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      scEpath: energy landscape-based inference of transition probabilities and cellular trajectories from single-cell transcriptomic data

      1 , 1 , 1 , 1 , 2


      Oxford University Press

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          Single-cell RNA-sequencing (scRNA-seq) offers unprecedented resolution for studying cellular decision-making processes. Robust inference of cell state transition paths and probabilities is an important yet challenging step in the analysis of these data.


          Here we present scEpath, an algorithm that calculates energy landscapes and probabilistic directed graphs in order to reconstruct developmental trajectories. We quantify the energy landscape using ‘single-cell energy’ and distance-based measures, and find that the combination of these enables robust inference of the transition probabilities and lineage relationships between cell states. We also identify marker genes and gene expression patterns associated with cell state transitions. Our approach produces pseudotemporal orderings that are—in combination—more robust and accurate than current methods, and offers higher resolution dynamics of the cell state transitions, leading to new insight into key transition events during differentiation and development. Moreover, scEpath is robust to variation in the size of the input gene set, and is broadly unsupervised, requiring few parameters to be set by the user. Applications of scEpath led to the identification of a cell-cell communication network implicated in early human embryo development, and novel transcription factors important for myoblast differentiation. scEpath allows us to identify common and specific temporal dynamics and transcriptional factor programs along branched lineages, as well as the transition probabilities that control cell fates.

          Availability and implementation

          A MATLAB package of scEpath is available at

          Supplementary information

          Supplementary data are available at Bioinformatics online.

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          Most cited references 40

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          Pseudo-temporal ordering of individual cells reveals dynamics and regulators of cell fate decisions

          Single-cell expression profiling by RNA-Seq promises to exploit cell-to-cell variation in gene expression to reveal regulatory circuitry governing cell differentiation and other biological processes. Here, we describe Monocle, a novel unsupervised algorithm for ordering cells by progress through differentiation that dramatically increases temporal resolution of expression measurements in a model of skeletal muscle differentiation. This reordering unmasks switch-like changes in expression of key regulatory factors, reveals sequentially organized waves of gene regulation, and exposes novel regulators of cell differentiation. A loss-of function screen revealed that many of these inhibitors act through regulatory elements also used by pro-myogenic factors to activate downstream genes. This study demonstrates that single-cell expression analysis by Monocle can uncover novel regulatory interactions governing differentiation. Cell differentiation is governed by a vast and complex gene regulatory program. During differentiation, each cell makes fate decisions independently by integrating a wide array of signals from other cells, executing a complex choreography of gene regulatory changes. Recently, several studies carried out at single-cell resolution have revealed high cell-to-cell variation in most genes during differentiation 1–5 , even among key developmental regulators. Although high variability complicates analysis of such experiments 6 , it might define biological progression between cellular states, revealing regulatory modules of genes that co-vary in expression across individual cells 7 . Prior studies have used approaches from computational geometry 8,9 and supervised machine learning 10 to order bulk cell populations from time-series microarray experiments by progress through a biological process. Applying this concept to order individual cells could expose fine-grained gene expression dynamics as they differentiate. We have developed Monocle, an algorithm that harnesses single cell variation to sort cells in “pseudo time” according to progress through differentiation. Applying Monocle to the classic model of myogenesis unveiled dynamics at unprecedented resolution and exposed novel regulatory factors. Skeletal myoblasts undergo a well-characterized sequence of morphological and transcriptional changes during differentiation 11 . Global expression and epigenetic profiles have reinforced the view that a small cohort of transcription factors (e.g. MYOD, MYOG, MRF4, and MYF5) orchestrates these changes 12 . However, efforts to expand this set of factors and map the broader myogenic regulatory network have been hampered by the temporal resolution of global expression measurements, with thousands of genes following a limited number of coarse kinetic trends 13 . Single-cell measurements of markers of myogenesis have made clear that cells do not progress through differentiation in synchrony. A population of cells captured at the same time may thus cover a range of distinct intermediate differentiation states. Drawing conclusions from a group of individuals based on the properties of their average is a hazardous practice because the average can mask important trends among the individuals, resulting in phenomena such as Simpson's paradox 14 . Experimental synchronization or stringent isolation of myogenic precursors is often challenging and dramatically alters differentiation kinetics. We hypothesized that capturing complete expression profiles of individual cells might avoid these problems and dramatically increase temporal resolution in global transcriptome dynamics. In essence, a single-cell RNA-Seq experiment might constitute a time-series, with each cell representing a distinct time point along a continuum. To test this hypothesis we investigated the single cell transcriptome dynamics during myogenesis. We expanded primary human myoblasts under high mitogen conditions (GM), and then induced differentiation by switching to low-mitogen media (DM). We then captured 50–100 cells at each of four time points following serum switch using the Fluidigm C1 microfluidic system. RNA from each cell was isolated and used to construct mRNA-Seq libraries, which were then sequenced to a depth of ~4 million reads per library, resulting in a complete gene expression profile for each cell (Fig 1a, S1). Averaging expression profiles of cells collected at the same time correlated well with the corresponding bulk RNA-Seq libraries, and moderately expressed genes were detectable (≥ 1 FPKM) in a majority of individual cells (Fig 1b, S2, S3). However, markers of mature myocytes were present at all time points following serum switch, and many other genes showed similar temporal heterogeneity (Fig 1c) We speculated that the high variability in cell-to-cell gene expression levels was due to unsynchronized differentiation, with myoblasts, intermediate myocytes, and mature myotubes residing in the same well concurrently. Indeed, large, multinucleated MYH2+ cells were abundant after 72 hours in DM, but these cells were present at lower frequency even at 24 hours (Fig 1c). We reasoned that informatically ordering the cells by their progress through differentiation, rather than by the time they were collected, would distinguish genes activated early in differentiation from those activated later. To this end, we developed a novel unsupervised algorithm, Monocle, which re-ordered the cells to maximize the transcriptional similarity between successive pairs (Fig 2a). The algorithm first represents the expression profile of each cell as a point in a high-dimensional Euclidean space, with one dimension for each gene. Second, it reduces the dimensionality of this space using Independent Component Analysis 15 . Third, Monocle constructs a minimum spanning tree (MST) on the cells, an approach now commonly used in other single-cell settings, such as flow or mass cytometry 16,17 . Fourth, the algorithm finds the longest path through the MST, corresponding to the longest sequence of transcriptionally similar cells. Finally, Monocle uses this sequence to produce a “trajectory” of an individual cell's progress through differentiation. Progress along a differentiation trajectory is measured in “pseudo-time”: the total transcriptional change a cell undergoes as it differentiates. This strategy is derived from a prior algorithm for temporally ordering microarray samples 8 , but extends it to allow for multiple cell fates stemming from a single progenitor cell type. As cells progress, they may diverge along two or more separate paths. After Monocle finds the longest sequence of similar cells, it examines cells not along this path to find alternative trajectories through the MST. These sub-trajectories are ordered and connected to the main trajectory, and each cell is annotated with both a trajectory and a pseudo-time value. Monocle thus orders cells by progress through differentiation and can reconstruct branched biological processes, which might arise when a precursor cell makes cell fate decisions that govern the generation of multiple subsequent lineages. Importantly, Monocle is unsupervised and needs no prior knowledge of specific genes that distinguish cell fates, and is thus suitable for studying a wide array of dynamic biological processes. Monocle decomposed myoblast differentiation into a two-phase trajectory and isolated a branch of non-differentiating cells (Fig 2b). The first phase of the trajectory was primarily composed of cells collected under high-mitogen conditions and which expressed markers of actively proliferating cells such as CDK1, while the second mainly consisted of cells collected at 24, 48, or 72 hours following serum switch. Cells in the second phase were positive for markers of muscle differentiation such as MYOG (Fig S4). A tightly grouped third population of cells branched from the trajectory near the transition between phases. These cells lacked myogenic markers but expressed PDGFRA and SPHK1, suggesting that they are contaminating interstitial mesenchymal cells and did not arise from the myoblasts. Such cells were recently shown to stimulate muscle differentiation 18 . Monocle's estimates of the frequency and proliferative status of these cells were consistent with estimates derived from immunofluorescent stains against ANPEP/CD13 and nuclear phosphorylated H3-Ser10 (Fig S4). Monocle thus enabled analysis of the myoblast differentiation trajectory without subtracting these cells by immunopurification, maintaining in vitro differentiation kinetics that resemble physiological cell crosstalk occurring in the in vivo niche. To find genes that were dynamically regulated as the cells progressed through differentiation, we modeled each gene's expression as a nonlinear function of pseudo-time. A total of 1,061 genes were dynamically regulated during differentiation (FDR = 0.8) to their relative order within the full data set. The algorithm retained the ability to detect dynamically regulated genes with high precision (>= 95%) over all designs and with increasing recall as more of the cells were included. (Fig S7) We next grouped genes with similar trends in expression, reasoning that such groups might share common biological functions and regulators. Clustering of genes according to direction and timing revealed six distinct trends (Fig 3). Genes downregulated early or upregulated late in pseudo-time were highly enriched for biological processes central to myogenesis, including cell-cycle exit and activation of muscle-specific structural proteins. However, the other clusters included many genes with broad roles in development, including mediators of cell-cell signaling, RNA export and translational control, and remodeling of cell morphology (Fig S8). A timeseries analysis of myoblast differentiation with bulk RNA-Seq identified up and down-regulated genes, but did not identify the transient clusters or distinguish the early from late regulation visible with pseudo-temporally ordered single cells (Fig S9). Furthermore, dynamic range of expression was compressed for most genes, confirming that failure to account for variability in progress through differentiation leads directly to the effects associated with Simpson's paradox. Pseudo-temporal cell ordering thus decomposes the coarse kinetic trends produced by conventional RNA-Seq into distinct, sequential waves of transcriptional reconfiguration. To identify factors driving myoblast differentiation, we performed a cis-regulatory analysis on genes in each pseudo-temporal cluster. Cis regulatory elements were first identified based on DNaseI hypersensitive sites in HSMM cells and HSMM-derived myotubes 20 , classified according to function according to histone marks 21 , and finally annotated with conserved transcription factor binding sites. While downregulated genes were enriched at near significant levels with binding sites for genes that play roles in proliferation (e.g. MAX, E2F, and NMYC), nearly all significantly enriched motifs fell near upregulated genes. These genes were highly enriched for regulatory elements containing binding motifs for 175 transcription factors, including numerous well-known regulators of myogenesis, such as MYOD, MYOG, PBX1, MEIS1, and the MEF2 family (Fig S10). Some, but not all, of these factors were revealed by a regulatory element analysis performed using bulk RNA-Seq data, underscoring the power of increased (pseudo) temporal resolution of single-cell analysis (Fig S11). A similar analysis of microRNA target sites identified miR-1, miR-206, miR-133, and numerous others as regulators of genes activated during myogenesis (Fig S12). Of these, only miR-1/206 target sites were significantly enriched among genes found to be transiently upregulated and then sharply downregulated. This may suggest that miR-1 and miR-206, which are expressed at an intermediate stage of myoblast differentiation, may act to strongly suppress a subset of genes activated earlier. Many of the transcription factors implicated by our cis regulatory analysis to govern differentiation had no previously appreciated role in muscle development. To test potential roles of these factors we performed an RNAi mediated loss of function screen for 11 candidates. Briefly, we virally expressed proliferating myoblasts with one of 44 distinct shRNAs targeting either one of these factors or a mock (non-targeting) control, followed by serum-induced differentiation for five days. We then measured the frequency and size of myosin heavy chain 2 (MYH2)-positive cells with a high-throughput immunofluorescence pipeline. Of the targets we tested, MZF1, ZIC1, XBP1, and USF1 showed significantly altered differentiation kinetics (Fig 4a,b, Fig S13) when depleted with two or more independent hairpins (FDR < 5%). Knockdown of XBP1, USF1, ZIC1, and MZF1 enhanced myotube formation, with larger myotubes containing a higher fraction of total nuclei than mock shRNA controls. Depletion of CUX1, ARID5B, POU2F1, and AHR also increased differentiation efficiency, albeit less significantly. Importantly, whole-well nuclei counts were similar between knockdowns and mock controls, indicating that enhanced differentiation was not simply a result of higher initial cell counts or increased proliferation. With the exception of ZIC1, forced overexpression did not substantially alter differentiation kinetics (data not shown). Notably, several of these factors have binding motifs that are highly enriched in promoters and enhancers that also have motifs for known muscle regulators (Fig 4c). For example, USF1 motifs are enriched in enhancers that also have MYOD motifs. Together, these results confirm that the transcription factors identified as possible regulators in fact play a role in myoblast differentiation, and demonstrate the power of Monocle for identifying key differentiation genes. Here, we report that individual myoblasts progress through differentiation in an unsynchronized manner, but that they can be reordered according to progress through differentiation. This pseudo-time ordering pinpoints key events in differentiation that are masked both by conventional bulk cell expression profiling, and by single-cell expression profiles ordered by time collected. The reordering resolves sequentially activated transcriptional sub-programs that are regulated by common factors. The temporal resolution offered by hundreds of ordered cells might enable future efforts to computationally infer novel gene-regulatory modules. For example, the enrichment of transiently upregulated genes for common microRNA target sites raises the question of whether those microRNAs are expressed later, curtailing what would have been higher levels of expression. Sequencing-based measurements of small RNAs and mRNAs from the same cell will provide answers to such systems-level questions. Moreover, single-cell analysis distinguishes cells of interest from contaminating cell types such as interstitial mesenchymal cells without experimental isolation that might disrupt cell-cell interactions important in the in vivo niche. We identified eight previously unappreciated transcription factors that dramatically influence the course of myoblast differentiation, thus proving the principle of pseudo-temporal analysis and expanding the catalog of regulators in this well-studied system. Several of the eight factors reported here may normally repress differentiation by competing with pro-myogenic factors for these regulatory elements. Alternatively, these inhibitors may co-occupy regulatory elements with pro-myogenic factors, preventing transactivation of their targets (Fig. 4d). Previous studies in other contexts provide mechanistic data supporting both of these models. USF1 inhibits MyoD autoactivation in Xenopus by competing with MyoD at its promoter through an alternative E-box 22 . Our results suggest that USF1 may repress a broad array of targets via E-box competition. CUX1 represses targets in several developmental contexts through binding site competition 23 . XBP1 was recently reported to inhibit myoblast differentiation in mice, potentially through the mechanisms proposed here 24 . Further experiments in these HSMM cells and myoblasts from other anatomic depots will be needed to confirm the mechanism of these factors. While the positive regulators of myogenesis have been well characterized, only a handful of inhibitors have been identified. The eight inhibitors reported here may shed light on how the balance of proliferation and differentiation is maintained during development and regeneration. Ordering the expression profiles of individual cells by biological progress is thus a powerful new tool for studying cell differentiation, and could in principle be used to map regulatory networks that govern a much wider array of biological processes. Supplementary Material 1
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            A Tutorial on Spectral Clustering

            In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.
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              Reconstructing lineage hierarchies of the distal lung epithelium using single cell RNA-seq

              The mammalian lung is a highly branched network, in which the distal regions of the bronchial tree transform during development into a densely packed honeycomb of alveolar air sacs that mediate gas exchange. Although this transformation has been studied by marker expression analysis and fate-mapping, the mechanisms that control the progression of lung progenitors along distinct lineages into mature alveolar cell types remain obscure, in part due to the limited number of lineage markers 1 - 3 and the effects of ensemble averaging in conventional transcriptome analysis experiments on cell populations 1 – 5 . We used microfluidic single cell RNA sequencing (RNA-seq) on 198 individual cells at 4 different stages encompassing alveolar differentiation to measure the transcriptional states which define the developmental and cellular hierarchy of the distal mouse lung epithelium. We empirically classified cells into distinct groups using an unbiased genome-wide approach that did not require a priori knowledge of the underlying cell types or prior purification of cell populations. The results confirmed the basic outlines of the classical model of epithelial cell type diversity in the distal lung and led to the discovery of many novel cell type markers and transcriptional regulators that discriminate between the different populations. We reconstructed the molecular steps during maturation of bipotential progenitors along both alveolar lineages and elucidated the full lifecycle of the alveolar type 2 cell lineage. This single cell genomics approach is applicable to any developing or mature tissue to robustly delineate molecularly distinct cell types, define progenitors and lineage hierarchies, and identify lineage-specific regulatory factors.

                Author and article information

                Role: Associate Editor
                Oxford University Press
                15 June 2018
                05 February 2018
                05 February 2018
                : 34
                : 12
                : 2077-2086
                [1 ]Department of Mathematics and Center for Complex Biological Systems
                [2 ]Department of Development and Cell Biology, University of California, Irvine, CA, USA
                Author notes
                To whom correspondence should be addressed. Email: qnie@
                © The Author(s) 2018. Published by Oxford University Press.

                This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact

                Page count
                Pages: 10
                Funded by: National Institute of Health
                Award ID: P50GM76516, R01GM107264, R01ED023050, R01NS095355, R01GM123731
                Funded by: National Science Foundation 10.13039/100000001
                Award ID: DMS1161621, DMS1562176
                Funded by: Jayne Koskinas Ted Giovanis Foundation for Health and Policy
                Funded by: Breast Cancer Research Foundation 10.13039/100001006
                Funded by: National Institutes of Health 10.13039/100000002
                Original Papers
                Gene Expression

                Bioinformatics & Computational biology


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