Determination of cell-cell interaction
We employed the expression of immune-related ligands and receptors to assess the cell-cell interactions (Ma et al., 2020). The possible ligand-receptor interactions between one set of receptor-expressing cells and then next ligand-expressing cells were determined as the average of the product of receptor and ligand expression (respectively from set one and two) across all single-cell pairs:
\documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym} 				\usepackage{amsfonts} 				\usepackage{amssymb} 				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$I = \mathop \sum \limits_{i}^{n} I_{i} \times \mathop \sum \limits_{j}^{m} r_{j} \left(\frac{1}{m*n}\right)$$\end{document}I=∑inIi×∑jmrj1m∗nwhere I refers to the interaction score between receptor expressing cells in set one and ligand-expressing cells in set two, Ii stands for the ligand expression of cell i in cell set one, rj represents the receptor expression of cell j in cell set two, n stands for the number of cells in set one and m denotes the number of cells in set two.
In the gene list, there were 168 pairs of well-annotated ligands and receptors, among which were co-stimulators, chemokines and cytokines. The possible interactions between two cell types were orchestrated by receptor-ligand pairs by the product of the average expression levels of the ligand in one cell type and the respective receptor in the other cell type.