MACS Matchmaker

Langmuir 1:2 (Heterogeneous Ligand)

Two independent ligand populations on the same surface — for example a partially modified protein or two binding sites — each binding the analyte 1:1 with their own kinetics. The observed response is the sum of the two Langmuirs and shows a characteristic two-phase association/dissociation.

Reaction
AanalyteL1A·L1L2A·L2
R(t)=R1(t)+R2(t),dRidt=kon,i C (Rmax,i−Ri)−koff,i RiR(t) = R_1(t) + R_2(t),\quad \frac{dR_i}{dt} = k_{on,i}\, C\, (R_{max,i} - R_i) - k_{off,i}\, R_i

Two independent Langmuir 1:1 sub-reactions add together. Each has its own kon, koff, and Rmax. The faster site dominates early; the slower site dominates late.

Assumptions
  • Two independent ligand populations, no cross-talk.
  • Each site obeys Langmuir 1:1 with its own rate constants.
  • Pseudo-first order; mass transport not limiting.
  • Both sites are fully reversible.
Parameters
Site 1 (typically the faster / higher-affinity site)

kon,1 (M⁻¹ s⁻¹)

koff,1 (s⁻¹)

Site 2 (typically the slower / lower-affinity site)

kon,2 (M⁻¹ s⁻¹)

koff,2 (s⁻¹)

Concentration series (nM)
Kinetic mode
Single-cycle: concentrations are injected sequentially on the same surface, no regeneration.

Noise σ (pg/mm²)

Derived

KD,1 = 2 nM

KD,2 = 1 µM

Req,1 (highest C) = 70 pg/mm²

Req,2 (highest C) = 13 pg/mm²

Diagnostic cues
  • Dissociation that visibly bends (fast drop then slow tail) is the classic two-component signature.
  • If the two KD values are within ~3× of each other the signature is hard to distinguish from a single Langmuir 1:1.
  • Try setting kon,1 = kon,2 — the model collapses to a single Langmuir 1:1 with summed Rmax.
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