical mechanical model to predict the structure and folding stability of the RNA/RNA kissing-loop complex. One of the key ingredients of the theory is the conformational entropy for the RNA/RNA kissing complex. We employ the recently developed virtual bond-based RNA folding model (Vfold model) to evaluate the entropy parameters for the different types of kissing loops. A benchmark test against experiments suggests that the entropy calculation is reliable. As an application of the model, we apply the model to investigate the structure and folding thermodynamics for the kissing complex of the HIV-1 dimerization initiation signal. With the physics-based energetic parameters, we compute the free energy landscape for the HIV-1 dimer. From the energy landscape, we identify two minimal free energy structures, which correspond to the kissing-loop dimer and the extended-duplex dimer, respectively. The results support the two-step dimerization process for the HIV-1 replication cycle. Furthermore, based on the Vfold model and energy minimization, the theory can predict the native structure as well as the local minima in the free energy landscape. The root-mean-square deviations (RMSDs) for the predicted kissing-loop dimer and extended-duplex dimer are ∼3.0 Å. The method developed here provides a new method to study the RNA/RNA kissing complex.     

Evidence that folding of an RNA tetraloop hairpin is less cooperative than its DNA counterpart

Hairpin secondary structural elements play important roles in the folding and function of RNA and DNA molecules. Previous work from our lab on small DNA hairpin loop motifs, d(cGNAg) and d(cGNABg) (where B is C, G, or T), showed that folding is highly cooperative and obeys indirect coupling, consistent with a concerted transition. Herein, we investigate folding of the related, exceptionally stable RNA hairpin motif, r(cGNRAg) (where R is A or G). Previous NMR characterization identified a complex network of seven hydrogen bonds in this loop. We inserted three carbon (C3) spacers throughout the loop and found coupling between G1 of the loop and the CG closing base pair, similar to that found in DNA. These data support a GNRA motif being expandable at any position but before the G. Thermodynamic measurements of nucleotide-analogue-substituted oligonucleotides revealed pairwise-coupling free energies ranging from weak to strong. When coupling free energies were remeasured in the background of changes at a third site, they remained essentially unchanged even though all of the sites were coupled to each other. This type of coupling, referred to as "direct", is peculiar to the RNA loop. The data suggest that, for small stable loops, folding of RNA obeys a model with nearest-neighbor interactions, while folding of DNA follows a more concerted process in which the stabilizing interactions are linked through a conformational change. The lesser cooperativity in RNA loops may provide a more robust loop that can withstand mutations without a severe loss in stability. These differences may enhance the ability of RNA to evolve.     

Does conformational free energy distinguish loop conformations in proteins?

Limitations in protein homology modeling often arise from the inability to adequately model loops. In this paper we focus on the selection of loop conformations. We present a complete computational treatment that allows the screening of loop conformations to identify those that best fit a molecular model. The stability of a loop in a protein is evaluated via computations of conformational free energies in solution, i.e., the free energy difference between the reference structure and the modeled one. A thermodynamic cycle is used for calculation of the conformational free energy, in which the total free energy of the reference state (i.e., gas phase) is the CHARMm potential energy. The electrostatic contribution of the solvation free energy is obtained from solving the finite-difference Poisson-Boltzmann equation. The nonpolar contribution is based on a surface area-based expression. We applied this computational scheme to a simple but well-characterized system, the antibody hypervariable loop (complementarity-determining region, CDR). Instead of creating loop conformations, we generated a database of loops extracted from high-resolution crystal structures of proteins, which display geometrical similarities with antibody CDRs. We inserted loops from our database into a framework of an antibody; then we calculated the conformational free energies of each loop. Results show that we successfully identified loops with a "reference-like" CDR geometry, with the lowest conformational free energy in gas phase only. Surprisingly, the solvation energy term plays a confusing role, sometimes discriminating "reference-like" CDR geometry and many times allowing "non-reference-like" conformations to have the lowest conformational free energies (for short loops). Most "reference-like" loop conformations are separated from others by a gap in the gas phase conformational free energy scale. Naturally, loops from antibody molecules are found to be the best models for long CDRs (> or = 6 residues), mainly because of a better packing of backbone atoms into the framework of the antibody model.     

Synthesis, spectroscopy, computational evaluation and first X-ray structural characterization of a primary amine containing boronium ion

Stable (CF₃SO₂)₂N⁻, I⁻ and salts of the boronium ion [(tert-butylamine)(1-methylimidazole)BH₂]⁺ have been isolated and characterized. A single-crystal X-ray structure of the salt provides the first unambiguous proof for a boronium ion supported by a primary amine ligand.     

Coarse-Grained Prediction of RNA Loop Structures

One of the key issues in the theoretical prediction of RNA folding is the prediction of loop structure from the sequence. RNA loop free energies are dependent on the loop sequence content. However, most current models account only for the loop length-dependence. The previously developed “Vfold” model (a coarse-grained RNA folding model) provides an effective method to generate the complete ensemble of coarse-grained RNA loop and junction conformations. However, due to the lack of sequence-dependent scoring parameters, the method is unable to identify the native and near-native structures from the sequence. In this study, using a previously developed iterative method for extracting the knowledge-based potential parameters from the known structures, we derive a set of dinucleotide-based statistical potentials for RNA loops and junctions. A unique advantage of the approach is its ability to go beyond the the (known) native structures by accounting for the full free energy landscape, including all the nonnative folds. The benchmark tests indicate that for given loop/junction sequences, the statistical potentials enable successful predictions for the coarse-grained 3D structures from the complete conformational ensemble generated by the Vfold model. The predicted coarse-grained structures can provide useful initial folds for further detailed structural refinement.     

Leaf chlorophyll fluorescence, reflectance, and physiological response to freshwater and saltwater flooding in the evergreen shrub, Myrica cerifera

Photosynthesis, water relations, chlorophyll fluorescence, and leaf reflectance were used to evaluate stress due to freshwater and saltwater flooding in the evergreen coastal shrub, Myrica cerifera, under controlled conditions. M. cerifera forms large monospecific thickets that facilitate scaling up from leaf-level measurements to the landscape. Based on physiological responses, stress began by day 3 in flooded plants treated with 5, 10, and 15 g L⁻¹ salinity, as seen by significant decreases in stomatal conductance and net photosynthesis relative to control plants. Decreases in physiological measurements occurred by day 9 in freshwater flooded plants. Visible signs of stress occurred by day 5 for plants treated with 15 g L⁻¹, day 8 for flooded plants exposed to 10 g L⁻¹, and day 10 for those treated with 5 g L⁻¹ salinity. Significant differences in light-adapted fluorescence yield () were observed by day 3 in plants flooded with 5, 10, and 15 g L⁻¹ salinity and day 6 in freshwater flooded plants. Non-photochemical quenching (Φ_NPQ) increased with decreasing . In comparison, statistical differences in dark-adapted fluorescence yield (F_v/F_m) were observed by day 12 in plants flooded with 5, 10, and 15 g L⁻¹ salinity, well after visible signs of stress were apparent. Fluorescence parameters were successful at detecting and distinguishing both freshwater and saltwater flooding stress. A positive, linear correlation (r² = 0.80) was observed between and the physiological reflectance index (PRI). Xanthophyll-cycle dependent energy dissipation appears to be the underlying mechanism in protecting photosystem II from excess energy in saltwater flooded plants. was useful in detecting stress-induced changes in the photosystem before any visible signs of damage were evident at the leaf-level. This parameter may be linked to hyperspectral reflectance data for rapid detection of stress at the canopy-level.     

Protozoan predation on nitrification performance and microbial community during bioaugmentation

The effects of predation on nitrification performance and microbial community during bioaugmentation were investigated. Although most of the nitrification ability of the seed source was lost in the seeded reactors, bioaugmentation significantly enhanced the activity and community of the nitrifiers. The ammonium uptake rate (AUR) increased from 2.59 to 15.25 mg -N/L h and 2.88 to 13.36 mg -N/L h, and the nitrite uptake rate (NUR) increased from 0.80 to 4.02 mg -N/L h and 0.76 to 4.34 mg -N/L h for the reactors with and without protozoa inhibition, respectively. The population of nitrifiers increased, and the dominant nitrite oxidizing bacteria (NOB) transferred from Nitrospira to Nitrobacter. Predation had an evident influence on the microbial community of nitrifiers, especially the K-strategist, which was more vulnerable to predation than r-strategist during bioaugmentation due to its low growth rate. However, predation did not have a significant effect on the nitrification performance.