MACS Matchmaker

Equilibrium Evaluation

Equilibrium evaluation extracts a steady-state dissociation constant (K_D) from the plateau response at each analyte concentration. It complements kinetic fitting: kinetics give k_on and k_off from the time-course, equilibrium gives K_D from the height of the plateau. The two should agree when binding is well-behaved 1:1 — disagreement is diagnostic. See BIA → Equilibrium for the underlying physics.

When to choose Equilibrium over kinetic analysis

You only need affinity (K_D), not residence time or rate constants.
Kinetic fitting is unstable on your data — for example mass-transport limited association, complex curve shapes, or surface decay.
You want a robust cross-check against a kinetic K_D obtained from the same trace.

Data requirements

What the software accepts is a single phase with at least two ASSOCIATION injections of the same analyte at different concentrations, or two or more grouped traces with one association each. Single-cycle-format and MCK-format data are both accepted. Two points cannot identify a four-parameter curve, so acceptance here is not sufficiency — see the concentration requirement below.
A valid concentration must be set on each association. Injections without concentrations are silently excluded; if fewer than two remain, the evaluation aborts with an error.
What an interpretable result needs is at least six non-zero concentrations — the zero-concentration blank is required as well and does not count toward the six — spanning two decades, on both sides of the inflection (≥2 below, ≥2 above) and including points near both asymptotes. With four free parameters and fewer points than that, the optimizer still returns a value; it is underdetermined rather than measured.
A BASELINE injection before each cycle's association, or before the first association of a titration, gives the default offset removal a clean reference. Without one, the offset is measured on the start of the association.

How to run it

Add the measurement to a project, or open the evaluation wizard and use Add Raw Data to Project from its Data step.
From the project home, open Kinetics and Affinity, then chooseEquilibrium Analysis.
Select eligible raw data, processed data, or an existing evaluation's inputs. Configure cleanup actions in Cleanup, choose the fitting settings in Parameters, review the setup, and choose Run.
Results appear in the evaluation view: per-sensor 4PL fits, the aggregate K_D with its spread across molograms, and exportable plots.

Configuration

Parameter	Purpose
Model	Four Parametric Logistic Regression (4PL). Fits plateau response vs. concentration and reports K_D, Hill slope, and the bottom/top asymptotes.
Fit Equilibrium	When enabled, fits an exponential saturation curve to each association and uses the extrapolated steady-state value (r_eq). Use this when association windows are too short to actually reach the plateau. When disabled (default), the response is the mean signal over the fractional window below.
Response / Fitting Interval	Dimensionless fractional window from 0 to 1 used for response extraction. Default `[0.9, 0.95]` averages the signal over the last stretch of the association, from 90% to 95% of its length, which approximates equilibrium for well-saturated traces. Both values must lie in the dimensionless [0, 1] interval with start < end.
Cleanup Actions	The Cleanup step previews the selected response and lets you add, edit, or remove actions before running the analysis. These actions are stored with the evaluation input, and the analysis uses the data exactly as they leave it. Applicable defaults appear in the same list: immobilization normalization, blank subtraction (or removal of blank groups that cannot be subtracted), and offset removal. A multi-cycle measurement is split into its cycles, and each cycle is zeroed on its own baseline so the cycles overlay. A titration is zeroed once on its first baseline, then grouped into its injection groups, leaving out groups without an association. For a reused evaluation with multiple data inputs, the editor updates the first input while the remaining inputs retain their existing actions and receive their own applicable defaults. Use Save as processed data only to make the cleaned input reusable outside the wizard.
Save Intermediate Fits	Stores the per-injection exponential saturation fits when Fit Equilibrium is on, so each association curve can be inspected. This less frequently changed option is in the collapsedAdvanced Parameters section.

How K_D is calculated

For each sensor, the plateau responses at each concentration are fit with the four-parameter logistic model:

y(x) = (min − max) / (1 + (x / POI)^slope) + max

POI (point of inflection) — reported as the apparent K_D: the concentration at half-maximum response.
min, max — bottom and top asymptotes.
slope — Hill slope; equals 1 for a true 1:1 Langmuir isotherm.

The fitted bottom and top define the response range. The point of inflection is the half-maximum concentration reported as the apparent K_D; the Hill slope controls how sharply the curve transitions between the two plateaus.

If the concentration range does not bracket the inflection, the fitter constrains POI to the sampled range. The returned K_D is then a boundary value, not a measurement — extend the range and re-run.

Results

K_D, Hill slope, and min/max asymptote per sensor.
Aggregate K_D reported as the median across accepted molograms with the 2.5th–97.5th percentile interval across them. That interval is the empirical spread between sensors, not a confidence interval for the median.
Dose-response plots (per-sensor and overlay), normalized binding-trace plots per ligand, per-sensor timetrace HTML plots, PDF report, and CSV exports of the fitted parameters. In the binding-trace plots, a grey band marks the part of each association the response is computed from.

Cross-check against kinetic K_D

The same trace can be evaluated both ways. Agreement within the experiment's uncertainty supports the binding model; disagreement is informative:

Symptom	Possible causes	What to do
K_{D, kinetic} > K_{D, equilibrium}	Mass transport, surface decay over the run, or a ligand population the kinetic model does not describe can each pull the kinetic estimate away from the transport-independent equilibrium one; the direction alone does not identify which.	Repeat at a higher flow rate or lower ligand density and compare both estimates again.
K_{D, equilibrium} > K_{D, kinetic}	Association too short, so no plateau was reached; also concentration error, or a non-specific contribution that inflates the plateau.	Extend association time, or enable Fit Equilibrium.
Hill slope ≠ 1	Cooperativity, heterogeneous ligand or avidity — but equally incomplete equilibration, transport limitation, or asymptotes the series never bracketed.	Check residuals and assay design, then use a richer model only when its mechanism is supported.
K_D sits at the edge of the concentration range	Range does not bracket K_D.	Add concentrations below or above and re-run.

Troubleshooting

“Insufficient data for equilibrium fitting” — fewer than two ASSOCIATION injections carried valid concentrations. Check that every association has its analyte concentration set.
“No successful equilibrium fits” — the 4PL did not converge on any sensor. Likely causes: response amplitude near noise, non-monotonic dose-response, or all concentrations on a single asymptote.
“Baseline inferred from association” — no BASELINE injection was found before an association; the preprocessor used the early portion of the association as a substitute. Where the measured baseline supports that reading, adding an explicit short baseline before each association avoids the warning; where it does not, the warning is telling you the substitute was wrong and the responses it produced should not be trusted.
K_D looks unreasonably round (exactly the highest or lowest concentration) — the fitter has clipped the inflection to the sampled range. Extend the concentration range.