Modeling the uptake of fluorescent molecules into 3D cellular spheroids
Rokas Astrauskas
Vilnius University
Feliksas Ivanauskas
Vilnius University
Greta Jarockytė
National Cancer Institute
Vitalijus Karabanovas
National Cancer Institute / Vilnius Gediminas Technical University
Ričardas Rotomskis
National Cancer Institute / Vilnius University
Published 2019-09-26


diffusion reaction equations,
cellular spheroids
rhodamine 6G
wheat germ agglutinin
mathematical modeling

How to Cite

Astrauskas R., Ivanauskas F., Jarockytė G., Karabanovas V. and Rotomskis R. (2019) “Modeling the uptake of fluorescent molecules into 3D cellular spheroids”, Nonlinear Analysis: Modelling and Control, 24(5), pp. 838–852. doi: 10.15388/NA.2019.5.9.


Three mathematical models were developed to analyze the dynamics of fluorescent dyes penetration into 3D cellular spheroids. Two fluorescent dyes were chosen to verify mathematical models: rhodamine 6G (R6G) as a small molecule, which can freely penetrate through the cells, and wheat germ agglutinin (WGA) conjugated with Alexa488 fluorescent label, which reacts with the cells plasma membrane, and its cellular penetration is significantly lower. Dye penetration and binding to cells were modeled with nonlinear diffusion–reaction equations. System of differential equations was solved using numerical methods, and good correspondence with physical experiment was shown. Diffusion coefficients in extracellular matrix were determined for both fluorescent dyes, and the influence of reactions parameters to WGA penetration was analyzed. Dynamics of dyes accumulation into cell spheroids were also determined.

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