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

Abstract

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.