Efficient calculation of accurate masses of isotopic peaks

Abstract

This paper presents a new method for calculating accurate masses of isotopic peaks. It is based on breaking the calculation into a binary series of calculations. The molecule is built up by a series of such calculations. At each step the accurate masses are calculated as a probability weighted sum of the masses of the contributing peaks. The method is computationally efficient and accurate for both mass and relative abundance. T his paper addresses the problem of calculating the accurate masses of isotopic peaks in an isotopic distribution of a compound of known chemical formula. For the purposes of this paper an "isotopic peak" consists of all molecules having the same number of nucleons, regardless of the isotopic fine structure of the peak. For example, the compound CO has an isotopic peak containing 29 nucleons. Although this peak has an isotopic fine structure with contributions from both 12 C 17 O and 13 C 16 O, each of which has a slightly different mass, for the purposes of the present paper these will not be considered as two separate peaks but as a single isotopic peak with an accurate mass of 28.998297 Da.There are several methods for calculating masses of isotopic peaks. The accuracy and speed of an isotopic calculation both depend strongly on the method used. Kubinyi [1] and Rockwood and Van Orden [2] have described fast methods that also produce semi-accurate masses. The method of reference [2] is extremely fast and generally produces results within a few millimass units [2,3]. Although semi-accurate masses are useful for many applications, in some cases being more accurate than experimental measurements of masses [3], for other applications accurate masses would be preferable.Accurate masses of isotopic peaks can be calculated by several methods. Polynomial-based methods work well for low and medium molecular weight compounds, but become computationally inefficient at high molecular weights. Attempts to accelerate the polynomial-based methods by applying "pruning", which is the omission of small terms from the calculation, involve a tradeoff between speed and accuracy [4,5].In a second method, one might start with an algorithm that calculates profile-mode isotopic distributions centered on the accurate masses [4]. Numerical values of the accurate masses of the isotopic peaks would then be extracted by numerical quadrature or by peak fitting of the nominal isotopic peaks. However, considerable computational effort would still be involved in such a method.A third method is to perform a series of stepwise convolutions, building the full molecule by the stepwise addition of atoms to an accumulated "super atom". Masses of the individual isotopic peaks are calculated at each convolution step as a probability weighted sum of the contributions to each peak [3]. This method is accurate, but computational efficiency is not optimal.Recently, a new algorithm was presented for the calculation of accurate masses of isotopic peaks, and application examples were discussed [6]. This method combines very high compu...

Software Analysis of Uncorrelated MS1 Peaks for Discovery of Post-Translational Modifications

“…The averaged mass spectrum for retention time range is generated in profile mode and undergoes a peak picking step in which all spectral peaks not consistent with peptides are removed. The software then employs a custom version of the software Qmass [68,69] to generate theoretical isotopic distributions for the peptide ion of interest, and each theoretical peak is assigned to a corresponding experimental peak so long as the intensity exceeds 4% of the most abundant peak. The score is determined using a least squares approach comparing the theoretical peaks to the observed and is calculated as follows:…”

Reply to the Comment on:

“…For larger fluctuations of the masses and/or abundances of elemental isotopes, the effect on the isotopic distribution is even more pronounced and, in some cases, becomes troubling, as illustrated in Tables 2 and 3. The tables show the differences between the theoretical monoisotopic masses (Equation 24 in [1]) and theoretical average masses (Equation 25 in [1]) of 10 molecules [1] based upon the default isotope information used by BRAIN [1] and IsoDalton [3] (NIST), the IUPAC1997 standard [4], IsoPro [5], Mercury [6] and Emass [7], and NeutronCluster [8] (Table S1 in [1]). …”

A hierarchical algorithm for calculating the isotopic fine structures of molecules

“…There are another stepwise method [26] and an approximate method [27] to calculate the nominal peaks. Conversely, these methods do not provide the isotopic fine structure information of a molecule, and such information is required to fit experimental data from Fourier transform (see Figure 2) and sector instruments.…”