Isotope Abundance Correction

Invert a two-isotopologue natural-abundance correction matrix.

Description

Two-component isotope correction solves a supplied 2×2 mixing system and normalizes the recovered components.

Two-component isotope correction solves a supplied 2×2 mixing system and normalizes the recovered components. The correction matrix defines the entire model.^[1]

Invert a two-isotopologue natural-abundance correction matrix.

When to use Isotope Abundance Correction

Use this tool to invert a two-isotopologue natural-abundance correction matrix.

Prepare the measured profile, formula counts, upstream model outputs or caller-defined reference criteria requested. Keep paired entries aligned and units, sample basis and preprocessing consistent.

How to use Isotope Abundance Correction and understand its results

Prepare the measured profile, formula counts, upstream model outputs or caller-defined reference criteria requested. Keep paired entries aligned and units, sample basis and preprocessing consistent.
Enter observedIsotopologues, naturalAbundanceMatrix using the field table and calculation rules, then run the tool.
Read correctedIsotopologues, sumCorrected. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
observedIsotopologues	Observed isotopologues	list of number	Required
naturalAbundanceMatrix	Natural abundance matrix	list of list of number	Required

Enter a 2×2 finite matrix and two finite observed values. Reject determinant magnitude<1e−12, negative recovered components and nonpositive recovered sum. Return normalized fractions and their sum.

raw=A^−1 observed; fractions=raw/Σraw

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
correctedIsotopologues	Corrected isotopologues	list of number
sumCorrected	Sum corrected	number

json

{
  "input": {
    "observedIsotopologues": [
      0.8,
      0.2
    ],
    "naturalAbundanceMatrix": [
      [
        1,
        0.1
      ],
      [
        0,
        0.9
      ]
    ]
  },
  "output": {
    "correctedIsotopologues": [
      0.7777777777777778,
      0.22222222222222224
    ],
    "sumCorrected": 1
  }
}

Limitations and assumptions

Signed matrix and observation entries are accepted; probability structure is not validated. This supports only two components and does not build a natural-abundance model.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Matrices are limited to 128 rows and 128 entries per row; other lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Isotopologue Distribution: Normalize M+0 through M+n isotopologues and count mean labeled carbons. For a complementary task, use MPLUS1 Carbon Estimate: Estimate carbon number from M+1 intensity using a caller-supplied per-carbon isotope contribution.

References

Isotope Abundance Correction — tool.io

Similar or alternative tools

Isotopologue Distribution
Normalize M+0 through M+n isotopologues and count mean labeled carbons.
MPLUS1 Carbon Estimate
Estimate carbon number from M+1 intensity using a caller-supplied per-carbon isotope contribution.