Test statistic 6: Is metabolite m exchanged by cell types t and u?#
Gene pairs can also be linked to metabolites by using the HarremanDB database (or to ligand-receptor pathways by using CellChatDB (Jin et al., Nature protocols, 2024)). Therefore, as \(H_{ab}^{t,u} = \sum_{i \in C_t}^{}\sum_{j \in C_u}^{} w_{ij}X_{ai}X_{bj}\) can be summed up for all gene pairs that exchange a given metabolite, we obtain the equation below:
where m is a given metabolite that is being exchanged by genes a and b. In this setting, we would be assessing if metabolite m is exchanged by cell types t and u.
Significance testing in this case also depends on which of the three possible null hypotheses defined in Test statistic 5 we are testing and, therefore, the shuffling strategy used. The null hypotheses in this case are defined as follows:
(1) The observed co-expression of all gene pairs associated with metabolite m across cell types t and u is no stronger than expected by chance, given the spatial co-localization of cell types t and u.
(2) The observed co-expression of metabolite m’s associated genes is not enriched in any specific cell type pair, that is, it is random with respect to which cell types express those genes.
(3) The observed spatial co-expression between the expression of metabolite m’s genes in a cell type of interest and the expression of those genes in another cell type u is no stronger than expected if gene expression in cell type u were random.
However, irrespective of the null hypothesis we want to test, the equation above is computed in each iteration. Eventually, p-values are computed (\(p-value = \frac{x+1}{M+1}\)) and adjusted using the Benjamini-Hochberg approach.