No evidence that mRNAs have lower folding free energies than random sequences with the same dinucleotide distribution

This work investigates whether mRNA has a lower estimated folding free energy than random sequences. The free energy estimates are calculated by the mfold program for prediction of RNA secondary structures. For a set of 46 mRNAs it is shown that the predicted free energy is not significantly different from random sequences with the same dinucleotide distribution. For random sequences with the same mononucleotide distribution it has previously been shown that the native mRNA sequences have a lower predicted free energy, which indicates a more stable structure than random sequences. However, dinucleotide content is important when assessing the significance of predicted free energy as the physical stability of RNA secondary structure is known to depend on dinucleotide base stacking energies. Even known RNA secondary structures, like tRNAs, can be shown to have predicted free energies indistinguishable from randomized sequences. This suggests that the predicted free energy is not always a good determinant for RNA folding.     

Prediction of alternative RNA secondary structures based on fluctuating thermodynamic parameters.

In this paper we present a new method for predicting a set of RNA secondary structures that are thermodynamically favored in RNA folding simulations. This method uses a large number of 'simulated energy rules' (SER) generated by perturbing the free energy parameters derived experimentally within the range of the experimental errors. The structure with the lowest free energy is computed for each SER. Structural comparisons are used to avoid multiple generation of similar structures. Computed structures are evaluated using the energy distribution of the lowest free energy structures derived in the simulation. Predicted be graphically displayed with their occurring frequencies in the simulation by dot-plot representations. On average, about 90% of phylogenetic helixes in the known models of tRNA, Group I self-splicing intron, and Escherichia coli 16 S rRNA, were predicted using the method.     

一种预测单链RNA分子二级结构的计算机算法

本文给出了一个利用已知能量数据构成具有最小自由能的单链RNA分子二级结构的计算机算法,并给出了此算法的可行性证明和应用实例。     

Applicability of urea in the thermodynamic analysis of secondary and tertiary RNA folding

The equilibrium folding of a series of self-complementary RNA duplexes and the unmodified yeast tRNA(Phe) is studied as a function of urea and Mg(2+) concentration with optical spectroscopies and chemical modification under isothermal conditions. Via application of standard methodologies from protein folding, the folding free energy and its dependence on urea concentration, the m value, are determined. The free energies of the RNA duplexes obtained from the urea titrations are in good agreement with those calculated from thermal melting studies [Freier, S. I., et al. (1986) Proc. Natl. Acad. Sci. U.S.A. 83, 9373]. The m value correlates with the length of the RNA duplex and is not sensitive to ionic conditions and temperature. The folding of the unmodified yeast tRNA(Phe) can be described by two Mg(2+)-dependent transitions, the second of which corresponds to the formation of the native tertiary structure as confirmed by hydroxyl radical protection and partial nuclease digestion. Both transitions are sensitive to urea and have m values of 0.94 and 1.70 kcal mol(-)(1) M(-)(1), respectively. Although the precise chemical basis of urea denaturation of RNA is uncertain, the m values for the duplexes and tRNA(Phe) are proportional to the amount of the surface area buried in the folding transition. This proportionality, 0.099 cal mol(-)(1) M(-)(1) A(-)(2), is very similar to that observed for proteins, 0.11 cal mol(-)(1) M(-)(1) A(-)(2) [Myers, J., Pace, N., and Scholtz, M. (1995) Protein Sci. 4, 2138]. These results indicate that urea titration can be used to measure both the free energy and the magnitude of an RNA folding transition.     

Detection of unusual RNA folding regions in HIV and SIV sequences

We have developed a method for detecting more stable and significantfolding regions relative to others in the sequence. The algorithmis based on the calculation of the lowest free energy of RNAsecondary structures and Monte Carlo simulation. For any givenRNA segment, the stability and statistical significance of RNAfolding are assessed by two measures: the stability score andthe significance score. The stability score measures the degreeof thermodynamic stability of the segment between all possiblebiological segments in the RNA sequence. The significance scorecharacterizes the specific arrangement of the nucleotides inthe segment that could imply a structural role for the sequenceinformation. Using these two measures, we are able to detecta series of distinct folding regions where highly stable andstatistically significant secondary structures occur in humanimmunodeficiency virus (HIV) and simian immunodeficiency virus(SIV) sequences. Received on April 4, 1990; accepted on October 2, 1990     

Evaluation of the suitability of free-energy minimization using nearest-neighbor energy parameters for RNA secondary structure prediction

Background

A detailed understanding of an RNA's correct secondary and tertiary structure is crucial to understanding its function and mechanism in the cell. Free energy minimization with energy parameters based on the nearest-neighbor model and comparative analysis are the primary methods for predicting an RNA's secondary structure from its sequence. Version 3.1 of Mfold has been available since 1999. This version contains an expanded sequence dependence of energy parameters and the ability to incorporate coaxial stacking into free energy calculations. We test Mfold 3.1 by performing the largest and most phylogenetically diverse comparison of rRNA and tRNA structures predicted by comparative analysis and Mfold, and we use the results of our tests on 16S and 23S rRNA sequences to assess the improvement between Mfold 2.3 and Mfold 3.1.

Results

The average prediction accuracy for a 16S or 23S rRNA sequence with Mfold 3.1 is 41%, while the prediction accuracies for the majority of 16S and 23S rRNA structures tested are between 20% and 60%, with some having less than 20% prediction accuracy. The average prediction accuracy was 71% for 5S rRNA and 69% for tRNA. The majority of the 5S rRNA and tRNA sequences have prediction accuracies greater than 60%. The prediction accuracy of 16S rRNA base-pairs decreases exponentially as the number of nucleotides intervening between the 5' and 3' halves of the base-pair increases.

Conclusion

Our analysis indicates that the current set of nearest-neighbor energy parameters in conjunction with the Mfold folding algorithm are unable to consistently and reliably predict an RNA's correct secondary structure. For 16S or 23S rRNA structure prediction, Mfold 3.1 offers little improvement over Mfold 2.3. However, the nearest-neighbor energy parameters do work well for shorter RNA sequences such as tRNA or 5S rRNA, or for larger rRNAs when the contact distance between the base-pairs is less than 100 nucleotides.     

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.     

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.     

A guide to ions and RNA structure

RNA folding into stable tertiary structures is remarkably sensitive to the concentrations and types of cations present; an understanding of the physical basis of ion-RNA interactions is therefore a prerequisite for a quantitative accounting of RNA stability. This article summarizes the energetic factors that must be considered when ions interact with two different RNA environments. "Diffuse ions" accumulate near the RNA because of the RNA electrostatic field and remain largely hydrated. A "chelated" ion directly contacts a specific location on the RNA surface and is held in place by electrostatic forces. Energetic costs of ion chelation include displacement of some of the waters of hydration by the RNA surface and repulsion of diffuse ions. Methods are discussed for computing both the free energy of the set of diffuse ions associated with an RNA and the binding free energies of individual chelated ions. Such calculations quantitatively account for the effects of Mg(2+) on RNA stability where experimental data are available. An important conclusion is that diffuse ions are a major factor in the stabilization of RNA tertiary structures.     

Stability of XGCGCp, GCGCYp, and XGCGCYp helixes: an empirical estimate of the energetics of hydrogen bonds in nucleic acids

The stabilizing effects of dangling ends and terminal base pairs on the core helix GCGC are reported. Enthalpy and entropy changes of helix formation were measured spectrophotometrically for AGCGCU, UGCGCA, GGCGCCp, CGCGCGp, and the corresponding pentamers XGCGCp and GCGCYp containing the GCGC core plus a dangling end. Each 5' dangling end increases helix stability at 37 degrees C roughly 0.2 kcal/mol and each 3' end from 0.8 to 1.7 kcal/mol. The free energy increments for dangling ends on GCGC are similar to the corresponding increments reported for the GGCC core [Freier, S. M., Alkema, D., Sinclair, A., Neilson, T., & Turner, D. H. (1985) Biochemistry 24, 4533-4539], indicating a nearest-neighbor model is adequate for prediction of stabilization due to dangling ends. Nearest-neighbor parameters for prediction of the free energy effects of adding dangling ends and terminal base pairs next to G.C pairs are presented. Comparison of these free energy changes is used to partition the free energy of base pair formation into contributions of "stacking" and "pairing". If pairing contributions are due to hydrogen bonding, the results suggest stacking and hydrogen bonding make roughly comparable favorable contributions to the stability of a terminal base pair. The free energy increment associated with forming a hydrogen bond is estimated to be -1 kcal/mol of hydrogen bond.     

Identification and characterization of E.coli ribosomal binding sites by free energy computation.

Sequences upstream from translational initiation sites of different E.coli genes show various degrees of complementarity to the Shine-Dalgarno (SD) sequence at the 3' end of the 16S rRNA. We propose a quantitative measure for the SD region on the mRNA, that reflects its degree of complementarity to the rRNA. This measure is based on the stability of the rRNA-mRNA duplex as established by free energy computations. The free energy calculations are based on the same principles that are used for folding a single RNA molecule, and are executed by similar algorithms. Bulges and internal loops in the rRNA and mRNA are allowed. The mRNA string with maximum free energy gain upon binding to the rRNA is selected as the most favorable SD sequence of a gene. The free energy value that represents the SD region provides a quantitative measure that can be used for comparing SD sequences of different genes. The distribution of this measure in more than 1000 E.coli genes is presented and discussed.     

Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information.

This paper presents a new computer method for folding an RNA molecule that finds a conformation of minimum free energy using published values of stacking and destabilizing energies. It is based on a dynamic programming algorithm from applied mathematics, and is much more efficient, faster, and can fold larger molecules than procedures which have appeared up to now in the biological literature. Its power is demonstrated in the folding of a 459 nucleotide immunoglobulin gamma 1 heavy chain messenger RNA fragment. We go beyond the basic method to show how to incorporate additional information into the algorithm. This includes data on chemical reactivity and enzyme susceptibility. We illustrate this with the folding of two large fragments from the 16S ribosomal RNA of Escherichia coli.     

A dynamic programming algorithm for finding alternative RNA secondary structures.

Dynamic programming algorithms that predict RNA secondary structure by minimizing the free energy have had one important limitation. They were able to predict only one optimal structure. Given the uncertainties of the thermodynamic data and the effects of proteins and other environmental factors on structure, the optimal structure predicted by these methods may not have biological significance. We present a dynamic programming algorithm that can determine optimal and suboptimal secondary structures for an RNA. The power and utility of the method is demonstrated in the folding of the intervening sequence of the rRNA of Tetrahymena. By first identifying the major secondary structures corresponding to the lowest free energy minima, a secondary structure of possible biological significance is derived.     

Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure.

An improved dynamic programming algorithm is reported for RNA secondary structure prediction by free energy minimization. Thermodynamic parameters for the stabilities of secondary structure motifs are revised to include expanded sequence dependence as revealed by recent experiments. Additional algorithmic improvements include reduced search time and storage for multibranch loop free energies and improved imposition of folding constraints. An extended database of 151,503 nt in 955 structures? determined by comparative sequence analysis was assembled to allow optimization of parameters not based on experiments and to test the accuracy of the algorithm. On average, the predicted lowest free energy structure contains 73 % of known base-pairs when domains of fewer than 700 nt are folded; this compares with 64 % accuracy for previous versions of the algorithm and parameters. For a given sequence, a set of 750 generated structures contains one structure that, on average, has 86 % of known base-pairs. Experimental constraints, derived from enzymatic and flavin mononucleotide cleavage, improve the accuracy of structure predictions.     

Predicting a set of minimal free energy RNA secondary structures common to two sequences

MOTIVATION: Function derives from structure, therefore, there is need for methods to predict functional RNA structures. RESULTS: The Dynalign algorithm, which predicts the lowest free energy secondary structure common to two unaligned RNA sequences, is extended to the prediction of a set of low-energy structures. Dot plots can be drawn to show all base pairs in structures within an energy increment. Dynalign predicts more well-defined structures than structure prediction using a single sequence; in 5S rRNA sequences, the average number of base pairs in structures with energy within 20% of the lowest energy structure is 317 using Dynalign, but 569 using a single sequence. Structure prediction with Dynalign can also be constrained according to experiment or comparative analysis. The accuracy, measured as sensitivity and positive predictive value, of Dynalign is greater than predictions with a single sequence. AVAILABILITY: Dynalign can be downloaded at http://rna.urmc.rochester.edu     

Structural RNA has lower folding energy than random RNA of the same dinucleotide frequency

We present results of computer experiments that indicate that several RNAs for which the native state (minimum free energy secondary structure) is functionally important (type III hammerhead ribozymes, signal recognition particle RNAs, U2 small nucleolar spliceosomal RNAs, certain riboswitches, etc.) all have lower folding energy than random RNAs of the same length and dinucleotide frequency. Additionally, we find that whole mRNA as well as 5'-UTR, 3'-UTR, and cds regions of mRNA have folding energies comparable to that of random RNA, although there may be a statistically insignificant trace signal in 3'-UTR and cds regions. Various authors have used nucleotide (approximate) pattern matching and the computation of minimum free energy as filters to detect potential RNAs in ESTs and genomes. We introduce a new concept of the asymptotic Z-score and describe a fast, whole-genome scanning algorithm to compute asymptotic minimum free energy Z-scores of moving-window contents. Asymptotic Z-score computations offer another filter, to be used along with nucleotide pattern matching and minimum free energy computations, to detect potential functional RNAs in ESTs and genomic regions.     

RNA大分子的二极结构预测

本文提出能预测单链核酸分子的具有最小自由能的二级结构的计算方法。方法的基础是拓扑平面图的最大C—匹配原理和现有的单链核酸分子折叠构象的热力学数据资料。为了说明算法的能力,对免疫球蛋白r1重链的mRNA片段序列(459个核苷酸残基)大肠杆菌16s rRNA片段序列(567一883)以及脊髓灰白质炎病毒RNA片段序列(1—74O)的二级结构进行了计算机预测并同现有的结构模型进行了比较和讨论。由计算机预测的大肠杆菌16s rRNA中心域的二级结构与Noller和Woese提出的结构模型基本一致。     

Statistics of RNA secondary structures

A statistical reference for RNA secondary structures with minimum free energies is computed by folding large ensembles of random RNA sequences. Four nucleotide alphabets are used: two binary alphabets, AU and GC, the biophysical AUGC and the synthetic GCXK alphabet. RNA secondary structures are made of structural elements, such as stacks, loops, joints, and free ends. Statistical properties of these elements are computed for small RNA molecules of chain lengths up to 100. The results of RNA structure statistics depend strongly on the particular alphabet chosen. The statistical reference is compared with the data derived from natural RNA molecules with similar base frequencies. Secondary structures are represented as trees. Tree editing provides a quantitative measure for the distance d_t, between two structures. We compute a structure density surface as the conditional probability of two structures having distance t given that their sequences have distance h. This surface indicates that the vast majority of possible minimum free energy secondary structures occur within a fairly small neighborhood of any typical (random) sequence. Correlation lengths for secondary structures in their tree representations are computed from probability densities. They are appropriate measures for the complexity of the sequence-structure relation. The correlation length also provides a quantitative estimate for the mean sensitivity of structures to point mutations. © 1993 John Wiley & Sons, Inc.