MACS Matchmaker

Concentration Determination

Concentration Determination estimates the concentration of an unknown sample by inverting a previously measured standard curve. A titration of known concentrations is fit with a four-parameter logistic (4PL), a three-parameter logistic (3PL) whose lower asymptote is fixed at zero, or a through-origin scaled cubic model (y ∝ x³). Each sensor reading from the unknown sample is then mapped back through the curve to a concentration. It is launched as a project-level workflow so a calibration measurement can be reused across many unknown samples acquired under matched conditions.

For the physics of dose-response measurements and how to design a useful titration, see BIA → Equilibrium. For 4PL and 3PL, the underlying logistic fit is the same one documented in Equilibrium Evaluation.

When to choose it

You have a stable, well-characterized analyte/ligand pair and want to quantify how much of that analyte is present in an unknown sample (potency assay, batch QC, supernatant titer).
You can run a titration of known concentrations once, then probe many unknowns against the same standard curve.
The unknown sample is dilutable: running the same sample at several dilutions and combining the back-calculated values is the most reliable way to land within the curve's linear range and confirm internal consistency.

Data requirements

Calibration source. A measurement, processed data, or saved Concentration Determination evaluation with a Calibration Curve, Titration Series, or Single Cycle Kinetics phase containing at least three ASSOCIATION injections at known concentrations. Aim for ≥6 concentrations bracketing the expected target. Logistic fits should include ≥2 concentrations below and ≥2 above the inflection; cubic fits should cover the full interval in which the cubic response is expected to hold. A titration must contain exactly one analyte, start with a blank association at 0 M, and record known molar concentrations for the nonblank associations.
Unknown source(s). One or more measurements, processed data, or saved Concentration Determination evaluations with an Unknown Concentration phase or compatible titration. An unknown titration must contain exactly one analyte, start with a blank association at 0 M, and leave nonblank molar concentrations unknown. Each association injection should carry a Dilution Factor set in the injection editor; if a sample was diluted before being injected, the dilution factor is what back-converts the curve-derived value to the original sample concentration. The selected input role determines how a titration is validated. Each selected unknown phase is evaluated separately.
Phase selection. Whole-measurement inputs use a retained Calibration Curve or Unknown Concentration phase for the selected role. If none remains after Cleanup, they use a titration. A raw measurement selected as Unknown that holds several Unknown Concentration phases is evaluated as one input per phase, in the order the phases ran, each labelled with its phase name. Processed data and inputs taken from a previous evaluation are used as saved, including their Cleanup, so they must be phase-scoped or retain exactly one Unknown Concentration phase. Calibration needs a single candidate. When a raw measurement picked as calibration holds several, the Data step asks which curve to fit; processed data must be phase-scoped or keep one after its Cleanup. An explicit phase selection takes precedence.
Unknowns inside the calibration range. A prediction is an interpolation. A response above the highest or below the lowest retained standard is reported as out of range — never extrapolated, never clamped to the nearest endpoint — and contributes nothing to the result. Bracket the expected concentration when choosing the standards, and dilute a sample that lands outside rather than reading a value off the end of the curve.
Matched conditions. Buffer, flow rate, ligand layout, and analyte chemistry must match between calibration and unknown for the curve to apply. The system does not detect or correct condition mismatches.
Normalization injections. Recommended uses immobilization when every selected input contains it after Cleanup. The injection before the first IMMOBILIZATION injection is mapped to 0, and that IMMOBILIZATION injection is mapped to 1. For a phase without its own immobilization, the nearest preceding Immobilization phase in the same measurement can supply these references if only Regeneration phases separate it from the titration. Cleanup time intervals use the selected phase's time origin when replayed for normalization. Keeping only a titration interval excludes the preceding immobilization. If any input lacks immobilization, Recommended evaluates all inputs without normalization so calibration and unknowns stay on the same response scale. For other references, choose Custom reference injections and set the 0 and 1 reference injections manually. No normalization always evaluates the selected phases without loading immobilization references.

How to run it

Open Concentration Determination from the project home and name the study.
Under Data, select one eligible calibration source and one or more unknown sources. Calibration and unknown data must use matched assay conditions.
Review each input under Cleanup, then configure normalization, sensor aggregation, and outlier handling under Parameters.
Under Fitting, choose the justified calibration model and inspect the curve, unknown distributions, traces, and findings. Exclude a complete injection or individual sensor observation when the plots show a documented problem.
Check the overall concentration, confidence interval, contributing unknowns, cleanup summary, and warnings under Review. Save only after the calibration brackets the retained unknown responses.

Configuration

Parameter	Purpose
Model	4-parameter logistic (4PL) is the default and fits both the lower and upper asymptotes. 3-parameter logistic (3PL) fixes the lower asymptote at 0, reducing the fit by one degree of freedom. Use 3PL when baseline subtraction represents a true zero; keep 4PL when the baseline may carry a residual offset. Cubic fits a scaled through-origin y ∝ x³ response. It is non-saturating and should be selected only when that response law is justified across the calibration and prediction interval. See Equilibrium Evaluation → How K_D is calculated for the logistic equation.
Concentration normalization	Recommended detects immobilization in the selected inputs. When every input has it, the preceding injection is mapped to 0 and the first IMMOBILIZATION injection to 1. If any input lacks immobilization, no inputs are normalized. No normalization disables normalization. Custom reference injections lets you choose the 0-reference and 1-reference injections by name. The labels match the cleanup-action injection selectors: injection index, injection name, and group. Those selected injection positions are applied to every unknown trace, so calibration and unknowns must use the same injection order at the selected positions. The 0 and 1 reference value percentiles are percentages from 0% to 100%, default to 5% and 95%, and can be adjusted for noisy reference injections. If any input contains a normalization cleanup action, select No normalization; Review remains unavailable otherwise. See the normalization cleanup actions for details.
Aggregate sensors	When on, a single calibration model is fit to the aggregate response across sensors — more robust when individual sensors are noisy but loses sensor-specific calibration fits. Unknown readings are still inverted and sensitivity-weighted per sensor using that shared curve. When off (default), each sensor gets its own fit and contributes independently to the predicted values.
Known concentration (nM)	Optional independently known concentration for a validation or QC sample. The value is entered in nanomolar under the collapsed Advanced Parameters section in Parameters and adds an accuracy analysis to the result.
Remove outliers	Toggleable in Parameters. For an aggregated calibration fit, automatic removal can reject at most one off-curve concentration using MAD-based residuals. In aggregated and per-sensor modes, an iterative IQR filter (1.5 × IQR, up to 5 passes) checks dilution-adjusted per-sensor predictions. Data-quality failures reject a sensor across the unknown's dilution groups, while range exclusions remain local to each group. The evaluation records each automatic quality trigger and whether it was a non-finite prediction, non-finite response, or IQR outlier. Median view lets you exclude a whole calibration injection, while Sensors view lets you exclude an individual sensor observation. These exclusions are tied to the injection and, where chosen, the sensor, remain selected when automatic removal is toggled, and are restored when a saved evaluation is re-evaluated.

Results

Fitting workspace. Calibration Curve contains the standard curve and its Median/Sensors control. The Result card above the workspace contains the overall result on every tab.Unknowns contains full-width per-injection sensor tables.Distribution contains the concentration boxplot. Accuracy appears only when a known concentration was supplied and an accuracy assessment is available. Active range and dilution-response findings appear above the calibration plot in a compact warning strip; Review presents the same decision-relevant warnings with summary text only.
Overall concentration in nM, with 95% confidence interval and the number of unknown groups that contribute positive effective weight.
Per-group statistics. One percentage-labelled tab per reported unknown / dilution group: median of the positive-effective-weight back-calculated sample concentrations with its confidence interval and a per-sensor table in the Unknowns workspace (measured response, prediction status, raw concentration, adjusted-for-dilution concentration, and the sensor's normalized share of that group's sensitivity). Point to a tab to see its full injection name. Its color marker matches the group in the plots, and the table expands without an internal scrollbar. Manually excluded rows remain visible with a 0% share so they can be restored. A Contribution chip on each tab shows the share of the Overall result that dilution group accounts for — computed as mean(weights) / dilution² normalized across all groups, which is the same formula the combiner uses. If one group's contribution is overwhelmingly high relative to the others, the Overall is effectively driven by that group alone.
Calibration plot. The Calibration Curve tab shows each sensor fit as solid over that sensor's retained-standard interval, and draws no extension beyond it. The plot also contains calibration standards and one colored median marker for each unknown / dilution group with a contributing prediction. Groups with at least two positive-effective-weight predictions also get an x-range box. Each group keeps the same color on the calibration plot and the boxplot so the same sample can be followed across both views. Select a whole calibration injection in Median view or an individual calibration observation in Sensors view. Individual sensor fits and finite, in-range sensor prediction dots are available through the Median/Sensors option above the chart but hidden by default to keep the QC view readable. The logarithmic concentration axis labels the actual positive standard concentrations in nM. The response axis shows normalized calibration data in a.u.; without normalization, coherent mass density is displayed in pg/mm² using the same single display conversion as the measured traces.
Boxplot. The Distribution tab shows positive-effective-weight back-calculated concentrations per dilution group, side-by-side, with a dashed line marking the Overall predicted result and a shaded band marking its 95% CI. Hover the line to see the numeric prediction and CI range.
Accuracy. When an independently known concentration was supplied and the prediction returns an accuracy assessment, the Accuracy tab reports agreement with that reference value. Runs without an accuracy assessment omit the tab.
Saved trace plots. The completed evaluation includes a calibration trace and one plot per unknown trace as artifacts, useful for spotting injection artefacts before trusting the numbers.
CSV export (when saved as a study): concentration_statistics.csv contains the Overall result, per-group statistics (with a Contribution (%) column matching the chip in the UI), and a per-sensor section listing raw value, adjusted value, and Weight Share (%) normalized within each reported group. Group statistics use contributing sensor results; explicit inclusion-status and exclusion-reason columns distinguish manually excluded injection and sensor rows from naturally zero-weight rows.
Saved evaluation statistics. Opening the completed evaluation from the Evaluations table shows findings first, followed by the Hologram Identifier and Filter by tags controls. The saved Overall result, dilution-group summaries, contributions, per-sensor values, plot artifacts, and downloadable CSV appear below those controls. Tag selections filter both the saved statistics view and the artifacts.
Deterministic findings. Every completed evaluation reports how many unknown groups remain usable. For logistic models, it also reports whether the calibration curves cover at least 90% of their fitted high-concentration plateau; this plateau assessment does not apply to the non-saturating cubic model. When any response is outside the fitted boundary or unavailable, a Calibration range finding reports aggregate counts with bounded per-group detail plus the affected sensor's measured response and status. Incomplete or unassessable logistic curves trigger a warning that includes the affected curve count and, when at least one curve is assessable, its median coverage, threshold, and highest retained standard used in the final fit. Automatic quality evidence records the exact injection and sensor trigger, its response or adjusted concentration when finite, and whether it was rejected for a non-finite value or IQR outlier behavior.
Dilution response compression. This advisory check uses the three highest sample fractions when they span at least 4× in dilution factor. For each sensor, their measured responses are normalized against the fitted response interval between the lowest and highest retained calibration standards. A sensor is compressed when all three responses stay at or above the 75% calibrated response position while spanning no more than 15% of that interval. The warning appears when at least four sensors are assessable and at least half are compressed. It indicates possible response saturation or a dilution-series inconsistency; it does not exclude observations or alter prediction weights.
Re-evaluation. Use the Re-evaluate icon for a completed Concentration Determination in the Evaluations table to open the workflow on its Cleanup step. Each data role is preselected on the raw data that role ran on, carrying the cleanup actions stored with it, so the fit reproduces the one the evaluation reports. Its model, normalization, aggregation, automatic outlier setting, and manual calibration exclusions, tied to the injection and, where chosen, the sensor, are restored, and the name carries the next version number. Saving creates a new evaluation and leaves the original unchanged.

Good data example

The two checks. An unknown is only quantifiable where the calibration curve still resolves it — between roughly 20% and 80% of saturation, since outside that band a large change in concentration moves the response very little. Back-calculating each dilution group separately then tests the result: groups that scatter around the combined value support it, while a monotonic trend across dilutions points at a matrix effect rather than a concentration. The calibration panel is schematic; the agreement panel plots the measured group medians.

A healthy standard-curve prediction should show dilution groups that agree after back-calculation, with the Overall result inside the shaded 95% CI band on the boxplot. In a representative good run the true sample concentration is 50.0 nM and the weighted combine reports 46.6 nM with a 95% CI of 45.6–48.5 nM across 255 sensor predictions.

Dilution factor	Adjusted group median	Sensor predictions
16×	44.5 nM	49
8×	52.7 nM	54
4×	48.7 nM	50
2×	43.6 nM	51
1×	47.3 nM	51

The group medians are not identical, but they stay in the same range and bracket the combined result. That is the pattern to look for before trusting the Overall prediction: agreement across dilutions, no single group dominating the contribution chips, and unknown points landing on the informative middle of the calibration curve.

How concentrations are calculated

The pipeline runs in three stages:

Build the calibration curve. The titration phase is normalized (see above), the baseline (zero-concentration) response is subtracted from each higher-concentration response to give a delta response, and the selected 4PL, 3PL, or scaled through-origin cubic model is fit to delta-response vs. concentration — either per sensor (default) or aggregated. Manually excluded sensor observations and whole injections, together with any automatically rejected calibration outlier, do not contribute to the fit.
Invert per sensor. For each association injection of the unknown trace, the delta response of each sensor is inverted through its fitted curve. Predictions between the lowest and highest retained standards used in the final fit use interpolation, including the two boundaries. A response outside the fitted response at those boundaries has no predicted concentration and zero effective weight; it is reported as below or above range rather than extrapolated or clamped to an endpoint. The retained value is the per-sensor diluted concentration x_d, which is multiplied by the injection's dilution factor d to recover the original sample concentration X = d · x_d.
Combine across dilutions. Each sensor also carries a sensitivity weight |x · dy/dx| at its reading point on the curve — high where the curve is steep and low where it is flat. Per dilution group, the median of X across in-range sensor predictions with a positive effective weight is the group estimate; positive weights do not otherwise change each sensor's rank in that median. Manually excluded observations and out-of-range responses have zero effective weight and do not enter the group median, CI, or count. Group estimates are then combined into a single Overall value as a weighted mean, with each group's weight equal to the mean of its per-sensor sensitivities — including zeros — divided by dilution². That mean uses the sensors retained by the shared cross-dilution quality mask as its denominator: a sensor unsupported only in one dilution contributes zero to that group's mean, while a sensor rejected globally for invalid data or outlier behavior is absent from every group's denominator.

Interpretation and troubleshooting

Symptom	Likely cause	What to do
Finding reports responses outside the calibration boundaries	The measured response is below or above the fitted response at the lowest or highest retained standard for that sensor.	Use another dilution or extend the retained standards so they bracket the unknown response. The affected sensor has no predicted concentration and zero effective weight, but remains visible in the Unknowns table with its measured response and status. Other in-range sensors and dilution groups can still contribute.
No usable concentration remains for the unknown	Every sensor response in every dilution group is outside the fitted calibration boundaries or otherwise unavailable.	Re-run the unknown at another dilution or extend the standard curve far enough to support the response.
“Calibration coverage”	For a logistic model, at least one assessable calibration fit reaches less than 90% of its fitted dynamic range at the highest retained standard, or a curve could not be assessed. Predictions near or above that standard may be unreliable. Cubic fits do not have an asymptotic plateau, so their informational finding states that plateau assessment is not applicable instead of producing this warning.	Add higher calibration concentrations until the response approaches a stable plateau. Inspect the affected curve count, median coverage, and highest standard, when available, in Technical details.
“Dilution response compression”	Across the three highest sample fractions, at least half of four or more assessable sensors remain near the upper end of their fitted calibration response interval and change very little despite a dilution span of at least 4×. This can indicate response saturation or an inconsistent dilution series.	Inspect the per-injection tables in Unknowns, verify the dilution factors and sample preparation, and measure a further dilution that moves the response into the informative part of the curve. Treat the adjusted concentrations as less reliable; the warning itself does not remove data or change their weights.
Per-group medians cluster within a factor of two, but the Overall sits near the extreme of one group	One group still dominates the weighted mean despite the `1 / dilution²` correction — its sensitivity is several orders of magnitude larger than the others.	Inspect the boxplot. Consider rerunning with that group removed (e.g. drop the diluted-too-low or diluted-too-high injection), or add intermediate dilutions to spread the weight.
Wide 95% CI on Overall	Low sensitivity at the reading point — unknown response sits on an asymptote of the curve, or sensor-to-sensor noise is high.	Add a dilution that puts `x_d` closer to the curve inflection. If the issue is per-sensor noise, enable Aggregate sensors.
Per-group Adjusted Medians disagree by 10× or more across dilutions of the same sample	Calibration curve no longer applies — likely a condition mismatch (buffer, flow, ligand density) or the unknown is outside the assay's linear range at every dilution.	Repeat the calibration alongside the unknown under identical conditions; verify the dilution factors entered on each injection.
“Failed to fit calibration curve” or “No concentration predictions”	The selected model did not converge — too few concentrations, negative delta responses, or calibration points that do not support the selected curve shape.	Check that the titration has ≥3 distinct non-zero concentrations and that the baseline is not higher than the lowest titration step; clean up or re-acquire the calibration.