Abstract
The paper reports on a new mathematical model, starting with the original Hill equation which is derived to describe cell viability () while testing nanomaterials (NMs). Key information on the sample’s morphology, such as mean size () and size dispersity () 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: and ); dark: and ) is compared with the “morphological polydispersity” ( and ), the latter obtained from TEM (transmission electron microscopy). The fitted data are then used to simulate a series of responses. Two aspects are emphasized in the simulations: (i) fixing , one simulates versus and (ii) fixing , one simulates versus . Trends observed in the simulations are supported by a phenomenological model picture describing the monotonic reduction in as increases (; and are fitting parameters) and accounting for two opposite trends of versus : under light () and under dark ().
Highlights
The interest in conducting the mathematical modeling of biological data, in vitro standard assays, has grown tremendously in the last five decades from a few peer-reviewed publications in the early seventies to a few hundred in recent years, as witnessed by the records of scientific data [1]
The impact of the NM’s morphological aspects on the biological response will be explored in this study using Equation (4), starting with the fitting parameters extracted from the analysis of the cell viability assay (MTT assay) performed with the HepG2 cell line incubated with the F:Graphene quantum dots (GQDs), in the dark and under visible light illumination
The MTT test under visible light was performed to probe the capability of the F:GQD sample in generating reactive oxygen species (ROS) and to explore its future application in photodynamic therapy (PDT) [33]
Summary
The interest in conducting the mathematical modeling of biological data, in vitro standard assays, has grown tremendously (by about two orders of magnitude) in the last five decades from a few peer-reviewed publications in the early seventies to a few hundred in recent years, as witnessed by the records of scientific data [1]. The benefits of this trend are multifaceted, ranging from a minimization in the use of cell lines up to helping the improved planning of all biological assays, with the aim to maximize resources and minimize replication [2].
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