MODENA: a multi-objective RNA inverse folding

With an increase in the number of known biological functions of non-coding RNAs, the importance of RNA sequence alignment has risen. RNA sequence alignment problem has been investigated by many researchers as a mono-objective optimization problem where contributions from sequence similarity and secondary structure are taken into account through a single objective function. Since there is a trade-off between these two objective functions, usually we cannot obtain a single solution that has both the best sequence similarity score and the best structure score simultaneously. Multi-objective optimization is a widely used framework for the optimization problems with conflicting objective functions. So far, no one has examined how good alignments we can obtain by applying multi-objective optimization to structural RNA sequence alignment problem. We developed a pairwise RNA sequence alignment program, Cofolga2mo, based on multi-objective genetic algorithm (MOGA). We tested Cofolga2mo with a benchmark dataset which includes sequence pairs with a wide range of sequence identity, and we obtained at most 100 alignments for each inputted RNA sequence pair as an approximate set of weak Pareto optimal solutions. We found that the alignments in the approximate set give benchmark results comparable to those obtained by the state-of-the-art mono-objective RNA alignment algorithms. Moreover, we found that our algorithm is efficient in both time and memory usage compared to the other methods. Our MOGA programs for structural RNA sequence alignment can be downloaded at http://rna.eit.hirosaki-u.ac.jp/cofolga2mo/.

BackgroundRNA inverse folding is the problem of finding one or more sequences that fold into a user-specified target structure s0, i.e. whose minimum free energy secondary structure is identical to the target s0. Here we consider the ensemble of all RNA sequences that have low free energy with respect to a given target s0.ResultsWe introduce the program RNAdualPF, which computes the dual partition functionZ∗, defined as the sum of Boltzmann factors exp(−E(a,s0)/RT) of all RNA nucleotide sequences a compatible with target structure s0. Using RNAdualPF, we efficiently sample RNA sequences that approximately fold into s0, where additionally the user can specify IUPAC sequence constraints at certain positions, and whether to include dangles (energy terms for stacked, single-stranded nucleotides). Moreover, since we also compute the dual partition functionZ∗(k) over all sequences having GC-content k, the user can require that all sampled sequences have a precise, specified GC-content.Using Z∗, we compute the dual expected energy 〈E∗〉, and use it to show that natural RNAs from the Rfam 12.0 database have higher minimum free energy than expected, thus suggesting that functional RNAs are under evolutionary pressure to be only marginally thermodynamically stable.We show that C. elegans precursor microRNA (pre-miRNA) is significantly non-robust with respect to mutations, by comparing the robustness of each wild type pre-miRNA sequence with 2000 [resp. 500] sequences of the same GC-content generated by RNAdualPF, which approximately [resp. exactly] fold into the wild type target structure. We confirm and strengthen earlier findings that precursor microRNAs and bacterial small noncoding RNAs display plasticity, a measure of structural diversity.ConclusionWe describe RNAdualPF, which rapidly computes the dual partition functionZ∗ and samples sequences having low energy with respect to a target structure, allowing sequence constraints and specified GC-content. Using different inverse folding software, another group had earlier shown that pre-miRNA is mutationally robust, even controlling for compositional bias. Our opposite conclusion suggests a cautionary note that computationally based insights into molecular evolution may heavily depend on the software used.C/C++-software for RNAdualPF is available at http://bioinformatics.bc.edu/clotelab/RNAdualPF.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1280-6) contains supplementary material, which is available to authorized users.

The importance of non-coding RNAs and their informatics tools has grown for a decade due to a drastic increase of known non-coding RNAs. RNA sequence alignment is one of the most important technologies in such informatics tools. Recently, we have proposed a multi-objective genetic algorithm, Cofolga2mo, for obtaining an approximate set of weak Pareto optimal solutions for global pairwise RNA sequence alignment, where a sequence similarity and a secondary structure contribution are taken into account as objective functions. In the present study, we have developed a web server for obtaining RNA sequence alignments by Cofolga2mo and for assisting the decision making from the alignments. Furthermore, we introduced an index for reducing the number of alignments output by Cofolga2mo. As a result, we successfully reduced the maximum number of alignments for an input RNA sequence pair from fifty to ten without a significant loss of accurate alignments. By using the BRAliBase 2.1 benchmark dataset, we show that a set of alignments output by Cofolga2mo for an input RNA sequence pair, which has at most ten alignments, includes an accurate alignment compared to those of the previous mono-objective RNA sequence alignment programs.

The tremendous demand on computer memory and computing time for prediction of complex secondary structures limits the applicability of most RNA secondary structure prediction programs available to short RNA sequences. We propose to approach this problem by segmenting a long RNA sequence into shorter non-overlapping chunks, predicting the secondary structures of each chunk individually, and then assembling the prediction results to give the structure of the original sequence. The selection of cutting points is a crucial component of the approach. Noting that stem-loops and pseudoknots always contain an inversion, we developed two cutting methods, the centered and optimized methods, for segmenting long RNA sequences based on inversion excursions. For the majority of the sequences in a dataset of 50 RNAs from the RFAM database, the prediction algorithm PKnotsRG used with these cutting methods produces more accurate secondary structures than those predicted for the whole sequence without segmentation. Both the centered and optimized cutting methods outperform the naïve regular segmentation. These results support our claim that cutting is a promising approach for the prediction of long RNA sequences, and choosing the cutting points intelligently by considering sequence features such as inversion excursions can further enhance prediction accuracy.

Stochastic context-free grammars (SCFGs) have been applied to predicting RNA secondary structure. The prediction of RNA secondary structure can be facilitated by incorporating with comparative sequence analysis. However, most of existing SCFG-based methods lack explicit phylogenic analysis of homologous RNA sequences, which is probably the reason why these methods are not ideal in practical application. Hence, we present a new SCFG-based method by integrating phylogenic analysis with the newly defined profile SCFG. The method can be summarized as: 1) we define a new profile SCFG, M, to depict consensus secondary structure of multiple RNA sequence alignment; 2) we introduce two distinct hidden Markov models, λ and λ′, to perform phylogenic analysis of homologous RNA sequences. Here, λ is for non-structural regions of the sequence and λ′, is for structural regions of the sequence; 3) we merge λ and λ′, into M to devise a combined model for prediction of RNA secondary structure. We tested our method on data sets constructed from the Rfam database. The sensitivity and specificity of our method are more accurate than those of the predictions by Pfold.

RNA secondary structures are known to be important in many biological processes. Many available programs have been developed for RNA secondary structure prediction. Based on our knowledge, however, there still exist secondary structures of known RNA sequences which cannot be covered by these algorithms. In this paper, we provide an efficient algorithm that can handle all RNA secondary structures found in Rfam database. We designed a new stochastic context-free grammar named Rectangle Tree Grammar (RTG) which significantly expands the classes of structures that can be modelled. Our algorithm runs in O(n 6) time and the accuracy is reasonably high, with average PPV and sensitivity over 75%. In addition, the structures that RTG predicts are very similar to the real ones.

The RNAmute and MultiRNAmute interactive java programs were developed to predict deleterious point mutations in RNA sequences, which intently cause a global conformational rearrangement of the secondary structure of the functional RNA molecules and thereby disrupt their function. RNAmute was designed to deal with only single point mutations in a brute force manner, while the MultiRNAmute tool uses an efficient approach to deal with multiple point mutations. The approach used in MultiRNAmute is based on the stabilization of the suboptimal RNA folding solutions and/or destabilization of the optimal MFE structure of the wild type RNA molecule. Both programs utilize the Vienna RNA package to find the optimal and suboptimal (in case of MultiRNAmute) RNA secondary structures. The main limitation of both programs is their ability to predict only substitution mutations and these programs were not designed to work with deletion or insertion mutations. Herein we develop an efficient approach, based on suboptimal folding solutions, to predict multiple point mutations consisting of deletions, insertions and substitution mutations. All RNAmute algorithms were validated on the TPP-riboswitch and some other functional RNAs.

Optimal design of hysteretic dampers connecting adjacent structures using multi-objective genetic algorithm and stochastic linearization method

Motivation: Secondary structure prediction of RNA sequences is an important problem. There have been progresses in this area, but the accuracy of prediction from an RNA sequence is still limited. In many cases, however, homologous RNA sequences are available with the target RNA sequence whose secondary structure is to be predicted.Results: In this article, we propose a new method for secondary structure predictions of individual RNA sequences by taking the information of their homologous sequences into account without assuming the common secondary structure of the entire sequences. The proposed method is based on posterior decoding techniques, which consider all the suboptimal secondary structures of the target and homologous sequences and all the suboptimal alignments between the target sequence and each of the homologous sequences. In our computational experiments, the proposed method provides better predictions than those performed only on the basis of the formation of individual RNA sequences and those performed by using methods for predicting the common secondary structure of the homologous sequences. Remarkably, we found that the common secondary predictions sometimes give worse predictions for the secondary structure of a target sequence than the predictions from the individual target sequence, while the proposed method always gives good predictions for the secondary structure of target sequences in all tested cases.Availability: Supporting information and software are available online at: http://www.ncrna.org/software/centroidfold/ismb2009/.Contact: hamada-michiaki@aist.go.jpSupplementary information:Supplementary data are available at Bioinformatics online.

Most practical problems are formulated as multiobjective optimization problems (MOP) so as to meet the diversified demands of a decision maker. Usually, there is a trade-off relation among objective functions, and thus there does not necessarily exist the solution that optimizes all objective functions simultaneously in MOP. Therefore, Pareto optimal solution is used as a definition of solution to MOP. Recently, evolutionary algorithms have been developed remarkably in order to obtain approximate solutions to optimization problems. Particularly, multiobjective genetic algorithms (MOGA) have been developed for generating Pareto optimal solutions. However, there are two problems in MOGA: how to assign the fitness to individuals, and how to keep the diversification of individuals. Many existing MOGAs have made an effort in order to overcome these problems, and so does this paper. First, this paper suggests a fitness function in MOGA using generalized data envelopment analysis (GDEA) which was suggested for evaluating the relative efficiency of individuals under several items of assessment management science. It is shown that the GDEA method can approximate Pareto optimal solutions more effectively and faster than the ranking method which is mostly used in MOGA, and generate well-distributed Pareto optimal solutions. Furthermore, this paper suggests the aspiration-level based GDEA method to generate the most interesting part (not the whole Pareto optimal solutions) to an aspiration level of decision maker for choosing a final solution from many Pareto optimal solutions. Finally, this paper illustrates the effectiveness of the methods using GDEA through several numerical examples.

It is known that for two given secondary structures (defined by position of base pairings) an RNA string can easily be found that can fold into both structures. But for more than two secondary structures this is not necessarily possible. Moreover, when four or more secondary structures are given the problem to determine the least number of positions, such that after the removal of all incident base pairs, a compatible RNA sequence can be found, is known to be NP-complete (\cite{real_shapes}). In this paper we introduce pseudo edges that are used to forbid that certain base pairs can bind and therefore can be used to define the properties of possible RNA secondary structures. We study the complexity of the problem to design an RNA sequence that can fold into different secondary structures each of them is described by a set of required and forbidden base pairs. We refine the NP-completeness results of \cite{real_shapes} and show an analoguous NP-completeness result for the realization problem concerning the removal of (pseudo) edges. We also present a polynomial time method for checking the realizability of extended shape graphs. Furthermore, we empirically analyze the influence of pseudo edges on the realizability for sets of random RNA sequences and for sets of aptamers.

RNA has become an integral building material in synthetic biology. Dominated by their secondary structures, which can be computed efficiently, RNA molecules are amenable not only to in vitro and in vivo selection, but also to rational, computation-based design. While the inverse folding problem of constructing an RNA sequence with a prescribed ground-state structure has received considerable attention for nearly two decades, there have been few efforts to design RNAs that can switch between distinct prescribed conformations. We introduce a user-friendly tool for designing RNA sequences that fold into multiple target structures. The underlying algorithm makes use of a combination of graph coloring and heuristic local optimization to find sequences whose energy landscapes are dominated by the prescribed conformations. A flexible interface allows the specification of a wide range of design goals. We demonstrate that bi- and tri-stable "switches" can be designed easily with moderate computational effort for the vast majority of compatible combinations of desired target structures. RNAdesign is freely available under the GPL-v3 license.

Classification of RNA Secondary Structures Using the Techniques of Cluster Analysis

Cellular Manufacturing (CM) is an important application of Group Technology (GT) in which families of parts are produced in manufacturing cells or a group of various machines, which are physically close together and can entirely process a part family. The manufacturing system established based on such an idea is called Cellular Manufacturing System (CMS). A major problem associated with many CMSs is the existence of Exceptional Elements (EEs), i.e. bottleneck machines and exceptional parts. These are machines/parts that cannot be exclusively assigned to a machine cell/part family. In this paper a new model is presented for dealing with the EEs in the form of a Multi-objective Optimization Problem (MOP). This model aims to minimize: (1) intercellular parts movements, (2) total cost needed for machine duplication and part subcontracting, (3) the system's under-utilization, and (4) deviations among the cells' utilization. Attaining an ideal solution, which is optimal to all of the objectives is prohibited, as they conflict with each other. Hence, a Multi-Objective Genetic Algorithm (MOGA) is developed to provide the decision-maker with a set of non-dominated or Pareto-optimal solutions. Comparisons between the developed MOGA and three other MOGAs show its viability in three performance aspects, namely: quality, diversity and CPU time.

Multi-objective genetic algorithm (MOGA) and a data mining technique were applied to the multidisciplinary design optimization (MDO) of a hybrid rocket. In this study, a swirling-oxidizer-type hybrid rocket engine with a single cylindrical grain port was designed. MOGA was applied to solve the multi-objective problem using real-number cording and the Pareto ranking method. In this study, two objective functions were considered: one maximized the flight altitude and the other minimized the gross weight. Each objective function was empirically estimated. Many non-dominated solutions were obtained using MOGA, and a trade-off was observed between the two objective functions. To better understand the design problem, the MOGA results were visualized using a scatter plot matrix (SPM) and a data mining technique.