MACS Matchmaker

Langmuir 1:1 — Injection-Specific Non-Dissociation

This model assigns an independent non-dissociating fraction to every injection while sharing the same 1:1 rate constants and binding capacity. Use it when repeated injections leave different residual response fractions that a single shared fraction cannot describe.

Model

R_{\mathrm{non\text{-}diss},n}^{\mathrm{assoc}} = f_{n-1}\,R_{\mathrm{start},n},\quad R_{\mathrm{non\text{-}diss},n}^{\mathrm{diss}} = f_n\,R_{\mathrm{end},n},\quad f_0=f_{\mathrm{start}}

R_{\mathrm{diss},n}(t) = \left(R_{\mathrm{end},n} - R_{\mathrm{non\text{-}diss},n}\right)e^{-k_{\mathrm{off}}t} + R_{\mathrm{non\text{-}diss},n}

f_n is fitted separately for injection n. It sets the residual response floor during dissociation after that injection, then remains the carried fraction during association n + 1. The first association uses the fixed starting fraction, normally zero. The remaining response follows the standard Langmuir 1:1 equation.

Response, R_max, noise, and derived response floors use the workflow's normalized, dimensionless scale. Concentration, time, and rate constants retain their physical units.

When to use it

Repeated injections show different residual-to-peak ratios, not just one consistent sticky fraction.
k_on, k_off, and R_max remain shared across injections.
The f_n values are independent and need not increase monotonically.
Every added injection introduces another fitted parameter, so prefer the shared-fraction model unless the residual pattern supports this extra flexibility.
A fitted non-dissociating fraction describes the sensorgram; it does not by itself identify aggregation, avidity, or covalent capture as the mechanism.

Shared parameters

k_on (M⁻¹ s⁻¹)

k_off (s⁻¹)

R_max (normalized, dimensionless)

Association (s)

Dissociation (s)

Noise σ (normalized response)

Injection-specific parameters

Injection 1

Injection 1 concentration (nM)

f₁

Injection 2

Injection 2 concentration (nM)

f₂

Injection 3

Injection 3 concentration (nM)

f₃

Injection 4

Injection 4 concentration (nM)

f₄

Injection 5

Injection 5 concentration (nM)

f₅

Derived

Final residual floor = 0.59 (normalized)

Final association peak = 0.84 (normalized)

Final residual-to-peak ratio = 70%

Cycle results

1. 50.0 nM · f=0.10 · floor 0.058 (normalized)

2. 50.0 nM · f=0.25 · floor 0.18 (normalized)

3. 50.0 nM · f=0.40 · floor 0.31 (normalized)

4. 50.0 nM · f=0.55 · floor 0.45 (normalized)

5. 50.0 nM · f=0.70 · floor 0.59 (normalized)

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