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 RNA secondary structure by free energy minimization

RNA secondary structure is often predicted from sequence by free energy minimization. Over the past two years, advances have been made in the estimation of folding free energy change, the mapping of secondary structure and the implementation of computer programs for structure prediction. The trends in computer program development are: efficient use of experimental mapping of structures to constrain structure prediction; use of statistical mechanics to improve the fidelity of structure prediction; inclusion of pseudoknots in secondary structure prediction; and use of two or more homologous sequences to find a common structure.     

Computer simulation of tRNA secondary structure folding

Computer simulation results of folding linear RNA moleculesinto secondaty structures are presented. The structure is formedby two interacting processes: the RNA molecular chain growth(beginning from an initial length, L_o), and the structuring(secondary structure sequential growth in the region of theexisting molecular chain, based on the local free energy minimizationby sequential addition of elementary substruc tures-stems).It was found that the final secondary structure formation isgreatly influenced by the ‘structuring period’ T(the ratio of the molecular chain growth rate to the structuringrate), and the direction of RNA synthesis. The computer simulationhas been performed for 219 and 906 tRNA genes from two publishedcatalogues, on the whale two-dimensional domain (T,L₀) parameters,by using four known free-energy models. Minimwn stem lengthand molecular chain growth direction have been also varied Thecalculated secondary structures have been compared to the naturaltRNA structures given in the catalogues, and the region of bestcoincidence for the model parameters has been determined. Ithas been proved that, on average, >86% of the paired basesof natural tRNA structures appear in the folding simulation.     

RNA二级结构预测系统构建

运用下列RNA二级结构预测算法:碱基最大配对方法、Zuker极小化自由能方法、螺旋区最优堆积、螺旋区随机堆积和所有可能组合方法与基于一级螺旋区的RNA二级结构绘图技术, 构建了RNA二级结构预测系统Rnafold. 另外, 通过随机选取20个tRNA序列, 从自由能和三叶草结构两个方面比较了前4种二级结构预测算法, 并运用t检验方法分析了自由能的统计学差别. 从三叶草结构来看, 以随机堆积方法最好, 其次是螺旋区最优堆积方法和Zuker算法, 以碱基最大配对方法最差. 最后, 分析了两种极小化自由能方法之间的差别.     

Prediction of RNA secondary structure based on helical regions distribution

MOTIVATION: RNAs play an important role in many biological processes and knowing their structure is important in understanding their function. Due to difficulties in the experimental determination of RNA secondary structure, the methods of theoretical prediction for known sequences are often used. Although many different algorithms for such predictions have been developed, this problem has not yet been solved. It is thus necessary to develop new methods for predicting RNA secondary structure. The most-used at present is Zuker's algorithm which can be used to determine the minimum free energy secondary structure. However many RNA secondary structures verified by experiments are not consistent with the minimum free energy secondary structures. In order to solve this problem, a method used to search a group of secondary structures whose free energy is close to the global minimum free energy was developed by Zuker in 1989. When considering a group of secondary structures, if there is no experimental data, we cannot tell which one is better than the others. This case also occurs in combinatorial and heuristic methods. These two kinds of methods have several weaknesses. Here we show how the central limit theorem can be used to solve these problems. RESULTS: An algorithm for predicting RNA secondary structure based on helical regions distribution is presented, which can be used to find the most probable secondary structure for a given RNA sequence. It consists of three steps. First, list all possible helical regions. Second, according to central limit theorem, estimate the occurrence probability of every helical region based on the Monte Carlo simulation. Third, add the helical region with the biggest probability to the current structure and eliminate the helical regions incompatible with the current structure. The above processes can be repeated until no more helical regions can be added. Take the current structure as the final RNA secondary structure. In order to demonstrate the confidence of the program, a test on three RNA sequences: tRNAPhe, Pre-tRNATyr, and Tetrahymena ribosomal RNA intervening sequence, is performed. AVAILABILITY: The program is written in Turbo Pascal 7.0. The source code is available upon request. CONTACT: Wujj@nic.bmi.ac.cn or Liwj@mail.bmi.ac.cn      

RNA二级结构的最小自由能算法

RNA(即tRNA,rRNA,mRNA和SnRNA)有两大主要功能：一是某些病毒的遗传物质;二是参与蛋白质的合成,这些与细胞分化、代谢、记忆的储存等有重要关系,这些功能与RNA二级结构的稳定性。自由能密切相关．常用的计算自由能的方法有热力学微扰法及热力学微积分法等．本文以寻找最小自由能二级结构为目的,给出了RNA二级结构的最小自由能算法,该算法的时间复杂性不超过O(n^4)。     

Parsing nucleic acid pseudoknotted secondary structure: algorithm and applications.

Accurate prediction of pseudoknotted nucleic acid secondary structure is an important computational challenge. Prediction algorithms based on dynamic programming aim to find a structure with minimum free energy according to some thermodynamic ("sum of loop energies") model that is implicit in the recurrences of the algorithm. However, a clear definition of what exactly are the loops in pseudoknotted structures, and their associated energies, has been lacking. In this work, we present a complete classification of loops in pseudoknotted nucleic secondary structures, and describe the Rivas and Eddy and other energy models as sum-of-loops energy models. We give a linear time algorithm for parsing a pseudoknotted secondary structure into its component loops. We give two applications of our parsing algorithm. The first is a linear time algorithm to calculate the free energy of a pseudoknotted secondary structure. This is useful for heuristic prediction algorithms, which are widely used since (pseudoknotted) RNA secondary structure prediction is NP-hard. The second application is a linear time algorithm to test the generality of the dynamic programming algorithm of Akutsu for secondary structure prediction.Together with previous work, we use this algorithm to compare the generality of state-of-the-art algorithms on real biological structures.     

Structural changes and fluctuations of proteins: I. A statistical thermodynamic model

A general theory of the structural changes and fluctuations of proteins has been proposed based on statistical thermodynanic considerations at the chain level.The “structure” of protein was assumed to be characterized by the state of secondary bonds between unique pairs of specific sites on peptide chains. Every secondary bond changes between the bonded and unboned states by thermal agitation and the “structure” is continuously fluctuating. The free energy of the “structural state” that is defined by the fraction of secondary bonds in the bonded state has been expressed by the bond energy, the cooperative interaction between bonds, the mixing entropy of bonds, and the entropy of polypeptide chains. The most probable “structural state” can be simply determined by graphical analysis and the effect of temperature or solvent composition on it is discussed. The temperature dependence of the free energy, the probability distribution of structural states and the specific heat have been calculated for two examples of structural change.The theory predicts two different types of structural changes from the ordered to disordered state, a “structural transition” and a “gradual structural change” with rising temperature, In the “structural transition”, the probability distribution has two maxima in the temperature range of transition. In the “gradual structural change”, the probability distribution has only one maximum during the change.A considerable fraction of secondary bonds is in the unbonded state and is always fluctuating even in the ordered state at room temperature. Such structural fluctuations in a single protein molecule have been discussed quantitatively.The theory is extended to include small molecules which bind to the protein molecule and affect the structural state. The changes of structural state caused by specific and non-specific binding and allosteric effects are explained in a unified manner.     

长苞铁杉nrDNA内转录间隔区及5.8S的二级结构分析研究

核糖体RNA及相邻区域的二级结构研究,作为一个重要的工具,已在一些分类等级上被应用于系统发育的分析。以长苞铁杉为实验材料,通过克隆、测序,利用最小自由能原理预测nrDNA内转录间隔区及5.8S转录本的二级结构,分析它们的结构特点,探讨假基因化拷贝与功能拷贝结构上的差异。分析结果表明:(1)ITS1区的二级结构主要由几个延展的发夹结构组成,配对的亚重复单位在松科植物特有的保守序列处有部分重叠,未配对的亚重复单位通常能自身折叠,保守序列的部分碱基出现在发夹结构的环中;(2)假基因化拷贝二级结构的自由能比正常拷贝高;(3)与正常拷贝的二级结构相比,假基因化拷贝在进化速率很低的5.8S功能区发生较大的变异,且在5.8 S末端没有和26 S连接配对。     

Structural analysis of a group II intron by chemical modifications and minimal energy calculations.

Folding of the yeast mitochondrial group II intron aI5c has been analysed by chemical modification of the in vitro synthesised RNA with dimethylsulfate and diethylpyrocarbonate. Computer calculations of the intron secondary structure through minimization of free energy were also performed in order to study thermodynamic properties of the intron and to relate these to data obtained from chemical modification. Comparison of the two sets of data with the current phylogenetic model structure of the intron aI5 reveals close agreement, thus lending strong support for the existence of a typical group II intron core structure comprising six neighbouring stem-loop domains. Local discrepancies between the experimental data and the model structures have been analyzed by reference to thermodynamic properties of the structure. This shows that use of the latest refined set of free energy values improves the structure calculation significantly.     

Dependence among sites in RNA evolution

Although probabilistic models of genotype (e.g., DNA sequence) evolution have been greatly elaborated, less attention has been paid to the effect of phenotype on the evolution of the genotype. Here we propose an evolutionary model and a Bayesian inference procedure that are aimed at filling this gap. In the model, RNA secondary structure links genotype and phenotype by treating the approximate free energy of a sequence folded into a secondary structure as a surrogate for fitness. The underlying idea is that a nucleotide substitution resulting in a more stable secondary structure should have a higher rate than a substitution that yields a less stable secondary structure. This free energy approach incorporates evolutionary dependencies among sequence positions beyond those that are reflected simply by jointly modeling change at paired positions in an RNA helix. Although there is not a formal requirement with this approach that secondary structure be known and nearly invariant over evolutionary time, computational considerations make these assumptions attractive and they have been adopted in a software program that permits statistical analysis of multiple homologous sequences that are related via a known phylogenetic tree topology. Analyses of 5S ribosomal RNA sequences are presented to illustrate and quantify the strong impact that RNA secondary structure has on substitution rates. Analyses on simulated sequences show that the new inference procedure has reasonable statistical properties. Potential applications of this procedure, including improved ancestral sequence inference and location of functionally interesting sites, are discussed.     

Dynalign: an algorithm for finding the secondary structure common to two RNA sequences

With the rapid increase in the size of the genome sequence database, computational analysis of RNA will become increasingly important in revealing structure-function relationships and potential drug targets. RNA secondary structure prediction for a single sequence is 73 % accurate on average for a large database of known secondary structures. This level of accuracy provides a good starting point for determining a secondary structure either by comparative sequence analysis or by the interpretation of experimental studies. Dynalign is a new computer algorithm that improves the accuracy of structure prediction by combining free energy minimization and comparative sequence analysis to find a low free energy structure common to two sequences without requiring any sequence identity. It uses a dynamic programming construct suggested by Sankoff. Dynalign, however, restricts the maximum distance, M, allowed between aligned nucleotides in the two sequences. This makes the calculation tractable because the complexity is simplified to O(M(3)N(3)), where N is the length of the shorter sequence.The accuracy of Dynalign was tested with sets of 13 tRNAs, seven 5 S rRNAs, and two R2 3' UTR sequences. On average, Dynalign predicted 86.1 % of known base-pairs in the tRNAs, as compared to 59.7 % for free energy minimization alone. For the 5 S rRNAs, the average accuracy improves from 47.8 % to 86.4 %. The secondary structure of the R2 3' UTR from Drosophila takahashii is poorly predicted by standard free energy minimization. With Dynalign, however, the structure predicted in tandem with the sequence from Drosophila melanogaster nearly matches the structure determined by comparative sequence analysis.     

Boltzmann probability of RNA structural neighbors and riboswitch detection

MOTIVATION: We describe algorithms implemented in a new software package, RNAbor, to investigate structures in a neighborhood of an input secondary structure S of an RNA sequence s. The input structure could be the minimum free energy structure, the secondary structure obtained by analysis of the X-ray structure or by comparative sequence analysis, or an arbitrary intermediate structure. RESULTS: A secondary structure T of s is called a delta-neighbor of S if T and S differ by exactly delta base pairs. RNAbor computes the number (N(delta)), the Boltzmann partition function (Z(delta)) and the minimum free energy (MFE(delta)) and corresponding structure over the collection of all delta-neighbors of S. This computation is done simultaneously for all delta < or = m, in run time O (mn3) and memory O(mn2), where n is the sequence length. We apply RNAbor for the detection of possible RNA conformational switches, and compare RNAbor with the switch detection method paRNAss. We also provide examples of how RNAbor can at times improve the accuracy of secondary structure prediction. AVAILABILITY: http://bioinformatics.bc.edu/clotelab/RNAbor/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Trypanosoma congolense: structure and molecular organization of the surface glycoproteins of two early bloodstream variants

The complete primary structures of two variant specific glycoproteins (VSGs) of the nannomonad Trypanosoma (N.) congolense are presented. These coat proteins subserve the function of antigenic variation. The secondary structure potentials of both VSGs have been calculated. The amino acid sequences and secondary structure potentials of these VSGs have been compared with the primary structures and secondary structure potentials of several Trypanosoma brucei complex VSGs. In homologous regions, the T. brucei complex VSGs show a pattern of sharply contrasting secondary structure potentials. It has been suggested previously that this pattern gives rise to different folding structures in different members of this polygene protein family. Thus, different short regions of the polypeptide sequence are exposed as antigenic "caps" on the solvent-exposed surface of intact trypanosomes. A sharply contrasting secondary structure potential pattern is also found in regions of the two T. congolense VSGs. However, there is little homology of primary structure between each of the two T. congolense VSGs and any member of the T. brucei complex VSG polygene family whose primary structure has been determined.     

Calculation of the relative binding free energy of 2'GMP and 2'AMP to ribonuclease T1 using molecular dynamics/free energy perturbation approaches

We present a calculation of the relative changes in binding free energy between the complex of ribonuclease T1 (RNase Tr) with its inhibitor 2'-guanosine monophosphate (2'GMP) and that of RNase T1-2'-adenosine monophosphate (2'AMP) by means of a thermodynamic perturbation method implemented with molecular dynamics. Using the available crystal structure of the RNase T1-2'GMP complex, the structure of the RNase T1-2'AMP complex was obtained as a final structure of the perturbation calculation. The calculated difference in the free energy of binding (delta delta Gbind) was 2.76 kcal/mol. This compares well with the experimental value of 3.07 kcal/mol. The encouraging agreement in delta delta Gbind suggests that the interactions of inhibitors with the enzyme are reasonably represented. Energy component analyses of the two complexes reveal that the active site of RNase T1 electrostatically stabilizes the binding of 2'GMP more than that of 2'AMP by 44 kcal/mol, while the van der Waals' interactions are similar in the two complexes. The analyses suggest that the mutation from Glu46 to Gln may lead to a preference of RNase T1 for adenine in contrast to the guanine preference of the wild-type enzyme. Although the molecular dynamics equilibration moves the atoms of the RNase T1-2'GMP system about 0.9 A from their X-ray positions and the mutation of the G to A in the active site increases the deviation from the X-ray structure, the mutation of the A back to G reduces the deviation. This and the agreement found for delta delta Gbind suggest that the molecular dynamics/free energy perturbation method will be useful for both energetic and structural analysis of protein-ligand interactions.     

基于堆积协变信息与最小自由能预测含伪结的RNA二级结构

RNA伪结预测是RNA研究的一个难点问题。文中提出一种基于堆积协变信息与最小自由能的RNA伪结预测方法。该方法使用已知结构的RNA比对序列(ClustalW比对和结构比对)测试此方法, 侧重考虑相邻碱基对之间相互作用形成的堆积协变信息, 并结合最小自由能方法对碱基配对综合评分, 通过逐步迭代求得含伪结的RNA二级结构。结果表明, 此方法能正确预测伪结, 其平均敏感性和特异性优于参考算法, 并且结构比对的预测性能比ClustalW比对的预测性能更加稳定。文中同时讨论了不同协变信息权重因子对预测性能的影响, 发现权重因子比值在l1: l2=5:1时, 预测性能达到最优。     

Thermodynamics of the ColE1 cruciform. Comparisons between probing and topological experiments using single topoisomers

The sensitivity of the ColE1 cruciform to four enzyme and chemical probes of secondary structure has been studied as a function of plasmid topology. Purified topoisomers of pColIR515 have been probed with S1 nuclease, Bal31 nuclease, phage T4 endonuclease VII or osmium tetroxide, and site-specific reaction quantified. Closely similar profiles of reactivity as a function of linking difference were obtained for each probe. Electrophoresis of the pure topoisomers on polyacrylamide/agarose gels revealed a discontinuity in migration as a function of linking difference. Above a threshold linking difference, topoisomers exhibit pronounced reduction in mobility. The linking difference at which this band shift is found correlates precisely with that required for site-specific reaction with the four probes. We conclude that both probing and topological methods are valuable in the study of cruciform structure in supercoiled DNA. The band shift has been measured with accuracy to allow the calculation of the twist change that accompanies the transition, corresponding to delta Tw = -3.2 +/- 0.1. Using this value together with the critical linking difference we calculate a free energy of formation for this structure delta G = 18.4 +/- 0.5 kcal mol-1 (1 kcal = 4.184 kJ).     

Energy landscape of k-point mutants of an RNA molecule

MOTIVATION: A k-point mutant of a given RNA sequence s = s(1), ..., s(n) is an RNA sequence s' = s'(1),..., s'(n) obtained by mutating exactly k-positions in s; i.e. Hamming distance between s and s' equals k. To understand the effect of pointwise mutation in RNA, we consider the distribution of energies of all secondary structures of k-point mutants of a given RNA sequence. RESULTS: Here we describe a novel algorithm to compute the mean and standard deviation of energies of all secondary structures of k-point mutants of a given RNA sequence. We then focus on the tail of the energy distribution and compute, using the algorithm AMSAG, the k-superoptimal structure; i.e. the secondary structure of a < or =k-point mutant having least free energy over all secondary structures of all k'-point mutants of a given RNA sequence, for k' < or = k. Evidence is presented that the k-superoptimal secondary structure is often closer, as measured by base pair distance and two additional distance measures, to the secondary structure derived by comparative sequence analysis than that derived by the Zuker minimum free energy structure of the original (wild type or unmutated) RNA.     

A simple molecular model for thermophilic adaptation of functional nucleic acids

RNA molecules have numerous functions including catalysis and small molecule recognition, which typically arise from a tertiary structure. There is increasing interest in mechanisms for the thermostability of functional RNA molecules. Sosnick, Pan, and co-workers introduced the notion of "functional stability" as the free energy of the tertiary (functional) state relative to the next most stable (nonfunctional) state. We investigated the extent to which secondary structure stability influences the functional stability of nucleic acids. Intramolecularly folding DNA triplexes containing alternating T*AT and C+*GC base triples were used as a three-state model for the folding of nucleic acids with functional tertiary structures. A four-base-pair tunable region was included adjacent to the triplex-forming portion of the helix to allow secondary structure strength to be modulated. The degree of folding cooperativity was controlled by pH, with high cooperativity maintained by lower pH (5.5), and no cooperativity by higher pH (7.0). We find a linear relationship between functional free energy and the free energy of the secondary structure element adjacent to tertiary interactions, but only when folding is cooperative. We translate the definition of functional stability into equations and perform simulations of the thermodynamic data, which lend support to this model. The ability to increase the melting temperature of tertiary structure by strengthening base-pairing interactions separate from tertiary interactions provides a simple means for evolving thermostability in functional RNAs.