What's new in Monocle 3

Monocle 3 has been re-engineered to analyze large, complex single-cell datasets. The algorithms at the core of Monocle 3 are highly scalable and can handle millions of cells. Monocle 3 will add some powerful new features that enable the analysis of organism- or embryo-scale experiments:

  • A better structured workflow to learn developmental trajectories.
  • Support for the UMAP algorithm to initialize trajectory inference.
  • Support for trajectories with multiple roots.
  • Ways to learn trajectories that have loops or points of convergence.
  • Algorithms that automatically partition cells to learn disjoint or parallel trajectories using ideas from "approximate graph abstraction".
  • A new statistical test for genes that have trajectory-dependent expression.
  • A 3D interface to visualize trajectories and gene expression.

Monocle 3 is still under active development. This first early alpha release only includes some of the features listed above. We plan to release updates to Monocle 3 every few weeks that add the functionality you see mentioned here. Moreover, the above is only a partial list of the new features being added to Monocle 3, and more may be announced over the next few weeks and months. Note that some of Monocle 2's functions haven't yet been forward ported to Monocle 3. We welcome users' bug reports, comments and feedback.

The features discussed here will be described in more detail in upcoming manuscripts.

Below, you can find more details about some of the major new ideas and features in Monocle 3.

Uniform Manifold Approximation and Projection

Recently, Leland McInnes and John Healy introduced UMAP, a powerful new manifold learning technique that we've found works extremely well on single-cell RNA-seq data. Monocle 3 uses UMAP to embed cells in a low dimensional space, and then uses our principal graph embedding algorithms to learn a trajectory that fits the cells' UMAP coordinates. This approach enables Monocle 3 to learn very complex, potentially disjoint trajectories without much parameter optimization. Monocle 3 currently relies on the python implementation of UMAP. You can check out the preprint about UMAP here:

McInnes, L, Healy, J, UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction, ArXiv e-prints 1802.03426, 2018).

In Monocle 3 we provide a standard alone function UMAP to run umap. UMAP is also seamlessly integrated into the reduceDimension function.

Installing Monocle 3

Required software

Monocle runs in the R statistical computing environment. You will need R version 3.5 or higher, Bioconductor version 3.7, and monocle 2.99.0 or higher to have access to the latest features. To install Bioconductor:


Once you've installed Bioconductor, make sure you've installed Monocle 2 and all of its required dependencies:


Install DDRTree (simple-ppt-like branch) from our GitHub repo:

devtools::install_github("cole-trapnell-lab/DDRTree", ref="simple-ppt-like")

Install the latest version of L1-graph from our GitHub repo:


Install several python packages Monocle 3 depends on:

py_install('umap-learn', pip = T, pip_ignore_installed = T) # Ensure the latest version of UMAP is installed

Then pull the monocle3_alpha branch of the Monocle GitHub repo:

devtools::install_github("cole-trapnell-lab/monocle-release", ref="monocle3_alpha")

Testing the installation

To ensure that Monocle was installed correctly, start a new R session and type:


Getting help

Questions about Monocle 3 should be posted on our Google Group. Please use monocle.users@gmail.com for private communications that cannot be addressed by the Monocle user community. Please do not email technical questions to Monocle contributors directly.

The Monocle 3 workflow

Before we get into the details of ordering cells along a trajectory, it's important to understand what Monocle is doing. The ordering workflow shown above has five main steps, each of which involve a significant machine learning task.

Step 1: Normalizing and pre-processing the data

To analyze a single-cell dataset, Monocle first normalizes expression values to account for technical variation in RNA recovery and sequencing depth.

Step 2: Reducing the dimensionality of the data

Next, to eliminate noise and make downstream computations more tractable, it projects each cell onto the top 50 (by default) principal components. Then, you as the user choose whether to reduce the dimensionality further using one of two non-linear methods for dimensionality reduction: t-SNE or UMAP. The former is an extremely popular and widely accepted technique for visualizing single-cell RNA-seq data. The latter is faster, and often better preserves the global structure of the data but is also newer and therefore less well tested by the single-cell community. Then, Monocle 3 will cluster your cells, organize them into trajectories, or both.

Step 3: Clustering and partitioning the cells

Monocle 3 can learn multiple disconnected or "disjoint" trajectories. This is important because many experiments will capture a community of cells that are responding to a stimulus or undergoing differentiation, with each type of cell responding differently. Because Monocle 2 assumes that all of your data is part of a single trajectory, in order to construct individual trajectories you would have to manually split up each group of related cell types and stages into different sets, and then run the trajectory analysis separately on each group of cells. In contrast, Monocle 3 can detect that some cells are part of a different process than others in the dataset, and can therefore build multiple trajectories in parallel from a single dataset. Monocle 3 achieves this by "partitioning" the cells into "supergroups" using a method derived from "approximate graph abstraction" (AGA) (Wolf et al, 2017). Cells from different supergroups cannot be part of the same trajectory.

Step 4: Learning the principal graph

Monocle 3 provides three different ways to organize cells into trajectories, all of which are based on the concept of "reversed graph embedding". DDRTree is the method used in Monocle 2 to learn tree-like trajectories, and has received some important updates in Monocle 3. In particular, these updates have massively improved the throughout of DDRTree, which can now process millions of cells in minutes. SimplePPT works similarly to DDRTree in that it learns a tree-like trajectory, but it does not attempt to further reduce the dimensionality of the data. L1Graph is an advanced optimization method that can learn trajectories that have loops in them (that is, trajectories that aren't trees).

Once Monocle 3 has learned a principal graph that fits within the data, each cell is projected onto the graph. Then, the user selects one or more positions on the graph that define the starting points of the trajetory. Monocle measures the distance from these start points to each cell, traveling along the graph as it does so. A cell's pseudotime is simply the distance from each cell to the closest starting point on the graph.

Step 5: Differential expression analysis and visualization

Once this is complete, you can run tests for genes that are specific to each cluster, find genes that vary over the course of a trajectory, and plot your data in many different ways. Monocle 3 provides a suite of regression tests to find genes that differ between clusters and over trajectories. Monocle 3 also introduces a new test that uses the principal graph directly and can help find genes that vary in complex ways over a trajectory with loops and more intricate structures.

Tutorial 1: learning trajectories with Monocle 3

In this tutorial, we demonstrate how to use Monocle 3 (alpha release) to resolve multiple disjoint trajectories. We will mainly introduce:

  • How to learn tree-like trajectories with monocle 3 in two or three dimensions.
  • How to choose the starting point(s) for the trajectory.
  • How to visualize these trajectories in static 2D plots and interactive 3D plots.

Preliminaries: Load Monocle and the data

rm(list = ls())  # Clear the environment
options(warn=-1) # Turn off warning message globally
library(monocle) # Load Monocle

Let's load up the data from Paul et. al, which explored hematopoeisis at single-cell resolution. To save time, we'll just load a CellDataSet object. Monocle 3 makes some changes to the CellDataSet class, so we'll call a function to "upgrade" the old object to the new format. If you're starting from an expression matrix and building a new CellDataSet from scratch, you don't need to call updateCDS().

We'll also change the cluster IDs from the original study into easier to read names. Then we'll set up some colors for each of them that we'll use in some plots later.

cds <- readRDS(gzcon(url("http://trapnell-lab.gs.washington.edu/public_share/valid_subset_GSE72857_cds2.RDS")))

# Update the old CDS object to be compatible with Monocle 3
cds <- updateCDS(cds)

pData(cds)$cell_type2 <- plyr::revalue(as.character(pData(cds)$cluster),
                                        c("1" = 'Erythrocyte',
                                        "2" = 'Erythrocyte',
                                        "3" = 'Erythrocyte',
                                        "4" = 'Erythrocyte',
                                        "5" = 'Erythrocyte',
                                        "6" = 'Erythrocyte',
                                        "7" = 'Multipotent progenitors',
                                        "8" = 'Megakaryocytes',
                                        "9" = 'GMP',
                                        "10" = 'GMP',
                                        "11" = 'Dendritic cells',
                                        "12" = 'Basophils',
                                        "13" = 'Basophils',
                                        "14" = 'Monocytes',
                                        "15" = 'Monocytes',
                                        "16" = 'Neutrophils',
                                        "17" = 'Neutrophils',
                                        "18" = 'Eosinophls',
                                        "19" = 'lymphoid'))

cell_type_color <- c("Basophils" = "#E088B8",
                    "Dendritic cells" = "#46C7EF",
                    "Eosinophls" = "#EFAD1E",
                    "Erythrocyte" = "#8CB3DF",
                    "Monocytes" = "#53C0AD",
                    "Multipotent progenitors" = "#4EB859",
                    "GMP" = "#D097C4",
                    "Megakaryocytes" = "#ACC436",
                    "Neutrophils" = "#F5918A",
                    'NA' = '#000080')

Step 1: Noramlize and pre-process the data

We then estimate size factors for each cell and dispersion function for the genes in the cds as usual. Monocle 3 now performs these operations using the DelayedArray packages so they work on datasets with millions of cells. The dispersion calculation and several other operations rely on the DelayedArray package in Bioconductor, which splits the operation into blocks in order to avoid exhausting the computer's memory. You can control the block size and the verbosity of these operations as shown below:

# Pass TRUE if you want to see progress output on some of Monocle 3's operations

# Passing a higher value will make some computations faster but use more memory. Adjust with caution!

cds <- estimateSizeFactors(cds)
cds <- estimateDispersions(cds)

Next, run the preprocessCDS() function to project the data onto the top principal components:

cds <- preprocessCDS(cds, num_dim = 20)

Step 2: Reduce the dimensionality of the data

Then, apply a further round of (nonlinear) dimensionality reduction using UMAP:

cds <- reduceDimension(cds, reduction_method = 'UMAP')

Now we're ready to start learning trajectories!

Step 3: Partition the cells into supergroups

Rather than forcing all cells into a single developmental trajectory, Monocle 3 enables you to learn a set of trajectories that describe the biological process you're studying. For example, if you're looking at a community of immune cells responding to infection, each cell type will respond to antigen (and each other) in a different way, so they should be organized into distinct trajectories. This can also be helpful when you have small groups of outlier cells that for either technical or biological reasons are very dissimilar from the rest of the cells in your experiment. They can confuse a trajectory analysis. Monocle 3's partitioning strategy circumvents this issue because such groups often wind up in their own partition. In the Paul data, there is a small outgroup the authors classified as dendritic cells that Monocle automatically partitions away from the main trajectory.

In Monocle 3, we recognize "disjoint" trajectories by drawing on ideas from Alex Wolf and colleagues, who recently introduced the concept of abstract graph participation. Monocle 3 implements the test for cell community connectedness from Wolf et al via the partitionCells() function, which divides the cells into "supergroups".

cds <- partitionCells(cds)

Step 4: Learn the principal graph

Now that the cells are paritioned, we can organize each supergroup into a separate trajectory. The default method for doing this in Monocle 3 is SimplePPT, which assumes that each trajectory is a tree (albeit one that may have multiple roots). Learn these trees with the learnGraph function:

cds <- learnGraph(cds,  RGE_method = 'SimplePPT')

After you've learned the graph, it's time to assign each cell's pseudotime value with orderCells(). But before we get to that, let's see how to plot the trajectory so we know where the beginning of the trajectory should be.

Step 5: Visualize the trajectory

Once the you've learned the trajectory, you can visualize the it and color the cells in different ways.

                     color_by = "cell_type2") +
                     scale_color_manual(values = cell_type_color)

You can see that Monocle has learned two trajectories, one of which is tiny and essentially trivial. The other has one major branch. SimplePPT essentially is finding a principal graph that fits nicely within the cells as projected in the UMAP coordinate space.

Adjusting the start of pseudotime with orderCells

In the trajectory above, you can see that the "Multipotent progenitor" cells are located roughly in the middle of the longer trajectory segment. We know from extensive past study of hematopoeisis that these are the "root" cell state that generates all the others in the primary trajectory. We need to tell Monocle that these cells are the "beginning" of the trajectory. In Monocle 2, this wouldn't be possible, because the software required that the root be one of the leaves of the tree. Monocle 3 allows you to specify an internal part of the tree as the root. There are two ways to do this:

  1. You can specifiy the name of a specific cell or principal graph node as the root by passing it to orderCells().
  2. You can call orderCells() with no root specified and it will open a window for you to select the root(s) with your mouse cursor. This latter option is only available in interactive sessions, and doesn't work in Jupyter notebooks.

Once you select one or more roots, orderCells() computes the shortest path from each cell's location on the princiapl graph to the nearest root node. That is, a cell's pseudotime value is the geodesic distance from it to the nearest root, traveling over the graph. Any cell that is not reachable from some root will be assigned a pseudotime value of infinity.

You may find it helpful to automatically pick the root according to any number of biologically-driven criteria. For example, you could find the nodes at which cells expressing a certain marker gene are concentrated. Or we could select the node where cells from an early experimental timepoint land. Here, we provide one such helper function to show you how to do this kind of thing:

# a helper function to identify the root principal points:
get_correct_root_state <- function(cds, cell_phenotype, root_type){
  cell_ids <- which(pData(cds)[, cell_phenotype] == root_type)

  closest_vertex <-
  closest_vertex <- as.matrix(closest_vertex[colnames(cds), ])
  root_pr_nodes <-


In the above function, we are accessing pr_graph_cell_proj_closest_vertex which is just a matrix with a single column that stores for each cell, the ID of the principal graph node it's closest to. This is handy for computing statistics (e.g. with dplyr) about the principal graph nodes and which cells of what type map to them.

Now we can call this function to automatically find the node in the principal graph where our multipotent progenitors reside:

MPP_node_ids = get_correct_root_state(cds,
                                      cell_phenotype =
                                        'cell_type2', "Multipotent progenitors")
cds <- orderCells(cds, root_pr_nodes = MPP_node_ids)

In the figure shown below, we can see that the dendritic cells have a pseudotime value of infinity (shown in gray) because they are not reachable through the graph from the root we selected.

Learning and visualizing trajectories in 3D

Sometimes, projecting cells into three dimensions instead of two can make the biological process you're studying easier to interpret. In Monocle 3, we provide the plot_3d_cell_trajectory function to plot a dataset in 3 dimensions. The block of code below shows you how to learn a trajectory in 3D. Similarly to the 2d case, it:

  1. Reduces the data down into three dimensions using UMAP
  2. Learns and the trajectory trajectory and orders the cells
  3. Visualizes the 3D trajectory
cds <- reduceDimension(cds, max_components = 3,
                       reduction_method = 'UMAP',
                       verbose = F)

cds <- partitionCells(cds)

cds <- learnGraph(cds,
                  max_components = 3,
                  RGE_method = 'SimplePPT',
                  partition_component = T,
                  verbose = F)

cds <- orderCells(cds,
                  root_pr_nodes =
                                           cell_phenotype = 'cell_type2',
                                           "Multipotent progenitors"))

                          paste(getwd(), "/trajectory_3D.html", sep=""),

(You can left-click and drag your mouse to rotate the plot below. Scroll to zoom)

Identifying genes that vary in expression over a trajectory

We are often interested in finding genes that are differentially expressed across a single-cell trajectory. Monocle 3 introduces a new approach for finding such genes that draws on a powerful technique in spatial correlation analysis, the Moran’s I test. Moran’s I is a measure of multi-directional and multi-dimensional spatial autocorrelation. The statistic tells you whether cells at nearby positions on a trajectory will have similar (or dissimilar) expression levels for the gene being tested. Although both Pearson correlation and Moran’s I ranges from -1 to 1, the interpretation of Moran’s I is slightly different: +1 means that nearby cells will have perfectly similar expression (as in the right panel below); 0 represents no correlation (center), and -1 means that neighboring cells will be *anti-correlated* (left).

pr_graph_test <- principalGraphTest(cds, k=3, cores=1)

We can easily view the top differentially expressed genes as follows:

dplyr::add_rownames(pr_graph_test) %>%
    dplyr::arrange(plyr::desc(morans_test_statistic), plyr::desc(-qval)) %>% head(3)
rowname status pval morans_test_statistic morans_I gene_short_name qval
Gzmb OK 0 57.31594 0.8091045 Gzmb 0
H2-Eb1 OK 0 49.76385 0.7394550 H2-Eb1 0
Ermap OK 0 49.43468 0.7485182 Ermap 0

You can check out the test results for one or more genes like this:

pr_graph_test[fData(cds)$gene_short_name %in% c("Hbb-b1"),]
rowname status pval morans_test_statistic morans_I gene_short_name qval
Hbb-b1 OK 8.446106e-179 28.48717 0.4298683 Hbb-b1 3.131316e-177

The code below reports that overall, there are more than 2,300 DE genes over the whole trajectory:

nrow(subset(pr_graph_test, qval < 0.01))

Once you've identified differentially expressed genes, you'll often want to visualize their expression levels on the trajectory. The plot bleow shows each cell with detectable levels of Hbb-b1 superimposed on the trajectory. Hbb-b1 is a subunit of beta globin, a highly specific marker of erythroid cells. Indeed, it is largely restricted to the erythroid branch of the trajectory. Values are log-transformed and scaled into Z scores. Cells with no expression are not shown to avoid overplotting.

plot_3d_cell_trajectory(cds, markers = c('Hbb-b1'),
                        webGL_filename=paste(getwd(), "/beta_globin.html", sep=""),