Biosensor Binding Kinetics Simulator

Injection Phase

Analyte concentration 50 nM

Association rate k_on 1.0 ×10⁵ M⁻¹s⁻¹

Dissociation rate k_off 2.0 ×10⁻² s⁻¹

Bound fraction θ

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Equilibrium K_d

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Phase time

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Response R

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How it works

Each receptor site on the sensor surface (e.g. an immobilised antibody or aptamer) can be free or occupied. The fraction bound θ follows the real pseudo-first-order Langmuir binding equation used to interpret SPR and QCM sensorgrams:

dθ/dt = k_on·C·(1−θ) − k_off·θ
θ_eq  = C / (C + K_d),   K_d = k_off / k_on

During injection, analyte at concentration C drives θ up toward its concentration-dependent equilibrium. Switch to wash (C→0) and only the k_off term remains, so θ decays exponentially with time constant 1/k_off — exactly how a real sensorgram's association and dissociation phases look. The bound-molecule count on the chip is not decorative: at every frame it is recomputed from this ODE, then that many analyte spheres are actually moved onto empty receptor sites (or released back into solution) to match θ.

Analyte concentration C — higher C raises both the equilibrium response and the initial binding rate, but does not change K_d.
k_on — how fast a collision between analyte and receptor turns into a bond; sets how quickly the association phase approaches equilibrium.
k_off — how fast a bound complex falls apart; a low k_off gives a slow, "sticky" wash-out — the signature of a high-affinity assay.
Inject / Wash — toggles between the association phase (flowing analyte, C as set) and the dissociation phase (buffer only, C=0), the two halves of every real sensorgram run.

Simulation time runs 25× faster than real assay time so a full inject/wash cycle is visible in seconds rather than minutes — the rate relationships themselves are unscaled. A biosensor's practical limit of detection (LOD) is set by how small a θ (and therefore how small a C) can still be told apart from the noise of an unbound baseline; a low K_d (tight binding, small k_off/k_on ratio) is what lets a real assay push that LOD down.

Bound analyte Free (diffusing) Receptor site

Sensorgram — response vs time

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