Catalytic Motif Scaffolding (2D): Constraint-Satisfaction Backbone Folding

The 3D version of this simulator shows a diffusion model denoising a whole enzyme backbone at once. This 2D companion zooms into the actual optimization problem underneath that idea: a chain of connected residues, started as a random unfolded coil, is folded live — frame by frame — by a real simulated-annealing gradient-descent process that minimizes a geometric-constraint energy. A handful of residues along the chain are designated as the catalytic motif and are pulled toward a fixed target geometry (a Ser-His-Asp triad, a metal-binding site, or a Cys-His dyad), while spring and repulsion terms keep the rest of the chain connected and free of steric clashes. Watch the constraint-satisfaction-error readout fall from a large random value toward zero as the chain settles into a scaffold that genuinely holds the active site in the correct geometric arrangement — and watch it plateau above zero once the guidance-strength slider is turned down, exactly mirroring what happens to a designed enzyme's function when conditioning is too weak.