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Low-lying energy levels of amino acids and its implications for origin of life
Journal of Molecular Structure: THEOCHEM 756 (2005) 109–112 www.elsevier.com/locate/theochem
Low-lying energy levels of amino acids and its implications for origin of life Hong-Fang Ji, Liang Shen, Hong-Yu Zhang * Shandong Provincial Research Center for Bioinformatic Engineering and Technique, Center for Advanced Study, Shandong University of Technology, Zibo 255049, People’s Republic of China Received 5 July 2005; revised 11 August 2005; accepted 2 September 2005
Abstract A major challenge in understanding the origins of life is to elucidate how nature selects a small part of molecules from a large number of candidates as building blocks of life, e.g. amino acids and proteins. Inspired by the thermodynamic principle in protein-structure selection, we attempted to explore whether there exists a thermodynamic criterion to differentiate amino acids from their isomers. In this letter, the energies of 20 natural amino acid and corresponding isomers are calculated by quantum chemical methods. It is revealed that the energy levels of amino acids (especially small ones) are not distributed randomly but located at the bottom of the energy diagrams of their isomers, suggesting that thermodynamic factor plays an important role in selecting the basic building blocks of life. q 2005 Elsevier B.V. All rights reserved. Keywords: Amino acid; Energy; Origin of life; Quantum chemical calculation; Thermodynamics
1. Introduction
2. Methods
Origins and evolution of life is one of the most intriguing subjects in life sciences [1]. A major challenge in this area is to understand how nature selects limited building blocks of life, such as 20 amino acids and w1000 protein folds [2], from hundreds of thousands of candidates. Employing a simple lattice model of protein folding, Li et al. [3] revealed a thermodynamic principle in protein-structure selection. That is, nature tends to use thermodynamically stable proteins and proteins with stable-against-mutation structures (which can be characterized by designability) to constitute organisms. However, it is still elusive why nature chooses amino acids as starting points of life, because each amino acid corresponds to tens to thousands of isomers. The thermodynamic principle in protein structure selection arouses our interest to explore whether there exists a thermodynamic criterion for the amino acid selection by calculating the energies of 20 amino acids and corresponding isomers.
The isomers corresponding to each amino acid were collected by searching in CrossFire Beilstein database, which contains more than 9 million molecules available naturally or synthetically and is the World most comprehensive database of organic chemistry for compounds, reactions, properties and citations [4]. Totally, 8813 isomers (including different conformations of one isomer) were gathered and the intramolecular hydrogen bond (IHB) was taken into account to give the most stable conformation. Especially, double IHBs in a-amino acids were considered to reach the most stable conformation [5,6]. 8813 molecules were firstly optimized by semiempirical quantum chemical method AM1 [7] in vacuo to elicit a preliminary energy profile. Then, a part of the molecules (595 totally) were optimized by density functional theory (DFT) with B3LYP functional [8,9] on 6-31CG(d) basis set at 298.15 K and solvent (water) effect was considered by employing the self-consistent reaction field (SCRF) method with polarized continuum model (PCM) [10– 12]. During the in-solvent calculation, the zwitterions of all molecules were taken into account. All of the calculations were performed using Gaussian-98 program package [13].
* Corresponding author. Tel.: C86 533 278 0271; fax: C86 533 278 0271. E-mail address: [email protected] (H.-Y. Zhang).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.09.001
3. Results and discussion The AM1- and B3LYP/6-31GG(d)-derived energy diagrams are illustrated in Fig. 1. It is interesting to find that the
110
H.-F. Ji et al. / Journal of Molecular Structure: THEOCHEM 756 (2005) 109–112
Fig. 1. Energy levels of amino acids (in red) and their isomers. (a) AM1 results; (b) B3LYP/6-31CG(d) results with solvent (water) effect.
energies of amino acids (especially small amino acids) are not distributed randomly in the energy diagrams, but are located at the bottom of the energy levels (Fig. 1), indicating that thermostability is indeed an important factor to differentiate these basic building blocks from their isomers, not only in gas phase but also in water solution. As energy has to be injected (by sparking or discharge) into the vessel when synthesizing amino acids prebiotically [14], it is natural to speculate that the energies of amino acids should be rather high. But the present calculation reveals that the relative energies of amino acids are actually very low, which may result from the IHBs in parent amino acids and their zwitterions [15]. Although thermostability has been considered as an important factor in the selection of building blocks of life [16], our finding provides the first theoretical evidence to support the notion. More interestingly, there is likely a correlation between the relative energies of amino acids and their weights. That is, small amino acids, such as Gly, Ala, Ser, Thr, Glu, have low relative energies, while large amino acids, such as Arg, Trp, Tyr, Phe, His, possess relatively high energies (Fig. 1). As the entropy contributes little to the free energy, the low energy of a molecule means its high abundance among their isomers, provided that the thermodynamic equilibrium can be reached. This implies that large amino acids have less chance to occur spontaneously than the small ones, which is in line with the fact that Arg, Lys and His are more difficult to be synthesized than others [17]. Therefore, small amino acids were preferred to construct life at the beginning of origin of life, which agrees well with Wong’s proposal that amino acids emerged on the earth at different stages, Gly, Ala, Ser, Asp, Pro, Thr, Val and Glu occurring early, while His, Met, Lys, Phe, Tyr, Arg and Trp being biosynthesized later [18]. This discovery is also helpful to understanding the striking similarity between the products and the relative abundances of amino acids in Miller’s soup and Murchison meteorite [14,16]. Although DFT calculation cannot distinguish the energy difference between L- and D-amino acids (Tables 1 and 2), the calculation reveals that some nonnatural amino acids, such as b-amino acids, methyl-amino acids and N-alkyl-amino acids,
are less stable than the natural counterparts by several kcal/mol (Tables 1 and 2), regardless of in vacuo or in solvent. This finding suggests that these nonnatural amino acids are less abundant than the normal counterparts in the early stages of chemical evolution, which provides a complementary explanation to the interesting question: why these nonnatural amino acids were not employed by nature to construct organisms [16]? As revealed recently, life itself does not exclude nonnatural amino acids [19], which means that nonnatural amino acids are as efficient as the normal ones in building life. However, organisms just employ 20 natural amino acids as major building blocks. A reasonable explanation is that some (especially small) natural amino acids were indeed ubiquitous and easy-to-be-taken in the prebiotic world, due to their low energies. Our finding places some constraints on the basic life composition, which is of significance in predicting some primary features of life that consists of elements different from ours. For instance, silicon has been considered as a potential substituent of carbon to build life [20]. Thus, here comes an interesting question: does the silicon-based life use the building blocks similar to the carbon-based organisms? To address this question, we employed AM1 method to calculate the energies of silicon-based amino acids and corresponding isomers, which were constructed on the basis of carbon-based counterparts. It is interesting to note that most of the silicon-containing amino acids have rather high relative energies (Fig. 2), which likely results from the different orbital-hybridization- and bonding properties between carbon and silicon. This suggests that nature unlikely selects amino-acid-like structures to build silicon-based life. Therefore, if silicon-based life really exists somewhere in the universe, it will be much different from the carbon-based ones. 4. Conclusion Thermostability likely plays an important role in differentiating natural amino acids (especially small ones) from their isomers, which suggests that nature tends to use low-energy
Table 1 B3LYP/6-31CG(d)-calculated in vacuo relative energies (in kcal/mol) of natural amino acids (a-L-amino acids) and corresponding nonnatural isomers (a-D-amino acids, b-amino acids, a-methyl-amino acids and N-alkyl-amino acids) Gly
Asp
Glu
Lys
Pro
Gln
Asn
Cys
Ser
Thr
a-La-Dba-methylN-alkylAmino acidsa a-La-Dba-methylN-alkyl-
0.0 – – – – Ala 0.0 0.0 1.2 – 6.6
0.0 0.0 – 2.4 8.3 Val 0.0 0.1 – 7.1 7.8
0.0 0.0 0.9 2.5 10.2 Leu 0.0 0.0 K1.1 3.9 5.2
0.0 0.2 0.1 5.4 – Ile 0.0 0.0 – – –
0.0 1.9a – – – Arg 0.0 0.0 – – –
0.0 0.0 0.3 5.8 8.5 Met 0.0 0.0 – 0.1 4.9
0.0 0.1 0.4 2.8 4.1 Tyr 0.0 0.2 0.6 – –
0.0 0.0 –0.9 – – Phe 0.0 0.1 0.7 – –
0.0 0.0 – – 3.6 Trp 0.0 0.0 0.4 – –
0.0 0.0 – 1.2 1.8 His 0.0 0.0 – –
a
The higher energy results from the sterically hindered conformation of a-D-Pro.
Table 2 B3LYP/6-31CG(d)-calculated in-water relative energies (in kcal/mol) of natural amino acids (a-L-amino acids) and corresponding nonnatural isomers (a-D-amino acids, b-amino acids, a-methyl-amino acids and Nalkyl-amino acids), in which zwitterions forms are considered Amino acids
Gly
Asp
Glu
Lys
Pro
Gln
Asn
Cys
Ser
Thr
a-La-Dba-methylN-alkylAmino acidsa a-La-Dba-methylN-alkyl-
0.0 – – – – Ala 0.0 0.0 1.7 – 6.7
0.0 0.0 – 3.2 9.8 Val 0.0 0.0 – 4.5 6.2
0.0 0.0 0.8 3.5 4.2 Leu 0.0 0.0 0.5 2.4 3.5
0.0 0.2 0.9 2.6 – Ile 0.0 0.0 – – –
0.0 0.7a – – – Arg 0.0 0.2 – – –
0.0 0.1 0.1 1.8 1.9 Met 0.0 0.1 – 1.1 1.0
0.0 0.2 0.7 8.5 11.5 Tyr 0.0 0.0 0.2 – –
0.0 0.0 0.6 – – Phe 0.0 0.1 0.6 – –
0.0 0.0 – – 4.9 Trp 0.0 0.3 0.4 – –
0.0 0.0 – 5.4 7.1 His 0.0 0.1 – – –
a
H.-F. Ji et al. / Journal of Molecular Structure: THEOCHEM 756 (2005) 109–112
Amino acids
The higher energy results from the sterically hindered conformation of a-D-Pro.
111
112
H.-F. Ji et al. / Journal of Molecular Structure: THEOCHEM 756 (2005) 109–112
Acknowledgements This work is supported by the National Basic Research Program of China (2003CB114400) and the National Natural Science Foundation of China (30100035). We are grateful to Prof. Antonio Lazcano for his helpful suggestions. We also appreciate Mr Li Chen for his kind help in searching the CrossFire Beilstein database. References [1] [2] [3] [4] [5] [6] [7] Fig. 2. AM1-derived energy levels of silicon-based amino acids (in red) and their isomers, which were constructed on the basis of randomly selected carbon-based amino acids and isomers.
and thus ubiquitous molecules to constitute organisms. As natural amino acids possess other good properties than high thermostability, such as the high potential of forming polymers and the strong diversity and stability of the polymers, the employment of natural amino acids (especially small ones) in life seems to be a highly deterministic event, which supports the assumption proposed by Weber & Miller that the amino acids employed by life on other planets (if exist) will be similar to those on the earth [16].
[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
J.L. Bada, A. Lazcano, Science 296 (2002) 1982. C. Chothia, Nature 357 (1992) 543. H. Li, R. Helling, C. Tang, N. Wingreen, Science 273 (1996) 666. Beilstein Informationssysteme, Beilstein CROSSFIRE (Springer, Berlin). J.H. Jensen, M.S. Gordon, J. Am. Chem. Soc. 113 (1991) 7917. D. Yu, A. Rauk, D.A. Armstrong, J. Am. Chem. Soc. 117 (1995) 1789. M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B. 37 (1988) 785. A.D. Becke, J. Chem. Phys. 98 (1993) 1372. S. Miertus, E. Scrocco, J. Tomasi, Chem. Phys. 55 (1981) 117. S. Miertus, J. Tomasi, Chem. Phys. 65 (1982) 239. M. Cossi, V. Barone, J. Cammi, Chem. Phys. Lett. 255 (1996) 327. M.J. Frisch, et al. ‘Gaussian 98, Revision A.11’, Gaussian, Inc., Pittsburgh, PA, 2001. S.L. Miller, Origins Life 5 (1974) 139. S.W. Fox, Int. J. Quantum. Chem. Quantum. Biol. Symp. 13 (1986) 223. A.L. Weber, S.L. Miller, J. Mol. Evol. 17 (1981) 273. L. Miller, Cold Spring Harb. Symp. Quant. Biol. 52 (1987) 17. J.T. Wong, Microbiol. Sci. 5 (1988) 174. T. Hohsaka, M. Sisido, Curr. Opin. Chem. Biol. 6 (2002) 809 (and references therein). S.A. Benner, A. Ricardo, M.A. Carrigan, Curr. Opin. Chem. Biol. 8 (2004) 672.
Low-lying energy levels of amino acids and its implications for origin of life Hong-Fang Ji, Liang Shen, Hong-Yu Zhang * Shandong Provincial Research Center for Bioinformatic Engineering and Technique, Center for Advanced Study, Shandong University of Technology, Zibo 255049, People’s Republic of China Received 5 July 2005; revised 11 August 2005; accepted 2 September 2005
Abstract A major challenge in understanding the origins of life is to elucidate how nature selects a small part of molecules from a large number of candidates as building blocks of life, e.g. amino acids and proteins. Inspired by the thermodynamic principle in protein-structure selection, we attempted to explore whether there exists a thermodynamic criterion to differentiate amino acids from their isomers. In this letter, the energies of 20 natural amino acid and corresponding isomers are calculated by quantum chemical methods. It is revealed that the energy levels of amino acids (especially small ones) are not distributed randomly but located at the bottom of the energy diagrams of their isomers, suggesting that thermodynamic factor plays an important role in selecting the basic building blocks of life. q 2005 Elsevier B.V. All rights reserved. Keywords: Amino acid; Energy; Origin of life; Quantum chemical calculation; Thermodynamics
1. Introduction
2. Methods
Origins and evolution of life is one of the most intriguing subjects in life sciences [1]. A major challenge in this area is to understand how nature selects limited building blocks of life, such as 20 amino acids and w1000 protein folds [2], from hundreds of thousands of candidates. Employing a simple lattice model of protein folding, Li et al. [3] revealed a thermodynamic principle in protein-structure selection. That is, nature tends to use thermodynamically stable proteins and proteins with stable-against-mutation structures (which can be characterized by designability) to constitute organisms. However, it is still elusive why nature chooses amino acids as starting points of life, because each amino acid corresponds to tens to thousands of isomers. The thermodynamic principle in protein structure selection arouses our interest to explore whether there exists a thermodynamic criterion for the amino acid selection by calculating the energies of 20 amino acids and corresponding isomers.
The isomers corresponding to each amino acid were collected by searching in CrossFire Beilstein database, which contains more than 9 million molecules available naturally or synthetically and is the World most comprehensive database of organic chemistry for compounds, reactions, properties and citations [4]. Totally, 8813 isomers (including different conformations of one isomer) were gathered and the intramolecular hydrogen bond (IHB) was taken into account to give the most stable conformation. Especially, double IHBs in a-amino acids were considered to reach the most stable conformation [5,6]. 8813 molecules were firstly optimized by semiempirical quantum chemical method AM1 [7] in vacuo to elicit a preliminary energy profile. Then, a part of the molecules (595 totally) were optimized by density functional theory (DFT) with B3LYP functional [8,9] on 6-31CG(d) basis set at 298.15 K and solvent (water) effect was considered by employing the self-consistent reaction field (SCRF) method with polarized continuum model (PCM) [10– 12]. During the in-solvent calculation, the zwitterions of all molecules were taken into account. All of the calculations were performed using Gaussian-98 program package [13].
* Corresponding author. Tel.: C86 533 278 0271; fax: C86 533 278 0271. E-mail address: [email protected] (H.-Y. Zhang).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.09.001
3. Results and discussion The AM1- and B3LYP/6-31GG(d)-derived energy diagrams are illustrated in Fig. 1. It is interesting to find that the
110
H.-F. Ji et al. / Journal of Molecular Structure: THEOCHEM 756 (2005) 109–112
Fig. 1. Energy levels of amino acids (in red) and their isomers. (a) AM1 results; (b) B3LYP/6-31CG(d) results with solvent (water) effect.
energies of amino acids (especially small amino acids) are not distributed randomly in the energy diagrams, but are located at the bottom of the energy levels (Fig. 1), indicating that thermostability is indeed an important factor to differentiate these basic building blocks from their isomers, not only in gas phase but also in water solution. As energy has to be injected (by sparking or discharge) into the vessel when synthesizing amino acids prebiotically [14], it is natural to speculate that the energies of amino acids should be rather high. But the present calculation reveals that the relative energies of amino acids are actually very low, which may result from the IHBs in parent amino acids and their zwitterions [15]. Although thermostability has been considered as an important factor in the selection of building blocks of life [16], our finding provides the first theoretical evidence to support the notion. More interestingly, there is likely a correlation between the relative energies of amino acids and their weights. That is, small amino acids, such as Gly, Ala, Ser, Thr, Glu, have low relative energies, while large amino acids, such as Arg, Trp, Tyr, Phe, His, possess relatively high energies (Fig. 1). As the entropy contributes little to the free energy, the low energy of a molecule means its high abundance among their isomers, provided that the thermodynamic equilibrium can be reached. This implies that large amino acids have less chance to occur spontaneously than the small ones, which is in line with the fact that Arg, Lys and His are more difficult to be synthesized than others [17]. Therefore, small amino acids were preferred to construct life at the beginning of origin of life, which agrees well with Wong’s proposal that amino acids emerged on the earth at different stages, Gly, Ala, Ser, Asp, Pro, Thr, Val and Glu occurring early, while His, Met, Lys, Phe, Tyr, Arg and Trp being biosynthesized later [18]. This discovery is also helpful to understanding the striking similarity between the products and the relative abundances of amino acids in Miller’s soup and Murchison meteorite [14,16]. Although DFT calculation cannot distinguish the energy difference between L- and D-amino acids (Tables 1 and 2), the calculation reveals that some nonnatural amino acids, such as b-amino acids, methyl-amino acids and N-alkyl-amino acids,
are less stable than the natural counterparts by several kcal/mol (Tables 1 and 2), regardless of in vacuo or in solvent. This finding suggests that these nonnatural amino acids are less abundant than the normal counterparts in the early stages of chemical evolution, which provides a complementary explanation to the interesting question: why these nonnatural amino acids were not employed by nature to construct organisms [16]? As revealed recently, life itself does not exclude nonnatural amino acids [19], which means that nonnatural amino acids are as efficient as the normal ones in building life. However, organisms just employ 20 natural amino acids as major building blocks. A reasonable explanation is that some (especially small) natural amino acids were indeed ubiquitous and easy-to-be-taken in the prebiotic world, due to their low energies. Our finding places some constraints on the basic life composition, which is of significance in predicting some primary features of life that consists of elements different from ours. For instance, silicon has been considered as a potential substituent of carbon to build life [20]. Thus, here comes an interesting question: does the silicon-based life use the building blocks similar to the carbon-based organisms? To address this question, we employed AM1 method to calculate the energies of silicon-based amino acids and corresponding isomers, which were constructed on the basis of carbon-based counterparts. It is interesting to note that most of the silicon-containing amino acids have rather high relative energies (Fig. 2), which likely results from the different orbital-hybridization- and bonding properties between carbon and silicon. This suggests that nature unlikely selects amino-acid-like structures to build silicon-based life. Therefore, if silicon-based life really exists somewhere in the universe, it will be much different from the carbon-based ones. 4. Conclusion Thermostability likely plays an important role in differentiating natural amino acids (especially small ones) from their isomers, which suggests that nature tends to use low-energy
Table 1 B3LYP/6-31CG(d)-calculated in vacuo relative energies (in kcal/mol) of natural amino acids (a-L-amino acids) and corresponding nonnatural isomers (a-D-amino acids, b-amino acids, a-methyl-amino acids and N-alkyl-amino acids) Gly
Asp
Glu
Lys
Pro
Gln
Asn
Cys
Ser
Thr
a-La-Dba-methylN-alkylAmino acidsa a-La-Dba-methylN-alkyl-
0.0 – – – – Ala 0.0 0.0 1.2 – 6.6
0.0 0.0 – 2.4 8.3 Val 0.0 0.1 – 7.1 7.8
0.0 0.0 0.9 2.5 10.2 Leu 0.0 0.0 K1.1 3.9 5.2
0.0 0.2 0.1 5.4 – Ile 0.0 0.0 – – –
0.0 1.9a – – – Arg 0.0 0.0 – – –
0.0 0.0 0.3 5.8 8.5 Met 0.0 0.0 – 0.1 4.9
0.0 0.1 0.4 2.8 4.1 Tyr 0.0 0.2 0.6 – –
0.0 0.0 –0.9 – – Phe 0.0 0.1 0.7 – –
0.0 0.0 – – 3.6 Trp 0.0 0.0 0.4 – –
0.0 0.0 – 1.2 1.8 His 0.0 0.0 – –
a
The higher energy results from the sterically hindered conformation of a-D-Pro.
Table 2 B3LYP/6-31CG(d)-calculated in-water relative energies (in kcal/mol) of natural amino acids (a-L-amino acids) and corresponding nonnatural isomers (a-D-amino acids, b-amino acids, a-methyl-amino acids and Nalkyl-amino acids), in which zwitterions forms are considered Amino acids
Gly
Asp
Glu
Lys
Pro
Gln
Asn
Cys
Ser
Thr
a-La-Dba-methylN-alkylAmino acidsa a-La-Dba-methylN-alkyl-
0.0 – – – – Ala 0.0 0.0 1.7 – 6.7
0.0 0.0 – 3.2 9.8 Val 0.0 0.0 – 4.5 6.2
0.0 0.0 0.8 3.5 4.2 Leu 0.0 0.0 0.5 2.4 3.5
0.0 0.2 0.9 2.6 – Ile 0.0 0.0 – – –
0.0 0.7a – – – Arg 0.0 0.2 – – –
0.0 0.1 0.1 1.8 1.9 Met 0.0 0.1 – 1.1 1.0
0.0 0.2 0.7 8.5 11.5 Tyr 0.0 0.0 0.2 – –
0.0 0.0 0.6 – – Phe 0.0 0.1 0.6 – –
0.0 0.0 – – 4.9 Trp 0.0 0.3 0.4 – –
0.0 0.0 – 5.4 7.1 His 0.0 0.1 – – –
a
H.-F. Ji et al. / Journal of Molecular Structure: THEOCHEM 756 (2005) 109–112
Amino acids
The higher energy results from the sterically hindered conformation of a-D-Pro.
111
112
H.-F. Ji et al. / Journal of Molecular Structure: THEOCHEM 756 (2005) 109–112
Acknowledgements This work is supported by the National Basic Research Program of China (2003CB114400) and the National Natural Science Foundation of China (30100035). We are grateful to Prof. Antonio Lazcano for his helpful suggestions. We also appreciate Mr Li Chen for his kind help in searching the CrossFire Beilstein database. References [1] [2] [3] [4] [5] [6] [7] Fig. 2. AM1-derived energy levels of silicon-based amino acids (in red) and their isomers, which were constructed on the basis of randomly selected carbon-based amino acids and isomers.
and thus ubiquitous molecules to constitute organisms. As natural amino acids possess other good properties than high thermostability, such as the high potential of forming polymers and the strong diversity and stability of the polymers, the employment of natural amino acids (especially small ones) in life seems to be a highly deterministic event, which supports the assumption proposed by Weber & Miller that the amino acids employed by life on other planets (if exist) will be similar to those on the earth [16].
[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
J.L. Bada, A. Lazcano, Science 296 (2002) 1982. C. Chothia, Nature 357 (1992) 543. H. Li, R. Helling, C. Tang, N. Wingreen, Science 273 (1996) 666. Beilstein Informationssysteme, Beilstein CROSSFIRE (Springer, Berlin). J.H. Jensen, M.S. Gordon, J. Am. Chem. Soc. 113 (1991) 7917. D. Yu, A. Rauk, D.A. Armstrong, J. Am. Chem. Soc. 117 (1995) 1789. M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B. 37 (1988) 785. A.D. Becke, J. Chem. Phys. 98 (1993) 1372. S. Miertus, E. Scrocco, J. Tomasi, Chem. Phys. 55 (1981) 117. S. Miertus, J. Tomasi, Chem. Phys. 65 (1982) 239. M. Cossi, V. Barone, J. Cammi, Chem. Phys. Lett. 255 (1996) 327. M.J. Frisch, et al. ‘Gaussian 98, Revision A.11’, Gaussian, Inc., Pittsburgh, PA, 2001. S.L. Miller, Origins Life 5 (1974) 139. S.W. Fox, Int. J. Quantum. Chem. Quantum. Biol. Symp. 13 (1986) 223. A.L. Weber, S.L. Miller, J. Mol. Evol. 17 (1981) 273. L. Miller, Cold Spring Harb. Symp. Quant. Biol. 52 (1987) 17. J.T. Wong, Microbiol. Sci. 5 (1988) 174. T. Hohsaka, M. Sisido, Curr. Opin. Chem. Biol. 6 (2002) 809 (and references therein). S.A. Benner, A. Ricardo, M.A. Carrigan, Curr. Opin. Chem. Biol. 8 (2004) 672.