A Geometric Model of Nucleus-Constrained Frustrated Phagocytosis

Frustrated phagocytosis occurs when phagocytes fail to fully engulf large targets, yet the geometric origins of this physical limit remain poorly defined. Here we present a geometric model that identifies the cell nucleus as an intracellular constraint on engulfment. Extending membrane-limited frameworks, we distinguish an intrinsic phagocytic capacity set by membrane availability from an apparent capacity reduced by nuclear exclusion. Using minimal geometric assumptions, we derive closed-form expressions linking experimentally measurable parameters, including target coverage, volume ratio, and size, to phagocytic capacity and a normalized axial separation that quantifies nuclear accommodation. The model predicts a size- and curvature-independent geometric criterion for nuclear involvement applicable to both spherical and planar targets. These results establish nuclear geometry as a fundamental physical bottleneck in phagocytosis and provide a quantitative framework for interpreting stalled engulfment and nuclear deformation-dependent responses.