MACS Matchmaker

Langmuir 1:1 — Partially Non-Dissociative

A 1:1 model where a fixed fraction of bound analyte does not dissociate between cycles (covalent capture, sticky aggregates, slow conformer). Run several sequential injections at the same or different concentrations to see how the baseline creeps up cycle by cycle.

Reaction
time (sequential cycles)baseline driftcycle 1cycle 2cycle 3
Rnon-diss(n)=max⁡ ⁣( f⋅Rend(n),  Rnon-diss(n−1))R_{non\text{-}diss}^{(n)} = \max\!\left(\, f \cdot R_{end}^{(n)},\; R_{non\text{-}diss}^{(n-1)}\right)
Rassoc(t)=Req−(Req−Rdiss) e−kobst+Rnon-dissR_{assoc}(t) = R_{eq} - (R_{eq} - R_{diss})\, e^{-k_{obs} t} + R_{non\text{-}diss}

f: non-dissociable fraction · Rend: response at end of the current association · Rdiss: dissociable response carried into the cycle · Req = (kon·C/kobs)·(Rmax − Rnon-diss). The non-dissociable pool grows proportionally to Rend at the end of every association.

Assumptions
  • The non-dissociable fraction f is constant across cycles.
  • The non-dissociable pool only grows; it never decreases.
  • Dissociable fraction obeys standard Langmuir 1:1 kinetics against Rmax − Rnon-diss.
  • Cycles are sequential on the same surface; no regeneration.
Parameters

kon (M⁻¹ s⁻¹)

koff (s⁻¹)

Non-dissociable fraction f

Cycle concentrations (nM)

Noise σ (pg/mm²)

Derived

Final residual baseline = 80 pg/mm²

Last-cycle equilibrium = 95 pg/mm²

Residual share of equilibrium = 84%

Diagnostic cues
  • Baseline that does not return to zero between cycles is the hallmark.
  • Apparent koff looks slower than truth; apparent Rmax grows cycle-on-cycle.
  • Set f = 0 — the trace collapses to a stack of identical Langmuir 1:1 cycles.
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