DNA Nanorobot Lock Kinetics & Cargo Diffusion (2D)

This 2D companion strips the DNA-origami nanorobot box down to its two governing equations, each drawn as a native 2D diagram rather than a flattened 3D camera view. A reaction-coordinate ladder shows four toehold-mediated strand-displacement locks racing to satisfy an AND-gate threshold, with the exact analytical survival curve exp(−k_obs·t) plotted alongside the live stochastic trace. Below it, a genuine finite-difference solution of the 2D diffusion equation replaces individual jittering particles with a concentration field: cargo starts confined at high concentration inside a reflective-walled box, and once enough locks are displaced the wall opens and the field spreads outward exactly as Fick's law and the Stokes–Einstein diffusion coefficient predict. Tune toehold length, trigger concentration, the AND-gate threshold and temperature to see both the kinetics and the diffusion respond together.