Nanoparticle Endocytosis: The Membrane-Wrapping Model — 2D Cross-Section View

Before a drug-carrying nanoparticle can act inside a cell, it first has to get in — and that entry is its own physics problem. This 2D companion to the 3D membrane-wrapping simulator renders the exact same free-energy competition — bending cost, neck line tension, and receptor-adhesion gain — as a genuine cross-section: drag to pan and scroll to zoom around a real membrane profile that dimples, wraps and pinches free (or doesn't) around the particle. Tune nanoparticle radius, receptor density, membrane stiffness and line tension, watch live wrapping fraction and free energy, and see which endocytic route the outcome resembles. This version also fixes a stall-detection bug verified in the 3D source: most parameter settings pin the wrapping fraction at a genuine activation barrier right at the start, and the 3D widget's raw-velocity stall check never notices, leaving it stuck showing "Wrapping in progress…" forever — here the fix correctly reports "No uptake" instead.