An energy-based mathematical model of actin-driven protrusions in eukaryotic chemotaxis

In eukaryotic cell chemotaxis, many cells extend and retract transient actin-driven protrusions at their membrane that facilitate both the detection of external chemical gradients and directional movement via cell-matrix coupling and traction. Although extensive experimental work has detailed how cellular protrusions and morphology vary under different environmental conditions, the mechanistic principles linking protrusive activity to these factors remain poorly understood. Here, we model the extension of actin-based protrusions in chemotaxis as an optimisation problem, wherein cells balance the detection of chemical gradients with the energetic cost of protrusion formation. Our model, built on the assumption of maximal energetic efficiency during migration, provides a framework that qualitatively reproduces experimentally observed patterns of protrusive activity across a range of biological systems and environmental conditions, suggesting that energetic efficiency may underpin the morphology and chemotactic behaviour of motile eukaryotic cells. Additionally, we leverage the model to generate novel predictions regarding cellular responses to other, experimentally untested environmental perturbations, providing testable hypotheses for future experimental work that may be used to validate and refine the model presented here.