Modelling the size distribution and bioaccumulation of gold nanoparticles under mixture exposure

To assess the bioaccumulation and toxicity of nanoparticles (NPs), analyzing and modelling the relationship between the size distribution of NPs in organisms and the exposure particle size distribution represents an important challenge. Previous studies mostly focused on the NPs with single size. However, the size distribution of NPs is wide and variable in the natural environment. There is a lack of research on the NPs with mixed sizes. This study investigated the size distribution of three gold (Au) NPs with different sizes and their mixtures within a ciliate Tetrahymena thermophila under the same number concentration of particles. Results revealed that smaller particles tended to aggregate and bioaccumulate more in cells. Using expectation–maximization algorithm, a particle size distribution model of NPs in cells was established. This model effectively simulated the size distribution of NPs with mixed sizes in cells, demonstrating high accuracy with a mean absolute error of < 0.001, a root mean squared error of < 0.001, and a correlation coefficient exceeding 0.98. Experimental results further verified that the model reliably predicted the size distribution of NPs with mixed sizes in cells, and smaller particles accounted for a larger proportion of the size distribution and bioaccumulation. These results demonstrated the importance of particle size and size distribution of NPs in their environmental effects. Models developed here can provide guidance for future evaluation of the environmental risks of NPs mixtures.