Spatial optimization of transport and capture processes in extended cellular regions

Cellular functions such as autophagy, signaling, and endocytosis involve physical interaction or capture of transported organelles, proteins, and signaling molecules at specific locations within the cell. We model transport-and-capture processes in tubular cells to explore how the spatial arrangement of capture regions affects biological function. In neurons, autophagosomes carrying cellular material for degradation transport over long distances to interact and fuse with acidified lysosomes. Using a simple analytical model, we show that the flux of degraded material can be optimized by regulating the location of organelle interactions. Our model identifies key features and parameters that govern the interplay between autophagy and long-range transport. In contrast to motile lysosomes, stationary microtubule tips can also behave as capture regions for loading motor-driven cargo. Endocytosed vesicles and signaling molecules diffuse from their entry point until captured at a microtubule tip. We model this diffusive capture process and show that a dispersed microtubule tip arrangement can minimize capture time. Our results highlight important physical features of autophagy and microtubule-based transport, providing guiding principles for optimal spatial arrangements within the cell.