---
title: "Single Cell ATAC-seq Analysis with Cicero"
author: "Hannah Pliner"
date: "`r Sys.Date()`"
output:
html_document:
toc: true
theme: united
vignette: >
%\VignetteIndexEntry{Vignette from Cicero Website}
%\VignetteEngine{knitr::rmarkdown}
%\VignetteEncoding{UTF-8}
---
```{r setup, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
```
This vignette is a condensed version of the documentation pages on the
[Cicero website](https://cole-trapnell-lab.github.io/cicero-release). Please
check out the website for more details.
# Introduction:
The main purpose of Cicero is to use single-cell chromatin accessibility data
to predict regions of the genome that are more likely to be in physical
proximity in the nucleus. This can be used to identify putative
enhancer-promoter pairs, and to get a sense of the overall stucture of the
cis-architecture of a genomic region.
Because of the sparsity of single-cell data, cells must be aggregated by
similarity to allow robust correction for various technical factors in the
data.
Ultimately, Cicero provides a "Cicero co-accessibility" score between -1 and
1 between each pair of accessible peaks within a user defined distance where
a higher score indicates higher co-accessibility.
In addition, the Cicero package provides an extension toolkit for analyzing
single-cell ATAC-seq experiments using the framework provided by the
single-cell RNA-seq analysis software,
[Monocle](https://cole-trapnell-lab.github.io/monocle-release). This vignette
provides an overview of a single-cell ATAC-Seq analysis workflow with Cicero.
For further information and more options, please see the manual pages for the
Cicero R package, the
[Cicero website](https://cole-trapnell-lab.github.io/cicero-release) and our
publications.
Cicero can help you perform two main types of analysis:
* **Constructing and analyzing cis-regulatory networks.** Cicero analyzes
co-accessibility to identify putative cis-regulatory interactions, and uses
various techniques to visualize and analyze them.
* **General single-cell chromatin accessibility analysis.** Cicero also
extends the software package Monocle to allow for identification of
differential accessibility, clustering, visualization, and trajectory
reconstruction using single-cell chromatin accessibility data.
# Installing Cicero
1. Download the package from Bioconductor.
```{r getPackage, eval=FALSE}
if (!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install("cicero")
```
Or install the development version of the package from Github.
```{r, eval = FALSE}
BiocManager::install(cole-trapnell-lab/cicero)
```
2. Load the package into R session.
```{r Load, message=FALSE}
library(cicero)
```
# Constructing cis-regulatory networks
## Running Cicero
### The CellDataSet class
Cicero holds data in objects of the CellDataSet (CDS) class. The class is
derived from the Bioconductor ExpressionSet class, which provides a common
interface familiar to those who have analyzed microarray experiments with
Bioconductor. Monocle provides detailed documentation about how to generate an
input CDS [here](http://cole-trapnell-lab.github.io/monocle-release/docs/#the-celldataset-class).
To modify the CDS object to hold chromatin accessibility rather than expression
data, Cicero uses peaks as its feature data fData rather than genes or
transcripts. Specifically, many Cicero functions require peak information in the
form chr1_10390134_10391134. For example, an input fData table might look like
this:
| site_name | chromosome| bp1 | bp2
--------------------------|---------------------------|-----------|-----------|------------
chr10_100002625_100002940 | chr10_100002625_100002940 | 10 | 100002625 | 100002940
chr10_100006458_100007593 | chr10_100006458_100007593 | 10 | 100006458 | 100007593
chr10_100011280_100011780 | chr10_100011280_100011780 | 10 | 100011280 | 100011780
chr10_100013372_100013596 | chr10_100013372_100013596 | 10 | 100013372 | 100013596
chr10_100015079_100015428 | chr10_100015079_100015428 | 10 | 100015079 | 100015428
The Cicero package includes a small dataset called cicero_data as an example.
```{r}
data(cicero_data)
```
For convenience, Cicero includes a function called make_atac_cds. This function
takes as input a data.frame or a path to a file in a sparse matrix format.
Specifically, this file should be a tab-delimited text file with three columns.
The first column is the peak coordinates in the form
"chr10_100013372_100013596", the second column is the cell name, and the third
column is an integer that represents the number of reads from that cell
overlapping that peak. The file should not have a header line.
For example:
| |
--------------------------|--------|---------
chr10_100002625_100002940 | cell1 | 1
chr10_100006458_100007593 | cell2 | 2
chr10_100006458_100007593 | cell3 | 1
chr10_100013372_100013596 | cell2 | 1
chr10_100015079_100015428 | cell4 | 3
The output of make_atac_cds is a valid CDS object ready to be input into
downstream Cicero functions.
```{r, eval=TRUE}
input_cds <- make_atac_cds(cicero_data, binarize = TRUE)
```
### Create a Cicero CDS
Because single-cell chromatin accessibility data is extremely sparse, accurate
estimation of co-accessibility scores requires us to aggregate similar cells to
create more dense count data. Cicero does this using a k-nearest-neighbors
approach which creates overlapping sets of cells. Cicero constructs these sets
based on a reduced dimension coordinate map of cell similarity, for example,
from a tSNE or DDRTree map.
You can use any dimensionality reduction method to base your aggregated CDS on.
We will show you how to create two versions, tSNE and DDRTree (below). Both of
these dimensionality reduction methods are available from
[Monocle](http://cole-trapnell-lab.github.io/monocle-release/) (and loaded
by Cicero).
Once you have your reduced dimension coordinate map, you can use the function
make_cicero_cds to create your aggregated CDS object. The input to
make_cicero_cds is your input CDS object, and your reduced dimension coordinate
map. The reduced dimension map reduced_coordinates should be in the form of a
data.frame or a matrix where the row names match the cell IDs from the pData
table of your CDS. The columns of reduced_coordinates should be the coordinates
of the reduced dimension object, for example:
| ddrtree_coord1 | ddrtree_coord2
--------------|----------------|---------------
cell1 | -0.7084047 | -0.7232994
cell2 | -4.4767964 | 0.8237284
cell3 | 1.4870098 | -0.4723493
Here is an example of both dimensionality reduction and creation of a Cicero
CDS. Using Monocle as a guide, we first find tSNE coordinates for our input_cds:
```{r, eval=TRUE}
set.seed(2017)
input_cds <- detectGenes(input_cds)
input_cds <- estimateSizeFactors(input_cds)
input_cds <- reduceDimension(input_cds, max_components = 2, num_dim=6,
reduction_method = 'tSNE', norm_method = "none")
```
For more information on the above code, see the
[Monocle](http://cole-trapnell-lab.github.io/monocle-release/) website
section on clustering cells.
Next, we access the tSNE coordinates from the input CDS object where they are
stored by Monocle and run make_cicero_cds:
```{r, eval=TRUE}
tsne_coords <- t(reducedDimA(input_cds))
row.names(tsne_coords) <- row.names(pData(input_cds))
cicero_cds <- make_cicero_cds(input_cds, reduced_coordinates = tsne_coords)
```
### Run Cicero
The main function of the Cicero package is to estimate the co-accessiblity of
sites in the genome in order to predict cis-regulatory interactions. There are
two ways to get this information:
* **run_cicero, get Cicero outputs with all defaults** The function run_cicero will
call each of the relevant pieces of Cicero code using default values, and
calculating best-estimate parameters as it goes. For most users, this will be
the best place to start.
* **Call functions separately, for more flexibility** For users wanting more
flexibility in the parameters that are called, and those that want access to
intermediate information, Cicero allows you to call each of the component parts
separately. More information about running function separately is available on
the package manual pages and on the
[Cicero website](https://cole-trapnell-lab.github.io/cicero-release).
The easiest way to get Cicero co-accessibility scores is to run run_cicero. To
run run_cicero, you need a cicero CDS object (created above) and a genome
coordinates file, which contains the lengths of each of the chromosomes in your
organism. The human hg19 coordinates are included with the package and can be
accessed with data("human.hg19.genome"). Here is an example call, continuing
with our example data:
```{r, eval=TRUE}
data("human.hg19.genome")
sample_genome <- subset(human.hg19.genome, V1 == "chr18")
sample_genome$V2[1] <- 10000000
conns <- run_cicero(cicero_cds, sample_genome, sample_num = 2) # Takes a few minutes to run
head(conns)
```
## Visualizing Cicero Connections
The Cicero package includes a general plotting function for visualizing
co-accessibility called plot_connections. This function uses the Gviz framework
for plotting genome browser-style plots. We have adapted a function from the
Sushi R package for mapping connections. plot_connections has many options,
some detailed in the Advanced Visualization section on the
[Cicero website](https://cole-trapnell-lab.github.io/cicero-release), but
to get a basic plot from your co-accessibility table is quite simple:
```{r, fig.width = 7, fig.height = 4, fig.align='center', eval=TRUE}
data(gene_annotation_sample)
plot_connections(conns, "chr18", 8575097, 8839855,
gene_model = gene_annotation_sample,
coaccess_cutoff = .25,
connection_width = .5,
collapseTranscripts = "longest" )
```
## Comparing Cicero connections to other datasets
Often, it is useful to compare Cicero connections to other datasets with
similar kinds of links. For example, you might want to compare the output of
Cicero to ChIA-PET ligations. To do this, Cicero includes a function called
compare_connections. This function takes as input two data frames of connection
pairs, conns1 and conns2, and returns a logical vector of which connections from
conns1 are found in conns2. The comparison in this function is conducted using
the GenomicRanges package, and uses the max_gap argument from that package to
allow slop in the comparisons.
For example, if we wanted to compare our Cicero predictions to a set of
(made-up) ChIA-PET connections, we could run:
```{r, eval=TRUE}
chia_conns <- data.frame(Peak1 = c("chr18_10000_10200", "chr18_10000_10200",
"chr18_49500_49600"),
Peak2 = c("chr18_10600_10700", "chr18_111700_111800",
"chr18_10600_10700"))
conns$in_chia <- compare_connections(conns, chia_conns)
```
You may find that this overlap is too strict when comparing completely distinct
datasets. Looking carefully, the 2nd line of the ChIA-PET data matches fairly
closely to the last line shown of conns. The difference is only ~67 base pairs,
which could be a matter of peak-calling. This is where the max_gap parameter
can be useful:
```{r, eval=TRUE}
conns$in_chia_100 <- compare_connections(conns, chia_conns, maxgap=100)
head(conns)
```
In addition, Cicero's plotting function has a way to compare datasets visually.
To do this, use the comparison_track argument. The comparison data frame must
include a third columns beyond the first two peak columns called "coaccess".
This is how the plotting function determines the height of the plotted
connections. This could be a quantitative measure, like the number of ligations
in ChIA-PET, or simply a column of 1s. More info on plotting options in manual
pages ?plot_connections and in the Advanced Visualization section of the
[Cicero website](https://cole-trapnell-lab.github.io/cicero-release).
```{r, eval=TRUE}
# Add a column of 1s called "coaccess"
chia_conns <- data.frame(Peak1 = c("chr18_10000_10200", "chr18_10000_10200",
"chr18_49500_49600"),
Peak2 = c("chr18_10600_10700", "chr18_111700_111800",
"chr18_10600_10700"),
coaccess = c(1, 1, 1))
plot_connections(conns, "chr18", 10000, 112367,
gene_model = gene_annotation_sample,
coaccess_cutoff = 0,
connection_width = .5,
comparison_track = chia_conns,
include_axis_track = FALSE,
collapseTranscripts = "longest")
```
## Finding Cis-Coaccessibility Networks (CCANS)
In addition to pairwise co-accessibility scores, Cicero also has a function to
find Cis-Co-accessibility Networks (CCANs), which are modules of sites that are
highly co-accessible with one another. We use the Louvain community detection
algorithm (Blondel et al., 2008) to find clusters of sites that tend to be
co-accessible. The function generate_ccans takes as input a connection data
frame and outputs a data frame with CCAN assignments for each input peak. Sites
not included in the output data frame were not assigned a CCAN.
The function generate_ccans has one optional input called
coaccess_cutoff_override. When coaccess_cutoff_override is NULL, the function
will determine and report an appropriate co-accessibility score cutoff value
for CCAN generation based on the number of overall CCANs at varying cutoffs.
You can also set coaccess_cutoff_override to be a numeric between 0 and 1, to
override the cutoff-finding part of the function. This option is useful if you
feel that the cutoff found automatically was too strict or loose, or for speed
if you are rerunning the code and know what the cutoff will be, since the
cutoff finding procedure can be slow.
```{r, eval=TRUE}
CCAN_assigns <- generate_ccans(conns)
head(CCAN_assigns)
```
## Cicero gene activity scores
We have found that often, accessibility at promoters is a poor predictor of
gene expression. However, using Cicero links, we are able to get a better sense
of the overall accessibility of a promoter and it's associated distal sites.
This combined score of regional accessibility has a better concordance with
gene expression. We call this score the Cicero gene activity score, and it is
calculated using two functions.
The initial function is called build_gene_activity_matrix. This function takes
an input CDS and a Cicero connection list, and outputs an unnormalized table of
gene activity scores. **IMPORTANT**: the input CDS must have a column in the
fData table called "gene" which indicates the gene if that peak is a promoter,
and NA if the peak is distal. One way to add this column is demonstrated below.
The output of build_gene_activity_matrix is unnormalized. It must be normalized
using a second function called normalize_gene_activities. If you intend to
compare gene activities across different datasets of subsets of data, then all
gene activity subsets should be normalized together, by passing in a list of
unnormalized matrices. If you only wish to normalized one matrix, simply pass
it to the function on its own. normalize_gene_activities also requires a named
vector of of total accessible sites per cell. This is easily found in the pData
table of your CDS, called "num_genes_expressed". See below for an example.
```{r, eval=TRUE}
#### Add a column for the pData table indicating the gene if a peak is a promoter ####
# Create a gene annotation set that only marks the transcription start sites of
# the genes. We use this as a proxy for promoters.
# To do this we need the first exon of each transcript
pos <- subset(gene_annotation_sample, strand == "+")
pos <- pos[order(pos$start),]
pos <- pos[!duplicated(pos$transcript),] # remove all but the first exons per transcript
pos$end <- pos$start + 1 # make a 1 base pair marker of the TSS
neg <- subset(gene_annotation_sample, strand == "-")
neg <- neg[order(neg$start, decreasing = TRUE),]
neg <- neg[!duplicated(neg$transcript),] # remove all but the first exons per transcript
neg$start <- neg$end - 1
gene_annotation_sub <- rbind(pos, neg)
# Make a subset of the TSS annotation columns containing just the coordinates
# and the gene name
gene_annotation_sub <- gene_annotation_sub[,c(1:3, 8)]
# Rename the gene symbol column to "gene"
names(gene_annotation_sub)[4] <- "gene"
input_cds <- annotate_cds_by_site(input_cds, gene_annotation_sub)
head(fData(input_cds))
#### Generate gene activity scores ####
# generate unnormalized gene activity matrix
unnorm_ga <- build_gene_activity_matrix(input_cds, conns)
# remove any rows/columns with all zeroes
unnorm_ga <- unnorm_ga[!Matrix::rowSums(unnorm_ga) == 0, !Matrix::colSums(unnorm_ga) == 0]
# make a list of num_genes_expressed
num_genes <- pData(input_cds)$num_genes_expressed
names(num_genes) <- row.names(pData(input_cds))
# normalize
cicero_gene_activities <- normalize_gene_activities(unnorm_ga, num_genes)
# if you had two datasets to normalize, you would pass both:
# num_genes should then include all cells from both sets
unnorm_ga2 <- unnorm_ga
cicero_gene_activities <- normalize_gene_activities(list(unnorm_ga, unnorm_ga2), num_genes)
```
# Single-cell accessibility trajectories
The second major function of the Cicero package is to extend Monocle 2 for use
with single-cell accessibility data. The main obstacle to overcome with
chromatin accessibility data is the sparsity, so most of the extensions and
methods are designed to address that.
## Constructing trajectories with accessibility data
We strongly recommend that you consult the Monocle website, especially
[this section](http://cole-trapnell-lab.github.io/monocle-release/docs/#constructing-single-cell-trajectories)
prior to reading about Cicero's extension of the Monocle analysis described.
Briefly, Monocle infers pseudotime trajectories in three steps:
1. Choosing sites that define progress
2. Reducing the dimensionality of the data
3. Ordering cells in pseudotime
We will describe how each piece is modified for use with sparse single-cell
chromatin accessibility data.
### Aggregation: the primary method for addressing sparsity
The primary way that the Cicero package deals with the sparsity of single-cell
chromatin accessibility data is through aggregation. Aggregating the counts of
either single cells or single peaks allows us to produce a "consensus" count
matrix, reducing noise and allowing us to move out of the binary regime. Under
this grouping, the number of cells in which a particular site is accessible can
be modeled with a binomial distribution or, for sufficiently large groups, the
corresponding Gaussian approximation. Modeling grouped accessibility counts as
normally distributed allows Cicero to easily adjust them for arbitrary technical
covariates by simply fitting a linear model and taking the residuals with
respect to it as the adjusted accessibility score for each group of cells. We
demonstrate how to apply this grouping practically below.
#### aggregate_nearby_peaks
The primary aggregation used for trajectory reconstruction is between nearby
peaks. This keeps single cells separate while aggregating regions of the genome
and looking for chromatin accessibility within them. The function
aggregate_nearby_peaks finds sites within a certain distance of each other and
aggregates them together by summing their counts. Depending on the density of
your data, you may want to try different distance parameters. In published work
we have used 1,000 and 10,000.
```{r, eval=TRUE}
data("cicero_data")
input_cds <- make_atac_cds(cicero_data)
# Add some cell meta-data
data("cell_data")
pData(input_cds) <- cbind(pData(input_cds), cell_data[row.names(pData(input_cds)),])
pData(input_cds)$cell <- NULL
agg_cds <- aggregate_nearby_peaks(input_cds, distance = 10000)
agg_cds <- detectGenes(agg_cds)
agg_cds <- estimateSizeFactors(agg_cds)
agg_cds <- estimateDispersions(agg_cds)
```
## Choose sites for dimensionality reduction
### Choosing sites that define progress
There are several options for choosing the sites to use during dimensionality
reduction. Monocle has a discussion about the options
[here](http://cole-trapnell-lab.github.io/monocle-release/docs/#alternative-choices-for-ordering-genes).
Any of these options could be used with your new aggregated CDS, depending on
the information you have a available in your dataset. Here, we will show two
examples:
#### Choose sites by differential analysis
If your data has defined beginning and end points, you can determine which sites
define progress by a differential accessibility test. We use Monocle's
differentialGeneTest function looking for sites that are different in the
timepoint groups.
```{r, eval=TRUE}
# This takes a few minutes to run
diff_timepoint <- differentialGeneTest(agg_cds,
fullModelFormulaStr="~timepoint + num_genes_expressed")
# We chose a very high q-value cutoff because there are
# so few sites in the sample dataset, in general a q-value
# cutoff in the range of 0.01 to 0.1 would be appropriate
ordering_sites <- row.names(subset(diff_timepoint, qval < .5))
length(ordering_sites)
```
#### Choose sites by dpFeature
Alternatively, you can choose sites for dimensionality reduction by using
Monocle's dpFeature method. dpFeature chooses sites based on how they differ
among clusters of cells. Here, we give some example code reproduced from
Monocle, for more information, see the Monocle description.
```{r, fig.show='hold', eval=FALSE}
plot_pc_variance_explained(agg_cds, return_all = FALSE) #Choose 2 PCs
agg_cds <- reduceDimension(agg_cds,
max_components = 2,
norm_method = 'log',
num_dim = 2,
reduction_method = 'tSNE',
verbose = TRUE)
agg_cds <- clusterCells(agg_cds, verbose = FALSE)
plot_cell_clusters(agg_cds, color_by = 'as.factor(Cluster)') + theme(text = element_text(size=8))
clustering_DA_sites <- differentialGeneTest(agg_cds[1:10,], #Subset for example only
fullModelFormulaStr = '~Cluster')
# Not run because using Option 1 to continue
# ordering_sites <-
# row.names(clustering_DA_sites)[order(clustering_DA_sites$qval)][1:1000]
```
### Reduce the dimensionality of the data and order cells
However you choose your ordering sites, the first step of dimensionality
reduction is to use setOrderingFilter to mark the sites you want to use for
dimesionality reduction. In the following figures, we are using the
ordering_sites from "Choose sites by differential analysis" above.
```{r, eval=TRUE}
agg_cds <- setOrderingFilter(agg_cds, ordering_sites)
```
Next, we use DDRTree to reduce dimensionality and then order the cells along
the trajectory. Importantly, we use num_genes_expressed in our residual model
formula to account for overall assay efficiency.
```{r, fig.align='center', fig.height=4, fig.width=4, eval=TRUE}
agg_cds <- reduceDimension(agg_cds, max_components = 2,
residualModelFormulaStr="~num_genes_expressed",
reduction_method = 'DDRTree')
agg_cds <- orderCells(agg_cds)
plot_cell_trajectory(agg_cds, color_by = "timepoint")
```
Once you have a cell trajectory, you need to make sure that pseudotime proceeds
how you expect. In our example, we want pseudotime to start where most of the
time 0 cells are located and proceed towards the later timepoints. Further
information on this can be found
[here](http://cole-trapnell-lab.github.io/monocle-release/docs/#constructing-single-cell-trajectories)
on the Monocle website. We first color our trajectory plot by State, which is
how Monocle assigns segments of the tree.
```{r, fig.align='center', fig.height=4, fig.width=4, eval=TRUE}
plot_cell_trajectory(agg_cds, color_by = "State")
```
From this plot, we can see that the beginning of pseudotime should be from
state 4. We now reorder cells setting the root state to 4. We can then check
that the ordering makes sense by coloring the plot by Pseudotime.
```{r, fig.align='center', fig.height=4, fig.width=4, eval=TRUE}
agg_cds <- orderCells(agg_cds, root_state = 4)
plot_cell_trajectory(agg_cds, color_by = "Pseudotime")
```
Now that we have Pseudotime values for each cell (pData(agg_cds)$Pseudotime),
we need to assign these values back to our original CDS object. In addition,
we will assign the State information back to the original CDS.
```{r, fig.align='center', fig.height=4, fig.width=4, eval=TRUE}
pData(input_cds)$Pseudotime <- pData(agg_cds)[colnames(input_cds),]$Pseudotime
pData(input_cds)$State <- pData(agg_cds)[colnames(input_cds),]$State
```
## Differential Accessibility Analysis
Once you have your cells ordered in pseudotime, you can ask where in the genome
chromatin accessibility is changing across time. If you know of specific sites
that are important to your system, you may want to visualize the accessibility
at those sites across pseudotime.
### Visualizing accessibility across pseudotime
For simplicity, we will exclude the branch in our trajectory to make our
trajectory linear.
```{r, fig.width = 3, fig.height = 4, fig.align='center', eval=TRUE}
input_cds_lin <- input_cds[,row.names(subset(pData(input_cds), State != 5))]
plot_accessibility_in_pseudotime(input_cds_lin[c("chr18_38156577_38158261",
"chr18_48373358_48374180",
"chr18_60457956_60459080")])
```
### Running differentialGeneTest with single-cell chromatin accessibility data
In the previous section, we used aggregation of sites to discover cell-level
information (cell pseudotime). In this section, we are interested in a
site-level statistic (whether a site is changing in pseudotime), so we will
aggregate similar cells. To do this, Cicero has a useful function called
aggregate_by_cell_bin.
#### aggregate_by_cell_bin
We use the function aggregate_by_cell_bin to aggregate our input CDS object by
a column in the pData table. In this example, we will assign cells to bins by
cutting the pseudotime trajectory into 10 parts.
```{r, eval=TRUE}
pData(input_cds_lin)$cell_subtype <- cut(pData(input_cds_lin)$Pseudotime, 10)
binned_input_lin <- aggregate_by_cell_bin(input_cds_lin, "cell_subtype")
```
We are now ready to run Monocle's differentialGeneTest function to find sites
that are differentially accessible across pseudotime. In this example, we
include num_genes_expressed as a covariate to subtract its effect.
```{r, eval=TRUE}
diff_test_res <- differentialGeneTest(binned_input_lin[1:10,], #Subset for example only
fullModelFormulaStr="~sm.ns(Pseudotime, df=3) + sm.ns(num_genes_expressed, df=3)",
reducedModelFormulaStr="~sm.ns(num_genes_expressed, df=3)", cores=1)
head(diff_test_res)
```
# References
Blondel, V.D., Guillaume, J.-L., Lambiotte, R., and Lefebvre, E. (2008). Fast unfolding of communities in large networks.
Dekker, J., Marti-Renom, M.A., and Mirny, L.A. (2013). Exploring the three-dimensional organization of genomes: interpreting chromatin interaction data. Nat. Rev. Genet. 14, 390–403.
Sanborn, A.L., Rao, S.S.P., Huang, S.-C., Durand, N.C., Huntley, M.H., Jewett, A.I., Bochkov, I.D., Chinnappan, D., Cutkosky, A., Li, J., et al. (2015). Chromatin extrusion explains key features of loop and domain formation in wild-type and engineered genomes. . Proc. Natl. Acad. Sci. U. S. A. 112, E6456–E6465.
Sexton, T., Yaffe, E., Kenigsberg, E., Bantignies, F., Leblanc, B., Hoichman, M., Parrinello, H., Tanay, A., and Cavalli, G. (2012). Three-Dimensional Folding and Functional Organization Principles of the Drosophila Genome. . Cell 148:3, 458-472.
# Citation
```{r}
citation("cicero")
```
# Session Info
```{r}
sessionInfo()
```