The Effects of Non-Specific Binding Kinetics on Fluorescence Activated Cell Sorting (FACS)

Fluorescence activated cell sorting (FACS) is extensively used in biological studies to differentiate cells of interest (mutants) from control cells (wild-types). For mutant cells characterized by expression of a distinct membrane surface structure, fluorescent marker probes can be designed to bind specifically to those structures, resulting in a sufficiently high fluorescence intensity that indicates a mutant cell. However, endogenous membrane structures on wild-type cells may nonspecifically bind to the probes, resulting in false positive results. These same endogenous membrane structures would also be present on mutant cells, allowing both specific and non-specific binding to a single cell. We create a kinetic model of fluorescent probe binding dynamics by tracking populations of mutant and wild-type cells with differing numbers of probes bound specifically and non-specifically. By assuming the suspension is in equilibrium prior to cytometry, we analytically derive a likelihood function of the FACS output in order to infer the total number of mutant cells while accounting for the non-specific binding of probes. We further show how our model can be used to infer unknown binding rates of fluorescent markers if cell counts are a priori known.