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A general approach to calculating isotopic distributions for mass spectrometry
International Journal of Mass Spectrometry
and Ion Physics, 52 (1983)
337-349
337
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
A GENERAL APPROACH TO CALCULATING ISOTOPIC DISTRIBUTIONS FOR MASS SPECTROMETRY
JAMES A. YERGEY Middle Atlantic Mass Spectrometry Worfe Street, Baltimore, MD 21205
Fucidity, Johns Hopkins (U.S.A.)
School
of Medicine,
725 North
(Received 28 March 1983)
ABSTRACT Fundamental principles for obtaining mass spectral isotopic distributions are applied to a general computer program which can be used to calculate and present in tabular and graphic form the isotopic contributions for any molecular formula. A unique feature is the retention of the isotopic distribution, exact mass, and absolute abundance for all individual peaks at each mass. Special considerations have been made for the large number of isotopic combinations which occur for many higher mass compounds. The computer program accepts the input of a molecular formula followed by interactive input of a number of parameters which affect the final presentation of the theoretical distribution profile.
INTRODUCTION
Recent developments in desorption ionization techniques have stimulated growth in the mass spectrometric analysis of molecules with molecular weights between 1000 and 10000 daltons (middle molecules). Field desorption of polystyrene oligomers [l-3] as well as fast atom bombardment [4-61 and 252Cf plasma desorption [7] of bovine insulin are examples of recent progress in the field. In general, mass spectrometric techniques which are capable of analyzing middle molecules have focused upon obtaining molecular weight information for the molecules of interest. As molecular weight increases, molecular ion distributions of many compounds are no longer dominated by a single peak as observed at masses below 1000 daltons, but are complex distributions spread over many mass units 181. Abundances of monoisotopic mass ions become vanishingly low, and each peak at a given nominal mass contains numerous isotopic contributions whose separation requires a resolution better than 1 in lo6 [8]. The available algorithms describing the calculation of isotopic distributions for mass spectrometry which have been reported in the literature [9- 171 0020-7381/83/$03.00
0
1983
Elsevier Science Publishers B.V.
338
as well as the discussions included in mass spectrometry textbooks [ 18-201 have not addressed the representation of the complex distributions which occur in the middle molecule region. Earlier calculations were limited in their presentation of the data [9] or their ability to deal with the entire periodic table of elements [lo]. Most of the remaining algorithms El l- 161 allow for polyisotopic elements and present the calculated data as bar plots, but sum all of the contributing peaks at each nominal mass. Carrick and Glocking [ 171 describe a program especially designed for calculating distributions of organometallic compounds which retains the information about the individual peaks at each mass unit, but limits the molecules to five atoms each for three elements at most. The focus of this paper is the application of the fundamental principles for obtaining mass spectral isotopic distributions to a general computer program which can be used to calculate and present the isotopic contributions for any molecular formula, retaining the ,isotopic distribution, exact mass, and absolute abundance of all individual peaks at each mass. Special considerations have been made for the large number of isotopic combinations which occur for many higher mass compounds. The computer program accepts the input of a molecular formula followed by interactive input of a number of parameters which affect the final presentation of the theoretical distribution profile. PRINCIPLES
Mass spectral isotopic distributions can be calculated by expansion of a binomial expression for relatively small molecules or for molecules containing only elements with two isotopes. However, a rigorous treatment which can be applied to any molecular formula involves expansion of a polynomial expression. The isotopic distribution for a given molecule is described by the following product of polynomials 1151 ( a,+a,+a,+
. ..)m(b.+bz+b3...)“(cl+c,+c,+
. ..)“...
(1)
where a ,, a,, a3, etc., b,, b,, b,, etc., and c,, c2, c3, etc., represent the individual isotopes of the elements in the molecule, and the exponents m, n, o, etc., are the number of atoms of each element present in the molecule. The terms which result from the expansion of each polynomial can be used to describe the isotopic contributions, exact masses, and absolute abundances for each element’s contribution to the molecule. As an example, an expression describing all isotopic permutations of the m.w. = 3482) is given by pep tide molecule glucagon ( C , 53H,,,N,,O,,S, (12, + (32s
13q153(lH
+
33s
+2H)224(14N
+
34s
4
3%)
+
15~)42(16~
+
170
+
IS~)~O
(2)
339
If the polynomial for oxygen is expanded and the like terms collected, one where the coefficient is equal resulting term would be 58 000 160,,170,‘801, to the number of times the term appeared in the expansion. Like terms can be collected, in this application, since only the number distribution of the isotopes can be derived from a mass spectral peak, not the position of each isotope in the molecule. The contribution of each isotope is described by the subscripts of the expansion term. The exact mass (803.7585) and absolute abundance (1.518 X 10T3) for this permutation can be calculated from isotopic masses and relative abundances. It should be noted that preserving the isotopic contributions in the calculation permits the demonstration that another expansion term for the oxygen polynomial (1225 r60,,‘*0,) differs in mass by only 5 p.p.m. (803.7541) from the above example. The example also indicates that usually negligible isotopes such as I70 begin to have real contributions in the middle molecule mass range. Finally, this example illustrates the large number of permutations which occur when dealing with high mass compounds. If the product of polynomials in eqn. (2) are expanded with regard to the position of each atom there would be (2)153(2>224(2)42(3)50(4)1 = 3.9 X 10r5’ individual terms generated, which when collected to yield the like terms would still result in 7.9 X IO9 unique permutations. The large number of permutations generated for high mass compounds, coupled with the desire to preserve isotopic information concerning each permutation while including all isotopes in the calculation, necessitates that the program directly calculate only the unique permutations for each element. This is in contrast to calculation methods that expand each polynomial, followed by collection of like terms [9-163, which requires an excessive amount of computer time when applied to large molecules. An additional means of reducing the number of permutations and thereby the calculation time, is to stop the calculation of permutations for each element when all permutations having an absolute abundance greater than a user-defined threshold have been determined. Different means of applying the threshold can be understood by examining Table 1, which contains the first ten unique permutations generated by the expan$ion of the carbon polynomial ( ’ 2C + l3C) 153from eqn. (2). A commonly employed method to determine a threshold is to stop the calculation after a given number of permutations have been calculated [ 14,151. This method is satisfactory for small ,molecules containing elements whose most abundant isotope is also the lightest isotope, since the third or fourth peak in the distribution is almost always ( 1% of the first and most abundant peak. However, Table 1 illustrates that as the number of atoms of a given element becomes relatively large, the distribution shifts in a way that makes this method of determining a threshold invailid. A better method is to include only those permutations
34-o
TABLE
1
Distributions, abundances, and ‘*C 153 152 151 150 149 148 147 146 145
massesfor the first ten expansion terms of (“C+
13C 0
144
Absolute abundance
mass
0.18410 0.3 1327 0.2648 1 0.14825 0.06 183 0.02049 0.00562 0.00131 0.00027 0.00005
1836.000 1837.003 1838.007 1839.010 1840.013 1841.017 1842.020 1843.023 1844.027 1845.030
‘3C)‘53
Exact
whose abundance is greater than some absolute value. This method may also become invalid for higher molecular weight compounds, since there are so many permutations that the absolute abundance of even the most intense permutation can become very small (-c 0.01). Therefore, a threshold which can be applied to any molecular formula must be based on a percentage of the most abundant permutation’s absolute abundance; this method is used in the program described. The absolute value of the threshold will be based on the current permutation with the greatest abundance, and since the most abundant peak will usually change during the course of the calculation, the absolute value of the threshold will also change. The absolute abundances for each permutation can be described by the following combinational equation
(3) where n is the number of atoms of the element, rl, r,, I-~, etc., are the abundances of each isotope and a, b, c, etc., are the number distribution of the atoms in a given permutation [21]. Returning again to the example given for eqn. (2) of the expansion of the oxygen polynomial (I60 + I70 + 18O)5o of glucagon, it can now be shown that the absolute abundance of the 160,7’70,‘80, term is derived from the following equation (50)! A = (47)!(2)!(l)!
(r16)47tr17)2(r18)1
(4)
by substituting into eqn. (3) the number of atoms of oxygen (50) and the number distribution (47, 2, 1) of these atoms in this particular permutation.
341
Calculation of the ratio of factorials yields the coefficient of the expansion term, which is 58 000. The large number of atoms encountered in “middle molecules” requires an alternative approach to the calculation of each abundance since the large number of multiplication operations required by eqn. (3) for each abundance calculation would introduce serious computational errors, and require excessive calculation time. If the absolute abundance of any two permutations are divided by each other and the terms collected, the following equation is generated A
(4(b,)!(c,)!
_A
2-
.-*
’ (a,)!(b,)!(c,)!
. . .
)tc12-P,)(
(
pyc,,
p-y r2
r1
r3
.**
(5)
where subscripts denote the two different permutations. The program calculates the abundance of the first permutation using eqn. (3) and then proceeds by basing each subsequent abundance on that of the previous permutation, according to eqn. (5). The example in eqn. (4) would then be described by A
_-A 2-
’
(47)!(3)!(o)! (47)!(2)!(l)!
(
)(47--47)~
‘16
>“-“( r17
)(1--o) 118
(6)
or A2
=
3A1(57rh3)’
0)
which bases the abundance of the 160 4717021801 permutation ( A2) on that of the previous term 160d717O,‘“O, (A,). The total number of multiplication and division operations is greatly reduced using this formula, thereby reducing computational errors and saving substantial calculation time. ALGORITHMS The program which calculates and displays the molecular ion distributions consists of a main module (EXMASS) and four subroutines, which are outlined in the following paragraphs. PARAMETER statements at the beginning of each section of the program allow the operator to modify the common block array sizes easily, in order to accommodate vastly different types of molecules, e.g., polystyrene, II = 1000 (CS004H80,0), a large biomolecule such as insulin (C,,, H,,,N6507,S,), or an organometallic (Sn,C,,H,,), while still keeping the overall core requirement below 32K words. A molecular formula is input within subroutine DATAIN as elemental symbols which follow periodic table abbreviations, accompanied by the number of atoms of each element present in the molecule. The formula is decoded, and the exact mass and relative abundances of each isotope for elements in the formula are read from a disk file. The disk file presently
342
contains all naturally occurring isotopes of all stable elements, but can easily be modified to include isotopically-enriched species. An auxiliary program (UPDATE) is used to update information on the disk file which contains isotopic masses and abundances for each element. This routine can be used to input new elements, and to list, modify, or delete existing isotopic information, but must be run independently of program EXMASS. All unique permutations of each element are generated within subroutine PERMUT by a set of nine nested DO loops. The first permutation contains all atoms in the first isotope. The number of atoms in the first isotope are decremented and the remainder placed in the second isotope, forming a new permutation. The number in the second isotope is then decremented, placing the remainder in isotope three, etc. The loops are executed only to the level corresponding to one less than the number of isotopes for the element, therefore accommodating any element with ten or fewer isotopes. As each permutation is generated its absolute abundance is calculated and compared to the maximum abundance for that element. If the abundance is greater than the selected threshold, the isotopic distribution, absolute abundance, and exact mass of that permutation are saved. When appropriate, the maximum abundance for the element is also updated_ If too many permutations are generated for a particular element, as defined by PARAMETER MXPERM, subroutine RESET is used to reset the threshold, reduce the number of permutations, and inform the operator of the change in threshold. If no permutations are saved for a given number of atoms in the first isotope, any further decrementing of this number can only lead to permutations that will not be saved, and the calculation is therefore terminated. In subroutine FORMULA the permutations for each element are combined with the permutations for all other elements, generating complete molecular formulae. The permutations for the first element are saved as the initial combinations, and as the permutations for each successive element are completed they are combined with the existing combinations. This procedure accomplishes the multiplication of each successive polynomial described in eqn. (1) to complete the calculation of the isotopic distributions. Each combination is stored as a pointer to the isotopic distribution, or permutation, for each element, along with the exact mass and absolute abundance of the combination. The same threshold used in generating permutations is again applied to the combinations, and is reset, if necessary, according to the value of PARAMETER MXPEAK. After all elements have been permutated and combined into their final formulae, the combinations are ordered by increasing mass. The output of the program consists of two tables and a plot, which are generated within the main program module. The first table contains the isotopic distributions of each element for all combinations above threshold,’
343
along with the corresponding exact mass and absolute abundance. A second table summarizes the input data and calculated data, including nominal, monoisotopic, average, and most abundant masses. This table also includes a list of exact masses, relative abundances, p.p.m. spread, and multiplicity for integer mass groupings of the peaks in the first table. Finally, a plot is generated from a Gaussian distribution of the integer mass groupings. The resolution of the peaks in the plot is designated by the user, thereby allowing the user to compare more readily the distribution with experimental data. A bar plot is superimposed on the Gaussian distribution for clarity if the user-defined resolution is less than half the mass of the molecule. Program EXMASS and accompanying subroutines are written in FORTRAN IV, and consist of 1547 lines of code, including 805 comment statements. Most statements also contain an internal comment. Program UPDATE is also written in FORTRAN IV, and consist of 318 lines of code, of which 132 are comments. All disk I/O and dialog are accomplished by Data General RDOS FORTRAN cqmmands, which are readily converted to other operating systems. Dialog is designed for a Tektronix Model 4010 CRT, and output can be sent to either the CRT or to a hard copy device such as the Versatec Model 8OOA Printer/Plotter. Kratos DS-55 plot software is used in the present configuration but it can be readily exchanged for packages such as Tektronix Plot-10 software. The core size demanded varies with PARAMETER settings, but can operate in less than 32K words of core memory for most cases. RESULTS
An example of the dialog for executing the program is shown in Fig. 1. Note that, if desired, the program gives a complete introduction for each step of the dialog using bovine insulin as an example, and that default responses allow the operator to move through the dialog quickly and skip the extended table if desired. Tables 2 and 3 and Fig. 2 illustrate the output of the program for the same example. Only the first 16 peaks of the 290 peaks that were calculated and are usually presented, are included in Table 2. Note that Fig. 2 shows two plots, in order to illustrate the capability of the program to generate distributions at any user-selected plot resolution. Execution time depends on the number of elements, the number of isotopes per element, and the threshold selected, but typical examples include bovine insulin (&, H377N65075S), 30 s, and polystyrene n = 1000 lo-20 s is required to calculate the (C 8004 H,0,0)? 20 i. An additional Gaussian distribution for plotting. Documented listings of the program are available from the author. Individuals are also invited to correspond concerning “one-time” use of the program.
344 WELCOME
TO PROGRAM
EXMASS
THIS PROGRAM WAS DESIGNED TO ALLOW THE USER TO VISUALIZE THEORETICAL DISTRIBUTION PROFILES FOR ANY GIVEN MOLECULAR FORMULA. SPECIAL CONSIDERATIONS ARE MADE FOR THE LARGE NUMBER OF ISOTOPIC CONTRIBUTIONS WHICH OCCUR FOR MANY COMPOUNDS AT HIGHER MASSES. THE PROGRAM ACCEPTS THE INPUT OF A MOLECULAR FORMULA, FOLLOWED BY INTERACTIVE INPUT OF A NUMBER OF PARAMETERS WHICH AFFECT THE FINAL PRESENTATION OF THE THEORETICAL DISTRIBUTION PROFILE. DO YOU
DISIRE
A MORE
COMPLETE
INTRODUCTION
TO THE PROGRAM?
YES
THE PROGRAM WILL FIRST ASK YOU TO INPUT A MOLECULAR FORMULA. THE FORMULA MAY CONTAIN UP TO 9999 ATOMS OF ANY OF THE STABLE ELEMENTS OF THE PERIODIC TABLE. IT WILL CHECK TO ENSURE THAT THE FOLLOWING RULES ARE MET: 1) FIRST CHARACTER MUST BE A LETTER (ELEMENT NAME), 2) ELEMENT NAMES MUST BE TWO CHARACTERS OR SHORTER, FOLLOWING PERIODIC TABLE ABBREVIATIONS, 3) ANY NUMBER OF SINGLE SPACES MAY BE INCLUDED, BUT TWO IN ROW INDICATES THE END OF THE INPUT. TRY TO INPUT THE FORMULA FOR BOVINE INSULIN. TRY INCORRECTLY AT FIRST TO SEE THE RESPONSE *INPUT COMPOUNDS MOLECULAR FORMULA: 3CH2COOH
OF THE PROGRAM.
*INPUT ERRORS, *UNKNOWN ELEMENT. *MUST GIVE ELEMENT SYMBOL FIRST. *ELEMENT MUST HAVE LESS THAN 3 LETTERS. TRY AGAIN, THE FORMULA IS C254 H377 N65 075 S6. *INPUT COMPOUNDS C254H377N65075S6
MOLECULAR
FORMULA:
THE PROGRAM MUST LIMIT THE NUMBER OF POSSIBLE PERMUTATIONS FOR MANY COMPOUNDS, AND THEREFORE REQUESTS A THRESHOLD (5%OF THE BASE PEAK) TO BE USED AS A CUTOFF. THRESHOLD MUST BE > 0 and -z 100 OR IT WILL DEFAULT TO 1 E-10. TRY A THRESHOLD OF O.OL FOR THIS EXAMPLE. *INPUT 0.01
THRESHOLD
AS % OF BASE PEAK:
THE PROGRAM NOW COMPLETES IT CALCULATIONS OF THE THEORETICAL DISTRIBUTIONS, WHICH MAY REQUIRE A MEASURABLE AMOUNT OF TIME, AND MAY REQUIRE RESETTING THE THRESHOLD IF TOO MANY PERMUTATIONS ARE GENERATED, AS IN THIS EXAMPLE. NOTE THAT THE PROGRAM WILL INFORM YOU IF THIS IS NECESSARY; *TOO
MANY
PEAKS,
THRESHOLD
RESET TO 0.9999 E-3
AFTER COMPLETING THE CALCULATIONS, THE PROGRAM WILL ASK QUESTIONS CONCERNING THE DESIRED OUTPUT FORMAT. THE FIRST QUESTION IS WHETHER YOU WANT TO SEE THE ISOTOPIC DISTRIBUTIONS FOR EACH
345 ABOVE THRESHOLD PERMUTATION, OR GO ON TO THE TABLE OF PEAKS EACH INTEGER MASS AND THE PLOT. FOR THIS EXAMPLE REPLY “YES’ SIMPLY ” Y”. *OUTPUT’ YES
ISOTOPIC
DISTRIBUTIONS
FOR ALL
AT OR
PEAKS?
NEXT THE PROGRAM REQUESTS THE REPORT DEVICE: $VDU FOR THE CRT, WHICH IS THE DEFAULT DEVICE, OR $PPL FOR THE VERSATEC PRINTER/ PLOTTER. FOR THIS EXAMPLE REPLY WITH “$VDU” OR A CARRIAGE RETURN. *REPORT $VDU PLOT UNIT TION
DEVICE
RESOLUTION RESOLUTION OF 2500.
*PLOT 2500 LASTLY, *TITLE: BOVINE
IS SELECTED (10% VALLEY),
AT THIS POINT. THE DEFAULT BUT FOR THIS EXAMPLE TRY
VALUE IS A RESOLU-
RESOLUTION: THE PROGRAM INSULIN,
ASKS FOR A TITLE
FOR THE TABLES
AND
PLOT.
C254 H377 N65 075 S6
THE PROGRAM NOW OUTPUTS A TABLE OF EACH ABOVE THRESHOLD PEAK. FOR EACH PEAK, EVERY ELEMENT IS PRESENTED ALONGSIDE ITS ISOTOPIC DISTRIBUTION IN THAT PEAK. THE MASS AND ABSOLUTE ABUNDANCE ARE ALSO GIVEN FOR EACH PEAK. (See Table 2) THE FOLLOWiNG TABLE CONTAINS BOTH THE INPUT DATA AND A SUMMARY OF THE CALCULATED DATA, INCLUDING INTEGER MASS GROUPINGS OF THE PEAKS PRESENTED IN THE PREVIOUS TABLE. (See Table 3) FINALLY, A PLOT WILL BE GENERATED USING A GAUSSIAN DISTRIBUTION OF THE INTEGER MASS GROUPINGS OF THE PEAKS. NOTE THAT THE PROGRAM REQUESTS PATIENCE WHILE CALCULATING THE GAUSSIAN DISTRIBUTION. NOTE ALSO THAT A BAR PLOT IS GENERATED UNDER THE GAUSSIAN DISTRIBUTION. THE PROGRAM DOES THIS IN ALL CASES WHERE THE PLOT RESOLUTION IS LOW WHEN COMPARED TO THE MASS, MAKING IT DIFFICULT TO VISUALIZE THE INDIVIDUAL PEAKS. (See Figure 2) NOTE:
I) User responses are underlined_ 2) Only the text indicated by an asterisk (*) is output if a complete introduction is not requested.
Fig. 1. Example of dialog for program EXMASS
with extended introduction_
346 TABLE
2
Isotopic
distributions,
exact masses and absolute
bovine insulin molecular BOVINE PEAK
INSULIN,
NO.
abundances
of first 16 peaks for theoretical
ion envelope
C254 H377 N65 075
S6.
I : EXACT
MASS
= 5729.598
ABSOLUTE
ABUNDANCE
= 0_2753779E-
12C,,,1Hj,714N I40 PEAK NO. 2: E&C;
32s, MASS
= 5730.598
ABSOLUTE
ABUNDANCE
= 0.1304 147E- 1
= 5730.598
ABSOLUTE
ABUNDANCE
= 0.6647344E-2
MASS = 5730.602 “0 32S
ABSOLUTE
ABUNDANCE
= 0.7866999E-3
2 5730.602
ABSOLUTE
ABUNDANCE
= 0.7779628E-
= 5730.605
ABSOLUTE
ABUNDANCE
= O.l557495E-2
= 5731.594
ABSOLUTE
ABUNDANCE
= 0.73206 13E-2
ABSOLUTE
ABUNDANCE
= 0_789979OE-3
ABSOLUTE
ABUNDANCE
= 0.3148122E-3
ABSOLUTE
ABUNDANCE
= O.l87795OE-
ABSOLUTE
ABUNDANCE
= 0.4140522E-2
= 5731.602
ABSOLUTE
ABUNDANCE
= O.l899039E-3
= 5731.602
ABSOLUTE
ABUNDANCE
= 0.3759686E-3
ABSOLUTE
ABUNDANCE
= 0.36843 12E-2
ABSOLUTE
ABUNDANCE
= 0.2222484E-2
ABSOLUTE
ABUNDANCE
= 0.1094576
12C2~41H377’4N65’607~32S~33S1 PEAK NO. 3: EXACT MASS 12C,~~‘H~,7’4N~4’5N,‘60,532S6 PEAK NO. 4: EXACT ‘2C2541H377’4N I60 PEAK 12’253
NO. 5 : &AC? b&S ‘3C,‘H37714N65’607,3zS~
PEAK
NO.
12C,,4’H PEAK
6: EXACT
MASS
1
1
37a2H,14N65’607532S6 NO.
7: EXACT
MASS
12C2541H377’4N65’607532S~34SI PEAK NO. 8: EXACT MASS = 573 1.594 14Ns3’5N2160,532S6 12C,,,‘H 377 PEAK NO. 9: EXACT MASS = 5731.598 12C2,4~H377’4N~4’5N,160,532S533S, PEAK NO. IO: EXACT MASS = 5731.598 13C,‘H~7714Ns4’5N,‘607532S6 12c253 PEAK NO. 11: EXACT MASS = 5 73 1.602
1
12C2541H377’4N65160,4’80,32S6 PEAK NO. 12: EXACT MASS 12C2541H3,,‘4N64’5N,‘60,4170,32SG PEAK NO. 13: EXACT MASS
12C254’H376~H1’4N6415N1’607532S6 PEAK NO. 14: EXACT MASS = 573 1.602 ‘2c253
PEAK
13C1’H377’4N651607532S533S, NO.
15: EXACT
MASS
= 573 I .605
‘2C~j~13C,‘H37714N~5160,4170,32S~ PEAK NO. 16: EXACT MASS = 5731.605 ‘2C,,,
‘3C2’H37714N65’60,532S~
347 TABLE
3
Summary of input and calculated data for bovine insulin BOVINE INSULIN, INPUT DATA:
Czs4 H 377N65075 s,
ELEMENT
#ATOMS
#ISOTOPES
ISOTOPIC MASS
ISOTOPIC ABUNDANCE
C
254
2
12.OOoO 13.0034
0.98900 0.01 loo
H
377
2
1.0078 2.0141
0.99985 0.00015
N
65
2
14.003 1 15.0001
0.99630 0.00370
0
75
3
15.9949 16.9991 17.9992
0.99762 0.00038 0.00200
S
6
4
31.9721 32.9715 33.9679 35.967 1
0.95020 0.00750 0.042 10 0.00020
CALCULATED DATA: NOMINAL MASS = 5727 MONOISOTOPIC MASS = 5729.598 AVERAGE MASS = 5733.585 THRESHOLD = 0. ICKUKUIOE-2 TOTAL ABUNDANCE = 0.97975 10 MOST ABUNDANT PEAK = 573 1.605 MASS (MEAN) 5729.598 5730.598
573 1.602 5732.609 5733.609 5734.613 5735.609 5736.613 5737.617 5738.613 5739.62 1 5740.617
FRAC ABUN
PPM SPREAD
MULT
14.56 46.98 81.47 100.00 96.48 77.58 53.59 32.38 17.37 8.00 3.04 0.89
0.0 1.4 2.7 4.1 4.8 5.4 6.1 6.1 6.1 6.1 5.4 4.1
1 5 11 22 30 38 43 42 40 31 18 9
348 Plot PCsolUtlOn i 2500 Nominal
Plot re501ut1on = 5731
mE.5
Manosotoplc
nmss
90807060-
60 al ; 50
aI 50c” g 40-
8 5
40
30-
3 al 30 .s
.s
2o
= d
f%
IO-
: J
20 10
/
I
I
I,
I.
I
5730
I
I, 5735
m/z
I
, 5740
b30
mfz
4735
Fig. 2. Example of Gaussian distribution plots generated by program EXMASS insulin.
$740
for bovine
ACKNOWLEDGMENT
This work was supported by grants from the National Science Foundation, CHE-78 18396 and PCM-820 9954. REFERENCES 1 T. Matsuo, H. Matsuda and 1. Katakuse, Anal. Chem., 5 1 (1979) 133 1. 2 R.P. Lattimer, D.J. Harmon and G.E. Hansen, Anal. Chem., 52 (1980) 1808. 3 C. Fenselau, R. Cotter, G. Hansen, T. Chen and David Heller, J. Chromatogr., 218 (1981) 21. 4 A. Deli and H. Morris, Biochem. Biophys. Res. Cornmun., 106 (1982) 1456. 5 M. Barber, R.S. Bordoli, G.J. Elliott, R.D. Sedgwick, A.N. Tyler and B.N. Green, J. Chem. Sot., Chem. Commun., (1982) 936. 6 A.M. Buko, L.R. Phillips and B.A. Fraser, Biomed. Mass Spectrom., in press. 7 R.D. MacFarlane, Act. Chem. Res., (1982) 15. 8 J. Yergey, D. Heller, G. Hansen, R;J. Cotter and C. Fenselau, Anal. Chem., 55 (1983) 353. 9 J.L. Margrave and R.B. Polansky, J. Chem. Educ., 39 (1962) 335. 10 B. Boone, R.K. Mitchum and SE. Scheppele, Int. J. Mass Spectrom. Ion Phys., 5 (1970) 21. 1 I E. Hugentobler and J. Loliger, J. Chem. Educ., 49 (1972) 610. 12 B. Mattson and E. Carberry, J. Chem. Educ., 50 (1973) 511. 13 L.R. Crawford, Int. J. Mas Spectrom. Ion Phys., 10 (1972/3) 279. 14 Y.N. Sukharev, V.R. Sizoie and Y.S. Nekrasov, Org. Mass Spectrom., 16 (1981) 23. 15 M. Brownawell and J.S. Fillippo, Jr., J. Chem. Educ., 59 (1982) 663.
349 16 J.E. Campana, T.H. Risby and PC. Jurs, Anal. Chim. Acta, 112 (1979) 321. 17 A. Carrick and F. Glocking, J. Chem. Sot. A:, (1967) 40. 18 J-H. Beynon, Mass Spectrometry and Its Applications to Organic Chemistry, Elsevier, Amsterdam, 1960, p. 295. 19 K. Biemann, Mass Spectrometry Organic Chemical Applications, McGraw-Hill, New York, 1962, p. 59. 20 F.W. McLafferty, Interpretation of Mass Spectra, 3rd edn., University Science, Mill Valley, California, 1980, p_ 15. 21 R.E. Kirk, Introductory Statistics, Wadsworth, Belmont, California, 1978, p. 166.
and Ion Physics, 52 (1983)
337-349
337
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
A GENERAL APPROACH TO CALCULATING ISOTOPIC DISTRIBUTIONS FOR MASS SPECTROMETRY
JAMES A. YERGEY Middle Atlantic Mass Spectrometry Worfe Street, Baltimore, MD 21205
Fucidity, Johns Hopkins (U.S.A.)
School
of Medicine,
725 North
(Received 28 March 1983)
ABSTRACT Fundamental principles for obtaining mass spectral isotopic distributions are applied to a general computer program which can be used to calculate and present in tabular and graphic form the isotopic contributions for any molecular formula. A unique feature is the retention of the isotopic distribution, exact mass, and absolute abundance for all individual peaks at each mass. Special considerations have been made for the large number of isotopic combinations which occur for many higher mass compounds. The computer program accepts the input of a molecular formula followed by interactive input of a number of parameters which affect the final presentation of the theoretical distribution profile.
INTRODUCTION
Recent developments in desorption ionization techniques have stimulated growth in the mass spectrometric analysis of molecules with molecular weights between 1000 and 10000 daltons (middle molecules). Field desorption of polystyrene oligomers [l-3] as well as fast atom bombardment [4-61 and 252Cf plasma desorption [7] of bovine insulin are examples of recent progress in the field. In general, mass spectrometric techniques which are capable of analyzing middle molecules have focused upon obtaining molecular weight information for the molecules of interest. As molecular weight increases, molecular ion distributions of many compounds are no longer dominated by a single peak as observed at masses below 1000 daltons, but are complex distributions spread over many mass units 181. Abundances of monoisotopic mass ions become vanishingly low, and each peak at a given nominal mass contains numerous isotopic contributions whose separation requires a resolution better than 1 in lo6 [8]. The available algorithms describing the calculation of isotopic distributions for mass spectrometry which have been reported in the literature [9- 171 0020-7381/83/$03.00
0
1983
Elsevier Science Publishers B.V.
338
as well as the discussions included in mass spectrometry textbooks [ 18-201 have not addressed the representation of the complex distributions which occur in the middle molecule region. Earlier calculations were limited in their presentation of the data [9] or their ability to deal with the entire periodic table of elements [lo]. Most of the remaining algorithms El l- 161 allow for polyisotopic elements and present the calculated data as bar plots, but sum all of the contributing peaks at each nominal mass. Carrick and Glocking [ 171 describe a program especially designed for calculating distributions of organometallic compounds which retains the information about the individual peaks at each mass unit, but limits the molecules to five atoms each for three elements at most. The focus of this paper is the application of the fundamental principles for obtaining mass spectral isotopic distributions to a general computer program which can be used to calculate and present the isotopic contributions for any molecular formula, retaining the ,isotopic distribution, exact mass, and absolute abundance of all individual peaks at each mass. Special considerations have been made for the large number of isotopic combinations which occur for many higher mass compounds. The computer program accepts the input of a molecular formula followed by interactive input of a number of parameters which affect the final presentation of the theoretical distribution profile. PRINCIPLES
Mass spectral isotopic distributions can be calculated by expansion of a binomial expression for relatively small molecules or for molecules containing only elements with two isotopes. However, a rigorous treatment which can be applied to any molecular formula involves expansion of a polynomial expression. The isotopic distribution for a given molecule is described by the following product of polynomials 1151 ( a,+a,+a,+
. ..)m(b.+bz+b3...)“(cl+c,+c,+
. ..)“...
(1)
where a ,, a,, a3, etc., b,, b,, b,, etc., and c,, c2, c3, etc., represent the individual isotopes of the elements in the molecule, and the exponents m, n, o, etc., are the number of atoms of each element present in the molecule. The terms which result from the expansion of each polynomial can be used to describe the isotopic contributions, exact masses, and absolute abundances for each element’s contribution to the molecule. As an example, an expression describing all isotopic permutations of the m.w. = 3482) is given by pep tide molecule glucagon ( C , 53H,,,N,,O,,S, (12, + (32s
13q153(lH
+
33s
+2H)224(14N
+
34s
4
3%)
+
15~)42(16~
+
170
+
IS~)~O
(2)
339
If the polynomial for oxygen is expanded and the like terms collected, one where the coefficient is equal resulting term would be 58 000 160,,170,‘801, to the number of times the term appeared in the expansion. Like terms can be collected, in this application, since only the number distribution of the isotopes can be derived from a mass spectral peak, not the position of each isotope in the molecule. The contribution of each isotope is described by the subscripts of the expansion term. The exact mass (803.7585) and absolute abundance (1.518 X 10T3) for this permutation can be calculated from isotopic masses and relative abundances. It should be noted that preserving the isotopic contributions in the calculation permits the demonstration that another expansion term for the oxygen polynomial (1225 r60,,‘*0,) differs in mass by only 5 p.p.m. (803.7541) from the above example. The example also indicates that usually negligible isotopes such as I70 begin to have real contributions in the middle molecule mass range. Finally, this example illustrates the large number of permutations which occur when dealing with high mass compounds. If the product of polynomials in eqn. (2) are expanded with regard to the position of each atom there would be (2)153(2>224(2)42(3)50(4)1 = 3.9 X 10r5’ individual terms generated, which when collected to yield the like terms would still result in 7.9 X IO9 unique permutations. The large number of permutations generated for high mass compounds, coupled with the desire to preserve isotopic information concerning each permutation while including all isotopes in the calculation, necessitates that the program directly calculate only the unique permutations for each element. This is in contrast to calculation methods that expand each polynomial, followed by collection of like terms [9-163, which requires an excessive amount of computer time when applied to large molecules. An additional means of reducing the number of permutations and thereby the calculation time, is to stop the calculation of permutations for each element when all permutations having an absolute abundance greater than a user-defined threshold have been determined. Different means of applying the threshold can be understood by examining Table 1, which contains the first ten unique permutations generated by the expan$ion of the carbon polynomial ( ’ 2C + l3C) 153from eqn. (2). A commonly employed method to determine a threshold is to stop the calculation after a given number of permutations have been calculated [ 14,151. This method is satisfactory for small ,molecules containing elements whose most abundant isotope is also the lightest isotope, since the third or fourth peak in the distribution is almost always ( 1% of the first and most abundant peak. However, Table 1 illustrates that as the number of atoms of a given element becomes relatively large, the distribution shifts in a way that makes this method of determining a threshold invailid. A better method is to include only those permutations
34-o
TABLE
1
Distributions, abundances, and ‘*C 153 152 151 150 149 148 147 146 145
massesfor the first ten expansion terms of (“C+
13C 0
144
Absolute abundance
mass
0.18410 0.3 1327 0.2648 1 0.14825 0.06 183 0.02049 0.00562 0.00131 0.00027 0.00005
1836.000 1837.003 1838.007 1839.010 1840.013 1841.017 1842.020 1843.023 1844.027 1845.030
‘3C)‘53
Exact
whose abundance is greater than some absolute value. This method may also become invalid for higher molecular weight compounds, since there are so many permutations that the absolute abundance of even the most intense permutation can become very small (-c 0.01). Therefore, a threshold which can be applied to any molecular formula must be based on a percentage of the most abundant permutation’s absolute abundance; this method is used in the program described. The absolute value of the threshold will be based on the current permutation with the greatest abundance, and since the most abundant peak will usually change during the course of the calculation, the absolute value of the threshold will also change. The absolute abundances for each permutation can be described by the following combinational equation
(3) where n is the number of atoms of the element, rl, r,, I-~, etc., are the abundances of each isotope and a, b, c, etc., are the number distribution of the atoms in a given permutation [21]. Returning again to the example given for eqn. (2) of the expansion of the oxygen polynomial (I60 + I70 + 18O)5o of glucagon, it can now be shown that the absolute abundance of the 160,7’70,‘80, term is derived from the following equation (50)! A = (47)!(2)!(l)!
(r16)47tr17)2(r18)1
(4)
by substituting into eqn. (3) the number of atoms of oxygen (50) and the number distribution (47, 2, 1) of these atoms in this particular permutation.
341
Calculation of the ratio of factorials yields the coefficient of the expansion term, which is 58 000. The large number of atoms encountered in “middle molecules” requires an alternative approach to the calculation of each abundance since the large number of multiplication operations required by eqn. (3) for each abundance calculation would introduce serious computational errors, and require excessive calculation time. If the absolute abundance of any two permutations are divided by each other and the terms collected, the following equation is generated A
(4(b,)!(c,)!
_A
2-
.-*
’ (a,)!(b,)!(c,)!
. . .
)tc12-P,)(
(
pyc,,
p-y r2
r1
r3
.**
(5)
where subscripts denote the two different permutations. The program calculates the abundance of the first permutation using eqn. (3) and then proceeds by basing each subsequent abundance on that of the previous permutation, according to eqn. (5). The example in eqn. (4) would then be described by A
_-A 2-
’
(47)!(3)!(o)! (47)!(2)!(l)!
(
)(47--47)~
‘16
>“-“( r17
)(1--o) 118
(6)
or A2
=
3A1(57rh3)’
0)
which bases the abundance of the 160 4717021801 permutation ( A2) on that of the previous term 160d717O,‘“O, (A,). The total number of multiplication and division operations is greatly reduced using this formula, thereby reducing computational errors and saving substantial calculation time. ALGORITHMS The program which calculates and displays the molecular ion distributions consists of a main module (EXMASS) and four subroutines, which are outlined in the following paragraphs. PARAMETER statements at the beginning of each section of the program allow the operator to modify the common block array sizes easily, in order to accommodate vastly different types of molecules, e.g., polystyrene, II = 1000 (CS004H80,0), a large biomolecule such as insulin (C,,, H,,,N6507,S,), or an organometallic (Sn,C,,H,,), while still keeping the overall core requirement below 32K words. A molecular formula is input within subroutine DATAIN as elemental symbols which follow periodic table abbreviations, accompanied by the number of atoms of each element present in the molecule. The formula is decoded, and the exact mass and relative abundances of each isotope for elements in the formula are read from a disk file. The disk file presently
342
contains all naturally occurring isotopes of all stable elements, but can easily be modified to include isotopically-enriched species. An auxiliary program (UPDATE) is used to update information on the disk file which contains isotopic masses and abundances for each element. This routine can be used to input new elements, and to list, modify, or delete existing isotopic information, but must be run independently of program EXMASS. All unique permutations of each element are generated within subroutine PERMUT by a set of nine nested DO loops. The first permutation contains all atoms in the first isotope. The number of atoms in the first isotope are decremented and the remainder placed in the second isotope, forming a new permutation. The number in the second isotope is then decremented, placing the remainder in isotope three, etc. The loops are executed only to the level corresponding to one less than the number of isotopes for the element, therefore accommodating any element with ten or fewer isotopes. As each permutation is generated its absolute abundance is calculated and compared to the maximum abundance for that element. If the abundance is greater than the selected threshold, the isotopic distribution, absolute abundance, and exact mass of that permutation are saved. When appropriate, the maximum abundance for the element is also updated_ If too many permutations are generated for a particular element, as defined by PARAMETER MXPERM, subroutine RESET is used to reset the threshold, reduce the number of permutations, and inform the operator of the change in threshold. If no permutations are saved for a given number of atoms in the first isotope, any further decrementing of this number can only lead to permutations that will not be saved, and the calculation is therefore terminated. In subroutine FORMULA the permutations for each element are combined with the permutations for all other elements, generating complete molecular formulae. The permutations for the first element are saved as the initial combinations, and as the permutations for each successive element are completed they are combined with the existing combinations. This procedure accomplishes the multiplication of each successive polynomial described in eqn. (1) to complete the calculation of the isotopic distributions. Each combination is stored as a pointer to the isotopic distribution, or permutation, for each element, along with the exact mass and absolute abundance of the combination. The same threshold used in generating permutations is again applied to the combinations, and is reset, if necessary, according to the value of PARAMETER MXPEAK. After all elements have been permutated and combined into their final formulae, the combinations are ordered by increasing mass. The output of the program consists of two tables and a plot, which are generated within the main program module. The first table contains the isotopic distributions of each element for all combinations above threshold,’
343
along with the corresponding exact mass and absolute abundance. A second table summarizes the input data and calculated data, including nominal, monoisotopic, average, and most abundant masses. This table also includes a list of exact masses, relative abundances, p.p.m. spread, and multiplicity for integer mass groupings of the peaks in the first table. Finally, a plot is generated from a Gaussian distribution of the integer mass groupings. The resolution of the peaks in the plot is designated by the user, thereby allowing the user to compare more readily the distribution with experimental data. A bar plot is superimposed on the Gaussian distribution for clarity if the user-defined resolution is less than half the mass of the molecule. Program EXMASS and accompanying subroutines are written in FORTRAN IV, and consist of 1547 lines of code, including 805 comment statements. Most statements also contain an internal comment. Program UPDATE is also written in FORTRAN IV, and consist of 318 lines of code, of which 132 are comments. All disk I/O and dialog are accomplished by Data General RDOS FORTRAN cqmmands, which are readily converted to other operating systems. Dialog is designed for a Tektronix Model 4010 CRT, and output can be sent to either the CRT or to a hard copy device such as the Versatec Model 8OOA Printer/Plotter. Kratos DS-55 plot software is used in the present configuration but it can be readily exchanged for packages such as Tektronix Plot-10 software. The core size demanded varies with PARAMETER settings, but can operate in less than 32K words of core memory for most cases. RESULTS
An example of the dialog for executing the program is shown in Fig. 1. Note that, if desired, the program gives a complete introduction for each step of the dialog using bovine insulin as an example, and that default responses allow the operator to move through the dialog quickly and skip the extended table if desired. Tables 2 and 3 and Fig. 2 illustrate the output of the program for the same example. Only the first 16 peaks of the 290 peaks that were calculated and are usually presented, are included in Table 2. Note that Fig. 2 shows two plots, in order to illustrate the capability of the program to generate distributions at any user-selected plot resolution. Execution time depends on the number of elements, the number of isotopes per element, and the threshold selected, but typical examples include bovine insulin (&, H377N65075S), 30 s, and polystyrene n = 1000 lo-20 s is required to calculate the (C 8004 H,0,0)? 20 i. An additional Gaussian distribution for plotting. Documented listings of the program are available from the author. Individuals are also invited to correspond concerning “one-time” use of the program.
344 WELCOME
TO PROGRAM
EXMASS
THIS PROGRAM WAS DESIGNED TO ALLOW THE USER TO VISUALIZE THEORETICAL DISTRIBUTION PROFILES FOR ANY GIVEN MOLECULAR FORMULA. SPECIAL CONSIDERATIONS ARE MADE FOR THE LARGE NUMBER OF ISOTOPIC CONTRIBUTIONS WHICH OCCUR FOR MANY COMPOUNDS AT HIGHER MASSES. THE PROGRAM ACCEPTS THE INPUT OF A MOLECULAR FORMULA, FOLLOWED BY INTERACTIVE INPUT OF A NUMBER OF PARAMETERS WHICH AFFECT THE FINAL PRESENTATION OF THE THEORETICAL DISTRIBUTION PROFILE. DO YOU
DISIRE
A MORE
COMPLETE
INTRODUCTION
TO THE PROGRAM?
YES
THE PROGRAM WILL FIRST ASK YOU TO INPUT A MOLECULAR FORMULA. THE FORMULA MAY CONTAIN UP TO 9999 ATOMS OF ANY OF THE STABLE ELEMENTS OF THE PERIODIC TABLE. IT WILL CHECK TO ENSURE THAT THE FOLLOWING RULES ARE MET: 1) FIRST CHARACTER MUST BE A LETTER (ELEMENT NAME), 2) ELEMENT NAMES MUST BE TWO CHARACTERS OR SHORTER, FOLLOWING PERIODIC TABLE ABBREVIATIONS, 3) ANY NUMBER OF SINGLE SPACES MAY BE INCLUDED, BUT TWO IN ROW INDICATES THE END OF THE INPUT. TRY TO INPUT THE FORMULA FOR BOVINE INSULIN. TRY INCORRECTLY AT FIRST TO SEE THE RESPONSE *INPUT COMPOUNDS MOLECULAR FORMULA: 3CH2COOH
OF THE PROGRAM.
*INPUT ERRORS, *UNKNOWN ELEMENT. *MUST GIVE ELEMENT SYMBOL FIRST. *ELEMENT MUST HAVE LESS THAN 3 LETTERS. TRY AGAIN, THE FORMULA IS C254 H377 N65 075 S6. *INPUT COMPOUNDS C254H377N65075S6
MOLECULAR
FORMULA:
THE PROGRAM MUST LIMIT THE NUMBER OF POSSIBLE PERMUTATIONS FOR MANY COMPOUNDS, AND THEREFORE REQUESTS A THRESHOLD (5%OF THE BASE PEAK) TO BE USED AS A CUTOFF. THRESHOLD MUST BE > 0 and -z 100 OR IT WILL DEFAULT TO 1 E-10. TRY A THRESHOLD OF O.OL FOR THIS EXAMPLE. *INPUT 0.01
THRESHOLD
AS % OF BASE PEAK:
THE PROGRAM NOW COMPLETES IT CALCULATIONS OF THE THEORETICAL DISTRIBUTIONS, WHICH MAY REQUIRE A MEASURABLE AMOUNT OF TIME, AND MAY REQUIRE RESETTING THE THRESHOLD IF TOO MANY PERMUTATIONS ARE GENERATED, AS IN THIS EXAMPLE. NOTE THAT THE PROGRAM WILL INFORM YOU IF THIS IS NECESSARY; *TOO
MANY
PEAKS,
THRESHOLD
RESET TO 0.9999 E-3
AFTER COMPLETING THE CALCULATIONS, THE PROGRAM WILL ASK QUESTIONS CONCERNING THE DESIRED OUTPUT FORMAT. THE FIRST QUESTION IS WHETHER YOU WANT TO SEE THE ISOTOPIC DISTRIBUTIONS FOR EACH
345 ABOVE THRESHOLD PERMUTATION, OR GO ON TO THE TABLE OF PEAKS EACH INTEGER MASS AND THE PLOT. FOR THIS EXAMPLE REPLY “YES’ SIMPLY ” Y”. *OUTPUT’ YES
ISOTOPIC
DISTRIBUTIONS
FOR ALL
AT OR
PEAKS?
NEXT THE PROGRAM REQUESTS THE REPORT DEVICE: $VDU FOR THE CRT, WHICH IS THE DEFAULT DEVICE, OR $PPL FOR THE VERSATEC PRINTER/ PLOTTER. FOR THIS EXAMPLE REPLY WITH “$VDU” OR A CARRIAGE RETURN. *REPORT $VDU PLOT UNIT TION
DEVICE
RESOLUTION RESOLUTION OF 2500.
*PLOT 2500 LASTLY, *TITLE: BOVINE
IS SELECTED (10% VALLEY),
AT THIS POINT. THE DEFAULT BUT FOR THIS EXAMPLE TRY
VALUE IS A RESOLU-
RESOLUTION: THE PROGRAM INSULIN,
ASKS FOR A TITLE
FOR THE TABLES
AND
PLOT.
C254 H377 N65 075 S6
THE PROGRAM NOW OUTPUTS A TABLE OF EACH ABOVE THRESHOLD PEAK. FOR EACH PEAK, EVERY ELEMENT IS PRESENTED ALONGSIDE ITS ISOTOPIC DISTRIBUTION IN THAT PEAK. THE MASS AND ABSOLUTE ABUNDANCE ARE ALSO GIVEN FOR EACH PEAK. (See Table 2) THE FOLLOWiNG TABLE CONTAINS BOTH THE INPUT DATA AND A SUMMARY OF THE CALCULATED DATA, INCLUDING INTEGER MASS GROUPINGS OF THE PEAKS PRESENTED IN THE PREVIOUS TABLE. (See Table 3) FINALLY, A PLOT WILL BE GENERATED USING A GAUSSIAN DISTRIBUTION OF THE INTEGER MASS GROUPINGS OF THE PEAKS. NOTE THAT THE PROGRAM REQUESTS PATIENCE WHILE CALCULATING THE GAUSSIAN DISTRIBUTION. NOTE ALSO THAT A BAR PLOT IS GENERATED UNDER THE GAUSSIAN DISTRIBUTION. THE PROGRAM DOES THIS IN ALL CASES WHERE THE PLOT RESOLUTION IS LOW WHEN COMPARED TO THE MASS, MAKING IT DIFFICULT TO VISUALIZE THE INDIVIDUAL PEAKS. (See Figure 2) NOTE:
I) User responses are underlined_ 2) Only the text indicated by an asterisk (*) is output if a complete introduction is not requested.
Fig. 1. Example of dialog for program EXMASS
with extended introduction_
346 TABLE
2
Isotopic
distributions,
exact masses and absolute
bovine insulin molecular BOVINE PEAK
INSULIN,
NO.
abundances
of first 16 peaks for theoretical
ion envelope
C254 H377 N65 075
S6.
I : EXACT
MASS
= 5729.598
ABSOLUTE
ABUNDANCE
= 0_2753779E-
12C,,,1Hj,714N I40 PEAK NO. 2: E&C;
32s, MASS
= 5730.598
ABSOLUTE
ABUNDANCE
= 0.1304 147E- 1
= 5730.598
ABSOLUTE
ABUNDANCE
= 0.6647344E-2
MASS = 5730.602 “0 32S
ABSOLUTE
ABUNDANCE
= 0.7866999E-3
2 5730.602
ABSOLUTE
ABUNDANCE
= 0.7779628E-
= 5730.605
ABSOLUTE
ABUNDANCE
= O.l557495E-2
= 5731.594
ABSOLUTE
ABUNDANCE
= 0.73206 13E-2
ABSOLUTE
ABUNDANCE
= 0_789979OE-3
ABSOLUTE
ABUNDANCE
= 0.3148122E-3
ABSOLUTE
ABUNDANCE
= O.l87795OE-
ABSOLUTE
ABUNDANCE
= 0.4140522E-2
= 5731.602
ABSOLUTE
ABUNDANCE
= O.l899039E-3
= 5731.602
ABSOLUTE
ABUNDANCE
= 0.3759686E-3
ABSOLUTE
ABUNDANCE
= 0.36843 12E-2
ABSOLUTE
ABUNDANCE
= 0.2222484E-2
ABSOLUTE
ABUNDANCE
= 0.1094576
12C2~41H377’4N65’607~32S~33S1 PEAK NO. 3: EXACT MASS 12C,~~‘H~,7’4N~4’5N,‘60,532S6 PEAK NO. 4: EXACT ‘2C2541H377’4N I60 PEAK 12’253
NO. 5 : &AC? b&S ‘3C,‘H37714N65’607,3zS~
PEAK
NO.
12C,,4’H PEAK
6: EXACT
MASS
1
1
37a2H,14N65’607532S6 NO.
7: EXACT
MASS
12C2541H377’4N65’607532S~34SI PEAK NO. 8: EXACT MASS = 573 1.594 14Ns3’5N2160,532S6 12C,,,‘H 377 PEAK NO. 9: EXACT MASS = 5731.598 12C2,4~H377’4N~4’5N,160,532S533S, PEAK NO. IO: EXACT MASS = 5731.598 13C,‘H~7714Ns4’5N,‘607532S6 12c253 PEAK NO. 11: EXACT MASS = 5 73 1.602
1
12C2541H377’4N65160,4’80,32S6 PEAK NO. 12: EXACT MASS 12C2541H3,,‘4N64’5N,‘60,4170,32SG PEAK NO. 13: EXACT MASS
12C254’H376~H1’4N6415N1’607532S6 PEAK NO. 14: EXACT MASS = 573 1.602 ‘2c253
PEAK
13C1’H377’4N651607532S533S, NO.
15: EXACT
MASS
= 573 I .605
‘2C~j~13C,‘H37714N~5160,4170,32S~ PEAK NO. 16: EXACT MASS = 5731.605 ‘2C,,,
‘3C2’H37714N65’60,532S~
347 TABLE
3
Summary of input and calculated data for bovine insulin BOVINE INSULIN, INPUT DATA:
Czs4 H 377N65075 s,
ELEMENT
#ATOMS
#ISOTOPES
ISOTOPIC MASS
ISOTOPIC ABUNDANCE
C
254
2
12.OOoO 13.0034
0.98900 0.01 loo
H
377
2
1.0078 2.0141
0.99985 0.00015
N
65
2
14.003 1 15.0001
0.99630 0.00370
0
75
3
15.9949 16.9991 17.9992
0.99762 0.00038 0.00200
S
6
4
31.9721 32.9715 33.9679 35.967 1
0.95020 0.00750 0.042 10 0.00020
CALCULATED DATA: NOMINAL MASS = 5727 MONOISOTOPIC MASS = 5729.598 AVERAGE MASS = 5733.585 THRESHOLD = 0. ICKUKUIOE-2 TOTAL ABUNDANCE = 0.97975 10 MOST ABUNDANT PEAK = 573 1.605 MASS (MEAN) 5729.598 5730.598
573 1.602 5732.609 5733.609 5734.613 5735.609 5736.613 5737.617 5738.613 5739.62 1 5740.617
FRAC ABUN
PPM SPREAD
MULT
14.56 46.98 81.47 100.00 96.48 77.58 53.59 32.38 17.37 8.00 3.04 0.89
0.0 1.4 2.7 4.1 4.8 5.4 6.1 6.1 6.1 6.1 5.4 4.1
1 5 11 22 30 38 43 42 40 31 18 9
348 Plot PCsolUtlOn i 2500 Nominal
Plot re501ut1on = 5731
mE.5
Manosotoplc
nmss
90807060-
60 al ; 50
aI 50c” g 40-
8 5
40
30-
3 al 30 .s
.s
2o
= d
f%
IO-
: J
20 10
/
I
I
I,
I.
I
5730
I
I, 5735
m/z
I
, 5740
b30
mfz
4735
Fig. 2. Example of Gaussian distribution plots generated by program EXMASS insulin.
$740
for bovine
ACKNOWLEDGMENT
This work was supported by grants from the National Science Foundation, CHE-78 18396 and PCM-820 9954. REFERENCES 1 T. Matsuo, H. Matsuda and 1. Katakuse, Anal. Chem., 5 1 (1979) 133 1. 2 R.P. Lattimer, D.J. Harmon and G.E. Hansen, Anal. Chem., 52 (1980) 1808. 3 C. Fenselau, R. Cotter, G. Hansen, T. Chen and David Heller, J. Chromatogr., 218 (1981) 21. 4 A. Deli and H. Morris, Biochem. Biophys. Res. Cornmun., 106 (1982) 1456. 5 M. Barber, R.S. Bordoli, G.J. Elliott, R.D. Sedgwick, A.N. Tyler and B.N. Green, J. Chem. Sot., Chem. Commun., (1982) 936. 6 A.M. Buko, L.R. Phillips and B.A. Fraser, Biomed. Mass Spectrom., in press. 7 R.D. MacFarlane, Act. Chem. Res., (1982) 15. 8 J. Yergey, D. Heller, G. Hansen, R;J. Cotter and C. Fenselau, Anal. Chem., 55 (1983) 353. 9 J.L. Margrave and R.B. Polansky, J. Chem. Educ., 39 (1962) 335. 10 B. Boone, R.K. Mitchum and SE. Scheppele, Int. J. Mass Spectrom. Ion Phys., 5 (1970) 21. 1 I E. Hugentobler and J. Loliger, J. Chem. Educ., 49 (1972) 610. 12 B. Mattson and E. Carberry, J. Chem. Educ., 50 (1973) 511. 13 L.R. Crawford, Int. J. Mas Spectrom. Ion Phys., 10 (1972/3) 279. 14 Y.N. Sukharev, V.R. Sizoie and Y.S. Nekrasov, Org. Mass Spectrom., 16 (1981) 23. 15 M. Brownawell and J.S. Fillippo, Jr., J. Chem. Educ., 59 (1982) 663.
349 16 J.E. Campana, T.H. Risby and PC. Jurs, Anal. Chim. Acta, 112 (1979) 321. 17 A. Carrick and F. Glocking, J. Chem. Sot. A:, (1967) 40. 18 J-H. Beynon, Mass Spectrometry and Its Applications to Organic Chemistry, Elsevier, Amsterdam, 1960, p. 295. 19 K. Biemann, Mass Spectrometry Organic Chemical Applications, McGraw-Hill, New York, 1962, p. 59. 20 F.W. McLafferty, Interpretation of Mass Spectra, 3rd edn., University Science, Mill Valley, California, 1980, p_ 15. 21 R.E. Kirk, Introductory Statistics, Wadsworth, Belmont, California, 1978, p. 166.