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The delivery of nanoparticles into cells is important in therapeutic applications and in nanotoxicology. Nanoparticles are generally targeted to receptors on the surfaces of cells and internalized into endosomes by endocytosis, but the kinetics of the process and the way in which cell division redistributes the particles remain unclear. Here we show that the chance of success or failure of nanoparticle uptake and inheritance is random. Statistical analysis of nanoparticle-loaded endosomes indicates that particle capture is described by an over-dispersed Poisson probability distribution that is consistent with heterogeneous adsorption and internalization. Partitioning of nanoparticles in cell division is random and asymmetric, following a binomial distribution with mean probability of 0.52-0.72. These results show that cellular targeting of nanoparticles is inherently imprecise due to the randomness of nature at the molecular scale, and the statistical framework offers a way to predict nanoparticle dosage for therapy and for the study of nanotoxins.

Understanding nanoparticle uptake by biological cells is fundamentally important to wide-ranging fields from nanotoxicology to drug delivery. It is now accepted that the arrival of nanoparticles at the cell is an extremely complicated process, shaped by many factors including unique nanoparticle physico-chemical characteristics, protein-particle interactions and subsequent agglomeration, diffusion and sedimentation. Sequentially, the nanoparticle internalisation process itself is also complex, and controlled by multiple aspects of a cell’s state. Despite this multitude of factors, here we demonstrate that the statistical distribution of the nanoparticle dose per endosome is independent of the initial administered dose and exposure duration. Rather, it is the number of nanoparticle containing endosomes that are dependent on these initial dosing conditions. These observations explain the heterogeneity of nanoparticle delivery at the cellular level and allow the derivation of simple, yet powerful probabilistic distributions that accurately predict the nanoparticle dose delivered to individual cells across a population.

Assessing dose in nanoparticle–cell interactions is inherently difficult due to a complex multiplicity of possible mechanisms and metrics controlling particle uptake. The fundamental unit of nanoparticle dose is the number of particles internalized per cell; we show that this can be obtained for large cell populations that internalize fluorescent nanoparticles by endocytosis, through calibration of cytometry measurements to transmission electron microscopy data. Low-throughput, high-resolution electron imaging of quantum dots in U-2 OS cells is quantified and correlated with high-throughput, low-resolution optical imaging of the nanoparticle-loaded cells. From the correlated data, we obtain probability distribution functions of vesicles per cell and nanoparticles per vesicle. Sampling of these distributions and comparison to fluorescence intensity histograms from flow cytometry provide the calibration factor required to transform the cytometry metric to total particle dose per cell, the mean value of which is 2.4 million. Use of the probability distribution functions to analyze particle partitioning during cell division indicates that, while vesicle inheritance is near symmetric, highly variable vesicle loading leads to a highly asymmetric particle dose within the daughter cells.

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