Generally speaking, a well-designed experiment is one that is sufficiently powered and one in which technical artifacts and biological features that may systematically affect measurements are randomized, balanced, or controlled in some other way in order to minimize opportunities for multiple explanations for the effect(s) under study. Guidelines toward achieving this end have been reviewed for bulk RNA-seq studies [1, 2] and many of the same guidelines also hold for scRNA-seq. In short, to minimize potential artifacts and confounding, it is important to randomize or balance over as many factors as possible, ideally so that putatively interesting features that are observed in the data are not due to artifacts imposed during sample preparation and/or data collection. Although the specific factors that are important in any design are highly experiment-dependent, if multiple populations are being assessed, a primary candidate for randomization is the order with which cells from distinct populations are processed and libraries are constructed. If multiplexing is done, the assignment of barcoded samples should be randomized or balanced across multiple lanes to minimize potential lane effects.

While randomization should be carried out to the extent possible, it is important to point out that, in many cases, conducting a fully randomized experiment is not realistic. Limited samples, a fixed number of single-cell isolation platforms and sequencers, time constraints, and budgets often prohibit the theoretically ideal experiment from being realized in practice. In most cases, samples must be processed in multiple batches, with randomization occurring within batch. This is exemplified nicely in an experiment concerning embryonic development that profiles single-cell expression in oocytes and zygotes as well as in 2-cell, 4-cell, and 8-cell embryos [3]. In this study, within each batch, each developmental stage was represented and stages were randomized in an effort to ensure that batch and stage were not confounded. Further discussion of possible batch effects and a specific experimental design that reduces the confounding of batch effect with biological signal are given in Hicks et al. [4]. Specifically, they propose a design in which cells from the biological conditions under study are represented together in multiple batches, which are then randomized across sequencing runs, flow cells, and lanes as in bulk-RNA-Seq. With this design, one can model and adjust for batch effects that result from systematic experimental bias.

Experimental design considerations will also be affected by the various protocols and platforms available for scRNA-seq. Platforms for isolating single cells vary substantially with respect to capacity, cost, and time. Both Saliba et al. [5] and Kolodziejczyk et al. [6] review single-cell isolation practices in detail, with the latter including details on the more recent droplet methods. Additional consideration must be given to the protocols used for extracting RNA from each isolated cell and for its conversion to cDNA; common methods vary with respect to transcript coverage and strand specificity. Details are provided in reviews by Grün and van Oudenaarden [7], Saliba et al. [5] and Kolodziejczyk et al. [6]. Another issue concerns whether or not to include synthetic spike-ins (external transcripts added in known concentrations) or unique molecular identifiers (UMIs; short random sequences attached to individual cDNA molecules). While both have a number of theoretical advantages for normalization and expression estimation, practical challenges have prevented their routine use in scRNA-seq studies to date. In addition to the challenges detailed by Stegle et al. [8], spike-ins are typically added in an scRNA-seq experiment at very high relative concentrations and, consequently, they take up a relatively large proportion of reads, an important consideration during deliberations regarding experimental design. In addition, recent droplet technologies are not yet able to accommodate spike-ins. UMIs offer a great advantage in reducing noise resulting from amplification bias [9, 10], but protocols that implement UMIs sequence only the 5′ or 3′ end of each transcript, making them unsuitable for studies of isoforms or allele-specific expression.

Whatever the design, it is always beneficial (and requires almost no additional resources) to record and retain information on as many factors as possible to facilitate downstream diagnostics. Just as it is standard to check residuals following a linear regression, it should be standard in sequencing experiments to check that effects of interest are not confounded by variations in technician, sample processing date/time, reaction temperature, position on cell capture device, lane, batch, proportion of detected genes, and so on. Through such an analysis, Leng et al. [11] identified an artifact related to position on Fluidigm’s IFC array; once identified, the effects of such artifacts can be removed [12]. It is also important to note that the sources of variation in an scRNA-seq experiment are not yet completely understood, and there likely are systematic effects that will be important in scRNA-seq that have yet to be discovered. Novel methods to identify such factors are needed and are beginning to be developed [4].

While many of the design principles established for bulk RNA-seq hold in the single-cell setting, specific guidelines to define what is meant by 'sufficiently powered' in an scRNA-seq experiment are less clear. As with bulk-RNA-seq, guidelines will generally depend on the questions of interest.

While most studies do not address the question of determining the minimum number of cells required for a given task, identifying the sequencing depth at which the majority of human transcripts expressed in a cell, or population of cells, are detected is a question that has received considerable attention. The consensus is that, beyond one million reads, there is very little change (<5 %) in the number of reliably expressed genes detected in a cell [13]. In fact, the majority of genes seem to be detected at 500,000 reads; and over half are typically detected at 250,000 reads [13, 14]. Furthermore, Shalek et al. [15] demonstrated that one million reads is sufficient to estimate the fraction of detectably expressing cells within a population and also to estimate the mean and variance of a gene’s expression among detectably expressing cells.

More reads will be required for more refined tasks, such as fully characterizing transcript structure, estimating the expression of rare isoforms, or distinguishing cells on the basis of subtle differences. Fewer reads but larger cell numbers may be preferred when mapping out a large population, searching for rare but distinct cell types, or pooling cells in silico to obtain average gene-expression clusters. Guidelines have yet to be reported for these considerations, as well as for most analysis tasks such as sub-population identification and the identification of transcripts showing differential distributions across conditions. As with any power calculation, precise guidelines will depend not only on the task at hand but also on the signal-to-noise ratio inherent to a given system. Pollen et al. [14] have shown, for example, that 50,000 reads is sufficient for cell-type classification in a sample of 301 cells containing diverse cell types. Conversely, in a seemingly homogenous cell population, deeper sequencing may be required to detect heterogeneity that is due to rare subpopulations. Evaluating the trade-off that exists between sequencing depth and number of cells will also depend on budget and, albeit to a much lesser extent, on platform, protocol, base-pair length, and genome size.

Once reads from a well-designed experiment are obtained, quality control should be performed on the raw reads, on the aligned reads, and across the collection of cells in an effort to identify low-quality cells that should be removed prior to expression estimation. Low-quality refers to those cells that are broken or dead or to capture sites that are empty or contain multiple cells; a detailed discussion is provided in Ilicic et al. [16]. Microscopic inspection of capture sites is often used to identify and remove empty or multiple captures prior to sequencing [11, 17, 18], but such a visual inspection is not possible with all platforms, is not feasible in very large-scale experiments, and is not helpful in identifying subtle features associated with low quality [16]. Beyond visual inspection, many of the hallmarks of low quality are qualitatively the same as in bulk RNA-seq; consequently, existing tools are proving useful in the single-cell setting [8]. FASTQC [19], Kraken [20], and RNA-SeQC [21] are all popular tools for assessing the quality of raw and mapped reads within an individual sample. Each calculates read quality using summaries of per-base quality defined using the probability of an incorrect base call [22]. Cells with unusually high numbers of low-quality reads are flagged for removal. Graphical interfaces allow a user to assess quickly whether there is structure in the low-quality scores: an abundance of low-quality scores in the first few positions of many reads may indicate a transient problem with the run, whereas a decrease in quality in the last positions indicates a general degradation. Trimming may prove useful in the latter but is not suggested for the former. The FASTQC website discusses these and other issues in detail [19]. For samples with sufficiently high-quality reads, as evidenced by relatively few base-call errors, additional features should be assessed. For most genomes, in a complex library free of nucleotide composition, GC content, and/or amplification bias, the proportion of nucleotides should be approximately equal across read positions (at least after an initial bias that may be present due to certain priming protocols), GC content should be approximately normally distributed across reads with a mean and variance similar to that in the reference transcriptome and very few reads should be duplicated.

Additional criteria should be assessed once reads are mapped to a reference transcriptome. The most common metrics are total number or reads, number of transcripts sequenced or detected, the proportion of uniquely mapping reads, and the proportion of reads mapping to annotated exonic regions, where low numbers are indicative of sample degradation and/or bias. The proportion of reads mapping to the mitochondrial genome may also be useful in identifying low-quality cells because in a broken cell cytoplasmic RNA will be lost, while RNAs that are enclosed in the mitochondria will be retained [16]. If spike-ins are used, the ratio of reads mapping to synthetic and endogenous transcripts can be informative [23]. Specifically, a high ratio may indicate that a cell was broken during the capture process [16]. Patterns associated with coverage are also important [21, 24] and can be evaluated, for example, by considering the evenness of coverage as represented by the mean coefficient of variation across transcripts, 5′/3′ coverage as assessed by calculating the average coverage at each percentile of length from annotated 5′ and 3′ ends of known transcripts, and gaps in coverage. Levin et al. [24] discuss these metrics in detail and Li et al. [25] provide examples; RNA-SeQC provides a software package to facilitate straightforward calculation and visualization [21]. It is important to note that expected coverage patterns will depend on protocol and should be evaluated accordingly [7].

Given all the metrics potentially relevant in assessing a cell’s quality, it can be difficult to decide which samples to include. Specifically, what proportion of low-quality reads is considered unusually high? How many reads should be unique in a sufficiently complex library? FASTQC provides suggested thresholds that may be used for these and many of the other metrics discussed above. Although useful, thresholds will depend on many factors, including specific features of the transcriptome under study, read length, library preparation protocols, and the experimental design. For some measures, thresholds from bulk do not apply; mapping rates, for example, are typically lower in scRNA-seq. For these reasons, it can be helpful to compare metrics across many samples. QoRTs [26] and Qualimap2 [27] allow a user to assess the quality of individual cells in the ways just described, but also introduce metrics to assess quality across a collection of samples. This allows a user to identify outlier cells with respect to any of the metrics just discussed. It also allows for the identification of batch or other systematic artifacts that are not visible when considering individual samples in isolation. Caution must be exercised when discarding individual cells, or groups of cells, at this stage as a cell’s distinct features may be due to interesting biological processes and not technical artifacts. Keeping in mind that QoRTs and Qualimap2 were developed for bulk RNA-seq, in which outlier samples are more likely to be due to artifacts, extra caution should be exercised before discarding a cell that passes quality control individually but not in the group setting. Ilicic et al. [16] recently developed a supervised classification approach for identifying low-quality cells in the single-cell setting. Like QoRTs and Qualimap2, it considers a collection of cells; it also accommodates not only technical but also biological measures of cell quality and, because of its comprehensiveness, is likely to become one of the state-of-the art methods in this area.

With quality cells in hand, expression may be represented as counts from non-UMI data using HTSeq [28] or as expected counts using RSEM [29] or WemIQ [30]. If UMI-tagged data are available, counts can be obtained using approaches such as those detailed by Islam et al. [10] or Hashimshony et al. [31]. Measures of relative expression within a cell are also often used; these include transcripts per million mapped reads (TPM) or reads/fragments per kilobase per million mapped reads (RPKM or FPKM, respectively). As detailed below, these measures are not appropriate for comparing expression across cells in most cases because they assume that RNA content is constant across cells and that genes are equivalently expressed. For most downstream analyses, normalization among cells is needed.

Normalization commonly refers to adjusting for differences in expression levels that result from technical artifacts, so that expression may be compared within or between samples. It is widely recognized that many systematic sources of variation affect scRNA-seq read counts and should be adjusted for, including capture inefficiency, amplification biases, GC content, differences in total RNA content, sequencing depth, etc. In practice, however, it is difficult to estimate many of these variance sources and so most often scRNA-seq normalization amounts to adjusting for differences in sequencing depth. When well-behaved and representative synthetic spike-ins and/or UMIs are available, further refinement is possible. We first discuss methods for normalization that do not involve spike-ins or UMIs.

Several strategies have been proposed to reduce noise from both technical and biological sources in scRNA-seq experiments [9, 49]. In spite of considerable progress, challenges remain, and scRNA-seq protocols continue to have substantially increased levels of nuisance variation relative to bulk RNA-seq. Capture efficiency (percentage of mRNA molecules in the cell lysate that are captured and amplified), amplification bias (non-uniform amplification of transcripts), and sequencing efficiency (rate at which cDNAs in a library are sequenced) are major contributors to technical variation. These sources affect counts in both a gene- and a cell-specific manner and are observed to have the greatest effect on lowly expressed genes [48, 63, 64]. Considerable variation also results from differences among cells in cell-cycle stage or cell size, variation that is not typically observed in (unsynchronized) bulk RNA-seq experiments in which expression is profiled on average over thousands of cells. These biological sources of variation are not of interest in most experiments and hence contribute to nuisance variation, although we note that in some experiments (for example, investigations of cell-cycle genes), this variation will be of direct interest. Given the substantial variability present in scRNA-seq measurements, separating nuisance from meaningful biological variation is crucial for accurately characterizing sub-populations, identifying highly heterogeneous genes, and comparing expression levels among groups of cells; a number of statistical approaches have been developed toward this end.

One group of methods aims to estimate technical variability, with the goal of identifying genes that have overall variability that greatly exceeds that expected from technical sources [48, 54, 63]. These methods use spike-ins to estimate technical noise because spike-ins are exposed to most of the same experimental steps as endogenous genes but are free of biological variation. Specifically, Brennecke et al. [48] demonstrated a strong non-linear relationship between gene expression and CV² for spiked-in genes, where CV² represents the square of the coefficient of variation. By modeling this relationship, estimates of technical variability are obtained and genes whose expression variability greatly exceeds these estimates for a given biological variability threshold can be identified. Although useful, this approach does not fully capture cell-to-cell differences in technical variability [63] or give explicit estimates of biological variability [9]. More recent methods provide improvements by estimating biological variability [9] or by incorporating additional aspects of technical noise to estimate parameters that account for variation across cells using spike-ins [63] or jointly over spike-ins and genes [54].

A second group of methods aims to identify and adjust for nuisance variation imposed by oscillatory genes. Specifically, Buettner et al. [47] propose a single-cell latent variable model (scLVM) to adjust for the effects of cell-cycle oscillations. By adjusting for a structured source of variation (resulting from oscillations), the overall residual variance is reduced, increasing the signal-to-noise ratio and effectively increasing power. The scLVM approach estimates a covariance matrix for known cell-cycle genes using a Gaussian-process latent variable model. A linear mixed model is then fitted to each gene with random effects, modeling contributions from hidden factors represented by the covariance matrix, technical noise, and biological variation. Residuals from the fit produce so-called 'corrected' gene expression values in which the variation associated with the cell-cycle has been removed. Buettner et al. [47] demonstrated nicely that previously masked sub-populations associated with T-cell differentiation are revealed following removal of cell cycle-associated variation.

A related approach called Oscope [11] does not rely on oscillating genes being identified a priori. Rather, it was developed to identify and characterize oscillators in snapshot (non temporal) scRNA-seq experiments. When oscillations that are due to the cell cycle or other sources are not of interest but rather are nuisance variables masking the effects that are of interest, the oscillatory gene groups identified by Oscope may be used subsequently in a de-noising step, using either scLVM or, for specific groups of genes, OEFinder [12]. It should be noted that Oscope is useful not only when oscillators are nuisance variables but also when they are of direct interest. For example, Oscope could be used in studies that aim to identify new oscillators (see the “Pseudotemporal ordering and inference” section).

Two of the most common goals of an scRNA-seq experiment are identifying cell sub-populations within a biological condition and characterizing genes that have differential distributions (DD) across conditions. We discuss each separately. As with normalization, the majority of reported scRNA-seq studies use methods developed for bulk experiments. Specifically, hierarchical clustering and/or PCA is often performed on DE [3, 15, 65], highly expressed [66, 67], or highly variable genes [61, 62] (or gene sets [68]) to identify cell sub-populations. A nonlinear dimension-reduction method, t-SNE [69], has also been used for scRNA-seq data and is often applied to a subset of highly variable genes [60–62]. High variability in expression levels among cells of the same type, which is common in scRNA-seq, can cause underlying structure to be undetected by these otherwise useful approaches. In addition, PCA (and related methods such as factor analysis (FA)) can provide misleading results in the single-cell setting because of the presence of zeros [70]. Methods have been developed recently to address these limitations. ZIFA is a dimension-reduction approach that augments a latent variable factor analysis model to accommodate zeros [70]. Pierson and Yau [70] used simulation studies to show that ZIFA has comparable performance to PCA/FA when no (or few) zeros are present and has considerable advantages in the presence of zeros. SNN-Cliq is a computationally efficient clustering approach that relies on shared nearest neighbor (SNN) similarity measures, which utilize rankings of similarities (such as Euclidean distance) between gene expression values as opposed to their numerical values [71]. As the ranking of nodes usually retains meaning in the high-dimensional setting, even when primary similarity measures might not, SNN-cliq proves to be more robust and precise than traditional approaches. Like SNN-cliq, RaceID also provides advantages gained by clustering of processed data as opposed to gene-expression values [59]. Specifically, RaceID performs k-means clustering applied to a similarity matrix determined by Pearson’s correlation coefficients from pairs of cells, which is shown to yield improvements in cluster separation relative to using expression values directly. A second step allows for outlier cells to be regrouped into separate clusters in an effort to identify rare sub-populations. Once sub-populations are identified, it will be very interesting to determine if they correspond to a known cell type; toward this end, a cell-type-enrichment analysis approach similar to gene-set-enrichment analysis has been developed as part of SINCERA [72]. Finally, if data from multiple time points are available, single-cell clustering using bifurcation analysis (SCUBA) can be used to identify sub-populations at an initial time point and to extract lineage relationships between the sub- populations and cells at subsequent time points [73].

To identify genes that have expression differences across conditions in an scRNA-seq study, investigators often use methods from bulk RNA-seq that test for shifts in unimodal distributions across conditions [3, 31, 56, 67, 74, 75]. A number of groups have recognized the deficiencies in doing so: due to both biological and technical variability cell-to-cell, there is often an abundance of cells for which a given gene’s expression is measured at zero. Recent methods, including MAST [76] and SCDE [77], have been developed to accommodate bimodality in expression levels resulting from an abundance of zero (or low) values. In these mixture-model-based approaches, one component distribution accommodates unobserved, or dropout, measurements (which include zero and, optionally, thresholded low-magnitude observations) and a second unimodal component describes gene expression in cells where expression is observed. (Note that SCDE uses a three-component mixture to fit error models and to improve expression estimates but a two-component mixture for testing for differences in expression across conditions.) Although these approaches provide an advance over the unimodal models that are used in the bulk setting, they are insufficient for characterizing multi-modal expression data, which is common in scRNA-seq experiments. For example, cell heterogeneity often gives rise to bimodal distributions within the “observed” component [15, 65].

A recent method developed by Korthauer et al. [78] accommodates multi-modality to identify genes with DD across conditions. In their Bayesian modeling framework, called scDD, they accommodate four types of changes across two biological conditions: shifts in unimodal distributions (traditional DE); differences in the number of modes (DM); differences in the proportion of cells within modes (DP); or both DE and DM, which the authors refer to as DB. The scDD model provides posterior probabilities of DD for each gene and then, using those posterior probabilities, classifies each DD gene into one of the four patterns. By explicitly modeling the multi-modal expression, scDD is likely to have increased power to identify differences in many settings.

Dynamic processes such as stem cell renewal and differentiation are essential for normal tissue development, homeostasis, and repair, yet our understanding of these fundamental processes remains primitive. Bulk RNA-seq studies have enabled numerous insights, but averaging over thousands of cells obscures, and in some cases misrepresents, signals of interest [79]. Consequently, the ability to profile genome-wide expression in individual cells is critical to improving our understanding of the dynamic cellular processes associated with development, differentiation, and disease. Single-cell RNA-seq experiments provide for such profiling but they too are limited to snapshot experiments, meaning that continuous monitoring of genome-wide gene expression in individual cells over time is not possible. Fortunately, computational algorithms coupled with scRNA-seq data enable reconstruction of differentiation paths from a population of individual unsynchronized cells. The idea is that, at any given time point, an unsynchronized cell population contains cells at various stages of differentiation. (We refer to differentiation throughout, noting that other dynamic biological processes may also be studied using these approaches.) Expression dynamics may be resolved by reordering the cells according to their position along a differentiation path. A number of statistical and computational methods have been developed toward this end.

Although the details differ considerably among methods, most approaches perform some type of dimension reduction and then apply algorithms from graph theory (or extensions thereof) designed to traverse nodes in a graph efficiently. In short, of interest in many graph theoretic considerations is identifying the paths (orderings of nodes) that pass through selected nodes in a graph while minimizing some distance function. This problem is structurally similar to ordering cells along a differentiation path or paths; the goal is to order cells so that the distance between cells, determined by gene expression, is minimized. Typically, distance is defined using genes that explain a substantial proportion of variance or those known to be important in differentiation.

Monocle was the first robust and efficient computational method developed to order cells according to their position along a differentiation process [36]. To reconstruct the so-called pseudotemporal ordering, Monocle uses independent component analysis (ICA) for dimension reduction, then constructs a minimum-spanning tree (MST) through the dimension-reduced data. The longest path through the MST is used initially to place cells according to their progress through differentiation. Divergence among paths is accommodated and numerous trajectories are considered to order cells that are not well placed initially. Monocle’s motivating examples and analysis are done using data from four time points and the authors [36] note that selecting genes that are DE between time points allowed for robust ordering. It is possible to use Monocle for pseudotime ordering of data from a single time point, but doing so would require a user to identify salient, temporally related genes, which in some cases is not possible. Waterfall is similar to Monocle but uses unsupervised clustering and PCA in a pre-processing step to identify groups of ordered cells (temporal delineators are not required) that are then used to reconstruct a full ordering using an MST [80].

Methods that are based on diffusion maps have also been developed [81]. They allow for dimension reduction and reconstruction in a single step, are relatively robust to noise, accommodate zeros, and are largely insensitive to the underlying sampling distribution; but with these advantages comes a considerable computational burden. Specific implementations that consider subsets of paths can dramatically improve performance [82]; and Sincell provides a general implementation in which various options for dimension reduction and pseudotemporal reconstruction may be specified by a user [83].

A key assumption that enables pseudotemporal ordering is that genes do not change direction very often, and thus samples with similar transcriptional profiles should be close in order. If oscillatory processes are of interest, the aforementioned approaches are not appropriate because genes that follow the same oscillatory process need not have similar transcriptional profiles. Two genes with an identical frequency that are phase shifted, for example, will have little similarity. Oscope was developed to enable the identification and reconstruction of oscillatory trajectories [11]. Like other pseudotemporal reconstruction algorithms, Oscope capitalizes on the fact that cells from an unsynchronized population represent distinct states in a system. Unlike previous approaches, however, it does not attempt to construct a linear order that is based on minimizing change among adjacent samples. Instead, it utilizes co-regulation information among oscillators to identify groups of putative oscillating genes and then reconstructs the cyclic order of samples for each group, defined as the order that specifies each cell’s position within one cycle of the oscillation. There are likely other processes of interest whose dynamics are not well described by the pseudotemporal or cyclic order reconstruction methods that are currently available and novel methods in this domain will prove useful.

Elucidating the structure and function of transcriptional regulatory networks is a central goal of numerous studies and scRNA-seq provides unprecedented potential toward this end. This challenge is commonly viewed as a regulatory network reconstruction problem, in which genes or transcripts represent nodes and edges represent interactions or dependence among nodes. Of primary interest are identifying meaningful groups of nodes, estimating edges, and determining the ways in which the network changes following perturbation. The weighted gene co-expression network analysis (WGCNA) is an analysis approach widely used in bulk RNA-seq [84]. In this framework, edges represent co-expression, as determined by both correlation and relative interconnectedness. It is not clear how these measures will perform in general when applied to scRNA-seq, where zeros and sub-populations are common, and it is likely that some adjustment to the existing framework may prove beneficial. At the same time, WGCNA has already enabled important insights in an scRNA-seq study focused on embryonic development [53]. There, the authors applied WGCNA to cells at the same developmental stage, minimizing the potential for spurious results induced by high-correlation coefficients resulting from the presence of sub-populations.

WGCNA and other association network reconstruction approaches have facilitated considerable progress in bulk studies and are expected to do so for scRNA-seq as well, but they do not provide information about regulatory relationships among nodes. To do so, temporal or perturbation experiments are typically required. As described in the previous section, it is possible to derive at least partial ordering from snapshot scRNA-seq experiments; two recent methods leverage the information provided by pseudotemporal ordering approaches and combine it with traditional methods for regulatory network reconstruction to infer regulatory relationships among genes [85, 86]. In doing so, these exciting methods greatly expand upon the type of information that can now be obtained from snapshot scRNA-seq experiments.

The past decade of genome research has led to major advances in single-cell sequencing technologies and concomitant advances in computational and statistical methodologies. Yet a number of challenges remain and must be addressed to ensure that maximal information can be obtained from single-cell RNA-seq, as well as other types of single-cell experiments. Methods from bulk experiments are readily applicable, perhaps following straightforward extensions, for tasks such as quality control and expression estimation that involve raw data. In contrast, novel methods are required for tasks that are directly affected by features characteristic of single-cell data, including an abundance of zeros, increased heterogeneity, and complex expression distributions. These tasks include normalization, sub-population identification, assessment of differential dynamics, pseudotime reconstruction, and network inference. For questions that involve processed measurements (involving PCA, FA, or network inference methods, for example), a main challenge is how best to define distance. Standard measures of distance may be compromised in the single-cell setting given the frequency of strongly expressed genes that dominate such measures and given the abundance of missing data that are not missing at random but rather arise from both biological and technical sources. Once robust and informative measures of distance are developed, applications of traditional methods will result in much-improved performance.

We have focused primarily on analyses for which multiple tools are available, although we note that there are additional methodological challenges that are not highlighted here. For example, novel methods are beginning to be developed for studies of allele-specific expression [63] and isoform usage [87]. Methodological challenges are also introduced with the advent of technologies that increase sample size by allowing for routine profiling of tens of thousands of cells [61, 62, 88]. Some of the methods discussed here will enjoy improved performance, whereas others will require extensions or approximations to handle the computational burden. Advances will also facilitate the study of single-cell gene-expression profiles over time, space [89], or lineage [90], as well as of multiple types of -omics data within a single cell [91]. This progress will usher in unique opportunities to fully address fundamental questions associated with cell state, circuitry, and fate decisions during development, homeostasis, and disease. As we enter a period of unparalleled data accumulation and analysis, computational biology will undoubtedly continue to contribute important advances to our understanding of molecular systems.

Six publically available datasets (three bulk and three single cell) are shown in Fig. 1. Datasets bulk1, bulk3, and sc3 contained spike-ins that were removed prior to analysis. The six datasets are described in detail below.