Match values molecular formula

Since this matches our value from before, this must be the molecular formula of the compound. 

Fortunately, the atomic masses of isotopes are nonintegers (see Table 6.2 and Appendix C). This feature imparts a unique value to the molecular mass of each compound or each formula. A nominal mass may have several combinations of elemental compositions, but the accurate mass can match one composition only. For example, a few of the molecular formulas that can be assigned to a 70-u... 

At first sight, MS provides information on masses and abundances in the ion mixture obtained from the analyte. Isotope compositions and theoretical isotope distributions link these primary pieces of information. This connection is discussed in Subsection 8.3.3. Ideas from [98,168, 291] will be developed further to calculate match values for molecular formula candidates using mass, intensities and isotope patterns. Such quantities are used for ranking and selection of molecular formula candidates (Subsection 8.4.1). 

Match values for molecular formulas and structural formulas... 

The above proposition can be used to determine both a molecular formula and a structural formula from a mass spectrum I. We will use Proposition 8.12 to calculate a match value (MV) for a given candidate molecular or structural formula K that measures the plausibility that K explains spectrum I. Ideally, such a compatibility match value should fulfill several requirements It should be between 0 and 1... 

If there was a match value that fulfilled the above conditions, the verification step of our structure elucidation problem would be solved. Unfortunately, there is no ranking function for real mass spectra that fulfils the latter two requirements in general. However, if we assume an exact recording of mass spectra intensities we can at least define a ranking function for molecular formulas that satisfies requirements (R) and (T). 

This is all the information necessary for calculation of the molecular formula. In the following, we cover all subproblems relevant in calculation of this match value. First... 

Appendix C contains tables of molecular formula counts for various nominal masses between 1 and 1000. Appendix D lists all molecular formulas from of masses between 1 and 150 containing at least one C atom. As mentioned before, it makes sense to include formulas only whose nominal masses in fact appear in the mass spectrum when calculating match values. 

Example (Match value of / = C6H12O2 for spectrum I from Ex. 8.2) Table 8.5 lists the molecular formulas /S, c that satisfy (Frag), (Gr2), and (Con). The last column gives the value of x, as solution of Equation (8.7). 

Now that we are able to calculate match values for molecular formulas with respect to a mass spectrum and to establish ranking lists, there is another issue How meiny candidates in a hit list should be considered if the correct candidate is to be included with a predefined probability ... 

Let us consider the distribution of match values of correct candidates for the molecular formula with respect to the respective spectrum. For a random sample of n = 1000 spectra Ij we calculate the match values of the correct molecular formula p,. 

Fig. 8.8. Match values of the molecular formula candidates of mass 116.

Histogram of the match values of correct molecular formulas for a sample of 1000 mass... 

The quantiles assist us in determining the acceptance (or rejection) of a molecular formula candidate, given a prescribed probability. If all molecular formulas p of correct mass m = trip are generated for our data set with a prescribed probability and all p whose match value is MV(7, P) > qi p are selected, then the correct molecular formula is contained in our selection with probability p. 

Table 8.7. Quantiles for match values of correct molecular formulas, for various probabilities p.

As mentioned earlier, fragmentation in a mass spectrometer generally follows known reaction schemes. We will use this knowledge during calculation of a match value for structure candidate M with respect to experimental mass spectrum I. The calculation is similar to that for molecular formula candidates. However, in the case of structural formulas we can considerably restrict the set of possible fragment molecular formulas jSj. We will consider only such molecular formulas for which fragments exist that are derived from M by successive ionization and fragmentation reactions. To simulate these we go back to the previous work in Section 2.3. 

For match value calculation, those molecular formulas Pi,i n are determined, for which 7(m, ) > 0, and then... 

The next step in calculation of match values is the determination of fragment molecular formulas. Table 8.8 Usts all such molecular formulas where there is a peak in the spectrum corresponding to the mass of highest intensity, f(m ) > 0. The solution Xj of the optimization problem is given in the last column. We obtain a match value... 

Next, we examine whether the match value Is able to rank structure candidates according to their relevance for the experimental spectrum. We generate all constitutional isomers of molecular formula C6H12O2,1313 candidates in total. If these are ordered by decreasing match values, the correct candidate methyl n-pentanoate Is at position 16. Figure 8.18 shows the 24 highest-ranked structure candidates and their match values. The top 13 positions are occupied by cyclic structures, although the ratio of cycUc and acyclic structures for 6 1202 is rather balanced (641 acyclic, 672 cycUc structures). If the acycUc nature could be determined somehow from the spectrum, then the correct candidate would be at position 2. In Section 8.5 we will try to find criteria for these structural properties empirically. 

As for molecular formulas, we calculate the match values for structures M, from a sample of randomly selected n = 1000 spectra 7 . Figures 8.21 and 8.22 show a histogram and the distribution of match values Xj = MV(7j, M,). As expected, the match values are considerably smaller than for molecular formulas. There are a few possible explanations for this. Some spectra are dominated by one or a few very intense peaks that are not explained using the standard fragmentation rules. No predicted fragments for a very intense peak results in a very low match value. Alternatively, the database spectra may be of low quahty or the structures given may be incorrect. 

Based on the quantiles of molecular formula match values we now can select some relevant molecular formula candidates. If we want to find the correct molecular formula in our selection result with a reliability of 95 0, we have to consider all candidates with a match value MV(I, /3) > 0.8775297. This excludes C4H4O4 and C4H4O2S. 

For the remaining six molecular formula candidates there are 118,669 constitutions in total. Using the classifier results, methyl ester can be set as a required substructure, while 52 forbidden substructures are obtained from the 40 absent properties. Under these restrictions, 123 structures remain. Using the permanent badlist from [320] containing 32 substructures, the structure space is reduced by einother four candidates. Figure 8.35 shows the match values for the 123 structure candidates. Match values for the structures eliminated with the four permanent badlist entries are marked in grey. 

A particularly clear-cut result is obtained if structures are restricted to those of the correct molecular formula Cg Hj2 O2. This leaves us with four structure candidates, with the correct structure ranked top, with a match value of 0.60530 ... 

In the present section we describe how to define a match value based on MS/MS data and present several examples that demonstrate how this additional information helps to determine the molecular formula. The main focus is on small and medium-sized molecules with a mass range up to approximately 1000 Da. Match values that reflect the consistency with MS isotope peaks and MS/MS fragment patterns are computed for candidate molecular formulas, and we demonstrate that these match values outperform methods based on isotope peak intensities alone. 

Calculating a match value for molecular formula candidate /S with MS/MS data can be achieved by trying to explain every peak in the MS/MS spectrum with a subformula /S. False formula candidates for the parent ion are expected to explain fewer MS/MS peaks (i.e. there will be peaks where no subformula can be found). The idea of taking all possible subformulas of a molecular formula candidate into account for the calculation of a MS-related match value was first formulated in [98]. Formulating this mathematically, a subformula /S can explain a measured MS/MS peak if the calculated mass m of /S as a singly charged cation or anion matches the observed peak mass within a certain tolerance (depending mainly on the spectrometer s accuracy). 

Alternatively, peaks of greater mass might be more important for the identification of the molecular formula than lower mass peaks. A match value that takes the peak mass itself into account could be defined as ... 

In Subsection 8.8.2 we presented three match values for MS isotope peak comparison. Table 8.22 shows the number of formula candidates with at least one carbon atom as well as the absolute and relative ranking positions of the true formulas. Calculations are based on g and MS accuracy 5 = 10 ppm. Numbers in the row headers cross-reference with the compounds in Table 8.20. Using MS data alone, only two compounds have ARP = 1, of which one has only one possible candidate (i.e. a trivial result) and the other has only two possible candidates. Using the ARP, it is not possible to choose the best method for calculating MS match values. While NDP works best for most of the samples, NSSE yields the best result for maltopentaose, and NSAE is best for cyclosporin C. If we look at the RRP results, creatine is excluded (RRP is not defined for only one candidate), but calculation of the arithmetic mean is possible. Thus, it appears that NDP performs best on average for these ten samples, but the other methods deliver quite similar mean results, and considering the small number of samples, this conclusion is by no means a statistically reliable result. What is clear from these results, the MS match value alone is by no means sufficient to unambiguously determine the correct molecular formula in most cases without further information or restrictions. 

The work presented in the previous sections demonstrates clearly that HR-MS provides much more information for the determination of the molecular formula when compared with LR-MS data. Exact masses alone already assist in the limitation of candidate molecular formulas, but the combination with MS/MS data (where available) clearly adds a significant improvement in eliminating false candidate formulas fiom consideration, for example through the use of combined match value. 

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