Abstract Introduction The tumor microenvironment (TME) is a complex ecosystem where cellular interactions are spatially governed. Spatial transcriptomics (ST) technologies, sequencing-based Visium which only have spot level resolution and imaging-based Xenium which are limited by a small RNA panel, probe the complexity, but high dimensional data interpretation remains a challenge [1]. Current analyses rely on pre-defined cell annotation patterns, critically failing to account for higher-order structures in gene co-expression and cell co-localization [2]. Biologically, cellular function is defined by coordinated gene modules, not individual genes, and these relationships exhibit a hierarchical organization across multiple spatial scales. A simple gene expression matrix is insufficient to capture this multi-scale and hierarchical structure of gene–gene and cell–cell interactions, especially given that TME niches are highly variable and context-dependent, difficultly to make a fixed scale definition. Furthermore, the order of cells in discrete gene expression matrices can affect the ability of neural networks to analyze cell–cell interactions. To overcome this, we introduce CoSMIM (Covariance of Spatial Multi-scale Integrated Microenvironment) matrix. Our hypothesis is that gene–gene covariance matrices, computed across multiple scales of neighbor cells, provide a richer representation of the TME’s spatial heterogeneity functional architecture. We use a multi-decoder conditional variational autoencoder(CVAE) to learn a unified latent space for consistent cross-scale modeling. Its architecture can impute genes in targeted spatial panels and infer spatial covariance matrices for non-spatial single-cell data, thus bridging these modalities. Methodology Our framework consists of two core components: the construction of a CoSMIM niche representation and a CVAE generative model for learning a unified representation. The input to our method is ST data from dataset HEST-1 k and 10X human-breast cancer FFPE dataset [3,4] which has various ST platforms such as Visium, Xenium, CosMx, or MERFISH. The specific steps are as follows (Fig. 1b): Definition and construction of multi-scale neighborhoods Tumor spatial heterogeneity is not random but is driven by the organizational patterns of cellular communities at different scales. Precisely defining cellular niches within ST data remains a key challenge. Given the heterogeneity in cell size, defining neighborhoods using a fixed number of cells or a constant radius has limitations [5]. We propose an adaptive approach that constructs neighborhoods through a learned linear combination of different biological scales (Fig. 2&Eq.2). We predefine a series of spatial neighborhood representing distinct biological interaction ranges. The gene expression matrix of whole tissue is $\mathrm{X}\in{R}^{n\times g}$, $n$ is the number of cells and $\mathrm{g}$ is number of genes. Each cell has a muti-scale niches matrix ${E}_k^i\in{R}^{k\times g}\left(\mathrm{e}.\mathrm{g}.\mathrm{k}\in \mathrm{K}\left\{\mathrm{5,15,50}\right\}\right)$ of $k$ nearest neighbor cells (excluding the target cell $i$ itself). Let $\mathrm{Cov}\in{\mathrm{R}}^{g\times g}$ be the target cell $i$’s gene–gene covariance of $k$ nearest neighbor cells. $\overline{X}$ global mean gene expression of gene g and $\overline{E_k}$ is $k$ scale niche’s mean gene expression. We then evaluate and optimize the selection of these scales $K$ based on the discriminatory power of their corresponding eigenvalues in principal component analysis. These scales correspond to different biological contexts: Small-scale (5–15 cells) Primarily captures direct signaling and short-range paracrine signaling, such as direct contact between a tumor cell and an adjacent immune cell PD-1/PD-L1 or local growth factor support from a Cancer-Associated Fibroblast. Medium-scale (15–50 cells) Reflects the characteristics of a functional niche, such as an immunosuppressive or pro-angiogenic ‘community’ composed of several tumor, immune, and stromal cells. Large-scale (>$50cells) Characterizes the tissue region state, such as broad hypoxic zones, regions of lymphocytic infiltration, or fibrotic stromal areas, which are often governed by diffusive chemical gradients or physical barriers. The scale weights are learned by entropy-regularized log-det minimization: With $\varepsilon >0$ for numerical stability and $\lambda \ge 0$ (larger $\lambda \Rightarrow$ more uniform $w$; smaller $\lambda \Rightarrow$ more concentrated $w$). The weighted CoSMIM matrix can be conceptualized as a ‘multi-scale spatial fingerprint’ of a niche. Using the progression of breast cancer from Ductal Carcinoma in Situ (DCIS) to Invasive Ductal Carcinoma (IDC) as an example, we hypothesize that this spatial fingerprint undergoes a specific transformation. In the DCIS stage, cancer cells are confined within the duct. Their microenvironmental communication is dominated by small-scale interactions, and thus the CoSMIM-learned weights are likely biased towards smaller scales. Upon progression to IDC, cancer cells breach the basement membrane, initiating large-scale invasion, remodeling the surrounding stroma, inducing angiogenesis, and interacting with broader immune populations, leading to infiltration and fibrosis. At this stage, medium and large-scale interactions become critically important. Therefore, this learned and quantifiable shift in scale weights has the potential to serve as an early biomarker for assessing invasion risk in breast cancer. Traditional cell/spot-gene expression matrices are sensitive to the ordering of cells, which impacts model robustness. We employ a feature representation that is invariant to cell permutation, the gene–gene correlation covariance matrix. Beyond Ligand-Receptor Pair Analysis Conventional Ligand-Receptor (L-R) analysis often focuses on the co-expression of a few L-R pairs, overlooking downstream signaling cascades. The covariance matrix excels at capturing the holistic activation state of an entire ‘signaling module.’ Capturing Long- and Short-Range Signaling When calculating the CoSMIM covariance, we use the global mean gene expression as the centering baseline [Fig. 1a], rather than the conventional local neighborhood mean. This design enables CoSMIM to not only capture local signaling patterns reflecting autocrine, paracrine, and juxtacrine modes but also to identify long-range endocrine signaling between spatially distant cells in a tissue sample. Result and conclusion In a direct comparison using human breast cancer transcriptomes, our CoSMIM framework demonstrated superior accuracy over traditional covariance methods in defining the spatial interactome (Fig. 3). While both approaches pinpointed the well-established endothelial–immune axis, marked by strong PECAM1–CD93 and CLEC14A–CD93 co-expression, only CoSMIM could confirm that this interaction was a fundamental architectural feature, persisting across all spatial scales. This finding validates CD93 as a stable regulator of the angiogenic and immune-suppressive barrier. Traditional covariance analysis once suggested a highly correlated expression network linking NOSTRIN with genes involved in matrix remodeling (MMP2), cell proliferation (KLF5), and metabolism (SQLE) (Fig. 3). However, CoSMIM revealed that this apparent high correlation was likely a false-positive signal driven by spatial heterogeneity, and no strong correlation exists within its multiscale spatial niche. By confirming genuine interactions while systematically eliminating such spatial artifacts, CoSMIM offers a profoundly clearer view of the breast cancer microenvironment. It moves beyond simple co-expression to identify mechanistically robust signaling axes, providing a high-fidelity roadmap for prioritizing novel therapeutic targets. References 1. Haviv D., Remšík J., Gatie E.A.A. et al. ‘The Covariance Environment Defines Cellular Niches for Spatial Inference.’ Nature Biotechnology 2025;43:269–280. 2. Kojima Y. et al. ‘Single-Cell Colocalization Analysis Using a Deep Generative Model.’ Cell Systems 2024;15:180–192.e7.

The identification of cancer subtypes can help researchers understand hidden genomic mechanisms, enhance diagnostic accuracy and improve clinical treatments. With the development of high-throughput techniques, researchers can access large amounts of data from multiple sources. Because of the high dimensionality and complexity of multiomics and clinical data, research into the integration of multiomics data is needed, and developing effective tools for such purposes remains a challenge for researchers. In this work, we proposed an entirely unsupervised clustering method without harnessing any prior knowledge (MODEC). We used manifold optimization and deep-learning techniques to integrate multiomics data for the identification of cancer subtypes and the analysis of significant clinical variables. Since there is nonlinearity in the gene-level datasets, we used manifold optimization methodology to extract essential information from the original omics data to obtain a low-dimensional latent subspace. Then, MODEC uses a deep learning-based clustering module to iteratively define cluster centroids and assign cluster labels to each sample by minimizing the Kullback-Leibler divergence loss. MODEC was applied to six public cancer datasets from The Cancer Genome Atlas database and outperformed eight competing methods in terms of the accuracy and reliability of the subtyping results. MODEC was extremely competitive in the identification of survival patterns and significant clinical features, which could help doctors monitor disease progression and provide more suitable treatment strategies.

MOTIVATION: Evolve and resequence (E&R) experiments show promise in capturing real-time evolution at genome-wide scales, enabling the assessment of allele frequency changes SNPs in evolving populations and thus the estimation of population genetic parameters in the Wright-Fisher model (WF) that quantify the selection on SNPs. Currently, these analyses face two key difficulties: the numerous SNPs in E&R data and the frequent unreliability of estimates. Hence, a methodology for efficiently estimating WF parameters is needed to understand the evolutionary processes that shape genomes. RESULTS: We developed a novel method for estimating WF parameters (EMWER), by applying an expectation maximization algorithm to the Kolmogorov forward equation associated with the WF model diffusion approximation. EMWER was used to infer the effective population size, selection coefficients and dominance parameters from E&R data. Of the methods examined, EMWER was the most efficient method for selection strength estimation in multi-core computing environments, estimating both selection and dominance with accurate confidence intervals. We applied EMWER to E&R data from experimental Drosophila populations adapting to thermally fluctuating environments and found a common selection affecting allele frequency of many SNPs within the cosmopolitan In(3R)P inversion. Furthermore, this application indicated that many of beneficial alleles in this experiment are dominant. AVAILABILITY AND IMPLEMENTATION: Our C++ implementation of 'EMWER' is available at https://github.com/kojikoji/EMWER. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Recently, next-generation sequencing techniques have been applied for the detection of RNA secondary structures, which is referred to as high-throughput RNA structural (HTS) analyses, and many different protocols have been used to detect comprehensive RNA structures at single-nucleotide resolution. However, the existing computational analyses heavily depend on the experimental methodology to generate data, which results in difficulties associated with statistically sound comparisons or combining the results obtained using different HTS methods. RESULTS: Here, we introduced a statistical framework, reactIDR, which can be applied to the experimental data obtained using multiple HTS methodologies. Using this approach, nucleotides are classified into three structural categories, loop, stem/background, and unmapped. reactIDR uses the irreproducible discovery rate (IDR) with a hidden Markov model to discriminate between the true and spurious signals obtained in the replicated HTS experiments accurately, and it is able to incorporate an expectation-maximization algorithm and supervised learning for efficient parameter optimization. The results of our analyses of the real-life HTS data showed that reactIDR had the highest accuracy in the classification of ribosomal RNA stem/loop structures when using both individual and integrated HTS datasets, and its results corresponded the best to the three-dimensional structures. CONCLUSIONS: We have developed a novel software, reactIDR, for the prediction of stem/loop regions from the HTS analysis datasets. For the rRNA structure analyses, reactIDR was shown to have robust accuracy across different datasets by using the reproducibility criterion, suggesting its potential for increasing the value of existing HTS datasets. reactIDR is publicly available at https://github.com/carushi/reactIDR .

MOTIVATION: The analysis of RNA-Seq data from individual differentiating cells enables us to reconstruct the differentiation process and the degree of differentiation (in pseudo-time) of each cell. Such analyses can reveal detailed expression dynamics and functional relationships for differentiation. To further elucidate differentiation processes, more insight into gene regulatory networks is required. The pseudo-time can be regarded as time information and, therefore, single-cell RNA-Seq data are time-course data with high time resolution. Although time-course data are useful for inferring networks, conventional inference algorithms for such data suffer from high time complexity when the number of samples and genes is large. Therefore, a novel algorithm is necessary to infer networks from single-cell RNA-Seq during differentiation. RESULTS: In this study, we developed the novel and efficient algorithm SCODE to infer regulatory networks, based on ordinary differential equations. We applied SCODE to three single-cell RNA-Seq datasets and confirmed that SCODE can reconstruct observed expression dynamics. We evaluated SCODE by comparing its inferred networks with use of a DNaseI-footprint based network. The performance of SCODE was best for two of the datasets and nearly best for the remaining dataset. We also compared the runtimes and showed that the runtimes for SCODE are significantly shorter than for alternatives. Thus, our algorithm provides a promising approach for further single-cell differentiation analyses. AVAILABILITY AND IMPLEMENTATION: The R source code of SCODE is available at https://github.com/hmatsu1226/SCODE. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: RNA secondary structure around splice sites is known to assist normal splicing by promoting spliceosome recognition. However, analyzing the structural properties of entire intronic regions or pre-mRNA sequences has been difficult hitherto, owing to serious experimental and computational limitations, such as low read coverage and numerical problems. RESULTS: Our novel software, "ParasoR", is designed to run on a computer cluster and enables the exact computation of various structural features of long RNA sequences under the constraint of maximal base-pairing distance. ParasoR divides dynamic programming (DP) matrices into smaller pieces, such that each piece can be computed by a separate computer node without losing the connectivity information between the pieces. ParasoR directly computes the ratios of DP variables to avoid the reduction of numerical precision caused by the cancellation of a large number of Boltzmann factors. The structural preferences of mRNAs computed by ParasoR shows a high concordance with those determined by high-throughput sequencing analyses. Using ParasoR, we investigated the global structural preferences of transcribed regions in the human genome. A genome-wide folding simulation indicated that transcribed regions are significantly more structural than intergenic regions after removing repeat sequences and k-mer frequency bias. In particular, we observed a highly significant preference for base pairing over entire intronic regions as compared to their antisense sequences, as well as to intergenic regions. A comparison between pre-mRNAs and mRNAs showed that coding regions become more accessible after splicing, indicating constraints for translational efficiency. Such changes are correlated with gene expression levels, as well as GC content, and are enriched among genes associated with cytoskeleton and kinase functions. CONCLUSIONS: We have shown that ParasoR is very useful for analyzing the structural properties of long RNA sequences such as mRNAs, pre-mRNAs, and long non-coding RNAs whose lengths can be more than a million bases in the human genome. In our analyses, transcribed regions including introns are indicated to be subject to various types of structural constraints that cannot be explained from simple sequence composition biases. ParasoR is freely available at https://github.com/carushi/ParasoR .

BACKGROUND: Single-cell technologies make it possible to quantify the comprehensive states of individual cells, and have the power to shed light on cellular differentiation in particular. Although several methods have been developed to fully analyze the single-cell expression data, there is still room for improvement in the analysis of differentiation. RESULTS: In this paper, we propose a novel method SCOUP to elucidate differentiation process. Unlike previous dimension reduction-based approaches, SCOUP describes the dynamics of gene expression throughout differentiation directly, including the degree of differentiation of a cell (in pseudo-time) and cell fate. SCOUP is superior to previous methods with respect to pseudo-time estimation, especially for single-cell RNA-seq. SCOUP also successfully estimates cell lineage more accurately than previous method, especially for cells at an early stage of bifurcation. In addition, SCOUP can be applied to various downstream analyses. As an example, we propose a novel correlation calculation method for elucidating regulatory relationships among genes. We apply this method to a single-cell RNA-seq data and detect a candidate of key regulator for differentiation and clusters in a correlation network which are not detected with conventional correlation analysis. CONCLUSIONS: We develop a stochastic process-based method SCOUP to analyze single-cell expression data throughout differentiation. SCOUP can estimate pseudo-time and cell lineage more accurately than previous methods. We also propose a novel correlation calculation method based on SCOUP. SCOUP is a promising approach for further single-cell analysis and available at https://github.com/hmatsu1226/SCOUP.

MOTIVATION: Measuring the effects of base mutations is a powerful tool for functional and evolutionary analyses of RNA structures. To date, only a few methods have been developed for systematically computing the thermodynamic changes of RNA secondary structures in response to base mutations. RESULTS: We have developed algorithms for computing the changes of the ensemble free energy, mean energy and the thermodynamic entropy of RNA secondary structures for exhaustive patterns of single and double mutations. The computational complexities are O(NW(2)) (where N is sequence length and W is maximal base pair span) for single mutations and O(N(2)W(2)) for double mutations with large constant factors. We show that the changes are relatively insensitive to GC composition and the maximal span constraint. The mean free energy changes are bounded ~7-9 kcal/mol and depend only weakly on position if sequence lengths are sufficiently large. For tRNA sequences, the most stabilizing mutations come from the change of the 5(')-most base of the anticodon loop. We also show that most of the base changes in the acceptor stem destabilize the structures, indicating that the nucleotide sequence in the acceptor stem is highly optimized for secondary structure stability. We investigate the 22 tRNA genes in the human mitochondrial genome and show that non-pathogenic polymorphisms tend to cause smaller changes in thermodynamic variables than generic mutations, suggesting that a mutation which largely increases thermodynamic variables has higher possibility to be a pathogenic or lethal mutation. AVAILABILITY AND IMPLEMENTATION: The C++ source code of the Rchange software is available at http://www.ncrna.org/software/rchange/.

MOTIVATION: Measuring evolutionary conservation is a routine step in the identification of functional elements in genome sequences. Although a number of studies have proposed methods that use the continuous time Markov models (CTMMs) to find evolutionarily constrained elements, their probabilistic structures have been less frequently investigated. RESULTS: In this article, we investigate a sufficient statistic for CTMMs. The statistic is composed of the fractional duration of nucleotide characters over evolutionary time, F(d), and the number of substitutions occurring in phylogenetic trees, N(s). We first derive basic properties of the sufficient statistic. Then, we derive an expectation maximization (EM) algorithm for estimating the parameters of a phylogenetic model, which iteratively computes the expectation values of the sufficient statistic. We show that the EM algorithm exhibits much faster convergence than other optimization methods that use numerical gradient descent algorithms. Finally, we investigate the genome-wide distribution of fractional duration time F(d) which, unlike the number of substitutions N(s), has rarely been investigated. We show that F(d) has evolutionary information that is distinct from that in N(s), which may be useful for detecting novel types of evolutionary constraints existing in the human genome. AVAILABILITY: The C++ source code of the 'Fdur' software is available at http://www.ncrna.org/software/fdur/ CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The importance of RNA sequence analysis has been increasing since the discovery of various types of non-coding RNAs transcribed in animal cells. Conventional RNA sequence analyses have mainly focused on structured regions, which are stabilized by the stacking energies acting on adjacent base pairs. On the other hand, recent findings regarding the mechanisms of small interfering RNAs (siRNAs) and transcription regulation by microRNAs (miRNAs) indicate the importance of analyzing accessible regions where no base pairs exist. So far, relatively few studies have investigated the nature of such regions. RESULTS: We have conducted a detailed investigation of accessibilities around the target sites of siRNAs and miRNAs. We have exhaustively calculated the correlations between the accessibilities around the target sites and the repression levels of the corresponding mRNAs. We have computed the accessibilities with an originally developed software package, called 'Raccess', which computes the accessibility of all the segments of a fixed length for a given RNA sequence when the maximal distance between base pairs is limited to a fixed size W. We show that the computed accessibilities are relatively insensitive to the choice of the maximal span W. We have found that the efficacy of siRNAs depends strongly on the accessibility of the very 3'-end of their binding sites, which might reflect a target site recognition mechanism in the RNA-induced silencing complex. We also show that the efficacy of miRNAs has a similar dependence on the accessibilities, but some miRNAs also show positive correlations between the efficacy and the accessibilities in broad regions downstream of their putative binding sites, which might imply that the downstream regions of the target sites are bound by other proteins that allow the miRNAs to implement their functions. We have also investigated the off-target effects of an siRNA as a potential RNAi therapeutic. We show that the off-target effects of the siRNA have similar correlations to the miRNA repression, indicating that they are caused by the same mechanism. AVAILABILITY: The C++ source code of the Raccess software is available at http://www.ncrna.org/software/Raccess/ The microarray data on the measurements of the siRNA off-target effects are also available at the same site. CONTACT: [email protected]

MOTIVATION: Recent studies have shown that the methods for predicting secondary structures of RNAs on the basis of posterior decoding of the base-pairing probabilities has an advantage with respect to prediction accuracy over the conventionally utilized minimum free energy methods. However, there is room for improvement in the objective functions presented in previous studies, which are maximized in the posterior decoding with respect to the accuracy measures for secondary structures. RESULTS: We propose novel estimators which improve the accuracy of secondary structure prediction of RNAs. The proposed estimators maximize an objective function which is the weighted sum of the expected number of the true positives and that of the true negatives of the base pairs. The proposed estimators are also improved versions of the ones used in previous works, namely CONTRAfold for secondary structure prediction from a single RNA sequence and McCaskill-MEA for common secondary structure prediction from multiple alignments of RNA sequences. We clarify the relations between the proposed estimators and the estimators presented in previous works, and theoretically show that the previous estimators include additional unnecessary terms in the evaluation measures with respect to the accuracy. Furthermore, computational experiments confirm the theoretical analysis by indicating improvement in the empirical accuracy. The proposed estimators represent extensions of the centroid estimators proposed in Ding et al. and Carvalho and Lawrence, and are applicable to a wide variety of problems in bioinformatics. AVAILABILITY: Supporting information and the CentroidFold software are available online at: http://www.ncrna.org/software/centroidfold/.

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/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The importance of accurate and fast predictions of multiple alignments for RNA sequences has increased due to recent findings about functional non-coding RNAs. Recent studies suggest that maximizing the expected accuracy of predictions will be useful for many problems in bioinformatics. RESULTS: We designed a novel estimator for multiple alignments of structured RNAs, based on maximizing the expected accuracy of predictions. First, we define the maximum expected accuracy (MEA) estimator for pairwise alignment of RNA sequences. This maximizes the expected sum-of-pairs score (SPS) of a predicted alignment under a probability distribution of alignments given by marginalizing the Sankoff model. Then, by approximating the MEA estimator, we obtain an estimator whose time complexity is O(L(3)+c(2)dL(2)) where L is the length of input sequences and both c and d are constants independent of L. The proposed estimator can handle uncertainty of secondary structures and alignments that are obstacles in Bioinformatics because it considers all the secondary structures and all the pairwise alignments as input sequences. Moreover, we integrate the probabilistic consistency transformation (PCT) on alignments into the proposed estimator. Computational experiments using six benchmark datasets indicate that the proposed method achieved a favorable SPS and was the fastest of many state-of-the-art tools for multiple alignments of structured RNAs. AVAILABILITY: The software called CentroidAlign, which is an implementation of the algorithm in this article, is freely available on our website: http://www.ncrna.org/software/centroidalign/. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Base pairing probability matrices have been frequently used for the analyses of structural RNA sequences. Recently, there has been a growing need for computing these probabilities for long DNA sequences by constraining the maximal span of base pairs to a limited value. However, none of the existing programs can exactly compute the base pairing probabilities associated with the energy model of secondary structures under such a constraint. RESULTS: We present an algorithm that exactly computes the base pairing probabilities associated with the energy model under the constraint on the maximal span W of base pairs. The complexity of our algorithm is given by O(NW2) in time and O(N+W2) in memory, where N is the sequence length. We show that our algorithm has a higher sensitivity to the true base pairs as compared to that of RNAplfold. We also present an algorithm that predicts a mutually consistent set of local secondary structures by maximizing the expected accuracy function. The comparison of the local secondary structure predictions with those of RNALfold indicates that our algorithm is more accurate. Our algorithms are implemented in the software named 'Rfold.' AVAILABILITY: The C++ source code of the Rfold software and the test dataset used in this study are available at http://www.ncrna.org/software/Rfold/.

BACKGROUND: Aligning multiple RNA sequences is essential for analyzing non-coding RNAs. Although many alignment methods for non-coding RNAs, including Sankoff's algorithm for strict structural alignments, have been proposed, they are either inaccurate or computationally too expensive. Faster methods with reasonable accuracies are required for genome-scale analyses. RESULTS: We propose a fast algorithm for multiple structural alignments of RNA sequences that is an extension of our pairwise structural alignment method (implemented in SCARNA). The accuracies of the implemented software, MXSCARNA, are at least as favorable as those of state-of-art algorithms that are computationally much more expensive in time and memory. CONCLUSION: The proposed method for structural alignment of multiple RNA sequences is fast enough for large-scale analyses with accuracies at least comparable to those of existing algorithms. The source code of MXSCARNA and its web server are available at http://mxscarna.ncrna.org.

MOTIVATION: Recent transcriptomic studies have revealed the existence of a considerable number of non-protein-coding RNA transcripts in higher eukaryotic cells. To investigate the functional roles of these transcripts, it is of great interest to find conserved secondary structures from multiple alignments on a genomic scale. Since multiple alignments are often created using alignment programs that neglect the special conservation patterns of RNA secondary structures for computational efficiency, alignment failures can cause potential risks of overlooking conserved stem structures. RESULTS: We investigated the dependence of the accuracy of secondary structure prediction on the quality of alignments. We compared three algorithms that maximize the expected accuracy of secondary structures as well as other frequently used algorithms. We found that one of our algorithms, called McCaskill-MEA, was more robust against alignment failures than others. The McCaskill-MEA method first computes the base pairing probability matrices for all the sequences in the alignment and then obtains the base pairing probability matrix of the alignment by averaging over these matrices. The consensus secondary structure is predicted from this matrix such that the expected accuracy of the prediction is maximized. We show that the McCaskill-MEA method performs better than other methods, particularly when the alignment quality is low and when the alignment consists of many sequences. Our model has a parameter that controls the sensitivity and specificity of predictions. We discussed the uses of that parameter for multi-step screening procedures to search for conserved secondary structures and for assigning confidence values to the predicted base pairs. AVAILABILITY: The C++ source code that implements the McCaskill-MEA algorithm and the test dataset used in this paper are available at http://www.ncrna.org/papers/McCaskillMEA/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Structural RNA genes exhibit unique evolutionary patterns that are designed to conserve their secondary structures; these patterns should be taken into account while constructing accurate multiple alignments of RNA genes. The Sankoff algorithm is a natural alignment algorithm that includes the effect of base-pair covariation in the alignment model. However, the extremely high computational cost of the Sankoff algorithm precludes its application to most RNA sequences. RESULTS: We propose an efficient algorithm for the multiple alignment of structural RNA sequences. Our algorithm is a variant of the Sankoff algorithm, and it uses an efficient scoring system that reduces the time and space requirements considerably without compromising on the alignment quality. First, our algorithm computes the match probability matrix that measures the alignability of each position pair between sequences as well as the base pairing probability matrix for each sequence. These probabilities are then combined to score the alignment using the Sankoff algorithm. By itself, our algorithm does not predict the consensus secondary structure of the alignment but uses external programs for the prediction. We demonstrate that both the alignment quality and the accuracy of the consensus secondary structure prediction from our alignment are the highest among the other programs examined. We also demonstrate that our algorithm can align relatively long RNA sequences such as the eukaryotic-type signal recognition particle RNA that is approximately 300 nt in length; multiple alignment of such sequences has not been possible by using other Sankoff-based algorithms. The algorithm is implemented in the software named 'Murlet'. AVAILABILITY: The C++ source code of the Murlet software and the test dataset used in this study are available at http://www.ncrna.org/papers/Murlet/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The relations between the promoter sequences and their strengths were extensively studied in the 1980s. Although these studies uncovered strong sequence-strength correlations, the cost of their elaborate experimental methods have been too high to be applied to a large number of promoters. On the contrary, a recent increase in the microarray data allows us to compare thousands of gene expressions with their DNA sequences. RESULTS: We studied the relations between the promoter sequences and their strengths using the Escherichia coli microarray data. We modeled those relations using a simple weight matrix, which was optimized with a novel support vector regression method. It was observed that several non-consensus bases in the '-35' and '-10' regions of promoter sequences act positively on the promoter strength and that certain consensus bases have a minor effect on the strength. We analyzed outliers for which the observed gene expressions deviate from the promoter strength predictions, and identified several genes with enhanced expressions due to multiple promoters and genes under strong regulation by transcription factors. Our method is applicable to other procaryotes for which both the promoter sequences and the microarray data are available.