A statistical theory for flow cytometry profiles in terms of the binding of ligands to cell surface receptors and changes in gene expression.

Flow cytometry analysis is a technique used for obtaining light scattering and fluorescence intensity data in order to characterise a chosen cell line. From a sample of the data obtained, it is desired to infer the distribution of cell size, cell granularity and occupancy of cell surface receptors, by constructing histograms for the variables of interest. Often an attempt is made, for instance, to account for the changes in shape of these histograms in terms of alterations in gene expression, etc. In this paper we analyse the way that changes in the sample histograms can be interpreted in three frequently encountered situations, namely (a) when there is one cell line exposed to alterations in chemical potential of ligand, (b) when there are two cell lines exposed separately to saturating concentrations of the same ligand, and (c) when two ligands are added in saturating amounts, first separately, then together, to the same cell line. We demonstrate that, under a wide range of assumptions, the change in histogram shape can be accounted for in terms of a proportionate and absolute component and examples are given to illustrate this. Finally, a computer program to analyse experimental data in terms of estimated shift and stretch parameters is described.