Drybench Assay.

What the app shows, how it works and how it was built, in the words of its own write-up, followed by the parameter defaults and the data sources with their licences.

Standard-curve interpolation

The Standard curve mode fits linear least squares with a free intercept, a four-parameter logistic with the existing bounded fitter, or, for standard curves only, a five-parameter logistic (seven or more standards; asymmetry s within 0.1 to 10, refused at that edge; its midpoint parameter is not a C50). Concentrations retain their selected mass or molar unit. It averages standard responses per concentration and unknown responses per exact sample label and dilution factor before interpolation. Optional mean-blank subtraction applies equally to standards and unknowns. The original-sample estimate multiplies by the explicitly entered pre-assay dilution factor; reagent dilution shared with standards must not be applied again.

Only the retained standard-concentration range is reported. An unknown outside it has a status and no extrapolated concentration. This tested range does not establish LLOQ, ULOQ or a detection limit. R² is descriptive; standards' back-calculated recovery and residuals aid review. Each interpolated unknown carries a 95 percent inverse-prediction interval (classical inverse regression for a linear curve; an approximate delta-method interval for the 4PL and 5PL), with the reading variance pooled from every kept standard reading; it is withheld under weighting, when the standards have unequal numbers of kept readings, with fewer than three degrees of freedom on the standard concentrations (concentrations minus parameters), near an asymptote or when a bound leaves the standards; constant variance is assumed. No automatic outlier removal, model selection or clinical validation is provided. The model must be appropriate for the user's ELISA or protein-assay protocol. NIST/SEMATECH §2.3.6.6 supports linear inverse calibration; Cox et al., Assay Guidance Manual, Immunoassay Methods (2019), covers model choice, recovery and weighting. Methods and primary-source links are also available beside the calibration results.

What it does

Paste or drop a plate-reader export, map the plate, and every compound's dose-response curve is fitted in batch: a four-parameter logistic model in log concentration with any parameter fixable, an unweighted 95 percent profile extra-sum-of-squares interval (Wald as an alternative); weighted intervals are unavailable, the Hill slope, both plateaus and R², with a relative or an absolute C50 and the rules that decide when a value is shown and when it is withheld with its reason. Plate exports are read by recognised layouts at 96 and 384 wells and the header is discarded; a long or wide table with units in its column headers works too. The plate map is assigned by keyboard or touch, saved as a template for next week, or placed from a dilution plan sent by the calculators.

Every result carries its method: the equation, the algorithm, the weighting, the constraints, the interval method, the exclusions, the normalisation formula with the controls it used, Z′ per plate and the engine version, printed as a method block and copied as a paragraph for a methods section. The same settings go into the CSV for GraphPad Prism (XY table) and the R snippet (drc::drm), so a fit can be reproduced elsewhere. Structures are drawn beside potencies when a SMILES column is present, and the C50s are written as your numbers on the target and the compounds, where the other apps can read them.

How it works

The engine is a pure module the suite shares: a bounded Levenberg-Marquardt fit with an analytic Jacobian and deterministic starting values read off the data (the extremes, the half-response crossing and the direction), so the same data give the same fit on every run; unweighted least squares by default, or 1/Y² by the fitted curve, using fixed weights from the preceding fitted response in an IRLS iteration. The Wald interval takes its standard error from (JᵀJ)⁻¹s² at the solution; the profile interval walks logC50 out from the fit, refitting the other parameters, until the objective rises to its minimum times 1 + F(0.95; 1, n − p)/(n − p), and labels a bound not reached within ten log units as not bounded within the search. Constant, unidentifiable and unconverged data have no reportable midpoint. Steep or runaway finite searches are labelled numerically unresolved; this is not a global-minimum proof.

Six rules, applied in order, decide what is shown: fewer than four distinct concentrations refuses the fit; a two-sided within-plate rank permutation test requires response evidence at p < 0.05 under independent exchangeable readings; a C50 the tested concentrations do not bracket on both sides is withheld; a free plateau with fewer than two concentrations at or beyond its bend point (C50 × 4.6805 to the power ±1/|Hill|) withholds the relative C50; an absolute C50 needs two concentrations predicted on each side of 50 percent; and a profile interval wider than two log units, or unbounded, flags the value as poorly determined. Batches run in a Web Worker in chunks of 25 curves with the progress read out and a cancel that stops after the current chunk; one curve fits on the page itself. No account is needed for scientific work: scientific computation stays local, and your plate data are kept as an assay object in this browser and in the session file you export, never in a link.

How it is checked

The engine is compared with named oracles run offline on published fixtures it never saw: 33 synthetic curves from a checked-in generator with known parameters and seeded noise, covering Hill slopes of 0.5, 1 and 3, plateaus away from 0 and 100, missing plateaus, rising curves, raw counts, high noise, 1/Y² weighting, fixed parameters, the four-concentration boundary, a three-concentration refusal, a flat line and a step; the worked MTT plate with three compounds; four control sets for Z′; and six nested model comparisons. Compatible unweighted estimates and resolved intervals are checked against the archived R oracle; historical weighted loss, old reporting rules and unresolved bounds are not validation of version 2. Relative IRLS is separately checked against SciPy least_squares with weights frozen within each solve. Z′ and ordinary nested-comparison arithmetic retain their reference checks. The tolerances are absolute on the logarithm: log10 C50 within 0.00043, Wald bounds within 0.0022 and profile bounds within 0.0043 log10 units; Hill within 0.1 percent; the plateaus within 0.1 percent of the span; legacy rule outcomes archived; the version 2 permutation policy is tested separately. The fixture files, their hashes, the generator and the oracle script are published on the verification page. The wording stays draft until the independent reviewer signs the fixture file and the method page (Q-19); agreement with Prism has not been checked, and no claim is made about it.

Equations and defaults

The model

y = Bottom + (Top − Bottom)/(1 + 10^((logC50 − x)·Hill)), x = log10 of the concentration in mol/L, Hill below zero for a falling curve; the parameterisation Prism documents, mapped to drc's LL.4 by e = C50, b = −Hill, c = Bottom, d = Top. This is the default model; bell-shaped and biphasic forms are fitted only when chosen, each with its own methods entry; any parameter may be fixed (Top at 100, Bottom at 0, Hill at ±1 by direction).

The fit

Bounded Levenberg-Marquardt with analytic derivatives, projected-gradient convergence checks and deterministic starts. A converged, identifiable solution is required. Unweighted least squares is the default. Relative fitting uses IRLS: start unweighted, freeze 1/f_previous² weights for each solve, update until parameters stabilise, and refuse nonpositive observations, nonpositive predictions or nonconvergence. Positive observations are an app domain restriction. SD is proportional to response; variance is proportional to response squared (constant CV). No Prism numerical-equivalence claim.

No finite minimum

Numerically constant observations, unidentifiable parameters and unconverged fits have no reportable midpoint. Finite multistart and limit searches can identify unresolved steep-step or runaway cases, but do not prove a global minimum does not exist. Legacy report codes are retained for file compatibility; the UI says numerically unresolved.

Wald interval

logC50 ± t(0.975, n − p) × SE with the standard error from (JᵀJ)⁻¹s² at the solution, s² the residual variance with n − p degrees of freedom; the named alternative, and drc's default confint.

Profile extra-sum-of-squares interval

Profile extra-sum-of-squares interval, unweighted only: refit nuisance parameters at each midpoint until RSS exceeds RSS_min × (1 + F(0.95;1,n−p)/(n−p)). This is an approximate nonlinear Gaussian constant-variance interval. Failed refits trigger multistart fallback or an unresolved bound. A missing or failed profile bound reads “not resolved within the search”, never infinity. Relative-weighted and numerically zero-residual fits have no interval.

The six rules, in order

Numerical validity is checked first. (i) Fewer than four distinct positive doses refuses fitting. (ii) A two-sided permutation test of dose/response rank covariance must have p < 0.05, permuting within plate; exact enumeration through eight observations, otherwise 1999 seeded permutations and the plus-one p-value. A failed check leaves a descriptive curve and no midpoint. Four unreplicated doses cannot pass: the smallest two-sided exact p is 2/24. This app-specific reporting policy requires independent exchangeable observations within each block and establishes ordering, not biological activity. (iii) Require two doses on each side of C50. (iv) Require two doses beyond each free plateau bend at C50 × 4.6805^(±1/|Hill|); fixed plateaus are exempt. (v) A 50-percent-control crossing needs two doses on each side. (vi) A wide or unresolved unweighted profile is flagged. The flat-line F diagnostic never gates reporting.

Relative and absolute C50

The assay-intent setting names the endpoint: inhibition gives IC50, activation/agonism EC50, and unspecified C50. Intent is preserved in links, saved analyses, exports and object measurements. Direction alone cannot determine that meaning. Relative C50 is the fitted midpoint. Absolute C50 is the 50-percent-control crossing, logC50 − log10((Top−Bottom)/(50−Bottom)−1)/Hill, only on an appropriate percent-control scale with an in-range crossing.

Normalisation and Z′

percent = 100 × (y − μneg)/(μpos − μneg) with each plate's own control means, the formula shown with the wells it used; raw, percent of control and percent inhibition as named alternatives. Z′ = 1 − 3(σpos + σneg)/|μpos − μneg| with sample standard deviations (n − 1) and n shown, refused when either control has fewer than two wells, and read against the 0.5 convention of Zhang, Chung and Oldenburg 1999 as an observation.

Model comparison

Only unweighted Gaussian constant-variance fits: nested extra-sum-of-squares F comparisons are approximate nonlinear-model diagnostics. Flat versus logistic is nonregular because midpoint and slope are unidentified under the flat null. AICc uses K = regression parameters + residual variance and is descriptive model comparison. Relative-weighted F/AICc comparisons are unavailable.

Statistics

The F distribution's upper tail by the regularised incomplete beta function (a continued fraction, modified Lentz), the t quantile by bisection on the t distribution, log-gamma by Lanczos; all in src/lib/fit/stats.ts, checked against known values.

Plate exports

A plate block is recognised by its structure, never by a vendor's name in the header: a row of column numbers over lettered rows (the grid), a Plate: line with a Temperature header or a Results section with a read label, at 96 or 384 wells; byte-order marks, UTF-16 and a decimal comma are read; every line outside the plate block is counted and discarded. Tables are long (one row per well or point) or wide (one column per compound) with the unit in the concentration header, converted to mol/L by the suite's unit table.

Timing

Data sources, licences and versions

Times on screen are local time with the UTC offset; times in exports are UTC. Dates with no time are shown at the precision the source gave them.

The Export menu offers the results as CSV (compound, C50, log C50, the interval's bounds with the method named, Hill, Top, Bottom, R², points, replicates, exclusions, flags and whether relative or absolute, with the provenance sidecar and README), the session as a JSON project file (the plate blocks, the layout, the settings, the exclusions and the results with the engine version, so it reopens here), the small multiples as SVG or PNG with the provenance embedded, a printed report with the method block, the CSV for GraphPad Prism (XY table), the R snippet (drc::drm) with the data inline and the method paragraph as text. Copy link carries the view and fit settings only; a session file carries the data.

Release gate: before the app leaves the preview, its exports and printed reports will carry the data versions, parameters, limits and a timestamp needed to reproduce a result, as the regulatory position says. This section will describe each format as it ships.

Each module below is a set of automated tests in the app's source code, with the expected results written into the tests. They check the app's logic against recorded inputs and stored reference records; none of them calls a live service.

src/lib/fit/fixtures.test.ts

Compatible unweighted curves from pipeline/assay-analyser/fixtures/synthetic-curves.json and the MTT compounds against drc-reference.json: estimates, objectives and resolved Wald/profile bounds; historical relative-loss fixtures remain archival. Version 2 relative IRLS is checked separately against a SciPy fixed-weight reference; unresolved profile refits are labelled explicitly rather than forced to reproduce an old finite bound. Also checks the compatible unweighted statistics and historical flat-line F diagnostic, Z′ for the five control sets and six nested F-tests, within the stated tolerances (absolute on the logarithm, never a percentage of one); the files' hashes against manifest.json, so a changed fixture fails before any value is compared. The oracle is R 4.3.3 nls with drc 4.0-0 as a cross-check, run offline by reference.R.

src/lib/fit/fit.test.ts

The statistics against known values; Levenberg-Marquardt on a line with bounds; the 4PL gradient against finite differences; a noiseless curve recovered exactly and the same fit on every run; a numerically unresolved steep step; the refusals; the absolute C50 and the bend constant; the normalisation modes; Z′'s refusal; AICc and the F-test.

src/lib/table/table.test.ts

The eight synthetic plate files and two tables under pipeline/assay-analyser/plates against expected.json: every well read back, every header line discarded, the profile and delimiter detected; byte-order marks, UTF-16 and the decimal comma; the plate map's rectangles, roles, filled series, the plan from the calculators and the curves it reads.

pipeline/assay-analyser/generate_curves.py and reference.R

The generator (NumPy, seeded, fits nothing) and the oracle (R 4.3.3, nls and optim; drc 4.0-0, MASS and jsonlite), MIT; reference.R records the R and package versions, the scripts' and inputs' hashes and the date, and writes manifest.json. drc's source is never translated and its starting heuristic is not used.

Draft until the independent reviewer signs the fixture file and the method page (Q-19).

Release gate: before the app leaves the preview, each release will publish a verification dataset with expected outputs on this page, so you can run your own checks.

Scientific computation runs in your browser, and individual apps need no account. Optional Bench accounts and backups use the site server and configured providers. The privacy statement, the hosts it contacts and the headers its workspace is served with are generated from its registry entry, the same record that sets the browser's policy.

What leaves your browser

Hosts the app contacts

The app contacts no host but its own.

Headers the workspace is served with