Ab initio quantum mechanical calculations that include the asymmetric electroweak interaction have been performed in order to determine the parity non-conserving energy difference AEPNC of the binding energy in the electronic ground state for major biomolecules such as amino acids. Molecular structures of amino acids are more complicated than twisted ethylene but they are still manageable. Stephen Mason and his former assistant George Tranter (who moved since then to Oxford University and afterwards to industry) performed studies on the molecular wave function of a-alanine with its 48 electrons at London King's-College (Mason and Tranter 1983a, 1983b).
As we have seen in Chap. 2, a-alanine is the simplest chiral amino acid with its asymmetrically substituted a-carbon atom as stereogenic center. The enantiomer a-R-alanine corresponds to a-D-alanine and a-S-alanine is identical to a-L-alanine. In the a-S-alanine zwitterionic structure depicted in Fig. 5.5 the planar carboxylate-group is not fixed and can rotate around the carbon-carbon bond linking this group to the amino acid's central a-carbon atom.
Fig. 5.5 Chemical structure of the amino acid a-S-alanine indicating the torsion angle O of the plane of the carboxylate-group COO~ and the fixed C-Ca-H-plane. In the solid state of aggregation the conformation shows O = 62°. In liquid solution, the confirmation is determined by O = 0
The torsion angle O can range from 0 to 180°, resulting in different conformer structures of a-alanine. Mason and Tranter calculated value and sign of the parity non-conserving energy shift for a-alanine as a function of this torsion angle O. The result is depicted in Fig. 5.6.
The parity violating energy shift is a function of the torsion angle O. If EPNC is negative, the bonding energy is stabilized which is the case for a-S-alanine with values of O smaller than 50° and bigger than 130°. The parity non-conserving energy difference AEPNC is defined by Eq. (5.2).
In this range of O, EPNC is indeed smaller than zero, which means that a-S-alanine (L-alanine) is energetically preferred compared to its mirror image enantiomer the a-R-alanine (D-alanine). For the intermediate range of 50 ° < O < 130° the opposite is true and D-alanine is more stable than L-alanine. But this intermediate range is less realized in all possible alanine confirmations since the medial conformation of alanine is in the L-enantiomer preferring range. In aqueous solution - the most important matrix for prebiotic reactions of amino acids - alanine has a torsion angle O = 0°.
So one concluded that L-alanine - as it is used in biomolecules - is energetically preferred in comparison with D-alanine, the 'unnatural' enantiomer at least in the important aqueous solution state. This preference is very tiny and was quantified with AEPNC (a-alanine) = 2.5 • 10-20 a.u. = 0.7 • 10-18 eV (see Fig. 5.6). For chemists, this tiny value corresponds to 6.8 • 10-14 Joule/mol, an extremely small amount of energy. Quack et al. insist on the fact that more recent and improved AEPNC calculations performed by his team at ETH Zurich gave rise to AEPNC values that are at least one order of magnitude larger (Bakasov et al. 1996).
What about other amino acids? The extrapolation of the preference of the L-enantiomer in the case of a-alanine by the parity non-conserving energy difference toward other amino acids seems to be possible. In the case of twisted glycine, nearly identical results were obtained (Mason and Tranter 1983a; Rein 1992). Glycine, the simplest amino acid is relatively easy to calculate with quantum mechanical tools. Similar to twisted ethylene, glycine is chiral over most of the conformational range spanned by the rotation of the carboxylate plane about the bond to the a-carbon atom. Magnitude and sign of the parity non-conserving energy differences were calculated to give a similar sinusoidal dependence on the torsion angle for both glycine and L-alanine. Subsequent calculations for other zwitteri-onic amino acids in the aqueous solution state equally preferred the L-enantiomers relative to their D-enantiomers, as there are AEPNC (valine) = 4.6 • 10~20 a.u., AEPNC (serine) = 1.7 • 10~20 a.u., and AEPNC (aspartate anion) = 2.9 • 10~20 a.u. (MacDermott and Tranter 1989).
So how about the typical amino acid confirmation in proteins (enzymes) that are, as we know, important biocatalysts composed of 20 different amino acids in L-configuration? Quantum mechanical calculations show that fragments of such proteins (polypeptides) composed of L-amino acids are little more stable than polypeptides composed of D-amino acids. This stabilization was calculated for both a-helices7 and for P-sheet structures. A polypeptide chain composed of L-amino acids is stabilized by - 1.8 -10~19 eV per monomer unit compared to a mirror-image polypeptide chain of D-amino acid monomers. A L-polypeptide of n residues should therefore be stabilized relative to the D-polypeptide by - 1.8 n • 10~19 eV, but there may be additional contributions from cross-terms between residues, since these do not necessarily fall off with increasing residue separation (MacDermott and Tranter 1989). This calculation is valid for both a-helices and for P-sheet structures.
We will discuss and illustrate in Chap. 10 whether or not mechanisms involved in prebiotic evolution were capable of amplifying such a tiny difference in electronic energies of enantiomers.
Now, we will turn towards quantum mechanical ab initio calculations of sugar molecules, since we know that biopolymers of living organisms such as the nucleic acids DNA and RNA exclusively implement monomers of D-deoxyribose and D-ribose enantiomers into their molecular skeletons. Consequently we will now ask, "Are D- or L-sugar enantiomers preferred by AEPNC-values, too?"
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