Trajectory-based differential expression analysis for single-cell sequencing data

Trajectory inference has radically enhanced single-cell RNA-seq research by enabling the study of dynamic changes in gene expression. Downstream of trajectory inference, it is vital to discover genes that are (i) associated with the lineages in the trajectory, or (ii) differentially expressed between lineages, to illuminate the underlying biological processes. Current data analysis procedures, however, either fail to exploit the continuous resolution provided by trajectory inference, or fail to pinpoint the exact types of differential expression. We introduce tradeSeq, a powerful generalized additive model framework based on the negative binomial distribution that allows flexible inference of both within-lineage and between-lineage differential expression. By incorporating observation-level weights, the model additionally allows to account for zero inflation. We evaluate the method on simulated datasets and on real datasets from droplet-based and full-length protocols, and show that it yields biological insights through a clear interpretation of the data. Downstream of trajectory inference for cell lineages based on scRNA-seq data, differential expression analysis yields insight into biological processes. Here, Van den Berge et al. develop tradeSeq, a framework for the inference of within and between-lineage differential expression, based on negative binomial generalized additive models

Differential expression analysis with global network adjustment

<p>Background: Large-scale chromosomal deletions or other non-specific perturbations of the transcriptome can alter the expression of hundreds or thousands of genes, and it is of biological interest to understand which genes are most profoundly affected. We present a method for predicting a gene’s expression as a function of other genes thereby accounting for the effect of transcriptional regulation that confounds the identification of genes differentially expressed relative to a regulatory network. The challenge in constructing such models is that the number of possible regulator transcripts within a global network is on the order of thousands, and the number of biological samples is typically on the order of 10. Nevertheless, there are large gene expression databases that can be used to construct networks that could be helpful in modeling transcriptional regulation in smaller experiments.</p> <p>Results: We demonstrate a type of penalized regression model that can be estimated from large gene expression databases, and then applied to smaller experiments. The ridge parameter is selected by minimizing the cross-validation error of the predictions in the independent out-sample. This tends to increase the model stability and leads to a much greater degree of parameter shrinkage, but the resulting biased estimation is mitigated by a second round of regression. Nevertheless, the proposed computationally efficient “over-shrinkage” method outperforms previously used LASSO-based techniques. In two independent datasets, we find that the median proportion of explained variability in expression is approximately 25%, and this results in a substantial increase in the signal-to-noise ratio allowing more powerful inferences on differential gene expression leading to biologically intuitive findings. We also show that a large proportion of gene dependencies are conditional on the biological state, which would be impossible with standard differential expression methods.</p> <p>Conclusions: By adjusting for the effects of the global network on individual genes, both the sensitivity and reliability of differential expression measures are greatly improved.</p&gt

A statistical framework for testing functional categories in microarray data

Ready access to emerging databases of gene annotation and functional pathways has shifted assessments of differential expression in DNA microarray studies from single genes to groups of genes with shared biological function. This paper takes a critical look at existing methods for assessing the differential expression of a group of genes (functional category), and provides some suggestions for improved performance. We begin by presenting a general framework, in which the set of genes in a functional category is compared to the complementary set of genes on the array. The framework includes tests for overrepresentation of a category within a list of significant genes, and methods that consider continuous measures of differential expression. Existing tests are divided into two classes. Class 1 tests assume gene-specific measures of differential expression are independent, despite overwhelming evidence of positive correlation. Analytic and simulated results are presented that demonstrate Class 1 tests are strongly anti-conservative in practice. Class 2 tests account for gene correlation, typically through array permutation that by construction has proper Type I error control for the induced null. However, both Class 1 and Class 2 tests use a null hypothesis that all genes have the same degree of differential expression. We introduce a more sensible and general (Class 3) null under which the profile of differential expression is the same within the category and complement. Under this broader null, Class 2 tests are shown to be conservative. We propose standard bootstrap methods for testing against the Class 3 null and demonstrate they provide valid Type I error control and more power than array permutation in simulated datasets and real microarray experiments.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS146 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Comment on Mott Scattering in strong Laser Field

The first differential cross section for Mott scattering of a Dirac-Volkov electron is reviewed. The expression (26) derived by Szymanowski et al. [Physical Review A {\bf 56}, 3846,(1997)] is corrected. In particular, we disagree with the expression of $(\frac{d\sigma}{d\Omega})$ they obtained and we give the exact coefficients multiplying the various Bessel functions appearing in the scattering differential cross section.Comment: 16 pages, LaTex, added reference for section 3, corrected some typosReport no: LPHEA 02-0

Application of the averaging method to the gyrokinetic plasma

we show that the solution to an oscillatory-singularly perturbed ordinary differential equation may be asymptotically expanded into a sum of oscillating terms. Each of those terms writes as an oscillating operator acting on the solution to a non oscillating ordinary differential equation with an oscillating correction added to it. The expression of the non oscillating ordinary differential equations are defined by a recurrence relation. We then apply this result to problems where charged particles are submitted to large magnetic field

Statistical Tests for Detecting Differential RNA-Transcript Expression from Read Counts

As a fruit of the current revolution in sequencing technology, transcriptomes can now be analyzed at an unprecedented level of detail. These advances have been exploited for detecting differential expressed genes across biological samples and for quantifying the abundances of various RNA transcripts within one gene. However, explicit strategies for detecting the hidden differential abundances of RNA transcripts in biological samples have not been defined. In this work, we present two novel statistical tests to address this issue: a 'gene structure sensitive' Poisson test for detecting differential expression when the transcript structure of the gene is known, and a kernel-based test called Maximum Mean Discrepancy when it is unknown. We analyzed the proposed approaches on simulated read data for two artificial samples as well as on factual reads generated by the Illumina Genome Analyzer for two _C. elegans_ samples. Our analysis shows that the Poisson test identifies genes with differential transcript expression considerably better that previously proposed RNA transcript quantification approaches for this task. The MMD test is able to detect a large fraction (75%) of such differential cases without the knowledge of the annotated transcripts. It is therefore well-suited to analyze RNA-Seq experiments when the genome annotations are incomplete or not available, where other approaches have to fail