The 3D version animates two glowing dye spheres tethered by a wobbling linker and explicitly flips a two-state Markov switch (open/closed) with a hand-set relaxation time. This 2D view instead simulates the molecule's reaction coordinate x as a bead undergoing genuine overdamped Langevin diffusion in a bistable energy landscape:
U(x) = h(x^2-1)^2 - tilt . x
gamma.dx/dt = -U'(x) + sqrt(2.gamma.T).xi(t) (xi = white noise)
The two minima of U(x) at x ~ -1 and x ~ +1 are the closed and open conformations — there is no scripted jump. The molecule crosses the barrier stochastically, exactly as Kramers escape theory describes real conformational transitions. The switching-rate slider sets the friction gamma via the overdamped Kramers rate
k = sqrt(U''(xmin).|U''(xmax)|) / (2.pi.gamma) . exp(-h/T)
and the population-bias slider sets the potential's tilt so the two wells' equilibrium (Boltzmann) occupancy exp(-U/T) matches the requested closed-state fraction — the same physics that sets fold/unfold or open/closed equilibria in real free-energy landscapes.
The reaction coordinate x is mapped linearly onto a dye-dye distance r (nm), which drives the identical Forster law and photon-counting statistics as the 3D scene:
E(r) = 1 / (1 + (r / R0)^6)
Each detected photon is still assigned to the acceptor channel with probability E(r) and the donor channel otherwise. Donor detections tick green along the top rail of the trace panel, acceptor detections tick red along the bottom rail — a 2D-native stand-in for the flying photon particles in the 3D scene. The energy-landscape panel above the trace draws U(x) live (it reshapes as you move the bias slider) with a marker ball riding the actual simulated x(t).
- R0 — same Forster-radius meaning as the 3D scene: the distance at which E = 0.5.
- Switching rate k — sets the friction so the Kramers escape rate over the fixed barrier approximates k; mean dwell time is roughly 1/k.
- Closed-state population — sets the potential's tilt so the two wells' Boltzmann occupancy matches this fraction.
- Photon rate — detector brightness; low rates reveal shot noise in the green "measured E" trace against the gray "true E" trace.