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Molecular Connectivity: Treatment of the Electronic Structure of Amino Acids
October 1992 Volume 81, Number 10
JOURNAL OF PHARMACEUTICAL SCIENCES A publication of the American Pharmaceutical Assodation
ARTICLES
Molecular Connectivity: Treatment of the Electronic Structure of Amino Acids LIONELLO POGLIANI Received July 23, 1991, from the Dip8rtimento di Chimica, Universith della Calabria, 87030 Rend8 (CS), kaly. February 6, 1992. Ab8tmct 0 A molecular connectivity model of atomic charges on the second-row atoms in a-amino acids is discussed. A correlation was found between the valence delta (sy) index from molecular connectivity theory and the charges on atoms that belong to the same class, whereas
different classes of carbon atoms had the same slopes on the 0versus a" matrix, where 0 is the calculated charge distribution. A similar correlation was found for nucleotide bases.
Much effort in the realm of structur*activity work has been made in correlating activity with measured bulk molecular properties1 of nonionizable molecules. A QSAR (quantitative structure-activity relationship)model of the isoelectricpoints of amino acids has been presented.2 A correlation between connectivity indexes and isoelectric points is appropriate, because this bulk property (i.e., isoelectric point) depends highly on the presence of ionizable groups in the molecule.2 Most of the receptor maps rely strongly on localized charge patterns that mirror the supposed distribution in the molecule to be bound; therefore an effort to correlate activity with measured charges on particular atoms of a molecule would be highly rewarding. The problem is that charge distributions in an entire class of pharmacological molecules are largely unknown and normally have to be estimated from resonance structures and from electronegativities of particular atoms. Years ago, Del Re et al.3 presented a systematic study of the electronic structure of a-amino acids. Despite many crude approximations of the theoretical treatment, that study led to the determination of charge distributions that permitted a fairly quantitative interpretation of the proton chemical shifta of the amino acids. This paper presents a molecular connectivity model of the atomic charges in amino acids. Molecular connectivity indexes to encode electronic charges in alkanes calculated by the second version of the method of complete neglect of differential overlap (CNDOI2) have already been developed with very high precision.4 Also, a novel representation developed from chemical graph theory, the electrotopological state, has been successful in encoding computed oxygen partial charges (and their corresponding 00223549/92/1 oOa-0967$02.50/0 0 1992, Americ8n Pharmaceutical Association
Accepted for publication
1 7 0 chemical shiftd.6 The aims of this work were to find correlations between charges in amino acids and the 6 indexes from molecular connectivity theory and to extend the understanding of the two specific indexes, 6 and 8" (see Theoretical Section for definitions of 6 indexes).
Theoretical Section Two cardinal numbers developed by Kier and Hall1.6 within the context of molecular connectivity were used in this study: the delta ( 6 ) index and the valence delta (6") index. The 6 index (6 = u - h; where u is the sigma orbital and h is the number of hydrogen ions suppressed) represents the nonhydrogen, sigma-bonded electrons contributed by an atom in a molecule (i.e., 6 is the number of bonded neighbors other than hydrogens). The 6' index (6'' =' 2 - h = 0 + p + n - h; where 2" is the number of valence electrons, and u,p, and n are orbitals) represents the nonhydrogen valence electrons participating in CT,p, and n (lone-pair) orbitals on each atom in a molecule.
ResuIts Calculated charge distributions (QI; where I is C, N, or 0) of the different second-row atoms in the neutral forms of the a-amino acids from Del Re's works are given with the corresponding 6" values in Table I. Data in Table I can be condensed and more easily interpreted if the atomic charges are considered to be 20% accurate. Such an error is satisfacQ tory because of the crude approximations used to derive : (the power of nuclear magnetic resonance spectrometers in the 1960sdid not allow a precise analysis of the proton spectra of many amino acids), the lack of more recent data on the subject, and the limits of our purpose. Table II shows the second-rowatoms of the a-amino acids on a QIversus 6 (Q1lSv) matrix, where QIis -20% accurate (some crude correlations are emphasized by straight lines). The slopes of all correlations have the same sign, and many correlations also have nearly the same slopes. The most significant correlations are those linking (1)NH,, NH, and N, with slope (s)= 0.2; (2) C, (terminal carbon) and the different Ci (internal carbon) Journal of Pharmaceutic8l Sciences I 987 Vol. 81, No. 10, October 1992
Table CDlrMbutlon of Electronk Charges ( 0 , .IOOO) and 8’ In Neutral Forms of Amlno Acldr QJ6Y for: u-Amino Acid
c,
CS
IS0
312 4713 4413 4513 4413
-11011 -2113 -6912 -2313
Phe
4413
- 7512
4413
-7512
Trp
4613
-82/2
His
4513
-6812
Pro
3713
-6812
Ser
6013
Thr
5713
Asp
4813
Glu
4513
-6412
Asn
4713
- 5712
Gln
4513
-6512
LYS
4513
-6812
-7612
Arg
4513
-6612
-6712
-22/2
CYS
52/3
Met
4713
-8712 -6711 (S)” -5712
-35914 (NH) 22914 ((2‘)” -52513 (NH,),” -25114 (NH)
-8812
-4811 (S)‘
- 13511
GlY
Ala Val Leu
4012 -45615 (OH)” 8813 -46015 (OH)” -5412
-11911 -2813 -7412 -11911S lZ4’ -3113’ -3113’ -3113’ lZ4’ -2913’ - 1 813’ - 1 4314’ -47115 (OH)’ 2114’ 1114’ -3113’ -3113’ -3013’ -2513’ 7314’ -26714 (NH)d 3813’ 9014’ 3613’ -13415 (N)’ 9913’ -26914 (NH)O -6812
- 12011 -11911
-2112 -35814 (NH)”
- 10711
26414 (V)” - 12716 (0)” - 45715 (OH) -62/2
”
26514 (Co)” -12816 (0)” -45815 (OH)”
21014 (Co)” -13416 (0)” -52713 (NH,)” -6512
21 114 (Co)”
- 1 3516 (0)” -52813 (NH2)” -6812
-la2
- 53013 (NH4”
’
The QJSV values for COOH group are Co,272/4;0, -1 2716;and OH, -45615;for the NH, group, QJ6Y is -53013. Values refer to carbon atoms on the aromatic ring. Values refer to OH bonded to aromatic ring. Value refers to NH on heterocyclic ring. ’Values refer to carbon atoms on the imidazole ring. ‘Value refers to N on the imidazole ring. Value refers to NH on the imidazole ring. Values refer to the atom or group in parentheses that Is linked to or is a substituent of the reference carbon atom (CB,Cy,Cg,or C,). ’ The sulfur atom bridges two carbon groups.
”
atoms, with s = 0.05; (3) the different C atoms bonded to an NH function, with s = 0.05; and (4) the different C atoms bonded to an OH function, with an average s = 0.05. The two
links C, carbons can be extended to include C” and c”‘ carbons (solid and dotted lines in Table 11).
smallest correlations (those made up of only two different points in the Q,IF matrix) are those concerning the C, atoms, with s = 0.05, and the OH and 0 groups, with s = 0.4. If a value of 7 for (6” + 8) is assigned to a c” (and c”’)atom (C”is the carboxyl carbon, and c”’is the carbon of the guanidinium p u p of arginine), then the correlation, with s = 0.05, that
Discussion
968I Journal of Pharmaceutical Sciences Vol. 81, No. 10, October 1992
For nine valence states of second-row atoms, electronegativity is some function of 6 - 8.6 Atomic charge distributions of the second-rowatoms in a-amino acids, however, show only a crude correlation with 6;therefore, charge distribution in
TIM. Il-0' w m ~ 8 6v Matrix for Second-Row Atoms In a-Amino Acldr QI / 6"
2
1
4
3
5
6
-.500
-.310 -.120
-.071
\
-. 0 2 5
CISHI ci
-.012
CIYHzl
,003 .016 .037
.051 .084
.1 4 0 .240
\
C,
\\ \ \
Ca
CIW,NH)
C(0H 1 /F ( N )
i'
C( NH )
\C(OH, C'/C"
amino acids can be better encoded by an index that represents all valence electrons, including sigma electrons (6= a + p + n - h1.6 The only exception is for the C"carbon. This terminal carbon bonded to two highly electronegative atoms is a special case, and ita highly positive charge can be fairly well correlated with the C, charges (assuming a r index value of 7; r = 6 + 6). Because a similar sum succeeded in encoding the Bondi atomic volumea,B C" may be considered as a special atom with a cardinal number of r. Despite the low n values of our correlations, the similar s values of the correlations of the different classes of carbon atoms in amino acids is striking, and the different s values of the correlations of the heteroatoma is easily explained by their different electronegativities.
Charge values of the dipolar forms of the amino acids3 show consistent QI changes at the oxygens of the COO- function (-0.62) and at the nitrogens of the -NH,+ and -NH2+functions (0.13 and 0.35,respectively), other changes being negligible. The first nitrogen has a 6 value of 1,and we could aasign it the same QI value as that of C,, with a positive sign (0.12),because ammonium is positively charged. The second nitrogen has a 6 value of 2, and because the correlation among nitrogens has an s value of -0.2 (see Results), the charge a t this nitrogen should be -0.32,in good accord with the calculated charges. Changes in QI at the oxygen atoms cannot be 80 easily explained. The 6 index encodes fairly well information about partial electronic charges in u-amino acids. The qualitative predictability of the electronic charges determined by this index is practically encoded by its definition in the context of the molecular connectivity theory. In fact, this index encodes information about all nonhydrogen valence electrons. Therefore, changes in the value of 6 must reflect changes in electronic density in a series of homonuclear atoms other than hydrogen. Changes in the intercept on the ordinate along the different series of homonuclear a t o m can be explained in terms of differences in electronegativities. To emphasize these conclusions, the QIvalues of uracyl, cytosine, adenine, and guanine bases7 are given below. Amino acids and nucleotide bases are quite different molecules in their structure, substitution, and conjugation patterns and in the required calculations. Nevertheless, the Q I / 6 patterns of these bases are analogous to the QI/Sv patterns of a-amino acids: 6YN) = 5 shows a QI of --0.150 & 0.03,6(C")= 7 shows a QIof 0.250 f 0.020,G[C(NH)I= 4 shows a QI of 0.100 f 0.04,G[C(NH)I = 3 shows a QI of 0.0602 0.02, and 6(Ci) = 3 shows a Q1of -0.04 2 0.01. The =O group, typically with a 6 value of 6, shows a QI of -0.39 2 0.03(i.e., a QIvalue that would fit a 6v value of 5.5; see Table 11).In view of the resonance structures of the bases, a 6 value of 5.5 for the resonating group =O -OH is not inconsistent.
-
References and Notes 1. Kier, L. B.; Hall, L. H. Molecular Connectiui in Structure Activity Analysis; Wiley: Letchworth, U.K., 1 9 8 pp 43-101. 2. Poaliani. L. J . Phurm. Sci. 1992.81, 33-36. 3. Dei Re, G.; Pullman, B.; Yonezawa, T. Biochim. Biophys. Actu 1963.75, 153-182. 4. Hall, L. H.; Kier, L. B. Tetmhedmn 1977, 33, 1963-1967. 5. Hall, L. H.; Mohney, B.; Kier, L. B. J . Chem. Zf. Comput. Sci. 1991,31, 76-82. 6. Kier, L. B.; Hall, L. H. J . Phurm. Sci. 1981, 70, 683-689. 7. Ladik, J.; Appel, K. Theor. Chim. Acta 1966,4, 132-138.
Journal of PhannaceuHcel SciencesI @69 Vol. 81, No. 10. October 1992
JOURNAL OF PHARMACEUTICAL SCIENCES A publication of the American Pharmaceutical Assodation
ARTICLES
Molecular Connectivity: Treatment of the Electronic Structure of Amino Acids LIONELLO POGLIANI Received July 23, 1991, from the Dip8rtimento di Chimica, Universith della Calabria, 87030 Rend8 (CS), kaly. February 6, 1992. Ab8tmct 0 A molecular connectivity model of atomic charges on the second-row atoms in a-amino acids is discussed. A correlation was found between the valence delta (sy) index from molecular connectivity theory and the charges on atoms that belong to the same class, whereas
different classes of carbon atoms had the same slopes on the 0versus a" matrix, where 0 is the calculated charge distribution. A similar correlation was found for nucleotide bases.
Much effort in the realm of structur*activity work has been made in correlating activity with measured bulk molecular properties1 of nonionizable molecules. A QSAR (quantitative structure-activity relationship)model of the isoelectricpoints of amino acids has been presented.2 A correlation between connectivity indexes and isoelectric points is appropriate, because this bulk property (i.e., isoelectric point) depends highly on the presence of ionizable groups in the molecule.2 Most of the receptor maps rely strongly on localized charge patterns that mirror the supposed distribution in the molecule to be bound; therefore an effort to correlate activity with measured charges on particular atoms of a molecule would be highly rewarding. The problem is that charge distributions in an entire class of pharmacological molecules are largely unknown and normally have to be estimated from resonance structures and from electronegativities of particular atoms. Years ago, Del Re et al.3 presented a systematic study of the electronic structure of a-amino acids. Despite many crude approximations of the theoretical treatment, that study led to the determination of charge distributions that permitted a fairly quantitative interpretation of the proton chemical shifta of the amino acids. This paper presents a molecular connectivity model of the atomic charges in amino acids. Molecular connectivity indexes to encode electronic charges in alkanes calculated by the second version of the method of complete neglect of differential overlap (CNDOI2) have already been developed with very high precision.4 Also, a novel representation developed from chemical graph theory, the electrotopological state, has been successful in encoding computed oxygen partial charges (and their corresponding 00223549/92/1 oOa-0967$02.50/0 0 1992, Americ8n Pharmaceutical Association
Accepted for publication
1 7 0 chemical shiftd.6 The aims of this work were to find correlations between charges in amino acids and the 6 indexes from molecular connectivity theory and to extend the understanding of the two specific indexes, 6 and 8" (see Theoretical Section for definitions of 6 indexes).
Theoretical Section Two cardinal numbers developed by Kier and Hall1.6 within the context of molecular connectivity were used in this study: the delta ( 6 ) index and the valence delta (6") index. The 6 index (6 = u - h; where u is the sigma orbital and h is the number of hydrogen ions suppressed) represents the nonhydrogen, sigma-bonded electrons contributed by an atom in a molecule (i.e., 6 is the number of bonded neighbors other than hydrogens). The 6' index (6'' =' 2 - h = 0 + p + n - h; where 2" is the number of valence electrons, and u,p, and n are orbitals) represents the nonhydrogen valence electrons participating in CT,p, and n (lone-pair) orbitals on each atom in a molecule.
ResuIts Calculated charge distributions (QI; where I is C, N, or 0) of the different second-row atoms in the neutral forms of the a-amino acids from Del Re's works are given with the corresponding 6" values in Table I. Data in Table I can be condensed and more easily interpreted if the atomic charges are considered to be 20% accurate. Such an error is satisfacQ tory because of the crude approximations used to derive : (the power of nuclear magnetic resonance spectrometers in the 1960sdid not allow a precise analysis of the proton spectra of many amino acids), the lack of more recent data on the subject, and the limits of our purpose. Table II shows the second-rowatoms of the a-amino acids on a QIversus 6 (Q1lSv) matrix, where QIis -20% accurate (some crude correlations are emphasized by straight lines). The slopes of all correlations have the same sign, and many correlations also have nearly the same slopes. The most significant correlations are those linking (1)NH,, NH, and N, with slope (s)= 0.2; (2) C, (terminal carbon) and the different Ci (internal carbon) Journal of Pharmaceutic8l Sciences I 987 Vol. 81, No. 10, October 1992
Table CDlrMbutlon of Electronk Charges ( 0 , .IOOO) and 8’ In Neutral Forms of Amlno Acldr QJ6Y for: u-Amino Acid
c,
CS
IS0
312 4713 4413 4513 4413
-11011 -2113 -6912 -2313
Phe
4413
- 7512
4413
-7512
Trp
4613
-82/2
His
4513
-6812
Pro
3713
-6812
Ser
6013
Thr
5713
Asp
4813
Glu
4513
-6412
Asn
4713
- 5712
Gln
4513
-6512
LYS
4513
-6812
-7612
Arg
4513
-6612
-6712
-22/2
CYS
52/3
Met
4713
-8712 -6711 (S)” -5712
-35914 (NH) 22914 ((2‘)” -52513 (NH,),” -25114 (NH)
-8812
-4811 (S)‘
- 13511
GlY
Ala Val Leu
4012 -45615 (OH)” 8813 -46015 (OH)” -5412
-11911 -2813 -7412 -11911S lZ4’ -3113’ -3113’ -3113’ lZ4’ -2913’ - 1 813’ - 1 4314’ -47115 (OH)’ 2114’ 1114’ -3113’ -3113’ -3013’ -2513’ 7314’ -26714 (NH)d 3813’ 9014’ 3613’ -13415 (N)’ 9913’ -26914 (NH)O -6812
- 12011 -11911
-2112 -35814 (NH)”
- 10711
26414 (V)” - 12716 (0)” - 45715 (OH) -62/2
”
26514 (Co)” -12816 (0)” -45815 (OH)”
21014 (Co)” -13416 (0)” -52713 (NH,)” -6512
21 114 (Co)”
- 1 3516 (0)” -52813 (NH2)” -6812
-la2
- 53013 (NH4”
’
The QJSV values for COOH group are Co,272/4;0, -1 2716;and OH, -45615;for the NH, group, QJ6Y is -53013. Values refer to carbon atoms on the aromatic ring. Values refer to OH bonded to aromatic ring. Value refers to NH on heterocyclic ring. ’Values refer to carbon atoms on the imidazole ring. ‘Value refers to N on the imidazole ring. Value refers to NH on the imidazole ring. Values refer to the atom or group in parentheses that Is linked to or is a substituent of the reference carbon atom (CB,Cy,Cg,or C,). ’ The sulfur atom bridges two carbon groups.
”
atoms, with s = 0.05; (3) the different C atoms bonded to an NH function, with s = 0.05; and (4) the different C atoms bonded to an OH function, with an average s = 0.05. The two
links C, carbons can be extended to include C” and c”‘ carbons (solid and dotted lines in Table 11).
smallest correlations (those made up of only two different points in the Q,IF matrix) are those concerning the C, atoms, with s = 0.05, and the OH and 0 groups, with s = 0.4. If a value of 7 for (6” + 8) is assigned to a c” (and c”’)atom (C”is the carboxyl carbon, and c”’is the carbon of the guanidinium p u p of arginine), then the correlation, with s = 0.05, that
Discussion
968I Journal of Pharmaceutical Sciences Vol. 81, No. 10, October 1992
For nine valence states of second-row atoms, electronegativity is some function of 6 - 8.6 Atomic charge distributions of the second-rowatoms in a-amino acids, however, show only a crude correlation with 6;therefore, charge distribution in
TIM. Il-0' w m ~ 8 6v Matrix for Second-Row Atoms In a-Amino Acldr QI / 6"
2
1
4
3
5
6
-.500
-.310 -.120
-.071
\
-. 0 2 5
CISHI ci
-.012
CIYHzl
,003 .016 .037
.051 .084
.1 4 0 .240
\
C,
\\ \ \
Ca
CIW,NH)
C(0H 1 /F ( N )
i'
C( NH )
\C(OH, C'/C"
amino acids can be better encoded by an index that represents all valence electrons, including sigma electrons (6= a + p + n - h1.6 The only exception is for the C"carbon. This terminal carbon bonded to two highly electronegative atoms is a special case, and ita highly positive charge can be fairly well correlated with the C, charges (assuming a r index value of 7; r = 6 + 6). Because a similar sum succeeded in encoding the Bondi atomic volumea,B C" may be considered as a special atom with a cardinal number of r. Despite the low n values of our correlations, the similar s values of the correlations of the different classes of carbon atoms in amino acids is striking, and the different s values of the correlations of the heteroatoma is easily explained by their different electronegativities.
Charge values of the dipolar forms of the amino acids3 show consistent QI changes at the oxygens of the COO- function (-0.62) and at the nitrogens of the -NH,+ and -NH2+functions (0.13 and 0.35,respectively), other changes being negligible. The first nitrogen has a 6 value of 1,and we could aasign it the same QI value as that of C,, with a positive sign (0.12),because ammonium is positively charged. The second nitrogen has a 6 value of 2, and because the correlation among nitrogens has an s value of -0.2 (see Results), the charge a t this nitrogen should be -0.32,in good accord with the calculated charges. Changes in QI at the oxygen atoms cannot be 80 easily explained. The 6 index encodes fairly well information about partial electronic charges in u-amino acids. The qualitative predictability of the electronic charges determined by this index is practically encoded by its definition in the context of the molecular connectivity theory. In fact, this index encodes information about all nonhydrogen valence electrons. Therefore, changes in the value of 6 must reflect changes in electronic density in a series of homonuclear atoms other than hydrogen. Changes in the intercept on the ordinate along the different series of homonuclear a t o m can be explained in terms of differences in electronegativities. To emphasize these conclusions, the QIvalues of uracyl, cytosine, adenine, and guanine bases7 are given below. Amino acids and nucleotide bases are quite different molecules in their structure, substitution, and conjugation patterns and in the required calculations. Nevertheless, the Q I / 6 patterns of these bases are analogous to the QI/Sv patterns of a-amino acids: 6YN) = 5 shows a QI of --0.150 & 0.03,6(C")= 7 shows a QIof 0.250 f 0.020,G[C(NH)I= 4 shows a QI of 0.100 f 0.04,G[C(NH)I = 3 shows a QI of 0.0602 0.02, and 6(Ci) = 3 shows a Q1of -0.04 2 0.01. The =O group, typically with a 6 value of 6, shows a QI of -0.39 2 0.03(i.e., a QIvalue that would fit a 6v value of 5.5; see Table 11).In view of the resonance structures of the bases, a 6 value of 5.5 for the resonating group =O -OH is not inconsistent.
-
References and Notes 1. Kier, L. B.; Hall, L. H. Molecular Connectiui in Structure Activity Analysis; Wiley: Letchworth, U.K., 1 9 8 pp 43-101. 2. Poaliani. L. J . Phurm. Sci. 1992.81, 33-36. 3. Dei Re, G.; Pullman, B.; Yonezawa, T. Biochim. Biophys. Actu 1963.75, 153-182. 4. Hall, L. H.; Kier, L. B. Tetmhedmn 1977, 33, 1963-1967. 5. Hall, L. H.; Mohney, B.; Kier, L. B. J . Chem. Zf. Comput. Sci. 1991,31, 76-82. 6. Kier, L. B.; Hall, L. H. J . Phurm. Sci. 1981, 70, 683-689. 7. Ladik, J.; Appel, K. Theor. Chim. Acta 1966,4, 132-138.
Journal of PhannaceuHcel SciencesI @69 Vol. 81, No. 10. October 1992