Protein Concentration (BCA/Bradford standard curve) mechanism

Model scope

The algebraic formula is standard for an ordinary least-squares linear standard curve, but the specification is incomplete about regression details, concentration units, validated linear range, blank handling, and dilution correction. Because those ambiguities affect the meaning of the reported concentration, the instrument needs review before being labeled fully verified.

• c=(A-b)/m is correct when ordinary least-squares regression models absorbance A as the dependent variable and concentration c as the independent variable.
• The specification does not explicitly define the regression method; ordinary least squares should be stated, including whether weighting, replicate averaging, or blank subtraction is used.
• BCA and Bradford assays are only approximately linear over validated concentration ranges; the instrument must enforce or clearly label the usable linear range rather than treating any standard set as linear.
• The output omits dilution-factor correction. If a sample was diluted before measurement, final concentration should be c_final=c_curve×dilution_factor.
• R² alone is not sufficient to validate a standard curve; residuals, standard range, blank behavior, and acceptable slope/intercept criteria may also be needed.

Units and conventions

• Absorbance A and intercept b are dimensionless absorbance units, commonly reported as AU or OD.
• Standard concentrations c and resulting sample concentrations must use the same concentration unit within a regression.
• The slope m has units of absorbance per concentration unit, so (A-b)/m has the chosen concentration unit.
• The sample absorbance must be measured under the same assay conditions as the standards and within the validated linear range.
• The vectors assume no dilution correction unless a dilution factor is explicitly supplied.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "standard_concentrations_mg_per_mL": [
      0,
      1,
      2,
      3
    ],
    "standard_absorbances_AU": [
      0.05,
      0.25,
      0.45,
      0.65
    ],
    "sample_absorbances_AU": [
      0.35,
      0.05
    ]
  },
  "expected_outputs": {
    "slope_m_AU_per_mg_per_mL": 0.2,
    "intercept_b_AU": 0.05,
    "R_squared": 1,
    "sample_concentrations_mg_per_mL": [
      1.5,
      0
    ]
  },
  "working": "The points lie exactly on A=0.20c+0.05: for c=0,1,2,3, predicted A values are 0.05, 0.25, 0.45, 0.65. Therefore m=0.20 AU/(mg/mL), b=0.05 AU, and every residual is 0, so SSE=0 and R²=1−SSE/SST=1. For sample A=0.35: c=(0.35−0.05)/0.20=0.30/0.20=1.5 mg/mL. For sample A=0.05: c=(0.05−0.05)/0.20=0/0.20=0 mg/mL. The second sample is the zero-concentration/intercept edge case."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The regression is undefined when all standard concentrations are identical, and the specification does not state validation behavior for negative inferred concentrations or ambiguous signed absorbance values. The specification also has no actual multi-regime formula branch despite a potential slope-sign boundary.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json