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Title: Cancer homogeneity in single cell revealed by Bi-state model and Binary matrix factorization

Paper content:
Single cell RNA sequencing (scRNAseq) technology enables quantifying gene expression profiles by individual cells within cancer.
Dimension reduction methods have been commonly used for cell clustering analysis and visualization of the data.
Current dimension reduction methods tend overly eliminate the expression variations correspond to less dominating characteristics, such we fail to find the homogenious properties of cancer development.
In this paper, we proposed a new and clustering analysis method for scRNAseq data, namely BBSC, via implementing a binarization of the gene expression profile into on/off frequency changes with a Boolean matrix factorization.
The low rank representation of expression matrix recovered by BBSC increase the resolution in identifying distinct cell types or functions.
Application of BBSC on two cancer scRNAseq data successfully discovered both homogeneous and heterogeneous cancer cell clusters.
Further finding showed potential in preventing cancer progression.
Cancer the biggest deadly threat to human has been a huge puzzle since its determination in 1775.
From once considered as contagious to nowadays cancer immunotherapy, the modern medication continues to evolve in tackling this problem (Dougan et al., 2019) .
And yet, not enough to make a huge difference, 1,762,450 people have been diagnosed with cancer and 606,880 has died in 2018 (Siegel et al., 2019) .
The development of single cell RNA sequencing (scRNA-seq), which measures each single cell in cancer tissue with over 20,000 dimension of genes (features), picturized the hologram of cancer and its micro-environment with high resolution (Picelli et al., 2014; Puram et al., 2017; Tirosh et al., 2016) .
As illustrated in Figure 1A , classic analysis pipeline takes a linear (PCA) or non-linear (t-SNE) dimension reduction of the high dimensional input data, by which loadings of the top bases are further used for cell clustering and visualization (Tirosh et al., 2016) .
Figure 1: Classic analysis pipeline for scRNA-seq data and Melanoma example Cancer cell heterogeneity hampers theraputic development.
We use the melanoma dataset as an example.
Cells in a scRNA-seq data are always with multiple crossed conditions, such as types of cancer, origin of patients and different cell types.
By analyzing melanoma scRNA-seq data with classic pipeline, we differentiated the cell type of each cell in its cancer microenvironment (CME) (figure 1B).
All cell types other than cancer cell are constituted by multiple patients ( figure 1C ), validated the accuracy of classic pipeline in cell type identification.
While on cancer cell, each patient forms a distinct cluster (highlighted in shadow), suggesting confounding patient-wise heterogeneity.
Similar phenomenon also exists in breast cancer and head and neck cancer.
On the other hand, being an investment-heavy industry like medical industry, the uniqueness of each cancer patient contradicts its general principle as to
In addition, f follows a beta distribution accounting for the collective effect of the probability to shift the expression from off to on (k on ) and from on to off (k of f ).
y denotes the true expression of gene i inside cell j and x is the observation of y with Gaussian error.
Recent study revealed that, regulated by enhancers, burst frequency f is the major facilitator of cell type specific gene expression landscape (Larsson et al., 2019) .
Though f and k size cannot be precisely fitted from our observed data, since y follows the Poisson distribution of the pure product of k size and f , we could still capture the most significant frequency changes across different cells.
That is, we could infer whether f is above or equal to zero, corresponding to expression/no-expression of the gene, from our observed data.
Counting this property, we thus propose the following approximate gene expression bi-state models.
where F denotes a latent binary matrix of f , which is considered as a low rank representation of k different cell types, generated by the Boolean product of two binary matrix A and B plus a Boolean flipping error E. Y denotes the true quantitative expression level generated from F , and X is considered as a measure of Y with i.i.d. Gaussian error .
Here our approach takes the approximating Y by Hadamard product between X andÂ n×k ⊗B k×m , i.e.
whereÂ n×k andB k×m are the estimation of A n×k and B k×m .
Bi-state and Boolean matrix factorization for scRNA-seq data (BBSC).
In sight of this, we developed a novel scRNA-seq pattern mining and analysis pipeline namely BBSC (Figure 2 ), by implementing a data binarization process for the inference of ON/OFF bi-state expression patterns.
In addition, we proposed a fast binary matrix factorization (BMF) method, namely PFAST, adapting to the large scale of scRNA-seq data.
BBSC can be easily implemented with classic dimension reduction based analysis procedure.
Application of BBSC on scRNA-seq of the head and neck cancer and melanoma data successfully revealed the cancer homogeneity hence increased the sensitivity in identifying sub types of cells.
In addition, cancer cell clusters expressing the epithelial mesenchymal transition (EMT) markers were specifically identified by BBSC in head and neck cancer study, which consist cancer cells from different patient samples, suggesting heterogeneous cancer cells may adopt a similar strategy in cancer metastasis process.
We summarize our contributions as follows:
• We constructed a scRNA-seq analysis pipeline, BBSC, for retrieving cancer homogeneity properties.
BBSC is by far the first analysis pipeline accounting the fundamental interplay between cell type and gene expression in the analysis of scRNA-seq data.
• As a major component in BBSC pipeline, we proposed a fast and efficient BMF algorithm, PFAST, in adapting to the large scale of scRNA-seq data.
• In the analysis of head and neck cancer data, BBSC identified that cancer cell may adapt similar strategies in metastasis.
This finding could be applied to prevent cancer progression.
Enabled by the development of single cell technology, we now can observe the complicated biological process like cancer with unprecedented resolution.
However, the classic analysis pipeline fails to deliver detailed information:
1) it does not reveal common characteristic of cancer cell in different cancer patients.
2) Even it separates functional cells; it fails to reveal intra-cluster heterogeneity.
To solve above problems, we have developed BBSC analysis pipeline.
Rooted from casting the frequency change in gene expression, we have applied BMF in the feature selection process, which avoids adding new expensive and potentially noisy information.
We have applied tailored binarizing process for each dataset.
Moreover, to deal with big scale tall matrix like scRNAseq data, we have developed a fast and efficient algorithm called PFAST.
Letting alone its fast speed in handling large-scale data, it shows high accuracy compared with state-of-art BMF algorithms.
We have applied BBSC on two high quality cancer studies, head and neck cancer and melanoma.
In both datasets, BBSC shutters the big clusters into several sub clusters, and promotes a gateway to analysis intra-cluster heterogeneity.
Moreover, BBSC manages to get common cancer sub cell clusters in both datasets, and decreases the patient-wise heterogeneity that hindered cancer therapeutic development.
We next have justified the biological meanings of BBSC derived sub clusters by looking into the sub cancer clusters in head and neck cancer.
By analyzing their detailed expression profile, We find out that the common clusters are in the EMT transition process indicating these cancer cells play an important part in cancer metastasis.
While patient specific clusters are in the early EMT process indicating that these cells are still in the original cancer micro environment.
These findings have first justified the biological importance of BBSC derived sub clusters.
Secondly, it brings much insightful ideas in the clinical application.
We now can hypothesize that when cancer cells seek metastasis, they will transform into similar states that are common across different patients.
The characteristic of the common clusters may serve as target in preventing cancer metastasis.
Furthermore, we validate that the heterogeneity of cancer comes from the original cancer tissue.
Also BBSC shows promising results in deciphering this kind of heterogeneity.
Especially in head and neck cancer study, BBSC distinctly divides cancer cells from the same patient into two sub clusters.
Due to our limited expertise in cancer biology, we did not look closely in this property.
However, we believe this would bring insightful ideas in the cause of cancer origin heterogeneity.
Overall BBSC is an efficient and valuable analysis platform for scRNAseq or other single cell data.
It is capable to bring insightful knowledge for our detailed understanding of complicated biological process.

assistant: text: Our finding shed lights in preventing cancer progression