Vfold Model Research Articles

Predicting RNA Structure with Vfold.

In order to carry out biological functions, RNA molecules must fold into specific three-dimensional (3D) structures. Current experimental methods to determine RNA 3D structures are expensive and time consuming. With the recent advances in computational biology, RNA structure prediction is becoming increasingly reliable. This chapter describes a recently developed RNA structure prediction software, Vfold, a virtual bond-based RNA folding model. The main features of Vfold are the physics-based loop free energy calculations for various RNA structure motifs and a template-based assembly method for RNA 3D structure prediction. For illustration, we use the yybP-ykoY Orphan riboswitch as an example to show the implementation of the Vfold model in RNA structure prediction from the sequence.

Slope heuristics and V-Fold model selection in heteroscedastic regression using strongly localized bases

We investigate the optimality for model selection of the so-called slope heuristics, $V$-fold cross-validation and $V$-fold penalization in a heteroscedastic with random design regression context. We consider a new class of linear models that we call strongly localized bases and that generalize histograms, piecewise polynomials and compactly supported wavelets. We derive sharp oracle inequalities that prove the asymptotic optimality of the slope heuristics---when the optimal penalty shape is known---and $V$ -fold penalization. Furthermore, $V$-fold cross-validation seems to be suboptimal for a fixed value of $V$ since it recovers asymptotically the oracle learned from a sample size equal to $1-V^{-1}$ of the original amount of data. Our results are based on genuine concentration inequalities for the true and empirical excess risks that are of independent interest. We show in our experiments the good behavior of the slope heuristics for the selection of linear wavelet models. Furthermore, $V$-fold cross-validation and $V$-fold penalization have comparable efficiency.

VfoldCPX Server for RNA/RNA Complex Structure Prediction

RNA/RNA interactions are essential for genomic RNA dimerization and regulation of gene expression. Predicting the structure and folding stabilities of RNA/RNA complexes is a biologically significant problem. We recently developed a new web server, VfoldCPX, to predict two-dimensional (2D) structures of RNA/RNA complexes from the sequence. The server is based on a new Vfold model that employs coarse-grained entropy parameters for the different structural motifs. By taking into account both the intra- and inter-molecular interactions, the model can predict RNA/RNA structures with cross-linked tertiary contacts. Furthermore, in addition to the minimum free energy structure, the server can predict multiple energetically stable structures ranked by their stabilities. The predicted structures can offer users with extensive insights into the folding and conformational switches in RNA biological functions. The web server is freely accessible at “http://rna.physics.missouri.edu”.

Physics-based RNA structure prediction.

Despite the success of RNA secondary structure prediction for simple, short RNAs, the problem of predicting RNAs with long-range tertiary folds remains. Furthermore, RNA 3D structure prediction is hampered by the lack of the knowledge about the tertiary contacts and their thermodynamic parameters. Low-resolution structural modeling enables us to estimate the conformational entropies for a number of tertiary folds through rigorous statistical mechanical calculations. The models lead to 3D tertiary folds at coarse-grained level. The coarse-grained structures serve as the initial structures for all-atom molecular dynamics refinement to build the final all-atom 3D structures. In this paper, we present an overview of RNA computational models for secondary and tertiary structures’ predictions and then focus on a recently developed RNA statistical mechanical model—the Vfold model. The main emphasis is placed on the physics behind the models, including the treatment of the non-canonical interactions in secondary and tertiary structure modelings, and the correlations to RNA functions.

Vfold: a web server for RNA structure and folding thermodynamics prediction.

BackgroundThe 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.ResultsThe 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.ConclusionsThe 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”.

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.

Statistical mechanical modeling of RNA folding: from free energy landscape to tertiary structural prediction.

In spite of the success of computational methods for predicting RNA secondary structure, the problem of predicting RNA tertiary structure folding remains. Low-resolution structural models show promise as they allow for rigorous statistical mechanical computation for the conformational entropies, free energies, and the coarse-grained structures of tertiary folds. Molecular dynamics refinement of coarse-grained structures leads to all-atom 3D structures. Modeling based on statistical mechanics principles also has the unique advantage of predicting the full free energy landscape, including local minima and the global free energy minimum. The energy landscapes combined with the 3D structures form the basis for quantitative predictions of RNA functions. In this chapter, we present an overview of statistical mechanical models for RNA folding and then focus on a recently developed RNA statistical mechanical model -- the Vfold model. The main emphasis is placed on the physics underpinning the models, the computational strategies, and the connections to RNA biology.

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.

Predicting loop-helix tertiary structural contacts in RNA pseudoknots.

Tertiary interactions between loops and helical stems play critical roles in the biological function of many RNA pseudoknots. However, quantitative predictions for RNA tertiary interactions remain elusive. Here we report a statistical mechanical model for the prediction of noncanonical loop-stem base-pairing interactions in RNA pseudoknots. Central to the model is the evaluation of the conformational entropy for the pseudoknotted folds with defined loop-stem tertiary structural contacts. We develop an RNA virtual bond-based conformational model (Vfold model), which permits a rigorous computation of the conformational entropy for a given fold that contains loop-stem tertiary contacts. With the entropy parameters predicted from the Vfold model and the energy parameters for the tertiary contacts as inserted parameters, we can then predict the RNA folding thermodynamics, from which we can extract the tertiary contact thermodynamic parameters from theory-experimental comparisons. These comparisons reveal a contact enthalpy (DeltaH) of -14 kcal/mol and a contact entropy (DeltaS) of -38 cal/mol/K for a protonated C(+)*(G-C) base triple at pH 7.0, and (DeltaH = -7 kcal/mol, DeltaS = -19 cal/mol/K) for an unprotonated base triple. Tests of the model for a series of pseudoknots show good theory-experiment agreement. Based on the extracted energy parameters for the tertiary structural contacts, the model enables predictions for the structure, stability, and folding pathways for RNA pseudoknots with known or postulated loop-stem tertiary contacts from the nucleotide sequence alone.

Biphasic Folding Kinetics of RNA Pseudoknots and Telomerase RNA Activity

Using a combined master equation and kinetic cluster approach, we investigate RNA pseudoknot folding and unfolding kinetics. The energetic parameters are computed from a recently developed Vfold model for RNA secondary structure and pseudoknot folding thermodynamics. The folding kinetics theory is based on the complete conformational ensemble, including all the native-like and non-native states. The predicted folding and unfolding pathways, activation barriers, Arrhenius plots, and rate-limiting steps lead to several findings. First, for the PK5 pseudoknot, a misfolded 5′ hairpin emerges as a stable kinetic trap in the folding process, and the detrapping from this misfolded state is the rate-limiting step for the overall folding process. The calculated rate constant and activation barrier agree well with the experimental data. Second, as an application of the model, we investigate the kinetic folding pathways for human telomerase RNA (hTR) pseudoknot. The predicted folding and unfolding pathways not only support the proposed role of conformational switch between hairpin and pseudoknot in hTR activity, but also reveal molecular mechanism for the conformational switch. Furthermore, for an experimentally studied hTR mutation, whose hairpin intermediate is destabilized, the model predicts a long-lived transient hairpin structure, and the switch between the transient hairpin intermediate and the native pseudoknot may be responsible for the observed hTR activity. Such finding would help resolve the apparent contradiction between the observed hTR activity and the absence of a stable hairpin.