Anal. Chem. 1996, 68, 2027-2030
Ultrahigh-Speed Calculation of Isotope Distributions Alan L. Rockwood* and Steven L. Van Orden†
Pacific Northwest National Laboratory, P.O. Box 999, Battelle Boulevard, Richland, Washington 99352
This paper introduces an ultrahigh-speed algorithm for calculating isotope distributions from molecular formulas, elemental isotopic masses, and elemental isotopic abundances. For a given set of input data (molecular formula, elemental isotopic masses, and elemental isotopic abundances), and assuming round-off error to be negilgible, the new algorithm rigorously produces isotope distributions whose mean and standard deviation are “correct” in the sense that an error-free algorithm would produce a distribution having the same mean and standard deviation. The peak heights are also “correct” in the sense that the height of each nominal isotope peak from the ultrahigh-speed calculation equals the integrated peak area of the corresponding nominal isotope peak from an exact calculation. As a consequence of these properties, the algorithm generally places isotope peaks within millidaltons of their true centroids. The method uses Fourier transform methods and relates closely to two other recently introduced algorithms. The suite of capabilities provided by these three algorithms is sufficient to solve an extremely wide range of problems requiring isotope distribution simulation. Several methods have been devised for calculating isotopic mass distributions of compounds from their molecular formulas and elemental compositions.1-7 Most rely on the expansion of a polynomial expression.4-6 The polynomial-based approach is a straightforward extension of the binomial probability distribution. When applied to isotopically complex molecules, polynomialbased methods have very unfavorable scaling properties because the number of terms to be calculated undergoes a combinatorial explosion as molecular weight increases, and calculation time and memory requirements rapidly grow to levels that make the method impractical.1,2 Recently, Rockwood et al. developed an approach using Fourier transform methods that enables calculations to be done both rapidly and accurately, even on very large molecules.1,2 For example, on a 50 MHz microcomputer using a 486 processor, the * Author to whom correspondence should be addressed. Present address: Sensar Corp., 1652 West 820 North, Provo, UT 84601. † Present address: Bruker Analytical Systems Inc., Manning Park, 19 Fortune Dr., Billerica, MA 01821. (1) Rockwood, A. L. Rapid Commun. Mass Spectrom. 1995, 9, 103. (2) Rockwood, A. L.; Van Orden, S. L.; Smith, R. D. Anal. Chem. 1995, 67, 2699. (3) Rockwood, A. L.; Van Orden, S. L.; Smith, R. D. Rapid Commun. Mass Spectrom. 1996, 10, 54. (4) Yergey, J. A. Int. J. Mass Spectrom. Ion Phys. 1983, 52, 337. (5) Brownawell, J. A.; San Filipo, J., Jr. J. Chem. Educ. 1982, 59, 663. (6) Hsu, C. S. Anal. Chem. 1984, 56, 1356. (7) Kubinyi, H. Anal. Chim. Acta 1991, 247, 107. S0003-2700(95)01158-9 CCC: $12.00
© 1996 American Chemical Society
isotope distribution of a 124 kDa DNA molecule took
