Abstract
Phagocytosis is a fundamental cellular process by which cells engulf external particles, controlled by receptor-ligand binding and actin-driven membrane dynamics. While a number of mathematical models have been developed to describe this process, they often overlook membrane tension, a key physical parameter known to influence membrane deformation and cytoskeletal behaviour. To address this gap, we present an enhanced mathematical model of receptor motion during phagocytosis that explicitly incorporates the role of membrane tension. Further, we introduce a signalling component that is coupled to receptor dynamics via the membrane tension. We find that including tension results in fundamentally different engulfment behaviour, which is slower than that predicted by models without tension. In particular, unlike in the previous version of this model, we show that tension can lead to stalled engulfment, an experimentally-observed phenomenon known as frustrated phagocytosis. We also find that signalling is able to modify engulfment behaviour, especially at later stages, and is able to alter cup growth to become linear in time without the need for receptor drift as introduced in previous models. These findings offer new insights into the role of membrane tension and biophysical regulation in phagocytosis, with implications for immune function, cell motility and targeted drug delivery.