Nanowire Biosensor: Reversible Binding Chain (2D)

This 2D companion to the 3D piezoresistive nanowire biosensor models the same real device, but computes it two genuinely different ways. Instead of a single deterministic saturation curve, each of the wire's 60 binding sites runs its own real reversible Langmuir reaction — molecules bind and unbind as independent Poisson processes, so coverage settles into a fluctuating dynamic equilibrium set by the ratio of on-rate to off-rate, not a one-way saturation. And instead of assuming the whole beam bends with one uniform curvature, the wire is split into 30 segments, each computing its own local curvature from its own local surface stress, and the full bent shape is built by chain-integrating those local curvatures end to end — a discretized elastica. The result is a spatially-resolved simulation that can show something the aggregate-only 3D model cannot: the same total number of bound molecules bends the tip differently depending on whether they cluster near the free end or spread evenly along the wire, exactly the kind of local detail a real functionalised-surface assay actually has.