Single-cell RNA sequencing (scRNA-seq) has become a popular experimental method to study variation of gene expression within a population of cells. However, obtaining an accurate picture of the diversity of distinct gene expression states that are present in a given dataset is highly challenging because of the sparsity of the scRNA-seq data and its inhomogeneous measurement noise properties. Although a vast number of different methods is applied in the literature for clustering cells into subsets with 'similar' expression profiles, these methods generally lack rigorously specified objectives, involve multiple complex layers of normalization, filtering, feature selection, dimensionality-reduction, employ ad hoc measures of distance or similarity between cells, often ignore the known measurement noise properties of scRNA-seq measurements, and include a large number of tunable parameters. Consequently, it is virtually impossible to assign concrete biophysical meaning to the clusterings that result from these methods. Here we address the following problem: Given raw unique molecule identifier (UMI) counts of an scRNA-seq dataset, partition the cells into subsets such that the gene expression states of the cells in each subset are statistically indistinguishable, and each subset corresponds to a distinct gene expression state. That is, we aim to partition cells so as to maximally reduce the complexity of the dataset without removing any of its meaningful structure. We show that, given the known measurement noise structure of scRNA-seq data, this problem is mathematically well-defined and derive its unique solution from first principles. We have implemented this solution in a tool called Cellstates which operates directly on the raw data and automatically determines the optimal partition and cluster number, with zero tunable parameters. We show that, on synthetic datasets, Cellstates almost perfectly recovers optimal partitions. On real data, Cellstates robustly identifies subtle substructure within groups of cells that are traditionally annotated as a common cell type. Moreover, we show that the diversity of gene expression states that Cellstates identifies systematically depends on the tissue of origin and not on technical features of the experiments such as the total number of cells and total UMI count per cell. In addition to the Cellstates tool we also provide a small toolbox of software to place the identified cellstates into a hierarchical tree of higher-order clusters, to identify the most important differentially expressed genes at each branch of this hierarchy, and to visualize these results.

Gene regulatory networks are ultimately encoded by the sequence-specific binding of (TFs) to short DNA segments. Although it is customary to represent the binding specificity of a TF by a position-specific weight matrix (PSWM), which assumes each position within a site contributes independently to the overall binding affinity, evidence has been accumulating that there can be significant dependencies between positions. Unfortunately, methodological challenges have so far hindered the development of a practical and generally-accepted extension of the PSWM model. On the one hand, simple models that only consider dependencies between nearest-neighbor positions are easy to use in practice, but fail to account for the distal dependencies that are observed in the data. On the other hand, models that allow for arbitrary dependencies are prone to overfitting, requiring regularization schemes that are difficult to use in practice for non-experts. Here we present a new regulatory motif model, called dinucleotide weight tensor (DWT), that incorporates arbitrary pairwise dependencies between positions in binding sites, rigorously from first principles, and free from tunable parameters. We demonstrate the power of the method on a large set of ChIP-seq data-sets, showing that DWTs outperform both PSWMs and motif models that only incorporate nearest-neighbor dependencies. We also demonstrate that DWTs outperform two previously proposed methods. Finally, we show that DWTs inferred from ChIP-seq data also outperform PSWMs on HT-SELEX data for the same TF, suggesting that DWTs capture inherent biophysical properties of the interactions between the DNA binding domains of TFs and their binding sites. We make a suite of DWT tools available at dwt.unibas.ch, that allow users to automatically perform 'motif finding', i.e. the inference of DWT motifs from a set of sequences, binding site prediction with DWTs, and visualization of DWT 'dilogo' motifs.

Although correlations between residues occurring at different positions within multiple protein alignments have long been used to infer directly interacting residues, most of these methods suffer from the frequent occurrence of indirectly correlated residues.Recently, a number of methods have been proposed that incorporate the entire set of observed frequencies of amino acid pairs for all pairs of positions into rigorous probabilistic models; these models have been shown to strongly improve the prediction of directly interacting residues by successfully distinguishing direct from indirect correlations.Some of these methods make use of the maximum entropy principle, originating in statistical physics.It has recently been argued that there is no reason to assume that protein sequences should follow maximum entropy distributions and that it is therefore puzzling that the max-ent formalism is successful for predicting interacting residues in proteins.In this brief review I will argue that such apparent puzzles result from a misconception of the meaning of the max-ent formalism and, more generally, on the meaning of probabilities.

Because DNA packaging in nucleosomes modulates its accessibility to transcription factors (TFs), unraveling the causal determinants of nucleosome positioning is of great importance to understanding gene regulation. Although there is evidence that intrinsic sequence specificity contributes to nucleosome positioning, the extent to which other factors contribute to nucleosome positioning is currently highly debated. Here we obtained both in vivo and in vitro reference maps of positions that are either consistently covered or free of nucleosomes across multiple experimental data-sets in Saccharomyces cerevisiae. We then systematically quantified the contribution of TF binding to nucleosome positioning using a rigorous statistical mechanics model in which TFs compete with nucleosomes for binding DNA. Our results reconcile previous seemingly conflicting results on the determinants of nucleosome positioning and provide a quantitative explanation for the difference between in vivo and in vitro positioning. On a genome-wide scale, nucleosome positioning is dominated by the phasing of nucleosome arrays over gene bodies, and their positioning is mainly determined by the intrinsic sequence preferences of nucleosomes. In contrast, larger nucleosome free regions in promoters, which likely have a much more significant impact on gene expression, are determined mainly by TF binding. Interestingly, of the 158 yeast TFs included in our modeling, we find that only 10-20 significantly contribute to inducing nucleosome-free regions, and these TFs are highly enriched for having direct interactions with chromatin remodelers. Together our results imply that nucleosome free regions in yeast promoters results from the binding of a specific class of TFs that recruit chromatin remodelers.

MOTIVATION: Probabilistic approaches for inferring transcription factor binding sites (TFBSs) and regulatory motifs from DNA sequences have been developed for over two decades. Previous work has shown that prediction accuracy can be significantly improved by incorporating features such as the competition of multiple transcription factors (TFs) for binding to nearby sites, the tendency of TFBSs for co-regulated TFs to cluster and form cis-regulatory modules and explicit evolutionary modeling of conservation of TFBSs across orthologous sequences. However, currently available tools only incorporate some of these features, and significant methodological hurdles hampered their synthesis into a single consistent probabilistic framework. RESULTS: We present MotEvo, a integrated suite of Bayesian probabilistic methods for the prediction of TFBSs and inference of regulatory motifs from multiple alignments of phylogenetically related DNA sequences, which incorporates all features just mentioned. In addition, MotEvo incorporates a novel model for detecting unknown functional elements that are under evolutionary constraint, and a new robust model for treating gain and loss of TFBSs along a phylogeny. Rigorous benchmarking tests on ChIP-seq datasets show that MotEvo's novel features significantly improve the accuracy of TFBS prediction, motif inference and enhancer prediction. AVAILABILITY: Source code, a user manual and files with several example applications are available at www.swissregulon.unibas.ch.

Predicting protein structure from primary sequence is one of the ultimate challenges in computational biology. Given the large amount of available sequence data, the analysis of co-evolution, i.e., statistical dependency, between columns in multiple alignments of protein domain sequences remains one of the most promising avenues for predicting residues that are contacting in the structure. A key impediment to this approach is that strong statistical dependencies are also observed for many residue pairs that are distal in the structure. Using a comprehensive analysis of protein domains with available three-dimensional structures we show that co-evolving contacts very commonly form chains that percolate through the protein structure, inducing indirect statistical dependencies between many distal pairs of residues. We characterize the distributions of length and spatial distance traveled by these co-evolving contact chains and show that they explain a large fraction of observed statistical dependencies between structurally distal pairs. We adapt a recently developed Bayesian network model into a rigorous procedure for disentangling direct from indirect statistical dependencies, and we demonstrate that this method not only successfully accomplishes this task, but also allows contacts with weak statistical dependency to be detected. To illustrate how additional information can be incorporated into our method, we incorporate a phylogenetic correction, and we develop an informative prior that takes into account that the probability for a pair of residues to contact depends strongly on their primary-sequence distance and the amount of conservation that the corresponding columns in the multiple alignment exhibit. We show that our model including these extensions dramatically improves the accuracy of contact prediction from multiple sequence alignments.

BACKGROUND: MicroRNAs have emerged as important regulatory genes in a variety of cellular processes and, in recent years, hundreds of such genes have been discovered in animals. In contrast, functional annotations are available only for a very small fraction of these miRNAs, and even in these cases only partially. RESULTS: We developed a general Bayesian method for the inference of miRNA target sites, in which, for each miRNA, we explicitly model the evolution of orthologous target sites in a set of related species. Using this method we predict target sites for all known miRNAs in flies, worms, fish, and mammals. By comparing our predictions in fly with a reference set of experimentally tested miRNA-mRNA interactions we show that our general method performs at least as well as the most accurate methods available to date, including ones specifically tailored for target prediction in fly. An important novel feature of our model is that it explicitly infers the phylogenetic distribution of functional target sites, independently for each miRNA. This allows us to infer species-specific and clade-specific miRNA targeting. We also show that, in long human 3' UTRs, miRNA target sites occur preferentially near the start and near the end of the 3' UTR. To characterize miRNA function beyond the predicted lists of targets we further present a method to infer significant associations between the sets of targets predicted for individual miRNAs and specific biochemical pathways, in particular those of the KEGG pathway database. We show that this approach retrieves several known functional miRNA-mRNA associations, and predicts novel functions for known miRNAs in cell growth and in development. CONCLUSION: We have presented a Bayesian target prediction algorithm without any tunable parameters, that can be applied to sequences from any clade of species. The algorithm automatically infers the phylogenetic distribution of functional sites for each miRNA, and assigns a posterior probability to each putative target site. The results presented here indicate that our general method achieves very good performance in predicting miRNA target sites, providing at the same time insights into the evolution of target sites for individual miRNAs. Moreover, by combining our predictions with pathway analysis, we propose functions of specific miRNAs in nervous system development, inter-cellular communication and cell growth. The complete target site predictions as well as the miRNA/pathway associations are accessible on the ElMMo web server.

In our manuscript on miRNA target predictions [1] we made use of a number of genome alignments that we obtained from the UCSC genome browser. We regret that, due to a misunderstanding, we failed to explicitly acknowledge the sequencing centers that made the genome sequences, that were used to construct these alignments, available before publication.

Over the last two decades a large number of algorithms has been developed for regulatory motif finding. Here we show how many of these algorithms, especially those that model binding specificities of regulatory factors with position specific weight matrices (WMs), naturally arise within a general Bayesian probabilistic framework. We discuss how WMs are constructed from sets of regulatory sites, how sites for a given WM can be discovered by scanning of large sequences, how to cluster WMs, and more generally how to cluster large sets of sites from different WMs into clusters. We discuss how 'regulatory modules', clusters of sites for subsets of WMs, can be found in large intergenic sequences, and we discuss different methods for ab initio motif finding, including expectation maximization (EM) algorithms, and motif sampling algorithms. Finally, we extensively discuss how module finding methods and ab initio motif finding methods can be extended to take phylogenetic relations between the input sequences into account, i.e. we show how motif finding and phylogenetic footprinting can be integrated in a rigorous probabilistic framework. The article is intended for readers with a solid background in applied mathematics, and preferably with some knowledge of general Bayesian probabilistic methods. The main purpose of the article is to elucidate that all these methods are not a disconnected set of individual algorithmic recipes, but that they are just different facets of a single integrated probabilistic theory.

BACKGROUND: MicroRNAs (miRNAs) are endogenous 21 to 23-nucleotide RNA molecules that regulate protein-coding gene expression in plants and animals via the RNA interference pathway. Hundreds of them have been identified in the last five years and very recent works indicate that their total number is still larger. Therefore miRNAs gene discovery remains an important aspect of understanding this new and still widely unknown regulation mechanism. Bioinformatics approaches have proved to be very useful toward this goal by guiding the experimental investigations. RESULTS: In this work we describe our computational method for miRNA prediction and the results of its application to the discovery of novel mammalian miRNAs. We focus on genomic regions around already known miRNAs, in order to exploit the property that miRNAs are occasionally found in clusters. Starting with the known human, mouse and rat miRNAs we analyze 20 kb of flanking genomic regions for the presence of putative precursor miRNAs (pre-miRNAs). Each genome is analyzed separately, allowing us to study the species-specific identity and genome organization of miRNA loci. We only use cross-species comparisons to make conservative estimates of the number of novel miRNAs. Our ab initio method predicts between fifty and hundred novel pre-miRNAs for each of the considered species. Around 30% of these already have experimental support in a large set of cloned mammalian small RNAs. The validation rate among predicted cases that are conserved in at least one other species is higher, about 60%, and many of them have not been detected by prediction methods that used cross-species comparisons. A large fraction of the experimentally confirmed predictions correspond to an imprinted locus residing on chromosome 14 in human, 12 in mouse and 6 in rat. Our computational tool can be accessed on the world-wide-web. CONCLUSION: Our results show that the assumption that many miRNAs occur in clusters is fruitful for the discovery of novel miRNAs. Additionally we show that although the overall miRNA content in the observed clusters is very similar across the three considered species, the internal organization of the clusters changes in evolution.

A central problem in the bioinformatics of gene regulation is to find the binding sites for regulatory proteins. One of the most promising approaches toward identifying these short and fuzzy sequence patterns is the comparative analysis of orthologous intergenic regions of related species. This analysis is complicated by various factors. First, one needs to take the phylogenetic relationship between the species into account in order to distinguish conservation that is due to the occurrence of functional sites from spurious conservation that is due to evolutionary proximity. Second, one has to deal with the complexities of multiple alignments of orthologous intergenic regions, and one has to consider the possibility that functional sites may occur outside of conserved segments. Here we present a new motif sampling algorithm, PhyloGibbs, that runs on arbitrary collections of multiple local sequence alignments of orthologous sequences. The algorithm searches over all ways in which an arbitrary number of binding sites for an arbitrary number of transcription factors (TFs) can be assigned to the multiple sequence alignments. These binding site configurations are scored by a Bayesian probabilistic model that treats aligned sequences by a model for the evolution of binding sites and "background" intergenic DNA. This model takes the phylogenetic relationship between the species in the alignment explicitly into account. The algorithm uses simulated annealing and Monte Carlo Markov-chain sampling to rigorously assign posterior probabilities to all the binding sites that it reports. In tests on synthetic data and real data from five Saccharomyces species our algorithm performs significantly better than four other motif-finding algorithms, including algorithms that also take phylogeny into account. Our results also show that, in contrast to the other algorithms, PhyloGibbs can make realistic estimates of the reliability of its predictions. Our tests suggest that, running on the five-species multiple alignment of a single gene's upstream region, PhyloGibbs on average recovers over 50% of all binding sites in S. cerevisiae at a specificity of about 50%, and 33% of all binding sites at a specificity of about 85%. We also tested PhyloGibbs on collections of multiple alignments of intergenic regions that were recently annotated, based on ChIP-on-chip data, to contain binding sites for the same TF. We compared PhyloGibbs's results with the previous analysis of these data using six other motif-finding algorithms. For 16 of 21 TFs for which all other motif-finding methods failed to find a significant motif, PhyloGibbs did recover a motif that matches the literature consensus. In 11 cases where there was disagreement in the results we compiled lists of known target genes from the literature, and found that running PhyloGibbs on their regulatory regions yielded a binding motif matching the literature consensus in all but one of the cases. Interestingly, these literature gene lists had little overlap with the targets annotated based on the ChIP-on-chip data. The PhyloGibbs code can be downloaded from http://www.biozentrum.unibas.ch/~nimwegen/cgi-bin/phylogibbs.cgi or http://www.imsc.res.in/~rsidd/phylogibbs. The full set of predicted sites from our tests on yeast are available at http://www.swissregulon.unibas.ch.