Modeling the uptake of fluorescent molecules into 3D cellular spheroids

Abstract

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.

3D Cell Aggregates Amplify Diffusion Signals

“…of dye penetration into cellular spheroids in which the unitary ratio is employed to model the boundary condition [12]. Leedale et al (2020) proposed a diffusion model for drug transport and metabolism that is developed in a multiscale spheroid framework, accounting for microscale processes where the concentration at the boundary is simply assumed to be equal to the outside concentration [13].…”

“…Despite its importance, the amplification BC has not been comprehensively characterized in the literature, and different types of models have been proposed by various authors. Some works define the amplification BC as a unitary ratio, implying that the concentration is the same inside and outside the 3DCA border [12][13][14][15].…”

“…Despite its importance, the amplification BC has not been comprehensively characterized in the literature, and different types of models have been proposed by various authors. Some works define the amplification BC as a unitary ratio, implying that the concentration is the same inside and outside the 3DCC border [10][11][12][13] . Astrauskas et al ( 2019) presented a reaction-diffusion equation model for analysis of dye penetration into cellular spheroids in which the unitary ratio is employed to model the boundary condition 10 .…”

“…Some works define the amplification BC as a unitary ratio, implying that the concentration is the same inside and outside the 3DCC border [10][11][12][13] . Astrauskas et al ( 2019) presented a reaction-diffusion equation model for analysis of dye penetration into cellular spheroids in which the unitary ratio is employed to model the boundary condition 10 . Leedale et al (2020) developed a diffusion model of drug transport and metabolism that is developed in a multiscale spheroid framework, accounting for microscale processes where the concentration at the boundary is simply assumed to be equal to the outside concentration 11 .…”

Spheroidal Molecular Communication via Diffusion: Signaling Between Homogeneous Cell Aggregates

“…Several studies have attempted to model the process of mass transport in a spheroidal environment. The authors of [3] modeled the penetration and diffusion of dyes within multicellular spheroids using diffusion-reaction equations. They assumed constant concentrations of molecules at the inside and outside of the outer spheroid's boundary.…”