Mathematical Modeling for an MTT Assay in Fluorine-Containing Graphene Quantum Dots

The paper reports on a new mathematical model, starting with the original Hill equation which is derived to describe cell viability ([Formula: see text]) while testing nanomaterials (NMs). Key information on the sample’s morphology, such as mean size ([Formula: see text]) and size dispersity ([Formula: see text]) is included in the new model via the lognormal distribution function. The new Hill-inspired equation is successfully used to fit MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) data from assays performed with the HepG2 cell line challenged by fluorine-containing graphene quantum dots (F:GQDs) under light (400–700 nm wavelength) and dark conditions. The extracted “biological polydispersity” (light: [Formula: see text] and [Formula: see text]); dark: [Formula: see text] and [Formula: see text]) is compared with the “morphological polydispersity” ([Formula: see text] and [Formula: see text]), the latter obtained from TEM (transmission electron microscopy). The fitted data are then used to simulate a series of [Formula: see text] responses. Two aspects are emphasized in the simulations: (i) fixing [Formula: see text] , one simulates [Formula: see text] versus [Formula: see text] and (ii) fixing [Formula: see text] , one simulates [Formula: see text] versus [Formula: see text]. Trends observed in the simulations are supported by a phenomenological model picture describing the monotonic reduction in [Formula: see text] as [Formula: see text] increases ([Formula: see text]; [Formula: see text] and [Formula: see text] are fitting parameters) and accounting for two opposite trends of [Formula: see text] versus [Formula: see text]: under light ([Formula: see text]) and under dark ([Formula: see text]).