Deconvolving Cell Type Fractions from Bulk Transcriptomics

A number of computational methods have been proposed to infer cell type abundance, cell type-specific GEPs, or both from bulk tissue expression profiles^{2 (link)–8 (link)}. These methods generally assume that biological mixture samples can be modeled as a system of linear equations, where a single mixture transcriptome m with n genes is represented as the product of H and f, where H represents an n × c cell type expression matrix consisting of expression profiles for the same n genes across c distinct cell types, and f represents a vector of size c, consisting of cell type mixing proportions.
To infer cell type abundance using this linear model within CIBERSORTx, let M be an n × k matrix with n genes and k mixture GEPs, let matrix B be a subset of H containing discriminatory marker genes for each of the c cell subsets (i.e., signature or basis matrix^{15 (link),74 (link),75 (link)}), and let M’ be the subset of M that contains the same marker genes as B. Given M’ and B, the following equation can then be used to impute F, a c × k fractional abundance matrix with columns [f₁,f₂,…,f_k]:
$$\mathrm{B}\times {\mathrm{F}}_{•,j}={\mathrm{M}}_{•,\mathrm{j}}^{\prime },1\le j\le k$$
where F_i,j≥ 0 for all i, j, the system is overdetermined (i.e., n > c), and expression data in M’ and B are represented in non-log linear space⁷⁶ . (Note that M_i,• and M_•,j denote row i and column j of matrix M, respectively). Many methods either normalize F or impose an additional constraint on F such that for each mixture sample, the inferred mixing coefficients sum to one, allowing F to be directly interpreted as cell type proportions (with respect to the cell subsets in B)^{3 (link)}. We previously introduced CIBERSORT as a method to estimate F using an implementation of ν-support vector regression, a machine learning technique that is robust to noise, unknown mixture content, and collinearity among cell type reference profiles^{15 (link)}. CIBERSORT was used to impute F in this work, and within this imputation workflow, the batch correction scheme described below was used for all cross-platform analyses, unless stated otherwise (Supplementary Table 1).