By determining two dimensions in chemical space (the C and N count) the degeneracy of possible formulae is reduced.
The astronomical number of possible formulae means that heuristic limitations are required to guide this combinatorial search.
(6) Further constraints can be placed on the possible formulas of unknown metabolites by making use of their fragmentation patterns.
The accurate mass data of the molecular ions were processed through the software program Data Analysis 4.0 (Bruker Daltonik, Bremen, Germany), which provided a list of possible elemental formulas using the Smart Formula algorithm.
In Section 2, we give two other possible formulas of solutions for the current systems by adopting the methods of integration by parts.
In this section, we present some sufficient conditions for finite time stability results for the desired system (1) by using three possible formulas of solutions, which do enrich the design methods in the practical problem.
For small molecule metabolites, maximal values for these dimensions might be close to 200 carbons and hydrogens, and lesser numbers of heteroatoms (see Materials and Methods), which still allows for a search space of 288,120,000 possible formulae.
Nevertheless, for all analyzed unknown metabolites, FragExtract performed a spectral cleanup and restricted the number of possible molecular formulas to one or two possibilities.
However, the number of possible chemical formulas and structures increases dramatically with mass, resulting in a very large number of "candidate formulas".
