GPseudoClust: deconvolution of shared pseudo-profiles at single-cell resolution.

MOTIVATION: Many methods have been developed to cluster genes on the basis of their changes in mRNA expression over time, using bulk RNA-seq or microarray data. However, single-cell data may present a particular challenge for these algorithms, since the temporal ordering of cells is not directly observed. One way to address this is to first use pseudotime methods to order the cells, and then apply clustering techniques for time course data. However, pseudotime estimates are subject to high levels of uncertainty, and failing to account for this uncertainty is liable to lead to erroneous and/or over-confident gene clusters. RESULTS: The proposed method, GPseudoClust, is a novel approach that jointly infers pseudotemporal ordering and gene clusters, and quantifies the uncertainty in both. GPseudoClust combines a recent method for pseudotime inference with non-parametric Bayesian clustering methods, efficient Markov Chain Monte Carlo sampling and novel subsampling strategies which aid computation. We consider a broad array of simulated and experimental datasets to demonstrate the effectiveness of GPseudoClust in a range of settings. AVAILABILITY AND IMPLEMENTATION: An implementation is available on GitHub: https://github.com/magStra/nonparametricSummaryPSM and https://github.com/magStra/GPseudoClust. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

GPseudoRank: a permutation sampler for single cell orderings.

MOTIVATION: A number of pseudotime methods have provided point estimates of the ordering of cells for scRNA-seq data. A still limited number of methods also model the uncertainty of the pseudotime estimate. However, there is still a need for a method to sample from complicated and multi-modal distributions of orders, and to estimate changes in the amount of the uncertainty of the order during the course of a biological development, as this can support the selection of suitable cells for the clustering of genes or for network inference. RESULTS: In applications to scRNA-seq data we demonstrate the potential of GPseudoRank to sample from complex and multi-modal posterior distributions and to identify phases of lower and higher pseudotime uncertainty during a biological process. GPseudoRank also correctly identifies cells precocious in their antiviral response and links uncertainty in the ordering to metastable states. A variant of the method extends the advantages of Bayesian modelling and MCMC to large droplet-based scRNA-seq datasets. AVAILABILITY AND IMPLEMENTATION: Our method is available on github: https://github.com/magStra/GPseudoRank. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Branch-recombinant Gaussian processes for analysis of perturbations in biological time series.

Motivation: A common class of behaviour encountered in the biological sciences involves branching and recombination. During branching, a statistical process bifurcates resulting in two or more potentially correlated processes that may undergo further branching; the contrary is true during recombination, where two or more statistical processes converge. A key objective is to identify the time of this bifurcation (branch or recombination time) from time series measurements, e.g. by comparing a control time series with perturbed time series. Gaussian processes (GPs) represent an ideal framework for such analysis, allowing for nonlinear regression that includes a rigorous treatment of uncertainty. Currently, however, GP models only exist for two-branch systems. Here, we highlight how arbitrarily complex branching processes can be built using the correct composition of covariance functions within a GP framework, thus outlining a general framework for the treatment of branching and recombination in the form of branch-recombinant Gaussian processes (B-RGPs). Results: We first benchmark the performance of B-RGPs compared to a variety of existing regression approaches, and demonstrate robustness to model misspecification. B-RGPs are then used to investigate the branching patterns of Arabidopsis thaliana gene expression following inoculation with the hemibotrophic bacteria, Pseudomonas syringae DC3000, and a disarmed mutant strain, hrpA. By grouping genes according to the number of branches, we could naturally separate out genes involved in basal immune response from those subverted by the virulent strain, and show enrichment for targets of pathogen protein effectors. Finally, we identify two early branching genes WRKY11 and WRKY17, and show that genes that branched at similar times to WRKY11/17 were enriched for W-box binding motifs, and overrepresented for genes differentially expressed in WRKY11/17 knockouts, suggesting that branch time could be used for identifying direct and indirect binding targets of key transcription factors. Availability and implementation: https://github.com/cap76/BranchingGPs. Supplementary information: Supplementary data are available at Bioinformatics online.

Machine learning based classification of cells into chronological stages using single-cell transcriptomics.

Age-associated deterioration of cellular physiology leads to pathological conditions. The ability to detect premature aging could provide a window for preventive therapies against age-related diseases. However, the techniques for determining cellular age are limited, as they rely on a limited set of histological markers and lack predictive power. Here, we implement GERAS (GEnetic Reference for Age of Single-cell), a machine learning based framework capable of assigning individual cells to chronological stages based on their transcriptomes. GERAS displays greater than 90% accuracy in classifying the chronological stage of zebrafish and human pancreatic cells. The framework demonstrates robustness against biological and technical noise, as evaluated by its performance on independent samplings of single-cells. Additionally, GERAS determines the impact of differences in calorie intake and BMI on the aging of zebrafish and human pancreatic cells, respectively. We further harness the classification ability of GERAS to identify molecular factors that are potentially associated with the aging of beta-cells. We show that one of these factors, junba, is necessary to maintain the proliferative state of juvenile beta-cells. Our results showcase the applicability of a machine learning framework to classify the chronological stage of heterogeneous cell populations, while enabling detection of candidate genes associated with aging.

Pseudotime estimation: deconfounding single cell time series.

MOTIVATION: Repeated cross-sectional time series single cell data confound several sources of variation, with contributions from measurement noise, stochastic cell-to-cell variation and cell progression at different rates. Time series from single cell assays are particularly susceptible to confounding as the measurements are not averaged over populations of cells. When several genes are assayed in parallel these effects can be estimated and corrected for under certain smoothness assumptions on cell progression. RESULTS: We present a principled probabilistic model with a Bayesian inference scheme to analyse such data. We demonstrate our method's utility on public microarray, nCounter and RNA-seq datasets from three organisms. Our method almost perfectly recovers withheld capture times in an Arabidopsis dataset, it accurately estimates cell cycle peak times in a human prostate cancer cell line and it correctly identifies two precocious cells in a study of paracrine signalling in mouse dendritic cells. Furthermore, our method compares favourably with Monocle, a state-of-the-art technique. We also show using held-out data that uncertainty in the temporal dimension is a common confounder and should be accounted for in analyses of repeated cross-sectional time series. AVAILABILITY AND IMPLEMENTATION: Our method is available on CRAN in the DeLorean package. CONTACT: john.reid@mrc-bsu.cam.ac.uk SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Conserved Cis-Regulatory Modules Control Robustness in Msx1 Expression at Single-Cell Resolution.

The process of transcription is highly stochastic leading to cell-to-cell variations and noise in gene expression levels. However, key essential genes have to be precisely expressed at the correct amount and time to ensure proper cellular development and function. Studies in yeast and bacterial systems have shown that gene expression noise decreases as mean expression levels increase, a relationship that is controlled by promoter DNA sequence. However, the function of distal cis-regulatory modules (CRMs), an evolutionary novelty of metazoans, in controlling transcriptional robustness and variability is poorly understood. In this study, we used live cell imaging of transfected reporters combined with a mathematical modelling and statistical inference scheme to quantify the function of conserved Msx1 CRMs and promoters in modulating single-cell real-time transcription rates in C2C12 mouse myoblasts. The results show that the mean expression-noise relationship is solely promoter controlled for this key pluripotency regulator. In addition, we demonstrate that CRMs modulate single-cell basal promoter rate distributions in a graded manner across a population of cells. This extends the rheostatic model of CRM action to provide a more detailed understanding of CRM function at single-cell resolution. We also identify a novel CRM transcriptional filter function that acts to reduce intracellular variability in transcription rates and show that this can be phylogenetically separable from rate modulating CRM activities. These results are important for understanding how the expression of key vertebrate developmental transcription factors is precisely controlled both within and between individual cells.

STEME: a robust, accurate motif finder for large data sets.

Motif finding is a difficult problem that has been studied for over 20 years. Some older popular motif finders are not suitable for analysis of the large data sets generated by next-generation sequencing. We recently published an efficient approximation (STEME) to the EM algorithm that is at the core of many motif finders such as MEME. This approximation allows the EM algorithm to be applied to large data sets. In this work we describe several efficient extensions to STEME that are based on the MEME algorithm. Together with the original STEME EM approximation, these extensions make STEME a fully-fledged motif finder with similar properties to MEME. We discuss the difficulty of objectively comparing motif finders. We show that STEME performs comparably to existing prominent discriminative motif finders, DREME and Trawler, on 13 sets of transcription factor binding data in mouse ES cells. We demonstrate the ability of STEME to find long degenerate motifs which these discriminative motif finders do not find. As part of our method, we extend an earlier method due to Nagarajan et al. for the efficient calculation of motif E-values. STEME's source code is available under an open source license and STEME is available via a web interface.

STEME: efficient EM to find motifs in large data sets.

MEME and many other popular motif finders use the expectation-maximization (EM) algorithm to optimize their parameters. Unfortunately, the running time of EM is linear in the length of the input sequences. This can prohibit its application to data sets of the size commonly generated by high-throughput biological techniques. A suffix tree is a data structure that can efficiently index a set of sequences. We describe an algorithm, Suffix Tree EM for Motif Elicitation (STEME), that approximates EM using suffix trees. To the best of our knowledge, this is the first application of suffix trees to EM. We provide an analysis of the expected running time of the algorithm and demonstrate that STEME runs an order of magnitude more quickly than the implementation of EM used by MEME. We give theoretical bounds for the quality of the approximation and show that, in practice, the approximation has a negligible effect on the outcome. We provide an open source implementation of the algorithm that we hope will be used to speed up existing and future motif search algorithms.

An alignment-free model for comparison of regulatory sequences.

MOTIVATION: Some recent comparative studies have revealed that regulatory regions can retain function over large evolutionary distances, even though the DNA sequences are divergent and difficult to align. It is also known that such enhancers can drive very similar expression patterns. This poses a challenge for the in silico detection of biologically related sequences, as they can only be discovered using alignment-free methods. RESULTS: Here, we present a new computational framework called Regulatory Region Scoring (RRS) model for the detection of functional conservation of regulatory sequences using predicted occupancy levels of transcription factors of interest. We demonstrate that our model can detect the functional and/or evolutionary links between some non-alignable enhancers with a strong statistical significance. We also identify groups of enhancers that are likely to be similarly regulated. Our model is motivated by previous work on prediction of expression patterns and it can capture similarity by strong binding sites, weak binding sites and even the statistically significant absence of sites. Our results support the hypothesis that weak binding sites contribute to the functional similarity of sequences. Our model fills a gap between two families of models: detailed, data-intensive models for the prediction of precise spatio-temporal expression patterns on the one side, and crude, generally applicable models on the other side. Our model borrows some of the strengths of each group and addresses their drawbacks. AVAILABILITY: The RRS source code is freely available upon publication of this manuscript: http://www2.warwick.ac.uk/fac/sci/systemsbiology/staff/ott/tools_and_software/rrs.

Variable structure motifs for transcription factor binding sites.

BACKGROUND: Classically, models of DNA-transcription factor binding sites (TFBSs) have been based on relatively few known instances and have treated them as sites of fixed length using position weight matrices (PWMs). Various extensions to this model have been proposed, most of which take account of dependencies between the bases in the binding sites. However, some transcription factors are known to exhibit some flexibility and bind to DNA in more than one possible physical configuration. In some cases this variation is known to affect the function of binding sites. With the increasing volume of ChIP-seq data available it is now possible to investigate models that incorporate this flexibility. Previous work on variable length models has been constrained by: a focus on specific zinc finger proteins in yeast using restrictive models; a reliance on hand-crafted models for just one transcription factor at a time; and a lack of evaluation on realistically sized data sets. RESULTS: We re-analysed binding sites from the TRANSFAC database and found motivating examples where our new variable length model provides a better fit. We analysed several ChIP-seq data sets with a novel motif search algorithm and compared the results to one of the best standard PWM finders and a recently developed alternative method for finding motifs of variable structure. All the methods performed comparably in held-out cross validation tests. Known motifs of variable structure were recovered for p53, Stat5a and Stat5b. In addition our method recovered a novel generalised version of an existing PWM for Sp1 that allows for variable length binding. This motif improved classification performance. CONCLUSIONS: We have presented a new gapped PWM model for variable length DNA binding sites that is not too restrictive nor over-parameterised. Our comparison with existing tools shows that on average it does not have better predictive accuracy than existing methods. However, it does provide more interpretable models of motifs of variable structure that are suitable for follow-up structural studies. To our knowledge, we are the first to apply variable length motif models to eukaryotic ChIP-seq data sets and consequently the first to show their value in this domain. The results include a novel motif for the ubiquitous transcription factor Sp1.

Transcriptional programs: modelling higher order structure in transcriptional control.

BACKGROUND: Transcriptional regulation is an important part of regulatory control in eukaryotes. Even if binding motifs for transcription factors are known, the task of finding binding sites by scanning sequences is plagued by false positives. One way to improve the detection of binding sites from motifs is by taking cooperativity of transcription factor binding into account. We propose a non-parametric probabilistic model, similar to a document topic model, for detecting transcriptional programs, groups of cooperative transcription factors and co-regulated genes. The analysis results in transcriptional programs which generalise both transcriptional modules and TF-target gene incidence matrices and provide a higher-level summary of these structures. The method is independent of prior specification of training sets of genes, for example, via gene expression data. The analysis is based on known binding motifs. RESULTS: We applied our method to putative regulatory regions of 18,445 Mus musculus genes. We discovered just 68 transcriptional programs that effectively summarised the action of 149 transcription factors on these genes. Several of these programs were significantly enriched for known biological processes and signalling pathways. One transcriptional program has a significant overlap with a reference set of cell cycle specific transcription factors. CONCLUSION: Our method is able to pick out higher order structure from noisy sequence analyses. The transcriptional programs it identifies potentially represent common mechanisms of regulatory control across the genome. It simultaneously predicts which genes are co-regulated and which sets of transcription factors cooperate to achieve this co-regulation. The programs we discovered enable biologists to choose new genes and transcription factors to study in specific transcriptional regulatory systems.