Modeling the uptake of fluorescent moleculesinto 3D cellular spheroids

Abstract

Three mathematical models were developed to analyze the dynamics of fluorescent dyespenetration into 3D cellular spheroids. Two fluorescent dyes were chosen to verify mathematicalmodels: 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 withthe cells plasma membrane, and its cellular penetration is significantly lower. Dye penetration andbinding to cells were modeled with nonlinear diffusion–reaction equations. System of differentialequations was solved using numerical methods, and good correspondence with physical experimentwas 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 dyesaccumulation into cell spheroids were also determined