Single-Molecule FRET: Energy-Landscape View

This is a genuinely 2D-native counterpart to the 3D single-molecule FRET simulator: instead of animating a dye pair in 3D space with a scripted state switch, it integrates the molecule's own reaction coordinate forward in time as overdamped Langevin diffusion inside a bistable energy landscape U(x). The two wells of that landscape are the open and closed conformations; the molecule crosses the barrier between them stochastically, the way real biomolecules do, with the switching-rate and population-bias sliders shaping the landscape's barrier friction and tilt through the Kramers escape rate and Boltzmann occupancy respectively. The reaction coordinate still drives the identical Forster energy-transfer law E = 1/(1+(r/R0)^6) and the same photon-by-photon shot-noise detection model, so the live trace and efficiency histogram read exactly like the 3D version's — only the mechanism producing the underlying motion is different.