Mass Calculation

Peptacular calculates the molecular mass and isotopic patterns for amino acid (AA) sequences. This page presents the mathematical framework that underlies these calculations.

Base Mass

The base mass \(M_{base}\) of an AA sequence containing modifications is calculated as the sum of all constituent molecular components:

\[M_{base} = \sum_{i=1}^{n} m_{AA_i} + M_{N} + M_{C} + M_{S} + M_{I} + M_{R} + M_{U} + \mathbb{1}_{\textrm{precursor} \, \lor \, \textrm{neutral}} \cdot M_{L}\]

where:

  • \(n\) is the sequence length

  • \(m_{AA_i}\) is the mass of amino acid at position \(i\)

  • \(M_{N}\) is the total mass of N-terminal modifications

  • \(M_{C}\) is the total mass of C-terminal modifications

  • \(M_{S}\) is the total mass of static/fixed modifications (applied to sequence)

  • \(M_{I}\) is the total mass of position-specific modifications

  • \(M_{R}\) is the total mass of modifications within defined sequence intervals

  • \(M_{U}\) is the total mass of modifications with unknown positions

  • \(M_{L}\) is the total mass of labile modifications

  • \(\mathbb{1}_{\textrm{precursor} \, \lor \, \textrm{neutral}}\) is an indicator function: 1 for precursor and neutral ion types, 0 otherwise

Labile modifications are included only for precursor and neutral ion types, since they are lost during fragmentation.

Neutral Mass

The neutral mass \(M_{\textrm{neutral}}\) is calculated by combining the base mass with ion-type adjustments, isotope modifications, and neutral deltas:

\[M_{\textrm{neutral}} = M_{\textrm{base}} + M_{\textrm{ion}} + M_{\textrm{isotope}} + M_{\textrm{ndelta}}\]

where:

  • \(M_{\textrm{base}}\) is the peptide base mass from the previous section

  • \(M_{\textrm{ion}}\) is the ion-type-specific mass offset

  • \(M_{\textrm{isotope}}\) is the mass shift from a specific isotopic species

  • \(M_{\textrm{ndelta}}\) is the mass change from neutral losses/gains

Mass-to-charge Ratio

The mass-to-charge (m/z) ratio is calculated by incorporating charge carriers and electron mass corrections to the neutral mass:

\[\frac{m}{z} = \frac{M_{\textrm{neutral}} + M_{\textrm{adduct}} - z \cdot m_e}{|z|}\]

where:

  • \(M_{\textrm{neutral}}\) is the neutral fragment mass

  • \(M_{\textrm{adduct}}\) is the total mass of charge carriers

  • \(z\) is the total charge state (adduct charge plus any charge contributed by modifications), which may be negative for negative-mode ions

  • \(m_e = 0.00054857990946\) Da (electron mass)

The denominator uses \(|z|\) so that negative charge states still produce a positive m/z value.