Mathematical Modeling for an MTT Assay in Fluorine-Containing Graphene Quantum Dots - Paulo C. Morais; Dieime C. Silva (Nanomaterials, 2022)
The paper reports on a new mathematical model, starting with the original Hill equation which is derived to describe cell viability (<semantics>V</semantics>) while testing nanomaterials (NMs). Key information on the sample’s morphology, such as mean size (<semantics>⟨s⟩</semantics>) and size dispersity (<semantics>σ</semantics>) 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: <semantics>⟨sMTT⟩=1.77±0.02 nm</semantics> and <semantics>σMTT=0.21±0.02</semantics>); dark: <semantics>⟨sMTT⟩=1.87±0.02 nm</semantics> and <semantics>σMTT=0.22±0.01</semantics>) is compared with the “morphological polydispersity” (<semantics>⟨sTEM⟩=1.98±0.06 nm</semantics> and <semantics>σTEM=0.19±0.03</semantics>), the latter obtained from TEM (transmission electron microscopy). The fitted data are then used to simulate a series of <semantics>V</semantics> responses. Two aspects are emphasized in the simulations: (i) fixing <semantics>σ</semantics>, one simulates <semantics>V</semantics> versus <semantics>⟨s⟩</semantics> and (ii) fixing <semantics>⟨s⟩</semantics>, one simulates <semantics>V</semantics> versus <semantics>σ</semantics>. Trends observed in the simulations are supported by a phenomenological model picture describing the monotonic reduction in <semantics>V</semantics> as <semantics>⟨s⟩</semantics> increases (<semantics>V~pa/(s)p−a</semantics>; <semantics>p</semantics> and <semantics>a</semantics> are fitting parameters) and accounting for two opposite trends of <semantics>V</semantics> versus <semantics>σ</semantics>: under light (<semantics>V~σ</semantics>) and under dark (<semantics>V~1/σ</semantics>).