Isolating the sources of heterogeneity in nano-engineered particle–cell interactions

Abstract

<jats:p>Nano-engineered particles have the potential to enhance therapeutic success and reduce toxicity-based treatment side effects via the targeted delivery of drugs to cells. This delivery relies on complex interactions between numerous biological, chemical and physical processes. The intertwined nature of these processes has thus far hindered attempts to understand their individual impact. Variation in experimental data, such as the number of particles inside each cell, further inhibits understanding. Here, we present a mathematical framework that is capable of examining the impact of individual processes during particle delivery. We demonstrate that variation in experimental particle uptake data can be explained by three factors: random particle motion; variation in particle–cell interactions; and variation in the maximum particle uptake per cell. Without all three factors, the experimental data cannot be explained. This work provides insight into biological mechanisms that cause heterogeneous responses to treatment, and enables precise identification of treatment-resistant cell subpopulations.</jats:p>

Understanding nano-engineered particle–cell interactions: biological insights from mathematical models

“…Additionally, outside of specific classes of differential equations, these models do not include stochastic effects such as environmental or demographic stochasticity 66 . One implication of this is that all entities represented by a single quantity of interest are identical 63 . Further, given an initial state for the quantities of interest and a set of parameter values, the solution trajectory will always be the same 65 .…”

“…Models that incorporate particle transport, stochastic particle behaviour, and internalisation kinetics have been successfully employed to understand the phenomenon of heterogeneity in par-ticle dosage at an individual cell level 59,60,63,154,155 . Heterogeneity in particle dosage has potentially severe consequences for particle-based therapeutics, as successful treatment may rely on each cell internalising a threshold number of drug-loaded particles.…”

“…By extending the particle internalisation and transport model of Faria et al 55 to account for stochastic particle behaviour, Johnston et al 63 demonstrate that the heterogeneity in particle dosage can be explained by accounting for three factors: (i) stochastic particle motion; (ii) heterogeneity in the rate of particle-cell association, and; (iii) heterogeneity in the finite particle capacity of cells. Further, the authors show that all three factors are needed to explain experimental observations 63 . This systematic unpacking of complex phenomena to reveal the key governing mechanisms highlights the insight that can be gained by combining mathematical models and particle-cell experiments.…”

“…For example, it is not common in experimental protocols to distinguish between internalised particles and particles that are merely bound to the cell membrane 55,158,159 . To robustly calibrate the model, either the mathematical model must calculate the number of associated particles 55,63 , rather than internalised particles, or more complex experimental protocols must be implemented 158,159 . Another likely fruitful avenue for future research is the combination of existing models of particle internalisation in a multiscale framework.…”

Fluid Menisci andIn VitroParticle Dosimetry of Submerged Cells

“…While this is a fundamental phenomenon that concerns any open well that exhibits a fluid-air interface, mathematical models assume flat fluid surfaces, neglecting completely the meniscus. 3–13…”