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3D cell cultures are extensively used to study in vitro toxic effect of xenobiotics. When using multicellular spheroids, the question about their optimal size should be solved: small spheroids are difficult to manipulate, while large size of spheroids impairs the transport of nutrients and oxygen into the center. Mathematical models describing the distribution of substances in multicellular spheroids numerical procedure for solving differential equation system, which complicates their use in laboratory practice. We proposed and experimentally evaluated a new mathematical model describing oxygen distribution in HepaRG cell spheroids. Markers of functional activity were studied in spheroids of different size. The maximum size of spheroids that can be maintained in culture for 9 days without necrosis was determined.

Сасо-2 cell line is widely used in in vitro studies of the intestinal wall permeability for drugs, but transport activity of these cells has not been thoroughly studied. We analyzed localization and expression of nucleoside transporters of the ENT family transferring a number of anticancer and antiviral drugs. Immunocytochemical staining revealed apical localization of ENT1 and integral expression of ENT2 in Caco-2 cells. Based on these data and on the value of hypoxanthine uptake by these cells, we created a mathematical model allowing quantification of transporter expression on the apical and basolateral membranes of Caco-2 cells. The discrepancy between gene and protein expression of the transporter complicating prediction of patient's sensitivity to the drug upon individual therapy selection is discussed.

We studied the relationship between microcirculation parameters and functional status of HepaRG cells in spheroids and chose an optimal regimen within the physiologically permissible limits of mechanical impact for the cells that maintains the expression of functional genes of the liver.

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We studied the effects of silver nanoparticles (10 nm) on HepaRG cell spheroids simulating liver tissue. The mathematical model was proposed that describes nanoparticle diffusion in a spheroid consisting of 5000 cells depending on the external nanoparticle concentration. It was demonstrated that cells in the 3D model were less sensitive to the toxic effects of nanoparticles in comparison with 2D cultures. Impaired integrity of the cell membrane did not deteriorate cell viability (according to MTT test).

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