International Journal of Mass Spectrometry and Ion Physics, 52 (1983) 337-349

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

337

A GENERAL APPROACH TO CALCULATING ISOTOPIC DISTRIBUTIONS FOR MASS SPECTROMETRY

JAMES A. YERGEY

Middle Atlantic Mass Spectrometry Fucidity, Johns Hopkins School of Medicine, 725 North

Worfe Street, Baltimore, MD 21205 (U.S.A.)

(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 combina- tions 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 desorp- tion 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 molecu- lar weight information for the molecules of interest. As molecular weight increases, molecular ion distributions of many com-

pounds 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 contribu- tions whose separation requires a resolution better than 1 in lo6 [8].

The available algorithms describing the calculation of isotopic distribu- tions 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 distri- butions 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 contribu- tions 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 combina- tions 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 contain- ing 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 pep tide molecule glucagon ( C , 5 3 H,,,N,,O,,S, m.w. = 3482) is given by

(12, + 13q153(lH +2H)224(14N + 15~)42(16~ + 170 + IS~)~O

(32s + 33s + 34s 4 3%) (2)

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If the polynomial for oxygen is expanded and the like terms collected, one resulting term would be 58 000 160,,170,‘801, where the coefficient is equal 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 ele- ment. This is in contrast to calculation methods that expand each poly- nomial, 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 ( ’ 2 C + l3 C) 153 from 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 masses for the first ten expansion terms of (“C+ ‘3C)‘53

‘*C 13C Absolute Exact abundance mass

153 0 0.18410 1836.000 152 151 150 149 148 147 146 145 144

0.3 1327 1837.003 0.2648 1 1838.007 0.14825 1839.010 0.06 183 1840.013 0.02049 1841.017 0.00562 1842.020 0.00131 1843.023 0.00027 1844.027 0.00005 1845.030

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

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.

(4)

Calculation of the ratio term, which is 58 000.

The large number of

341

of factorials yields the coefficient of the expansion

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 exces- sive 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 _A

2- (4(b,)!(c,)! .-* ( )tc12-P,)( p-y pyc,,

’ (a,)!(b,)!(c,)! . . . r1 r2 r3 .** (5)

where subscripts denote the two different permutations. The program calcu- lates 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 (47)!(3)!(o)! ( 2-

’ (47)!(2)!(l)! ‘16 )(47--47)~

r17 >“-“(

118 )(1--o)

or

A2 = 3A1(57rh3)’

(6)

0) which bases the abundance of the 160 4717021801 permutation ( A2) on that of the previous term 160d717 O,‘“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 biomole- cule 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

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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 permuta- tions 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 permuta- tions that will not be saved, and the calculation is therefore terminated.

In subroutine FORMULA the permutations for each element are com- bined 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 permuta- tion, 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,’

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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 FOR- TRAN 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 soft- ware 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

(C 8004 H,0,0)? 20 i. An additional lo-20 s is required to calculate the Gaussian distribution for plotting.

Documented listings of the program are available from the author. Indi- viduals are also invited to correspond concerning “one-time” use of the program.

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WELCOME TO PROGRAM EXMASS

THIS PROGRAM WAS DESIGNED TO ALLOW THE USER TO VISUALIZE THEO- RETICAL DISTRIBUTION PROFILES FOR ANY GIVEN MOLECULAR FORMULA. SPECIAL CONSIDERATIONS ARE MADE FOR THE LARGE NUMBER OF ISO- TOPIC 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 OF THE PROGRAM. *INPUT COMPOUNDS MOLECULAR FORMULA: 3CH2COOH

*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 MOLECULAR FORMULA: C254H377N65075S6

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 THRESHOLD AS % OF BASE PEAK: 0.01

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 PERMUTA- TIONS 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 QUES- TIONS CONCERNING THE DESIRED OUTPUT FORMAT. THE FIRST QUESTION IS WHETHER YOU WANT TO SEE THE ISOTOPIC DISTRIBUTIONS FOR EACH

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ABOVE THRESHOLD PERMUTATION, OR GO ON TO THE TABLE OF PEAKS AT EACH INTEGER MASS AND THE PLOT. FOR THIS EXAMPLE REPLY “YES’ OR SIMPLY ” Y”.

*OUTPUT’ ISOTOPIC DISTRIBUTIONS FOR ALL PEAKS? YES

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 DEVICE $VDU

PLOT RESOLUTION IS SELECTED AT THIS POINT. THE DEFAULT VALUE IS UNIT RESOLUTION (10% VALLEY), BUT FOR THIS EXAMPLE TRY A RESOLU- TION OF 2500.

*PLOT RESOLUTION: 2500

LASTLY, THE PROGRAM ASKS FOR A TITLE FOR THE TABLES AND PLOT.

*TITLE: BOVINE INSULIN, 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 PRO- GRAM REQUESTS PATIENCE WHILE CALCULATING THE GAUSSIAN DISTRIBU- TION. 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_

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TABLE 2

Isotopic distributions, exact masses and absolute abundances of first 16 peaks for theoretical

bovine insulin molecular ion envelope

BOVINE INSULIN, C254 H377 N65 075 S6.

PEAK NO. I : EXACT MASS = 5729.598

12C,,,1Hj,714N I40 32s, PEAK NO. 2: E&C; MASS = 5730.598

12C2~41H377’4N65’607~32S~33S1

PEAK NO. 3: EXACT MASS = 5730.598

12C,~~‘H~,7’4N~4’5N,‘60,532S6

PEAK NO. 4: EXACT MASS = 5730.602

‘2C2541H377’4N I60 “0 32S

PEAK NO. 5 : &AC? b&S 2 5730.602

12’253 ‘3C,‘H37714N65’607,3zS~

PEAK NO. 6: EXACT MASS = 5730.605

12C,,4’H 37a2H,14N65’607532S6

PEAK NO. 7: EXACT MASS = 5731.594

12C2541H377’4N65’607532S~34SI

PEAK NO. 8: EXACT MASS = 573 1.594

12C,,,‘H 377 14Ns3’5N2160,532S6

PEAK NO. 9: EXACT MASS = 5731.598

12C2,4~H377’4N~4’5N,160,532S533S, PEAK NO. IO: EXACT MASS = 5731.598

12c253 13C,‘H~7714Ns4’5N,‘607532S6

PEAK NO. 11: EXACT MASS = 5 73 1.602

12C2541H377’4N65160,4’80,32S6

PEAK NO. 12: EXACT MASS = 5731.602

12C2541H3,,‘4N64’5N,‘60,4170,32SG

PEAK NO. 13: EXACT MASS = 5731.602

12C254’H376~H1’4N6415N1’607532S6

PEAK NO. 14: EXACT MASS = 573 1.602

‘2c253 13C1’H377’4N651607532S533S,

PEAK 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~

ABSOLUTE ABUNDANCE = 0_2753779E- 1

ABSOLUTE ABUNDANCE = 0.1304 147E- 1

ABSOLUTE ABUNDANCE = 0.6647344E-2

ABSOLUTE ABUNDANCE = 0.7866999E-3

ABSOLUTE ABUNDANCE = 0.7779628E- 1

ABSOLUTE ABUNDANCE = O.l557495E-2

ABSOLUTE ABUNDANCE = 0.73206 13E-2

ABSOLUTE ABUNDANCE = 0_789979OE-3

ABSOLUTE ABUNDANCE = 0.3148122E-3

ABSOLUTE ABUNDANCE = O.l87795OE- 1

ABSOLUTE ABUNDANCE = 0.4140522E-2

ABSOLUTE ABUNDANCE = O.l899039E-3

ABSOLUTE ABUNDANCE = 0.3759686E-3

ABSOLUTE ABUNDANCE = 0.36843 12E-2

ABSOLUTE ABUNDANCE = 0.2222484E-2

ABSOLUTE ABUNDANCE = 0.1094576

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TABLE 3

Summary of input and calculated data for bovine insulin

BOVINE INSULIN, Czs4 H 377N65075 s, INPUT DATA:

ELEMENT #ATOMS #ISOTOPES ISOTOPIC MASS

ISOTOPIC ABUNDANCE

C 254 2 12.OOoO 0.98900 13.0034 0.01 loo

H 377 2 1.0078 0.99985 2.0141 0.00015

N 65 2 14.003 1 0.99630 15.0001 0.00370

0 75 3 15.9949 0.99762 16.9991 0.00038 17.9992 0.00200

S 6 4 31.9721 0.95020 32.9715 0.00750 33.9679 0.042 10 35.967 1 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)

FRAC ABUN

PPM SPREAD

MULT

5729.598 14.56 0.0 1 5730.598 46.98 1.4 5 573 1.602 81.47 2.7 11 5732.609 100.00 4.1 22 5733.609 96.48 4.8 30 5734.613 77.58 5.4 38 5735.609 53.59 6.1 43 5736.613 32.38 6.1 42 5737.617 17.37 6.1 40 5738.613 8.00 6.1 31 5739.62 1 3.04 5.4 18 5740.617 0.89 4.1 9

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Plot PCsolUtlOn i 2500 Plot re501ut1on = 5731 Nominal mE.5

Manosotoplc nmss

90-

80-

70-

60-

aI 50- c” g 40-

: 30-

J

.s 2o

f% IO-

/ I I I, I. I I I, I ,

5730 5735 5740

m/z

60

al ; 50

8 5 40

3 al 30

.s

= d

20

10

b30 4735 $740 mfz

Fig. 2. Example of Gaussian distribution plots generated by program EXMASS for bovine insulin.

ACKNOWLEDGMENT

This work was supported by grants from the National Science Founda- tion, CHE-78 18396 and PCM-820 9954.

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