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

The Influence of Liquid Menisci on Nanoparticle Dosimetry in Submerged Cells

Understanding the interaction between cells and nanoparticles (NPs) is vital to understand the hazard associated with nanoparticles. This requires quantifying and interpreting dose-response relationships. Experiments with cells cultured in vitro and exposed to particle dispersions mainly rely on mathematical models that estimate the received nanoparticle dose. However, models need to consider that aqueous cell culture media wets the inner surface of hydrophilic open wells, which results in a curved liquid-air interface called the meniscus. Here the impact of the meniscus on nanoparticle dosimetry is addressed in detail. Experiments and build an advanced mathematical model, to demonstrate that the presence of the meniscus may bring about systematic errors that must be considered to advance reproducibility and harmonization is presented. The script of the model is co-published and can be adapted to any experimental setup. Finally, simple and practical solutions to this problem, such as covering the air-liquid interface with a permeable lid or soft rocking of the cell culture well plate is proposed.

On predicting heterogeneity in nanoparticle dosage

Nanoparticles are increasingly employed as a vehicle for the targeted delivery of therapeutics to specific cell types. However, much remains to be discovered about the fundamental biology that dictates the interactions between nanoparticles and cells. Accordingly, few nanoparticle-based targeted therapeutics have succeeded in clinical trials. One element that hinders our understanding of nanoparticle-cell interactions is the presence of heterogeneity in nanoparticle dosage data obtained from standard experiments. It is difficult to distinguish between heterogeneity that arises from stochasticity in nanoparticle-cell interactions, and that which arises from heterogeneity in the cell population. Mathematical investigations have revealed that both sources of heterogeneity contribute meaningfully to the heterogeneity in nanoparticle dosage. However, these investigations have relied on simplified models of nanoparticle internalisation. Here we present a stochastic mathematical model of nanoparticle internalisation that incorporates a suite of relevant biological phenomena such as multistage internalisation, cell division, asymmetric nanoparticle inheritance and nanoparticle saturation. Critically, our model provides information about nanoparticle dosage at an individual cell level. We perform model simulations to examine the influence of specific biological phenomena on the heterogeneity in nanoparticle dosage in the absence of heterogeneity in the cell population. Under certain modelling assumptions, we derive analytic approximations of the nanoparticle dosage distribution. We demonstrate that the analytic approximations are accurate, and show that nanoparticle dosage can be described by a Poisson mixture distribution with rate parameters that are a function of Beta-distributed random variables. We discuss the implications of the analytic results with respect to parameter estimation and model identifiability from standard experimental data. Finally, we highlight extensions and directions for future research.

Equation learning to identify nano-engineered particle-cell interactions: an interpretable machine learning approach

Designing nano-engineered particles capable of the delivery of therapeutic and diagnostic agents to a specific target remains a significant challenge. Understanding how interactions between particles and cells are impacted by the physicochemical properties of the particle will help inform rational design choices. Mathematical and computational techniques allow for details regarding particle-cell interactions to be isolated from the interwoven set of biological, chemical, and physical phenomena involved in the particle delivery process. Here we present a machine learning framework capable of elucidating particle-cell interactions from experimental data. This framework employs a data-driven modelling approach, augmented by established biological knowledge. Crucially, the model of particle-cell interactions learned by the framework can be interpreted and analysed, in contrast to the 'black box' models inherent to other machine learning approaches. We apply the framework to association data for thirty different particle-cell pairs. This library of data contains both adherent and suspension cell lines, as well as a diverse collection of particles. We consider hyperbranched polymer and poly(methacrylic acid) particles, from 6 nm to 1032 nm in diameter, with small molecule, monoclonal antibody, and peptide surface functionalisations. Despite the diverse nature of the experiments, the learned models of particle-cell interactions for each particle-cell pair are remarkably consistent: out of 2048 potential models, only four unique models are learned. The models reveal that nonlinear saturation effects are a key feature governing particle-cell interactions. Further, the framework provides robust estimates of particle performance, which facilitates quantitative evaluation of particle design choices.

Identifying cell-to-cell variability in internalization using flow cytometry

Biological heterogeneity is a primary contributor to the variation observed in experiments that probe dynamical processes, such as the internalization of material by cells. Given that internalization is a critical process by which many therapeutics and viruses reach their intracellular site of action, quantifying cell-to-cell variability in internalization is of high biological interest. Yet, it is common for studies of internalization to neglect cell-to-cell variability. We develop a simple mathematical model of internalization that captures the dynamical behaviour, cell-to-cell variation, and extrinsic noise introduced by flow cytometry. We calibrate our model through a novel distribution-matching approximate Bayesian computation algorithm to flow cytometry data of internalization of anti-transferrin receptor antibody in a human B-cell lymphoblastoid cell line. This approach provides information relating to the region of the parameter space, and consequentially the nature of cell-to-cell variability, that produces model realizations consistent with the experimental data. Given that our approach is agnostic to sample size and signal-to-noise ratio, our modelling framework is broadly applicable to identify biological variability in single-cell data from internalization assays and similar experiments that probe cellular dynamical processes.

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

Understanding the interactions between nano-engineered particles and cells is necessary for the rational design of particles for therapeutic, diagnostic and imaging purposes. In particular, the informed design of particles relies on the quantification of the relationship between the physicochemical properties of the particles and the rate at which cells interact with, and subsequently internalise, particles. Quantitative models, both mathematical and computational, provide a powerful tool for elucidating this relationship, as well as for understanding the mechanisms governing the intertwined processes of interaction and internalisation. Here we review the different types of mathematical and computational models that have been used to examine particle-cell interactions and particle internalisation. We detail the mathematical methodology for each type of model, the benefits and limitations associated with the different types of models, and highlight the advances in understanding gleaned from the application of these models to experimental observations of particle internalisation. We discuss the recent proposal and ongoing community adoption of standardised experimental reporting, and how this adoption is an important step toward unlocking the full potential of modelling approaches. Finally, we consider future directions in quantitative models of particle-cell interactions and highlight the need for hybrid experimental and theoretical investigations to address hitherto unanswered questions.