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# Gene Expression Algorithms Overview

The computational pipeline cellranger count or multi for 3' Single Cell Gene Expression involves the following analysis steps:

The key read processing steps are outlined in this figure and described in the text below:

## Alignment

This section on read trimming applies to 3' gene expression assays.

A full length cDNA construct is flanked by the 30 bp template switch oligo (TSO) sequence, AAGCAGTGGTATCAACGCAGAGTACATGGG, on the 5' end and poly-A on the 3' end. Some fraction of sequencing reads are expected to contain either or both of these sequences, depending on the fragment size distribution of the sequencing library. Reads derived from short RNA molecules are more likely to contain either or both TSO and poly-A sequence than longer RNA molecules.

Since the presence of non-template sequence in the form of either TSO or poly-A, low-complexity ends confound read mapping, TSO sequence is trimmed from the 5' end of read 2 and poly-A is trimmed from the 3' end prior to alignment. Trimming improves the sensitivity of the assay as well as the computational efficiency of the software pipeline.

Tags ts:i and pa:i in the output BAM files indicate the number of TSO nucleotides trimmed from the 5' end of read 2 and the number of poly-A nucleotides trimmed from the 3' end. The trimmed bases are present in the sequence of the BAM record, and the CIGAR string shows the position of these soft-clipped sequences.

### Genome alignment

Cell Ranger uses an aligner called STAR, which performs splicing-aware alignment of reads to the genome. Cell Ranger then uses the transcript annotation GTF to bucket the reads into exonic, intronic, and intergenic, and by whether the reads align (confidently) to the genome. A read is exonic if at least 50% of it intersects an exon, intronic if it is non-exonic and intersects an intron, and intergenic otherwise.

For reads that align to a single exonic locus but also align to 1 or more non-exonic loci, the exonic locus is prioritized and the read is considered to be confidently mapped to the exonic locus with MAPQ 255.

### Transcriptome alignment

Cell Ranger further aligns confidently mapped exonic and intronic reads to annotated transcripts by examining their compatibility with the transcriptome. As shown below, reads are classified based on whether they are exonic (light blue) or intronic (red) and whether they are sense or antisense (purple).

To exclude intronic reads, include-introns must be set to false. In this case, Cell Ranger still uses transcriptomic (blue) reads with sense alignments (and ignores antisense alignments) for UMI counting, however a read is now classified as antisense if it has any alignments to a transcript exon on the opposite strand and no sense alignments.

Furthermore, a read is considered uniquely mapping if it is compatible with only a single gene. Only uniquely mapping reads are carried forward to UMI counting (see this page for methods to check for multi-mapped reads).

### 10x barcode correction

To determine whether barcode sequence is correct, Cell Ranger compares 10x Barcodes to the known barcodes for a given assay chemistry, which are stored in a barcode whitelist file. For example, there are roughly 737,000 barcodes in the whitelist for the Single Cell 3' v2 and V(D)J assays, and ~3 million barcodes for the Single Cell 3' v3 and v3.1 chemistries.

Cell Ranger uses the following algorithm to correct putative barcode sequences against the whitelist:

1. Count the observed frequency of every barcode on the whitelist in the dataset.
2. For every observed barcode in the dataset that is not on the whitelist and is at most one Hamming distance away from the whitelist sequences:
• Compute the posterior probability that the observed barcode did originate from the whitelist barcode but has a sequencing error at the differing base (by base quality score).
• Replace the observed barcode with the whitelist barcode that has the highest posterior probability (>0.975).

The corrected barcodes are used for all downstream analysis and output files. In the output BAM file, the original uncorrected barcode is encoded in the CR tag, and the corrected barcode sequence is encoded in the CB tag. Reads that cannot be assigned a corrected barcode will not have a CB tag.

### UMI counting

Before counting UMIs, Cell Ranger attempts to correct for sequencing errors in the UMI sequences. Reads that were confidently mapped to the transcriptome are placed into groups that share the same barcode, UMI, and gene annotation. If two groups of reads have the same barcode and gene, but their UMIs differ by a single base (i.e., are one Hamming distance apart), then one of the UMIs was likely introduced by a substitution error in sequencing. In this case, the UMI of the less-supported read group is corrected to the UMI with higher support.

Cell Ranger again groups the reads by barcode, UMI (possibly corrected), and gene annotation. If two or more groups of reads have the same barcode and UMI, but different gene annotations, the gene annotation with the most supporting reads is kept for UMI counting, and the other read groups are discarded. In case of a tie for maximal read support, all read groups are discarded, as the gene cannot be confidently assigned.

After these two filtering steps, each observed barcode, UMI, gene combination is recorded as a UMI count in the unfiltered feature-barcode matrix. The number of reads supporting each counted UMI is also recorded in the molecule info file.

## Calling cell barcodes

Cell Ranger v3.0 and later have an improved cell-calling algorithm that is better able to identify populations of low RNA content cells, especially when low RNA content cells are mixed into a population of high RNA content cells. For example, tumor samples often contain large tumor cells mixed with smaller tumor infiltrating lymphocytes (TIL) and researchers may be particularly interested in the TIL population. The new algorithm is based on the EmptyDrops method (Lun et al., 2019).

The algorithm has two key steps:

1. It uses a cutoff based on total UMI counts for each barcode to identify cells. This step identifies the initial number of high RNA content cells (initial cells).
2. Then the algorithm uses the RNA profile of each remaining barcode to determine if it is an "empty" or a cell-containing partition. This second step captures low RNA content cells whose total UMI counts may be similar to empty GEMs.

In the first step, the original Cell Ranger cell calling algorithm is used to identify the primary mode of high RNA content cells, using a cutoff based on the total UMI count for each barcode. Cell Ranger may take as input an expected number of recovered cells (e.g., see --expect-cells for count), N, or as of Cell Ranger 7.0, estimate this number.

The order of magnitude algorithm (OrdMag) estimates the initial number of recovered cells such that barcodes are called cells if total UMI counts exceed m/10, where m is the 99th percentile of top N barcodes based on total UMI counts. The estimation of expect-cells then finds a value x that approximates OrdMag(x) by minimizing a loss function where expect-cells = minx(OrdMag(x) - x)2 / x. Cell Ranger's grid-search goes from 2 to ~262k cells. In the example below, the optimized value for expect-cells is 1,137:

In the second step, a set of barcodes with low UMI counts that likely represent "empty" GEM partitions is selected. A model of the RNA profile of selected barcodes is created. This model, called the background model, is a multinomial distribution over genes. It uses Simple Good-Turing smoothing to provide a non-zero model estimate for genes that were not observed in the representative empty GEM set. Finally, the RNA profile of each barcode not called as a cell in the first step is compared to the background model. Barcodes whose RNA profile strongly disagrees with the background model are added to the set of positive cell calls. This second step identifies cells that are clearly distinguishable from the profile of empty GEMs, even though they may have much lower RNA content than the largest cells in the experiment.

Below is an example of a challenging cell calling scenario where 300 high RNA content 293T cells are mixed with 2,000 low RNA content PBMC cells. On the left is the cell calling result with the cell calling algorithm prior to Cell Ranger 3.0 and on the right is the Cell Ranger 3.0 result. You can see that low RNA content cells are successfully identified by the new algorithm.

 Cell Ranger 2.2 Cell Ranger 3.0

The plot shows the count of filtered UMIs mapped to each barcode. Barcodes can be determined to be cell-associated based on their UMI count or by their RNA profiles. Therefore some regions of the graph can contain both cell-associated and background-associated barcodes. The color of the graph represents the local density of barcodes that are cell-associated.

In some cases the set of barcodes called as cells may not match the desired set of barcodes based on visual inspection. This can be remedied by either re-running count or reanalyze with the --force-cells option, or by selecting the desired barcodes from the raw feature-barcode matrix in downstream analysis. Custom barcode selection can also be done by specifying --barcodes to reanalyze.

## Calling cell barcodes in targeted gene expression

Cell Ranger 4.0 includes a new dedicated cell calling algorithm that is applied specifically to identify cells from Targeted Gene Expression datasets. The Targeted Gene Expression cell calling method relies on identification of a transition point based on the shape of the barcode rank plot to separate cell-associated barcodes from background partitions, and is designed to successfully classify cells for a wide variety of potential target gene panels.

Note: This method is distinct from the cell calling algorithm used for non-targeted Whole Transcriptome Analysis (WTA) {{platform.name}} single cell datasets, and it does not employ the EmptyDrops approach (Lun et al., 2019) due to the distinct features of Targeted Gene Expression datasets.

## Calling cell barcodes in Feature Barcode only analysis

When using Cell Ranger in Feature Barcode Only Analysis mode, only step 1 of the cell calling algorithm is used. The cells called by this step of the algorithm are returned directly.

## Estimating multiplet rates

When multiple genomes are present in the reference (for example, Human and Mouse, or any other pair), Cell Ranger runs a special multi-genome analysis to detect barcodes associated with partitions where cells from two different genomes were present. Among all barcodes called as cell-associated (See Calling cell barcodes), they are initially classified as Human or Mouse by which genome has more total UMI counts for that barcode. Barcodes with total UMI counts that exceed the 10th percentile of the distributions for both Human and Mouse are called as observed multiplets. Because Cell Ranger can only observe the (Human, Mouse) multiplets, it computes an inferred multiplet rate by estimating the total number of multiplets (including (Human, Human) and (Mouse, Mouse)). This is done by estimating via maximum likelihood the total number of multiplet GEMs from the observed multiplets and the inferred ratio of Human to Mouse cells. If this ratio is 1:1, the inferred multiplet rate is approximately twice the observed (Human, Mouse) multiplets.

## Secondary analysis of gene expression

### Dimensionality reduction

#### PCA

In order to reduce the gene expression matrix to its most important features, Cell Ranger uses Principal Components Analysis (PCA) to change the dimensionality of the dataset from (cells x genes) to (cells x M) where M is a user-selectable number of principal components (via num_principal_comps). The pipeline uses a python implementation of IRLBA algorithm, (Baglama & Reichel, 2005), which we modified to reduce memory consumption. The reanalyze pipeline allows the user to further reduce the data by randomly subsampling the cells and/or selecting genes by their dispersion across the dataset. Note that if the data contains Feature Barcode data, only the gene expression data will be used for PCA and subsequent analysis.

#### t-SNE

For visualizing data in 2-d space, Cell Ranger passes the PCA-reduced data into t-SNE (t-Stochastic Neighbor Embedding), a nonlinear dimensionality reduction method (Van der Maaten, 2014). The C++ reference implementation by Van der Maaten (2014) was modified to take a PRNG seed for determinism and to expose various parameters which can be changed in reanalyze. We also decreased its runtime by fixing the number of output dimensions at compile time to 2 or 3.

#### UMAP

Cell Ranger also supports visualization with UMAP (Uniform Manifold Approximation and Projection), which estimates a topology of the high dimensional data and uses this information to estimate a low dimensional embedding that preserves relationships present in the data (McInnes et al, 2018). The pipeline uses the python implementation of this algorithm by McInnes et al (2018). The reanalyze pipeline allows the user to customize the parameters for the UMAP, including n_neighbors, min_dist and metric etc. Below shows the t-SNE (left) and UMAP (right) visualizations of our public dataset 5k PBMCs.

 t-SNE UMAP

### Clustering

Cell Ranger uses two different methods for clustering cells by expression similarity, both of which operate in the PCA space.

#### Graph-based

The graph-based clustering algorithm consists of building a sparse nearest-neighbor graph (where cells are linked if they among the k nearest Euclidean neighbors of one another), followed by Louvain Modularity Optimization (LMO; Blondel, Guillaume, Lambiotte, & Lefebvre, 2008), an algorithm which seeks to find highly-connected "modules" in the graph. The value of k, the number of nearest neighbors, is set to scale logarithmically with the number of cells. An additional cluster-merging step is done to perform hierarchical clustering on the cluster-medoids in PCA space and merge pairs of sibling clusters if there are no genes differentially expressed between them (with B-H adjusted p-value below 0.05). The hierarchical clustering and merging is repeated until there are no more cluster-pairs to merge.

The use of LMO to cluster cells was inspired by a similar method in the R package Seurat.

#### K-Means

Cell Ranger also performs traditional K-means clustering across a range of K values, where K is the preset number of clusters. In the web summary prior to 1.3.0, the default selected value of K is that which yields the best Davies-Bouldin Index, a rough measure of clustering quality.

### Differential expression

In order to identify genes whose expression is specific to each cluster, Cell Ranger tests, for each gene and each cluster i, whether the mean expression in cluster i differs from the mean expression across all other cells.

For cluster i, the mean expression of a feature is calculated as the total number of UMIs from that feature in cluster i divided by the sum of the size factors for cells in cluster i. The size factor for each cell is the total UMI count in that cell divided by the median UMI count per cell (across all cells). The mean expression outside of cluster i is calculated in the same way. The log2 fold-change of expression in cluster i relative to other clusters is the log2 ratio of mean expression within cluster i and outside of cluster i. When computing the log2 fold-change, a pseudocount of 1 is added to both the numerator and denominator of the mean expression.

To test for differences in mean expression between groups of cells, Cell Ranger uses the exact negative binomial test proposed by the authors of the sSeq method (Yu, Huber, & Vitek, 2013). When the counts become large, Cell Ranger switches to the fast asymptotic negative binomial test used in edgeR (Robinson & Smyth, 2007).

Note that Cell Ranger's implementation differs slightly from the sSeq paper: the size factors are calculated using total UMI count instead of using DESeq's geometric mean-based definition of library size. As with sSeq, normalization is implicit in that the per-cell size factor parameter is incorporated as a factor in the exact and asymptotic probability calculations.

### Chemistry batch correction

To correct the batch effects between chemistries, Cell Ranger uses an algorithm based on mutual nearest neighbors (MNN; Haghverdi et al, 2018) to identify similar cell subpopulations between batches. The mutual nearest neighbor is defined as a pair of cells from two different batches that is contained in each other’s set of nearest neighbors. The MNNs are detected for every pair of user-defined batches to balance among batches, as proposed in (Park et al, 2018).

The cell subpopulation matches between batches will then be used to merge multiple batches together (Hie et al, 2018). The difference in expression values between cells in a MNN pair provides an estimate of the batch effect. A correction vector for each cell is obtained as a weighted average of the estimated batch effects, where a Gaussian kernel function up-weights matching vectors belonging to nearby points (Haghverdi et al, 2018).

The batch effect score is defined to quantitatively measure the batch effect before and after correction. For every cell, we calculate how many of its 100 nearest-neighbors belong to the same batch and normalize it by the expected number of same batch cells when there is no batch effect. The batch effect score is calculated as the average of this normalized score in a randomly sampled subset (10%) of cells. If there isn't a batch effect, we would expect that each cells’ nearest neighbors are evenly shared across all batches and the batch effect score is close to one. There is a batch effect if the batch effect score is greater than one. The batch effect score value is not comparable across experiments with different numbers and/or batch sizes.

In the example below, the PBMC mixture was profiled separately by Single Cell 3' v2 (brown) and Single Cell 3' v3 (blue). On the left is the t-SNE plot after aggregating two libraries without the batch correction, and on the right is the t-SNE plot with the batch correction. The batch effect score decreased from 1.81 to 1.31 with the chemistry batch correction.

 Without Chemistry Batch Correction With Chemistry Batch Correction

## References

Baglama, J. & Reichel, L. Augmented Implicitly Restarted Lanczos Bidiagonalization Methods. SIAM Journal on Scientific Computing 27, 19–42 (2005).

Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment 2008, (2008).

Haghverdi, L., Lun, A. T., Morgan, M. D., & Marioni, J. C. Batch effects in single-cell RNA-sequencing data are corrected by matching mutual nearest neighbors. Nature biotechnology, 36(5), 421 (2018).

Hie, B. L., Bryson, B., & Berger, B. Panoramic stitching of heterogeneous single-cell transcriptomic data. bioRxiv 2018.

Lun, A., Riesenfeld, S., Andrews, T., Dao, T.P., Gomes. T., Participants in the 1st Human Cell Atlas Jamboree, Marioni, J. Distinguishing cells from empty droplets in droplet-based single-cell RNA sequencing data. Genome Biology 2019

McInnes, L, Healy, J, UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction. arXiv 2018

Park, J. E., Polanski, K., Meyer, K., & Teichmann, S. A. Fast Batch Alignment of Single Cell Transcriptomes Unifies Multiple Mouse Cell Atlases into an Integrated Landscape. bioRxiv 2018.

Robinson, M. D. & Smyth, G. K. Small-sample estimation of negative binomial dispersion, with applications to SAGE data. Biostatistics 9, 321–332 (2007). Link to edgeR source.

Van der Maaten, L.J.P. Accelerating t-SNE using Tree-Based Algorithms. Journal of Machine Learning Research 15, 3221-3245 (2014).

Yu, D., Huber, W. & Vitek, O. Shrinkage estimation of dispersion in Negative Binomial models for RNA-seq experiments with small sample size. Bioinformatics 29, 1275–1282 (2013).