Isotopologue Mass Delta Calculation

isotopologue-mass-delta-calculation

Summary

Systematically compute theoretical m/z mass shifts for all combinations of stable isotope substitutions (13C, typically M0 through M6) and ionization adducts (M+H, M+NH4, M+Na, M+HCl+H, M+K, M+ACN+H), organizing results into a reference grid ('khipu grid') used to match observed LC-MS features to theoretical ion species and infer neutral mass via linear regression.

When to use

When constructing a reference mass-matching framework for untargeted metabolomics or isotope-tracing LC-MS data, before pattern-matching observed features to isotopic and adduct variants. Specifically, generate a khipu grid when you have a neutral mass or chemical formula and need to predict all plausible m/z values across a defined isotope range and adduct set, in order to search an experimental feature table and build connected ion networks.

When NOT to use

• Input is already a feature table with observed m/z values — use this skill to generate the reference grid before feature matching, not as a feature extraction tool.
• Adduct list or isotope range is unknown or experiment-specific and has not been validated — confirm adduct formation and isotope labeling strategy first.
• Mass precision of the LC-MS instrument is significantly coarser than the chosen ppm tolerance (e.g., instrument ± 50 ppm, grid tolerance ± 5 ppm) — reconcile tolerances before grid construction.

Inputs

• neutral mass (Da) or chemical formula
• isotopologue range specification (e.g., M0 through M6)
• list of target adduct types with mass offsets (in Da)

Outputs

• khipu grid: 7×6 matrix of theoretical m/z values (rows = isotopologues M0–M6, columns = adducts)
• structured table (JSON or tab-delimited) with m/z predictions for feature matching

How to apply

Define the isotopologue series (typically M0 through M6, each differing by 1.00335 Da for 13C substitution). List the target adduct types with their precise mass offsets: M+H (+1.00783 Da), M+NH4 (+18.03383 Da), M+Na (+22.98922 Da), M+HCl+H (+36.99865 Da), M+K (+38.96315 Da), M+ACN+H (+42.03356 Da). For each isotopologue-adduct pair, calculate the theoretical m/z by adding the neutral mass (or formula mass) to the combined isotope and adduct mass offset. Organize results into a 7×6 matrix (rows = M0–M6, columns = six adduct types), with each cell containing the precise theoretical m/z value. This grid serves as the lookup table during feature matching; mass differences between observed features and grid rows/columns within a defined ppm tolerance (typically ≤ 5 ppm) indicate valid isotopic or adduct relationships.

Related tools

• mass2chem (formula-to-mass conversion and search functions used to calculate m/z offsets and match features to theoretical grid values) — https://github.com/shuzhao-li-lab/mass2chem
• Python 3 (scripting environment for defining isotopologue ranges, adduct mass offsets, and matrix computation)
• khipu (post-grid-construction: ingests the theoretical khipu grid and uses it to annotate feature networks and infer neutral masses via linear regression) — https://github.com/shuzhao-li/khipu

Examples

# Python: construct isotopologue m/z grid using mass2chem
from mass2chem.mass2chem_engine import find_adducts_from_mass
neutral_mass = 180.063  # e.g., glucose
adduct_list = [('M+H', 1.007276), ('M+NH4', 18.033826), ('M+Na', 22.989276), ('M+HCl+H', 36.983976), ('M+K', 38.963158), ('M+ACN+H', 42.033825)]
isotope_delta = 1.00335  # 13C - 12C
grid = {}
for isotope_num in range(7):
    grid[f'M{isotope_num}'] = {adduct_name: neutral_mass + isotope_delta*isotope_num + offset for adduct_name, offset in adduct_list}
print(grid)

Evaluation signals

• Grid dimensions are exactly 7 rows (M0–M6) × 6 columns (six adducts); all cells populated with numeric m/z values.
• Each isotopologue row increases by exactly 1.00335 Da relative to the previous row, consistent across all adduct columns.
• Adduct mass offsets match published values (M+H = 1.00783, M+NH4 = 18.03383, M+Na = 22.98922, M+HCl+H = 36.99865, M+K = 38.96315, M+ACN+H = 42.03356 Da); verify at least one cell by hand calculation.
• Grid matches observed feature m/z values in experimental data within defined ppm tolerance; feature pairs separated by predicted isotope or adduct shifts should align with network-matching expectations.
• Linear regression using grid values and observed ions yields a neutral mass with residuals (fit error) consistent with instrument mass accuracy.

Limitations

• Grid assumes 13C isotope substitution only; other isotopes (2H, 15N, 18O) require separate grid extension or custom isotope pattern definitions.
• Adduct list is fixed; for non-standard or experiment-specific adducts (e.g., in-source clustering, uncommon salt complexes), grid must be manually extended or redefined by user.
• Grid does not account for in-source neutral loss, fragmentation, or multiply-charged ions; apply only to singly-charged adducts in typical LC-MS conditions.
• Mass precision depends on accurate neutral mass input; incorrect or rounded input masses propagate directly to all grid cells and degrade feature-matching sensitivity.
• Grid construction assumes uniform isotope enrichment (e.g., all M+1, M+2, etc. correspond to uniformly distributed 13C); non-uniform labeling (e.g., site-specific or partial 13C) requires separate pattern definitions.

Evidence

• [other] Define the 13C isotopologues range as M0 through M6 (representing 0 to 6 carbon-13 substitutions, each differing by 1.00335 Da from the previous isotopologue).: "Define the 13C isotopologues range as M0 through M6 (representing 0 to 6 carbon-13 substitutions, each differing by 1.00335 Da from the previous isotopologue)."
• [other] Define the six adduct types with their respective mass offsets: M+H (+1.00783 Da), M+NH4 (+18.03383 Da), M+Na (+22.98922 Da), M+HCl+H (+36.99865 Da), M+K (+38.96315 Da), M+ACN+H (+42.03356 Da).: "Define the six adduct types with their respective mass offsets: M+H (+1.00783 Da), M+NH4 (+18.03383 Da), M+Na (+22.98922 Da), M+HCl+H (+36.99865 Da), M+K (+38.96315 Da), M+ACN+H (+42.03356 Da)."
• [other] For each combination of isotopologue and adduct type, calculate the theoretical m/z value using mass2chem or direct formula-to-mass conversion.: "For each combination of isotopologue and adduct type, calculate the theoretical m/z value using mass2chem or direct formula-to-mass conversion."
• [readme] Based on available ions and the theoretical "khipu grid", the neutral mass can be obtained via linear regression.: "Based on available ions and the theoretical "khipu grid", the neutral mass can be obtained via linear regression."
• [other] The khipu grid is constructed as a 7×6 matrix where rows represent isotopologues M0, 13C/12C×1 through 13C/12C×6, and columns represent adducts M+H[+], M+NH4[+], M+Na[+], M+HCl+H[+], M+K[+], M+ACN+H[+]: "The khipu grid is constructed as a 7×6 matrix where rows represent isotopologues M0, 13C/12C×1 through 13C/12C×6, and columns represent adducts M+H[+], M+NH4[+], M+Na[+], M+HCl+H[+], M+K[+],"