Modelo matemático para predecir la internalización celular de nanopartículas de oro

Abstract

This work develops and implements a compartmental mathematical model based on ordinary differential equations to quantitatively describe and predict the size-dependent cellular internalization dynamics of gold nanoparticles, in the context of oncological therapeutic applications through radiotherapy and hyperthermia. The model coherently integrates multiple physical and temporal scales, incorporating cell membrane thermodynamics, diffusion transport kinetics, cluster formation through FCC packing, and receptor-mediated endocytosis. From the energy balance between membrane curvature and receptor-ligand adhesion, a minimum thermodynamic barrier of Rmin = 23.09 nm was identified, determining the internalization threshold. The model was validated through direct comparison with experimental data from Chithrani et al. (2007) for spherical gold nanoparticles of 14 nm, 50 nm, and 74 nm in diameter, achieving a global coefficient of determination R² = 0.9786 and individual errors below 5.2%, correctly reproducing the non-monotonic dependence of cellular uptake on particle size, with a maximum at 50 nm.