TABLES AND AN ALGORITHM FOR CALCULATING FUNCTIONAL GROUPS OF ORGANIC

MOLECULES IN HIGH RESOLUTION MASS SPECTROMETRY

Joshua Lederberg
Professor of Genetics
School of Medicine
Stanford University

STAR (Scientific and Technical Aerospace Reports)

No. N6N -2)}4 26

Submitted April 1, 1964 to NASA as an interim report under Grant No,
NsG 81-60, "Cytochemical studies of planetary microorganisms",
 

TABLES AND AN ALGORITHM FOR CALCULATING FUNCTIONAL GROUPS OF ORGANIC
MOLECULES IN HIGH RESOLUTION MASS SPECTROMETRY

Joshua Lederberg
Stanford University

Introduction

The pioneering work of Beynon! has demonstrated the salient power
of high resolution mass spectrometry for the structural analysis of organic
molecules. Instruments with resolution capabilities of 1 part in 10,000
to 100,000 are becoming commercially available, There remains the problem
of computing the molecular composition from_the experimentally found mass.
Tables for this purpose have been published® but are necessarily limited in
scope by the sheer number of possible combinations.

On the atomic mass scale 12¢ 2 12,00000, the fractional mass is
attributable exclusively to the non-carbon part of a molecule, so these
parts can be tabulated separately and much more compactly than complete
tables of composition, Such tables have been computed over the range of

H from 0 to 124, N from 0 to 6 and O from 0 to 11, and published elsewhere?
to make them generally accessible.

An alternative approach was also generated, which gives even more

compact tables and an algorithm more suitable for computer-oriented analysis,
and is presented here,

The CHy=14 Algorithm

 

Where molecules in homologous series are in question, or the
investigator has a definite combination of functional groups in mind, the
CH2=14 algorithm will more than justify some additional arithmetic on the
part of the specialized user. Furthermore, its tables are even more com-
pact: roughly speaking, where an independent variable of the C=l2 system
is the number of H atoms, plausibly from 0 to 124, in the CHj=14 system
we use degrees of unsaturation from 0 to 30. This permits us to encompass
most molecules and radicals, N from 0 to 8 and © from 0 to 13 in Table 2.
In addition, the entries appear in an order related to the complexity of
the molecule. The topmost, simpler areas of the tables may become quite
familiar with extensive use, since e.g. alkanes, monocarboxylic acids,

dicarboxylic acids, monoketones, etc, each have a singular location in the
tables,

The logic of extracting the formula by division and examining the
remainder is similar to that of the C#=12 system, However, as Kendrick
has pointed out, using CHo as a base relates the formula to the structural

 
)
:
.
|
.
:
4
:
:
:

 

2.

concept of a fundamental hydrocarbon, with functional substituents, Instead
of taking C, H, 0, N as the variables, we take a formula as Terminal H +

CH), Cz, 0, NH

parts, i.e. saturated carbons, double bonds, oxygen, and amino-functions.
For computational purposes, -N= is regarded as -NH=- +C:, -CH»-CH=N- is
treated as BO ae’ This leads to a mathematical fiction in treating

molecules which have more double bonds than C atoms. "Double bonds" includes
rings (equivalent to one double bond each) and -C=C= functions (equivalent to
two C:), i.e. C: can be read as "degrees of unsaturation" together with an
equal number of C atoms.

In principle we can implement this scheme of extracting the CH part
by shifting to a mass scale 12cHy = 14,.00000, and then dividing by 14.
This would be done by multiplying the found mass by 0,99888337 =
(14,00000/14,01565),. We would then tabulate the mass defect, the amount
by which the decimal value falls short of an integral mass number, There
will be a characteristic defect on this scale for every class of organic
compound, A few classes of compounds exemplified by ethane, ethyl radical,
and ethylamine have a mass excess, i.e. negative defect, -.01339, ~.00669
and ~,00753 respectively; i.e. their masses are 30.01339, 29,00669 and
43,00753, respectively, when expressed on the CH,=14 scale, while higher
monologues with n additional CH, groups will be precisely 14n larger, In
these cases their functional groups fail to overbalance the mass excess of
the two terminal hydrogens of the basic structure, Alkenes, Coons will
have a defect of zero,

Other functional groups will have equally characteristic mass defects,
simply the sum of the contribution of each part (see Table 3).

In actual computation the multiplier .99888 is clumsy and inefficient,
Where m = exact mass on ““scale, it is better to take m (0,99888337) =
m~.00111663m, especially as the factor can usually be truncated, and only
the decimal corrections need be kept in hand, This will be readily seen in
working through the examples, Table 1 calculates the correction from the
integer part of the mass (with reasonable precision for most purposes) so
the only arithmetic actually needed is to subtract the entry of Table 1
from the observed mass, and use the difference in scanning the main table
(Table 2) °

Terminal H numbers 2 for complete molecules, 1 for radicals, the
latter being signified by * in the table,

Example. An alkaloid analysed to contain about N, and Og to Og
returned a mass reading of 718.37430 + ,00600.

Quotient Residue Decimal
1, From Table 1, 718,37430 = 51 (x 14) + 4 + » 37430
2. Calculate m (1-0,00111663), From Table 1:

718 — 30174"
637430 ——> 37430

Defect 42744 + 600

 
OE ORE EE

 

3.

(*The table gives the value for the integer 718. A more precise
measure of the defect by interpolation or direct multiplication
would be 80216 - 37430 = 42786; with practice, the interpolation
can be done by eye if necessary.)

3. From Table 2, integer residue class 4, the following entries are within
the range 42144 - 43344 and are intact molecules (not*);

 

 

Defect Cz NH 0 =(CH),
42192 17 8 7 31
42325 12 4 11 27
42378 30 6 0 32
42511 25 2 4 28
42727 8 6 13 28
42779 26 8 2 33
42912 21 4 6 29
43045 16 0 10 25
43314 17 6 8 30

Of these, only 42912 satisfies the compositional requirements with
respect to N and O, It may be interpreted as follows:

2H + 21C: + 4NH + 60 + (51-29) # 22CHo

Extensions

The proper extent of the tables is a compromise between the bulk
and cost of a larger table as against the effort of additional arithmetic.
The most frequent extension may be in the range of NH, here limited to 8.
If so indicated, 9NH can be extracted from the experimental mass by sub-
tracting 135,09809; the entries in the table will then correspond to NH
from 9 to 17 in place of 0 to 8.

Further extended versions of the tables can be computed if their
utility warrants. Alternatively, other special cases can be handled with
the present tables with some additional arithmetic. If additional atoms
are suspected, their weights should simply be subtracted from the mass
numbers found, Eeg.s, if monochloro compounds are in question the corres-
ponding dichloro radicals are formed by subtracting 35¢1 or 3%c1,

The tables are presented to 5 significant figures, which is an
optimistic projection of instrumental capacity. The Sth digit is subject
to rounding error of computation, The values refer to the mass of the
neutral molecule rather than the positive ion, as the mass of neutral
reference molecules is usually set down in calibrating the mass spectrometer,

Constants

The constants used in the computation are (on the 12¢ scale):
H = 1,00782522, N = 14,003074, 0 = 15.994915, They are taken from the
IUPAC report.

 

 
 

4.
Acknowledgments

These tables represent an exercise in the application of computers
to biochemical problems. Research connected with this program has been
supported by grants from the National Aeronautics and Space Administration
(NsG 81-60), National Science Foundation (NSF G-6411), and National
Institutes of Health (NB-04270-01 and 02, and AI-5160-06). I am grateful
to Professor Carl Djerassi for having challenged the computer to generate
the extended tables, to which the present algorithms are a rebuttal.

The programs were run under the Subalgol monitor on the IBM 7090
at Stanford University Computation Center, whose assistance to academic
research is supported by an NSF grant (NSF=GP948). I am indebted to the
staff of the Computation Center for their unstinting cooperation and to
Mrs, Margaret Wightman for skilled and loyal assistance.

The actual operation of these programs required about one second
of main frame computer time per page of tabular output.

References

1. J. He. Beynon, Mass Spectrometry and Its Applications to Organic

Chemistry, Elsevier, Amsterdam, 1960,

2, J. H. Beynon and A. E, Williams, Mass and Abundance Tables for Use
in Mass Spectrometry, Elsevier, Amsterdam, 1963.

3. J. Lederberg, The Computation of Molecular Formulas for Mass
Spectrometry, Holden-Day, San Francisco, 1964,

4, Prior to the completion of this report a similar proposal was
enunciated by E. Kendrick, A mass scale based on CH5 = 14,0000 for
high resolution mass spectrometry of organic compounds, Analytical
Chemistry 35:2146, 1963, His implementation, oriented towards
petroleum constituents, is substantially different, but the under-
lying concept closely anticipates the present scheme.

5, A, E, Cameron and E. Wichers, Report of the International Commission

E
on Atomic Weights (1961), Journal of the American Chemical Society,
84: 4175, 1962.

  
 

BALGOL PROGRAM

For Computation of Tables of Mass Defects by Composition

2 MIN3000 LEDERBERG MASSCORRECTIONS.».14 ALGORITHM

STANFORD UNIVERSITY COMPILER -- VERSION OF 1/27/64

144.46 COMMENT### OUTPUT ON TAPE $

*-SYMBOL

#-SPACE
144.464 COMMENT##* OUTPUT ON TAPE 648$
144.24. INTEGER OTHERWISES
144.66 GLOBAL INTEGER COLUMNS$
144.006 ARRAY A(2000%10)$
144e«+ PROCEDURE COLGUT(LINESsCOLS $ VAR:V1sV2sV3 $ OUT,FORM) $
156006 BEGIN INTEGER OTHERWISE $ SL = V2sLINES $
161... M = (CGLS-1)SL + VL $ COLUMNS = COLS $ SM = SL + V1 — V2 $
lTbess COMMENT WRITES MIN( LINES*COLS » (V34V2-V1)/V2 ) OUTS $
2OT eee FOR I = (VleV2_sSM) $ BEGIN
213006 UNTIL M LEQ V3 $ (M = M-SL $ COLUMNS = COLUMNS~1) $
224ea0 WRITE($$0, FORM) $ M = M + V2 END $
233000 RETURN $ OUTPUT O(FOR VAR=(1I,SL»M) $ OUT())
25be0% END COLOUT() §
304.e. PROCEDURE COLIST{COLS $ I411,12,13 $ OUT, FORM) $
316... BEGIN INTEGER OTHERWISE $
31l6ee- J = 60 COLS.12 $
322e06 FOR K = (Il, Js 13) & COLOUT{60,COLS $ IsKsl2s13 $ OUT,FORM) $
35leae RETURN END COLIST{) $
372ee6 PROCEDURE SORTS(FILL»N » VALUES() » KEY()) $

#-PRINT

#PRINT
664ee6 FOR I=(Lsl,1000)$A(1,9)=1$
T0500 FOR M=(0,1,13)$ BEGIN

T4a2ece FUNCTION CR(D)=134000D + 58626NH +2294540 ~ 67000HR$
T5leece 1=0%

T52ece FOR D=(0,1,30)$

T6306 FOR NH =(071,8)$%

TTbese (( HR=-MOD{(M+NH,2)$

1011... { O = MOD{ M + 1398 + 2D — HR — NHe14)/2 ) ) $

L025ee6 FOR 0=0,0+7$(

1053... SUM = 12D + 15 NH + 160 + 2 + HR$

1055.66 J=L$ [=141$ FOR A(T sJ)=CRID) sDyNHeOsHReSUM/14$ J=J+1))$
LL62.e6 ILIM=I1$%

1164... SORTS(OsILIMs A029) 2Ale1))$

LL77... [LIM = MINLILIM,540)$

1204.06 COLIST(3$ KslelsILIM$ SOMEsNUMBERS)$

L214e06 ENDS

L215... OCUTPUT SOME(FOR I=A(K,9)$ FOR HR=A(1,5) $((ACT,1)-133950)/100,
1270... FOR J = 2239476 $ AlIeJIdIIS

1302.04 FORMAT NUMBERS ( $COLUMNS $(B69L57 By 213» 149 B, $—-HRS( #8) sS1tHRS(* *)5
134lece 13) 2W)$

134lee6 FINISHS

 

 

 

:
c
:
 

¥19T0°
zELot’
g0€9T°
89890°
647€90°
68280"
T2240"
97610"
TO?vT’
LO6TT*
LYZET’
78890"

02040°
7¥SS0°

647720"
cL1S0°
€z0S0°
T8820°
68S540°
00000°
66220°
GS600°
£S$200°-
69900°
6EETO"=

we

Ed

N
ec

Nr nwsnowwrwrnrnrnwonwo own wo Oo

aNNOdNOD dO ssv19
LOaigd SSWW dNdIsaa

suoyfqouny etdwts jo (aT#IsS »t=°HO) Sqoajoq sseR

Z900°OZ
91%26° 18
L1976°62
TLELE “LE
89916°SE
26786°8S
T8S00 °C?
O60TO"L7
8€196°L6
97716°18
£6916°L6

G6€000* 29
0S6990° 74
SYEL90'°76
087S00°7¢
6LE9TO*T9
CLL86°CE
7991720° SY
0847S00° 94
OETEO* 82
GS9SOT0°OE
G9SOTO'8T
6769720°LT
ZSZ8200°T
c9STO'Z

aH
24H

19H

LOH

10H
SNOH
ONOH
NOH
Yosty
fostn
Yoaty
fo0¢H
9999

£ (Ho) SHED
2oty
HOOO°HN
s¢H
CHNOOH
HOOOH
eyo=CHD
o¢HO
o°H

fuN

-H

Cy

ATVOS Z71=97_ dNNOdhOd
ASVA OL NOTINGINLINOD OL NOLLAGTYINOD

SSVW

*paqernotes Aysnoqzasid punoduos e Jo voTzeqinjizsd sazItTppe sey

€8¢20°
TOVLT*
LL69T°
L£€SZo°
8TOZO°
8c680°
06840"
S6S70"
OySST°
9YCET*
98ST"
£2280°

6SES0°
£8890"
88S40°
71S90°
£9€90°
O0@Z470°
876S0°
6€€T0"
VEIEO*

76220"
98S00°

69900°

Loadgad SSVW

°€ ®LqeL

S a
ot 24 18
g 3G 6L
8 TO LE
9 10 SE
t SNO
EL OND
Il NO
zt £oso
OT £os
ZI foo
4 0090
g- =D4
9 o£
¥ 0¢
€ OODHN
y S
1 HNOOD
Z 009
Z- =)-
0 O=D
z 0
I HN
I- -H
“HZ

3NdISHa WAOTINI anouo

TWNOILONNA

 

ANTYON TA

aq Inoud

AdInNOds

aadTYOTHD

da TYOTHO
aLVNVAOOTHL
GLVNVAD

TITYLIN

YUaALSA ALVATAS
dIOV OINOATAS
UALSA ITYOHdSOHd
GIOV AXOUCAH
aNAZNAT

TOTaL—

IOId~

QIOV ONINV
UHHLEOLHL 29 ‘TOTHL~
da Inv

aqIov OT0-

ONTY 20 ANd~
"IONA- 20 AZNO- 10 'IV-
YaHLA 120 ‘10-
ANIKV-

(TVOIGVa) ‘TANV-
aNV=

aWVN