🟦 1:1 Langmuir Binding (MCK)

The Gold Standard. This is the simplest and most desired model. It describes a simple interaction between one analyte molecule (A) and one ligand binding site (L).

The ODE

Observed Rate

k_obs is the rate at which the sensorgram approaches equilibrium during association. It increases linearly with analyte concentration — plotting k_obs vs [A] gives a straight line with slope = k_a and intercept = k_d. In practice, k_d from the intercept is unreliable (small lever arm, dominated by fitting noise) — use the dissociation phase instead.

Analytical Solution (Association)

where R_eq = R_max × [A] / ([A] + K_D). At equilibrium, the response is a hyperbolic function of concentration — this is the Langmuir isotherm. K_D = k_d / k_a.

Symbols

• R — instrument response (RU); proportional to bound analyte mass
• R_max — maximum binding capacity (RU); response when all ligand sites are occupied
• [A] — analyte concentration (M or nM)
• k_a — association rate constant (M⁻¹s⁻¹)
• k_d — dissociation rate constant (s⁻¹)
• K_D — equilibrium dissociation constant = k_d / k_a (M); the concentration at which half of all binding sites are occupied at equilibrium

Dissociation

Pure exponential decay. R₀ is the response at the start of dissociation (the end of the association phase); t is re-zeroed at that point. The dissociation phase depends only on k_d, not on analyte concentration. This is why dissociation is often the most reliable phase for extracting kinetic parameters.

Multi-Cycle Kinetics (MCK): Traditionally, kinetics are performed by injecting analyte at one concentration, regenerating the surface, and then injecting the next concentration. This is what the "MCK" toggle above simulates.

Assumptions

The 1:1 Langmuir model is valid when:

1. Monovalent analyte, monovalent ligand — 1:1 stoichiometry. No multivalent or avidity effects.
2. Homogeneous ligand population — all binding sites are equivalent. No mixture of active/inactive or high/low affinity sites.
3. No mass transport limitation — the reaction is rate-limited, not diffusion-limited. Analyte reaches the surface faster than it binds.
4. No conformational change upon binding — the complex AL does not rearrange into a tighter state AL*.
5. Analyte concentration >> surface depletion — pseudo-first-order conditions. The bulk analyte concentration stays constant during binding.

When 1:1 Langmuir Fails

Watch for these residual signatures when the 1:1 model breaks down:

• Systematic curvature in residuals — the fit deviates consistently at the start or end of the association phase, often indicating a two-step binding mechanism. Try the Two-State (Conformational Change) model.
• Biphasic dissociation — a fast initial drop followed by a slow tail suggests a mixture of binding sites or affinities. Try the Heterogeneous Ligand model.
• Concentration-dependent off-rates — k_d that varies with [A] is a hallmark of mass transport limitation. Try the Mass Transport model.

Still unsure? See the Model Selection Guide for a decision tree.