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

Abstract

The paper reports on a new mathematical model, starting with the original Hill equation which is derived to describe cell viability (V) while testing nanomaterials (NMs). Key information on the sample’s morphology, such as mean size (⟨s⟩) and size dispersity (σ) 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: ⟨sMTT⟩=1.77±0.02 nm and σMTT=0.21±0.02); dark: ⟨sMTT⟩=1.87±0.02 nm and σMTT=0.22±0.01) is compared with the “morphological polydispersity” (⟨sTEM⟩=1.98±0.06 nm and σTEM=0.19±0.03), the latter obtained from TEM (transmission electron microscopy). The fitted data are then used to simulate a series of V responses. Two aspects are emphasized in the simulations: (i) fixing σ, one simulates V versus ⟨s⟩ and (ii) fixing ⟨s⟩, one simulates V versus σ. Trends observed in the simulations are supported by a phenomenological model picture describing the monotonic reduction in V as ⟨s⟩ increases (V~pa/(s)p−a; p and a are fitting parameters) and accounting for two opposite trends of V versus σ: under light (V~σ) and under dark (V~1/σ).