Calculation of Isotopic Distributions

As long as we are dealing with molecular masses in a range of up to some 10 u, it is possible to separate ions which differ by 1 u in mass. The upper mass limit for their separation depends on the resolution of the instrument enployed. Consequently, the isotopic composition of the analyte is directly reflected in the mass spectrum - it can be regarded as an elemental fingerprint. 

Even if the analyte is chemically perfectly pure it represents a mixture of different isotopic compositions, provided it is not composed of monoisotopic elements only. Therefore, a mass spectrum normally superimposes the mass spectra of all isotopic species involved [18]. The isotopic distribution or isotopic pattern of molecules containing one chlorine or bromine atom is listed in Table 3.1. But what about molecules containing two or more di-isotopic or even polyisotopic elements While it may seem, at the first glance, to complicate the interpretation of mass spectra, isotopic patterns are in fact an ideal source of analytical information. 

In the mass spectrum of methane (Fig. 1.4), there is a tiny peak at m/z 17 that has not been mentioned in the introduction. As one can infer from Table 3.1 this should result from the content of natural carbon which is an Xh-1 element according to our classification. 

Example Imagine a total of 1000 CH4 molecules. Due to a content of 1.1% there will be 11 molecules containing instead of the remaining 989 molecules are CUt. Therefore, the ratio of relative intensities of the peaks at m/z 16 and tn/z 17 is defined by the ratio 989/11 or by usual normalization 100/1.1. 

In a more general way, carbon consists of and in a ratio r that can be written as r = c/(100 - c) where c is the abundance of Then, the probability to have only in a molecular ion M consisting of w carbons, i.e., the probability of monoisotopic ions Pm is given by [19] 

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The polynomial approach is the logical expansion of the binomial approach. It is useful for the calculation of isotopic distributions of polyisotopic elements or for formulas composed of several non-monoisotopic elements. [2,14] In general, the isotopic distribution of a molecule can be described by a product of polynominals... 

Kubinyi, H. Calculation of Isotope Distributions in Mass Spectrometry. A Trivial Solution for a Non-Trivial Problem. Anal. Chim. Acta 1991, 247, 107-119. 

Rockwood, A.L. and VanOrden, S.L. (1996) Ultrahigh-speed calculation of isotope distributions. Anal. Chem., 68 (13), 2027-30. 

Palmblad, M., Buijs, J., Hakansson, P. (2001) Automatic aneilysis of hydrogen/deuterium exchange mass spectra of peptides and proteins using calculations of isotopic distributions. J Am Soc Mass Spectrom, 12(11), 1153-1162. 

Calculation of isotope distributions based on precise masses gains importance in two cases. One is for large molecules, where the true mass differs considerably from the nominal mass. Several algorithms have been proposed for calculation of precise mass isotope distributions [253,254,255]. The second is for high resolution instruments such as Fourier transform ion cyclotron resonance (FT-ICR) and Orbitrap MS that are capable of resolving isotope fine structure, such that individual isotope peaks are seen for certain elements (e.g. S). The R package isopat implements the theory... 

A. Rockwood, S. Van Orden, and R. Smith. Rapid calculation of isotope distributions. AnaL Chem., 67 2699-2704,1995. 

H. Kubinyi, Calculation of isotope distributions in mass spectrometry. A trivial solution for a non-trivial problem, Anal. Chim. Acta 1991,247, 107. 

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