Thermodynamic Index Calculation

thermodynamic-index-calculation

Summary

Calculate thermodynamic and molecular indices (DBE, GFE, AImod, NOSC) from assigned FT-ICR MS molecular formulas to characterize metabolite properties including saturation, lability, and oxidation state. These indices enable rapid assessment of compound degradability and structural complexity across large peak datasets.

When to use

Apply this skill after molecular formula assignment and filtering of FT-ICR MS peaks, when you have elemental composition (C, H, O, N, S, P counts) and need to characterize metabolite thermodynamic stability, degree of oxidation, aromaticity, and unsaturation to compare compound reactivity across samples or predict microbial degradation potential.

When NOT to use

• Input peaks lack assigned molecular formulas or elemental composition data—indices cannot be calculated without this foundation.
• Peak data has not been filtered for isotopic contamination (13C) or formula assignment error (>0.5 ppm)—indices on low-confidence peaks will propagate uncertainty.
• Downstream analysis requires isomer-level differentiation—these indices are composition-based and cannot distinguish chemical isomers.

Inputs

• Filtered peak abundance matrix (CSV) with m/z, assigned molecular formula, and elemental composition (C, H, O, N, S, P atom counts)

Outputs

• CSV table with columns: m/z, molecular formula, NOSC (nominal oxidation state of carbon), GFE (Gibbs free energy of carbon oxidation), AImod (modified aromaticity index), DBE (double-bond equivalent), peak intensity

How to apply

For each peak with a valid assigned molecular formula, sequentially compute four indices from elemental composition using the equations in Supplementary Table 2: (1) nominal oxidation state of carbon (NOSC) reflects the average oxidation state of all carbons and predicts lability; (2) Gibbs free energy of carbon oxidation (GFE or ΔG°C-ox) derived from NOSC indicates thermodynamic degradation likelihood—more negative values suggest greater microbial oxidation potential; (3) modified Aromaticity Index (AImod) quantifies carbon-to-carbon double bond density and aromatic ring prevalence; (4) double-bond equivalent (DBE) counts total unsaturation and aromatic structures. Export results as a CSV table with columns for m/z, molecular formula, NOSC, GFE, AImod, DBE, and peak intensity. All peaks with valid formulas must receive all four index values with no missing or NaN entries.

Related tools

• NumPy (Vectorized arithmetic for element-wise computation of NOSC, GFE, AImod, DBE across peak arrays)
• pandas (Loading filtered peak data, organizing elemental composition columns, and exporting indexed results as CSV)
• Formularity (Upstream tool for signal processing and molecular formula assignment from raw FT-ICR MS data prior to index calculation)

Evaluation signals

• All peaks with valid assigned molecular formulas receive exactly four index values (NOSC, GFE, AImod, DBE); no peaks missing any index.
• No NaN or infinite values in output; indices fall within expected biological ranges (e.g., NOSC typically −2 to +1; DBE ≥ 0 and proportional to molecular weight).
• Indices vary monotonically with elemental composition changes: increasing carbon and aromatic character raises DBE and AImod; increasing oxygen content increases NOSC (more oxidized); index values are internally consistent (e.g., high DBE correlates with high AImod for aromatic compounds).
• CSV output rows match input peak count exactly; m/z and molecular formula columns are identical between input and output.
• Indices computed for reference standards (e.g., lipids, carbohydrates, lignin) match literature-reported or manually verified values, confirming equation implementation.

Limitations

• FT-ICR MS cannot distinguish chemical isomers; thus indices reflect only elemental composition and cannot capture structural isomerism or regioisomerism that may affect actual thermodynamic stability.
• Index equations assume organic matter in natural aquatic/terrestrial systems; applicability to other domains (synthetic organics, plasma samples) not validated in article.
• Indices are composition-based estimates; actual compound reactivity also depends on physical factors (bioavailability, particle association, pH, ionic strength) not captured by formula-derived indices.
• Peak intensity data may be subject to ion suppression or enhancement in direct-injection MS, affecting downstream interpretation of relative compound abundance—indices themselves are unaffected but their use in abundance-weighted comparisons may be biased.

Evidence

• [other] MetaboDirect calculates thermodynamic indices including double-bond equivalent (DBE), Gibbs free energy (GFE), aromaticity index (AI), and nominal oxidation state of carbon (NOSC) from the elemental composition of assigned molecular formulas: "MetaboDirect calculates thermodynamic indices including double-bond equivalent (DBE), Gibbs free energy (GFE), aromaticity index (AI), and nominal oxidation state of carbon (NOSC) from the elemental"
• [other] For each peak's elemental composition, calculate the nominal oxidation state of carbon (NOSC) using the elemental composition equation from Supplementary Table 2. Calculate Gibbs free energy (ΔG°C-ox or GFE) for each peak from NOSC to determine degradation likelihood using the equation in Supplementary Table 2.: "For each peak's elemental composition, calculate the nominal oxidation state of carbon (NOSC) using the elemental composition equation from Supplementary Table 2. 3. Calculate Gibbs free energy"
• [other] Calculate modified Aromaticity Index (AImod) reflecting carbon-to-carbon double bond density from elemental composition using Supplementary Table 2 equation. Calculate double bond equivalent (DBE) representing molecular unsaturation and aromatic structure presence from elemental composition using Supplementary Table 2 equation.: "Calculate modified Aromaticity Index (AImod) reflecting carbon-to-carbon double bond density from elemental composition using Supplementary Table 2 equation. 5. Calculate double bond equivalent (DBE)"
• [other] Validation: all peaks with valid molecular formulas receive four index values; no missing or NaN values in output; indices fall within expected biological ranges for organic matter.: "Validation: all peaks with valid molecular formulas receive four index values; no missing or NaN values in output; indices fall within expected biological ranges for organic matter."
• [other] Export computed indices as a CSV table with columns for m/z, molecular formula, NOSC, GFE, AImod, DBE, and peak intensity.: "Export computed indices as a CSV table with columns for m/z, molecular formula, NOSC, GFE, AImod, DBE, and peak intensity."