Model for random internalization of nanoparticles by cells.

Area of Science:

• Biophysics
• Cell Biology
• Nanotechnology

Background:

• Cellular uptake of nanoparticles is crucial for drug delivery and toxicology.
• Existing models, like Rees et al., explain overdispersion using gamma-distributed cell areas.
• A need exists for alternative stochastic models to capture nanoparticle internalization dynamics.

Purpose of the Study:

• To propose a novel stochastic model for nanoparticle internalization by cells.
• To formulate cellular uptake as a compound Poisson process with random probability of success.
• To provide an alternative explanation for overdispersion in nanoparticle uptake.

Main Methods:

• Utilizing a Poisson process for new pit formation.
• Employing a random Bernoulli process with beta-distributed probability for capturing and heterogeneity.
• Deriving an explicit formula for the distribution of pits containing nanoparticles.

Main Results:

• The model demonstrates self-reinforcement in nanoparticle capture.
• Ensemble-averaged nanoparticle uptake is represented by a Polya process.
• The negative binomial distribution is recovered in the limit of fast nucleation and low capture probability.

Conclusions:

• The proposed stochastic model offers a new framework for understanding nanoparticle cellular uptake.
• The model successfully explains overdispersion and connects to known distributions like Polya and negative binomial.
• This work provides a valuable tool for researchers in nanomedicine and cell biology.