3D Plasmon Field & Binding Dynamics

SPR Sensor Chip — 3D

Analyte concentration C 80 nM

Association rate k_on 1.0×

Dissociation rate k_off 0.25×

Coverage θ

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Shift Δλ

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K_d

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Bound molecules

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Click "Sample" to toggle Injecting (molecules diffuse in and dock, the field shell brightens) vs Wash (buffer only — watch bound molecules release and the field shell dim).

How it works

Target molecules (small spheres) execute a random walk through the solution above a gold nanoparticle sensor and occasionally collide with an empty receptor on its functionalized surface, sticking with a probability set by the association rate k_on; already-bound molecules can also detach at a rate k_off. Averaged over the whole population this is exactly the Langmuir binding-kinetics ODE:

dθ/dt = k_on·C·(1−θ) − k_off·θ,   θ_eq = C / (C + K_d)
Δλ = S · Δn_max · θ   (resonance-wavelength shift)

The translucent shell around the nanoparticle is the localized plasmon field: its radius, brightness and color temperature scale directly with θ — a sparsely-bound sensor glows faint and blue-white, a densely-bound one glows large, bright and amber, visualizing the same field enhancement that a real LSPR sensor reports as a shifted resonance wavelength Δλ (shown live in the readout).

Analyte concentration C — raises the collision rate with empty receptors, driving θ up faster and to a higher equilibrium plateau.
k_on — sticking efficiency per collision; higher values fill receptors faster without changing the final plateau by itself.
k_off — release rate of bound molecules; higher values cap the plateau lower and speed the field's decay during Wash.
Sample / Wash — Wash halts new arrivals (C→0) without stripping already-bound molecules, isolating the pure dissociation phase.

Real-world relevance: this is the physical picture behind every LSPR nanoparticle biosensor — a plasmon field that only "feels" molecules within nanometers of the metal surface, translating a chemical binding event directly into an optical signal, with no fluorescent label required.

Free target molecule Bound (occupied receptor) Plasmon field shell

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