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

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.