Graphical representation of gene expression in two cells from a homogeneous population but with different total mRNA content.

(a) Three biological genes have the same expression rates in both cells, however cell 1 doubles cell 2 in terms of total mRNA content. As a result, the expression counts in cell 1 will be roughly twice as much as those from cell 2, for all genes. In terms of the cell-specific size factors ϕ_j, an appropriate normalisation in this case would be e.g. ϕ₁ = 2, ϕ₂ = 1 (or any other values such that ϕ₁/ϕ₂ = 2). (b) The same cells after the addition of two molecules of a spike-in gene to each cell. Because the same number of spike-in molecules are added to each cell, the spike-in expression counts are independent of the total mRNA content of each cell. Therefore, the cell-specific size factors ϕ_j are not required when modelling the technical gene.