Tracking and line integration of diffuse cellular subdomains by mesh advection

Active molecular transport ensures a purposeful spatiotemporal distribution of cellular proteins and is therefore key to a wide range of processes such as morphogenesis, homeostasis or migration. However, redistributions of molecules in bulk are seldom quantified because the regions involved are too diffuse to be segmented consistently. To bridge this gap, we propose a Laplace-corrected Runge-Kutta advection that is based on mesh triangulation. Our framework can follow the movement and deformation of multiple parts of a diffuse region at once and offers a seamless combination with spatiotemporal line integration in Lagrangian coordinates. This allows the flexibility to taylor specific measures to the question at hand, e.g. mechanical work, bringing long-established physics concepts into biology grounds. We exemplify our approach by quantifying how the isotropy of intracellular protein distributions changes during cargo transport.