Analysis of the in-vitro nanoparticle-cell interactions via smoothing splines mixed effects model

Abstract

A mixed effects statistical model is developed to understand the nanoparticle(NP)- cell interactions and predict the cellular uptake rate of NPs. NP-cell interactions are crucial for targeted drug delivery systems, cell-level diagnosis, and cancer treatment. The NP cellular uptake depends on the size, charge, chemical structure, concentration of NPs, and incubation time. The vast number of combinations of those variable values disallows a comprehensive experimental study of NP-cell interactions. A mathematical model can, however, generalize the findings from some limited number of carefully designed experiments and can be used for the simulation of NP uptake rates for the alternative treatment design, planning, and comparisons. We propose a mathematical model based on the data obtained from in-vitro NPhealthy cell experiments conducted by the Nanomedicine and Advanced Technologies Research Center in Turkey. The proposed model predicts the cellular uptake rate of Silica, polymethyl methacrylate, and polylactic acid NPs given the incubation time, size, charge and concentration of NPs. This study implements the mixed model methodology in nanomedicine area for the first time and is the first mathematical model that predicts NP cellular uptake rate based on sound statistical principles. Our model provides a cost effective tool for researchers developing targeted drug delivery systems.