Memory‐efficient calculation of the isotopic mass states of a molecule

Abstract

Our previous work postulated a transition concept among different isotopic mass states (i.e., isotopic species) of a molecule, and developed a hierarchical algorithm for accurately calculating their masses and abundances. A theoretical mass spectrum can be generated by convoluting a peak shape function to these discrete mass states. This approach suffers from limited memory if a level in the hierarchical structure has too many mass states. Here we present a memory efficient divide-and-recursively-combine algorithm to do the calculation, which also improves the truncation method used in the previous hierarchical algorithm. Instead of treating all of the elements in a molecule as a whole, the new algorithm first 'strips' each element one by one. For the mass states of each element, a hierarchical structure is established and kept in the memory. This process reduces the memory usage by orders of magnitude (e.g., for bovine insulin, memory can be reduced from gigabytes to kilobytes). Next, a recursive algorithm is applied to combine mass states of elements to mass states of the whole molecule. The algorithm described above has been implemented as a computer program called Isotope Calculator, which was written in C++. It is freely available under the GNU Lesser General Public License from http://www.cs.brandeis.edu/~hong/software.html or http://people.brandeis.edu/~agar.

An Efficient Method to Calculate the Aggregated Isotopic Distribution and Exact Center-Masses

“…The returned monoisotopic mass of the molecule is identical to the mass reported in the paper of Olson and Yergey [18]. All other monoisotopic masses returned by NeutronCluster are identical to the ones calculated by Equation (24).…”

“…For large molecules, the calculation of exact center-masses of aggregated variants becomes fundamental, and the calculation is taken care of by our method. When information about the isotopic fine structure is required, other methods proposed in (e.g., [24], [25], [26], or [21]) can be used. If the molecule is not too large, the multinomial expansion [10] can be applied to infer the isotopic fine structure.…”

Molecular Isotopic Distribution Analysis (MIDAs) with Adjustable Mass Accuracy

“…MIDAs’s performance was evaluated against eight published methods: Mercury [19], Mercury5 [32], JFC [34], Isotope Calculator (IC) [33], Qmass [20], BRAIN [18, 31, 43], NeutronCluster (NC) [17], and Emass [21]. The first three published methods are Fourier-transform-based, IC utilizes a divide-and-recursively-combine algorithm, Qmass has its core based on FFT, BRAIN and NeutronCluster are polynomial-based, whereas Emass is based on a direct convolution approach related to the stepwise procedure and its improvement [36, 37].…”

“…To evaluate the performance of MIDAs, we have benchmarked it against eight methods: four of these methods—Mercury [19], NeutronCluster (NC) [17], Emass [21], and BRAIN [18, 31]—are the four best performing methods taking from a recent publication by Claesen et al [18]; four other methods included are Mercury5 (a new version of Mercury2) [32], Qmass [20], Isotope Calculator (IC) [33], and a Fourier-transform-based method recently published [34], which we refer to as JFC. JFC is an improved version of Isotopica [35], which incorporates BRAIN’s generating function.…”

Computational mass spectrometry for small molecules

“…Later approaches model the folding procedure as a Markov process [108,129,130]. IsoDalton implements the approach of Snider [108].…”