. Author manuscript; available in PMC: 2017 Aug 5.

Published in final edited form as: J Proteome Res. 2016 Jul 1;15(8):2422–2432. doi: 10.1021/acs.jproteome.5b01098

Table 1.

Symbol definitions

Symbol	Definition
S	A top-down tandem mass spectrum
Score(S, F)	The shared mass count between spectrum S and a proteoform F.
P	The unmodified protein sequence of the target proteoform with length m
F_i	The proteoform of P in which the ith amino acid is modified. The molecular mass of F_i matches the precursor mass of S.
Pr(F_i)	The prior probability of proteoform F_i
Pr(S)	The probability of the data (spectrum). In Bayesian models, it is usually computed as the sum of the prior probabilities of all hypotheses multiplied by their likelihoods.
Pr(S\|F_i)	The likelihood, the conditional probability of observing S given F_i
Pr(F_i\|S)	The posterior probability, the probability for F_i after taking into account S
T_i,j	The proteoform of P in which the first i amino acids are truncated and the jth amino acid is modified. The molecular mass of T_i,j matches the precursor mass of S.
𝒬_i	The set of proteoforms of P with a pair of ordered modifications (x_i, y_i)
𝒬_ij	The set of proteoforms satisfying that the first modification x_i occurs on the first j amino acids and the second modification y_i on the last m − j amino acids
ℱ₁	The set of all proteoforms of P with one common modification whose molecular masses match the precursor mass of S
ℱ₂	The set of all proteoforms of P with two common modifications whose precursor masses match the precursor mass of S