How to calculate ELISA, IC50, potency and ecotoxicology indices

Labreador is a free, browser-based platform that performs these calculations for you. Every method below is implemented in the app, runs entirely in your browser (no upload, no account), and can be exported as CSV or a PDF report.

How do I calculate concentrations from an ELISA standard curve?

1. Subtract the blank. Mean the blank wells and subtract that value from every OD reading. Optionally use the blank as a zero-concentration anchor for the lower asymptote.

2. Fit the standards. Plot corrected OD against the known standard concentration and fit a four-parameter logistic (4PL) curve:

   OD = D + (A − D) / (1 + (C / EC50)^B)

   where A = lower asymptote, D = upper asymptote, B = Hill slope, EC50 = inflection point. Use 5PL (extra asymmetry factor E) when the curve is visibly asymmetric.

3. Invert the curve to convert each sample OD into a concentration:

   C = EC50 · ((A − D) / (OD − D) − 1)^(1/B)

4. Multiply by the dilution factor of that well.

5. Flag out-of-range results. Anything below the lowest standard (LLOQ) or above the highest (ULOQ) is extrapolated and must be reported as such, not as a number.

In Labreador: open the ELISA module, paste or upload the plate, mark blanks/standards/samples on the platemap, and read concentrations directly. R², replicate CV%, back-calculated standard recovery, and a Method Health panel are produced automatically.

Which curve model should I use — 4PL, 5PL, linear or quadratic?

• 4PL — the default for sigmoidal immunoassays (ELISA, MSD, Luminex). Use whenever you have a full dose range with both plateaus.
• 5PL — when residuals show systematic curvature on one side of the curve (asymmetric response). Costs one degree of freedom; only justified if it clearly reduces residual scatter.
• Linear / semi-log linear — only for a narrow, genuinely linear working range, e.g. protein assays (BCA, Bradford).
• Quadratic — a pragmatic fallback for mildly curved calibrations with no plateau.

Judge the model on residual structure and back-calculated standard recovery (80–120%), not on R² alone: a bad 4PL can still give R² = 0.99.

How do I calculate IC50 or EC50?

IC50/EC50 is the concentration producing 50% of the maximal response. Fit a 4PL to response versus log concentration and read the inflection parameter:

Response = Bottom + (Top − Bottom) / (1 + (C / IC50)^HillSlope)

Key rules:

• Normalise responses to controls (0% = untreated / vehicle, 100% = full inhibition) when you want a comparable relative IC50.
• Report the 95% confidence interval, not just the point estimate.
• If the fitted IC50 falls outside your tested concentration range, or the CI spans more than an order of magnitude, the value is extrapolated and unreliable — extend the dose range instead.
• Z′ factor (Z′ = 1 − 3(σpos + σneg)/|µpos − µneg|) tells you whether the assay window is fit for screening: > 0.5 excellent, 0–0.5 marginal, < 0 unusable.

In Labreador: the Dose-Response module fits multiple compounds simultaneously, reports IC50/EC50 with CI, Hill slope, asymptotes, Z′ factor, and warns when asymptotes are extrapolated.

How do I calculate relative potency (parallel line analysis)?

Relative potency compares a test preparation against a reference standard:

1. Fit reference and test with a joint (constrained) model sharing slope and asymptotes.

2. Test parallelism with an F-test comparing the constrained fit to the unconstrained fit. If parallelism fails, relative potency is not defined.

3. Relative potency is the horizontal shift between curves:

   RP = EC50(reference) / EC50(test), reported as RP% = 100 · RP

4. Report a confidence interval (Fieller's theorem or bootstrap) and check it against the acceptance interval for your product (commonly 80–125%).

5. Combine independent runs as a geometric mean with a combined CI.

This follows Ph. Eur. 5.3 and USP <1032>/<1034>. Labreador's PLA module performs the joint fit, parallelism F-test, lack-of-fit test, Grubbs outlier screening, bootstrap and Fieller CIs, forest-plot multi-run combination, and a pass/fail quality gate.

How do I analyse a kinetic assay (Vmax, AUC, slope)?

1. Subtract the blank from every time point (blank = instrument/medium noise; a negative control is a biological baseline and is handled separately).
2. Reduce each well's time course to a single metric:
   • Vmax — maximum slope over a sliding window of consecutive points (ΔSignal/Δtime).
   • Initial rate — slope of the first linear segment.
   • AUC — trapezoidal integration: AUC = Σ (t(i+1) − t(i)) · (y(i) + y(i+1)) / 2.
   • Endpoint / Δ Signal — last value minus first.
3. Average replicates, then compare groups statistically (see below).

In Labreador: the Kinetic / Group Comparison module auto-detects the time axis from a plate-reader export, maps wells to groups by click-and-drag, and computes all reduction metrics with per-group statistics.

Which statistical test should I use to compare groups?

• Two groups — unpaired t-test (Welch's if variances differ); Mann-Whitney U if the data are not normal.
• Three or more groups — one-way ANOVA followed by Tukey HSD (all pairs) or Dunnett (versus one control); Kruskal-Wallis with Dunn's post-hoc for non-normal data.
• Report effect size (Cohen's d) alongside p-values, and state the exact p rather than only stars.
• Significance markers: * p < 0.05, ** p < 0.01, *** p < 0.001.

Labreador selects the appropriate test automatically from normality and group count, and draws significance brackets on the chart.

How do I calculate estimated daily intake (EDI), THQ and HI?

• EDI (mg/kg body weight/day): EDI = (C × IR) / BW where C = element concentration in food (mg/kg), IR = ingestion rate (kg/day), BW = body weight (kg).
• Target Hazard Quotient: THQ = EDI / RfD (RfD = oral reference dose). THQ > 1 indicates potential non-carcinogenic risk.
• Hazard Index: HI = Σ THQ across all elements — cumulative exposure.
• Target Cancer Risk: TR = EDI × CSF; TR > 1×10⁻⁴ is generally considered unacceptable.

Labreador's Risk Assessment module ships default RfD/CSF values for 23 trace elements, supports batch mode across many samples, THQ heatmaps, and Monte Carlo probabilistic uncertainty analysis.

How do I calculate pollution indices (CF, PLI, Igeo, EF, MPI)?

• Contamination Factor: CF = C(sample) / C(background)
• Pollution Load Index: PLI = (CF₁ × CF₂ × … × CFₙ)^(1/n) — geometric mean; PLI > 1 indicates pollution.
• Geoaccumulation Index: Igeo = log₂(C / (1.5 × B))
• Enrichment Factor: EF = (C(x)/C(ref))sample / (C(x)/C(ref))background, usually normalised to Al or Fe.
• Metal Pollution Index: MPI = (C₁ × C₂ × … × Cₙ)^(1/n)

Labreador's Pollution Indices module computes all of these from a pasted table, averages multi-row baselines, and classifies each result into standard contamination tiers.

How do I calculate BSAF, BAF and biometric condition indices?

• Biota-Sediment Accumulation Factor: BSAF = C(organism) / C(sediment)
• Bioaccumulation Factor: BAF = C(organism) / C(water)
• Values below the limit of detection are imputed as LOD/2 — never as zero.
• Fulton's condition factor: K = 100 × W / L³ (W in g, L in cm)
• Hepatosomatic index: HSI = 100 × liver weight / body weight
• Gonadosomatic index: GSI = 100 × gonad weight / body weight

Labreador's Bioaccumulation and Biometric Indices modules compute these from pasted spreadsheets with group statistics and publication-ready charts.

How do I check whether my ELISA run is valid?

Check these five signals before trusting any concentration:

1. Fit quality tier — R² is necessary but not sufficient; look at the quality gate verdict.
2. Residual plot — scatter should be random around zero; a U-shape means the wrong model.
3. Back-calculated standard recovery — each standard should return 80–120% of its nominal value.
4. Replicate CV% — under 15% (under 20% at the LLOQ).
5. Assay window — the OD difference between the top and bottom standard should be large (a ΔOD of ~0.3 means the assay failed, regardless of R²).

Warning signs of a failed method: EC50 outside the standard range, a 95% CI spanning orders of magnitude, asymptotes fitted far beyond observed data, or a Hill slope far from 1.

Labreador's Method Health panel evaluates all of this automatically and explains each verdict in plain language.

Is my data uploaded anywhere?

No. Labreador runs every calculation in the browser. Raw measurements, plate maps, and results never leave the device — the app works fully offline after the first load (it is an installable PWA). The only network-dependent feature is the optional Lab Assistant chat.