Morais Paulo C, Silva Dieime C
Genomic Sciences and Biotechnology Program, Catholic University of Brasília, Brasília 70790-160, Brazil.
Institute of Physics, University of Brasília, Brasília 70910-900, Brazil.
Nanomaterials (Basel). 2022 Jan 27;12(3):413. doi: 10.3390/nano12030413.
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 (Vpa/(s)p-a; p and a are fitting parameters) and accounting for two opposite trends of V versus σ: under light (Vσ) and under dark (V~1/σ).
该论文报道了一种新的数学模型，它始于最初的希尔方程，该方程是在测试纳米材料（NMs）时为描述细胞活力（V）而推导出来的。通过对数正态分布函数，样本形态的关键信息，如平均尺寸（⟨s⟩）和尺寸分散度（σ）被纳入新模型。这个受希尔方程启发的新方程成功地用于拟合在光照（波长400 - 700 nm）和黑暗条件下，用含氟石墨烯量子点（F:GQDs）处理的HepG2细胞系所进行的MTT（3-(4,5-二甲基噻唑-2-基)-2,5-二苯基四氮唑溴盐）检测数据。提取的“生物多分散性”（光照条件下：⟨sMTT⟩ = 1.77±0.02 nm且σMTT = 0.21±0.02；黑暗条件下：⟨sMTT⟩ = 1.87±0.02 nm且σMTT = 0.22±0.01）与“形态多分散性”（⟨sTEM⟩ = 1.98±0.06 nm且σTEM = 0.19±0.03）进行比较，后者是通过透射电子显微镜（TEM）获得的。然后，拟合数据用于模拟一系列V响应。模拟中强调了两个方面：（i）固定σ，模拟V与⟨s⟩的关系；（ii）固定⟨s⟩，模拟V与σ的关系。模拟中观察到的趋势得到了一个现象学模型图景的支持，该图景描述了随着⟨s⟩增加V的单调降低（Vpa/(s)p - a；p和a是拟合参数），并解释了V与σ的两种相反趋势：光照条件下（Vσ）和黑暗条件下（V~1/σ）。
