Parity-violating energy differences and the origin of biomolecular homochirality

J. theor. Biol. (1986) 119, 467-479

Parity-violating Energy Differences and the Origin of Biomolecular Homochirality G. E. TRANTER

Theoretical Chemistry Department, University of Oxford, Oxford OX1 3 TG, U.K. (Received 1 October 1985) The violation of parity by the weak interactions ensures that enantiomeric chiral molecules have inequivalent energies. These parity-violating energy differences have been calculated, using ab initio methods, for the series of a-amino acids glycine, alanine, valine, serine and aspartic acid, and for a set of polypeptide/protein fragments in both the a-helix and fl-sheet secondary structures. In each case the energy differences are found to favour the existence of the natural left-handed L-enantiomers over their unnatural mirror-image right-handed D-enantiomers. The variation of the parity-violating energy difference along a prebiotic reaction path leading to the formation of a possible precursor of alanine has also been determined. Under equilibrium conditions the energy difference is found to preferentially select the stereochemical reaction channel corresponding to the eventual formation of L-alanine rather than that for its unnatural D-enantiomer. The significance of these results in accounting for the prebiotic origins of the terrestrial biomolecular homochirality are discussed.

1. Introduction The biochemistry of terrestrial organisms is based upon chiral (optically active) molecules such as the a - a m i n o acids and sugars. Furthermore it is essentially homochiral, with only one of the two possible series of enantiomers (mirror-image isomers) being substantially adopted. Specifically terrestrial proteins, irrespective of their source, are based u p o n the "left-handed" L-a-amino acids to the almost complete exclusion of their mirror-image counterparts, the "right-handed" D-aamino acids. Similarly all nucleic acids are principally based upon D-sugars to the virtual exclusion of their L-enantiomers. Overall the " n a t u r a l " enantiomers, L-a-amino acids and D-sugars, dominate terrestrial biochemistry, with the ratio of D to L-glucose on Earth being estimated as at least 10ts: 1 (Lederberg, 1965). Despite this dominance a few "unnatural" D - a - a m i n o acids and L-sugars do occur with specific molecular roles, such as in bacteriai cell walls (but not bacterial protein) and antibiotics, ahhough even in these cases homochirality is maintained with the corresponding, otherwise dominating, enantiomers being excluded. Fortunately the perpetual degradation of homochirality by racemization (enantiomer inter-conversion) is minimal, although a connection with ageing has been suggested (Ulbricht, 1981). The existence of the homochiral biochemistry is generally accounted for by the stereo-chemical "key and lock" hypothesis of Fischer (1894a, b), and its subsequent 467

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developments. The resulting self-replicating systems are competitively selected for their kinetic efficiency and product economy. However the observed homochiral biochemistry, based substantially upon L-a-amino acids and D-sugars, has an alternative mirror-image counterpart based principally upon the D-a-amino acids and L-sugars. Classically the two alternative homochiral biochemistries are energetically equivalent, and the "key and lock" hypothesis is unable to distinguish the reason for the particular terrestrial selection over its mirror-image counterpart. It is generally held that a chemistry approaching a homochiral composition must have been in existence during the latter stages of the prebiotic era prior to the development of self-replicating biomolecular systems since the formation of the necessary prototype biopolymers, which occurs with relative ease in homochiral conditions, is considerably hindered otherwise (Joyce et al., 1984; Blair et al., 1981; Idelson & Blout, 1958). Conventionally the particular terrestrial homochiral selection has been ascribed to chance. Initially, due to the even-handedness (parity-conservation) of the classical gravitational and electromagnetic interactions, the prebiotic chemistry is expected to have had a time averaged racemic composition, with equal time-averaged quantities of both enantiomers of each chiral species present. Nonetheless the continual random fluctuations will have generated, with equal probability, small temporary excesses of either of the enantiomeric series. Such a small initial excess may then have propagated to its corresponding homochiral chemistry via some form of kinetic dissymmetry amplification. Recent investigations of which the latest results are reported here, have shown that the terrestrial homochiral selection may instead be the outcome of a small universal systematic bias towards one enantiomeric series, deriving from the parityviolation of the weak interactions, rather than a simple random event.

2. Parity-violating Energy Differences The discovery that parity (space inversion equivalence) is not conserved by the weak interactions (Lee & Yang, 1956) supported a minority chemical tradition deriving from Pasteur (1884a, b), which maintained that there is an intrinsic dissymmetric force inherent in the physical world. This dissymmetry pervades throughout all atomic and molecular properties, with optical activity emerging as a universal property of all atoms and molecules (Emmons et al., 1984a, b) in addition to the pure electromagnetic optical activity of chiral systems (Barron, 1982). Classically a chiral molecular system and its enantiomer have been considered energetically equivalent, however, the partity-violating weak interactions through their connection established with electromagnetism (Weinberg, 1967; Salam, 1968), ensure that this equivalence is no longer exact (Rein, 1974; Zel'dovich et al., 1977; Rein et aL, 1979; Hegstrom et al., 1980). Effectively they give a small "parity-violating energy shift" (PVES), Epo, to the state energy of a chiral system, and a similar shift of equal magnitude, but opposite sign, -Epv, to the corresponding state energy of the enantiomeric system. Consequently there is a "parity-violating energy difference" (PVED), AEp~, between the two systems aEpo = Epv - ( - E p o ) = 2Epo.

(1)

PVED AND BIOMOLECULAR HOMOCHIRALITY

469

The PVED may occur not only for a system in its chiral equilibrium geometry, but also for any chiral transient form, such as reaction transition state. Thus PVED can manifest itself in a number of ways, in particular, as an imbalance in the concentrations of enantiomeric species in classically racemic equilibrium, and also an inequivalence in the rate constants of enantiomeric reactions. The weak interactions can be partitioned into two types, the weak charged current (WCC) and the weak neutral current (WNC), mediated by the recently discovered charged (W ~) and neutral (Z °) bosons respectively (Walgate, 1983). In keeping with the very large masses observed for these bosons, the interactions are of exceptionally short range, and to very good approximation may be taken as contact phenomena. Both the WCC and WNC interactions violate parity, however the W C C interactions, while important for charge-transferring processes such as /3-decay, have only a minor, high-order, significance relative to that of the WNC interactions for charge retaining atomic and molecular properties. Within atomic and molecular systems the WNC interaction has two principal components, the electron-nucleon potential and the generally less important electron-electron potential. Due to the exceptional short range of the interactions the electron-nucleon potential is only active within the regions of the atomic nuclei, being reliant on the non-vanishing quantum mechanical probability of an electron in an atomic nucleus. The intrinsic PVED between enantiometic species and reactions in the prebiotic state provides an alternative, globally (universally) consistent, source of a small chiral bias and may specifically select the observed terrestrial series of enantiomers. Initial calculations, based upon the electron-nucleon component of the WNC interaction, indicate that the natural amino acid L-alanine is stabilized relative to its D-enantiomer for the conformation preferred in aqueous media (Mason & Tranter, 1983a, 1984, 1985), as is the L-enantiomer of one of its possible precursors (Tranter, 1985a). A similar stabilization of the natural enantiomers has been described for a limited set of peptide/protein fragments in both the a-helix and /3-sheet conformations (Mason & Tranter, 1983b, 1984, 1985). The investigation reported here extends the PVED ab initio calculations, employing an improved procedure, to a series of fundamental a-amino acids: glycine, analine, valine, serine and aspartic acid. The PVED of various peptide/protein fragments are also reported with increased accuracy and the variation of PVED along a reaction path leading to a possible precursor of alanine, of which preliminary results have been published (Tranter, 1985) is discussed. 3. Calculations

For a multi-particle system such as a molecule the Hamiltonian Hpv representing the typically dominating electron-nucleon potential of the parity-violating WNC interaction can be written to first order approximation as (Bouchiat & Bouchiat, 1974, 1975; Hegstrom et al., 1980; Mason & Tranter, 1984, 1985)

Hpv = - F Y~Y, Qa{p,. s,, 8 3 ( r , - ro)}+ a

i

(2)

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In which {~}+ denotes an anti-commutator and the two summations run over all the atomic nuclei (a) and electrons (i) of the system respectively. Each electron i has a linear momentum operator Pi and a spin momentum operator si combined by a scalar product, and its electron density at the nucleus a is determined by the three-dimensional Dirac delta function ~3(r~-ra). The constant F contains the inherent weakness of the interactions by combining the Fermi weak coupling constant GF with the electron mass me and the speed of light c r = GF/(m,c2

= 5"731

x

)

10 -17 a.u.

The parameter Qa of the atomic nucleus a is a weighted sum of its neutron number N~ and proton number Z~ Q~ = N~ - ( 1 - 4 s i n 20w)Z~

(4)

with the Weinberg angle 0w deriving from the unification of weak and electromagnetic interactions. Empirical values of sin 2 0w are given as 0.215 (Emmons et al., 1984a, b) or 0.23 (Abbott & Barnett, 1979), compared to a theoretical value of 0.25 (Taylor, 1979). Consequently the weighting of the proton number, if non-zero, remains small. For the theoretical value sin 2 0w = 0.25 (Taylor, 1979), adopted here, Q~ is effectively equivalent to the neutron number N~. This clearly illustrates the important role neutrons have in the weak interactions within atoms and molecules, a complete contrast to their ineffectiveness for electromagnetic interactions. The enantiomorphous element of Hpo is the electronic scalar product which, if non-zero, has a signed, pseudo-scalar, resultant that changes sign on spacial inversion (e.g. for Cartesian co-ordinates x, y, z ~ - x , - y , - z ) ; i.e. parallel or antiparallel electronic linear momentum and spin vectors. This may be compared with the more usual parity-conserving Hamiltonians, which typically have a dependence upon a pure scalar resultant, for example the Coulombic interaction is dependent upon inter-charge distances without any directional property. A comprehensive derivation of the expressions and procedure for the calculation of the PVES for a chiral molecule in a closed-shell singlet electronic state, such as the systems discussed here, using the Hamiltonian Hpo of equation (2), has recently been presented (Hegstrom et al., 1980; Mason & Tranter, 1984). Determination of the molecular orbitals and energies required in the calculations for the closed-shell singlet groundstates of each of the systems reported was achieved by the use of the G A U S S I A N 82 molecular orbital program (Binkley et al., 1982). In all cases the optimal (Mason & Tranter, 1984) standard split-valence basis set STO-6-31G was employed in the restricted Hartree-Fock method of the G A U S S I A N 82 program. The procedure employed includes an improvement in the method of determining the various electronic state energies required in the calculations, the details of which appeared in a recent publication (Tranter, 1985b). This improvement ensures an increased reliability in the calculated values of PVES. However it does not appear to appreciably affect the sign or overall order of magnitude of the PVES for small chiral molecules. Therefore within these limitations previous results remain valid.

PVED AND BIOMOLECULAR

HOMOCHIRALITY

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4. A m i n o Acids

Since the L and D-fOrlIlS of an a-amino acid are enantiomeric, it is only necessary to calculate the PVES for one of the enantiomers, the total PVED between the two following from equation (1). In keeping with the natural selection of L-a-amino acids, it was the L-enantiomers that were considered.

"'..

H

..0

t.._ . ~

I

.

i ./

i/ e"

FIG. 1. The structure of L-a-amino acids, showing the dihedral angle ~b defining the carboxylate orientation.

The five L-a-amino acids studied--glycine, alanine, valine, serine, and aspartic acid--are among the most fundamental biomolecules likely to be present prior to and during the prebiotic-biotic transition. All five have analogous structures as depicted in Fig. 1, each assumed io be in their common zwitterionic form varying only in their side-groups denoted by R. Each of these side-groups is illustrated in Fig. 2, the aspartic acid carboxylate side-group being assumed to be ionized to give the aspartate anion. The a-amino acids can exist in a multitude of molecular conformations. In particular a series of conformers, characterized by the dihedral angle ~b for the axial rotation of the carboxylate group around its bond to the central carbon atom, as shown in Fig. 1, can be identified. Whilst alanine is constrained to a conformation with ~b ~ 42 ° in the crystalline phase (Lehmann et al., 1972), when in aqueous media the preferred, solvated, conformation for the amino acids is that with ~b = 0 ° due to the enhanced solvation of the charged groups of the zwitterion so allowed. For the calculations reported here, each o f the amino acids was constrained to its conformation preferred in aqueous media, the orientations o f the various groups being as in Fig. 1 with ~b = 0 °. Likewise these conformational constraints were extended to the differing side-groups and were taken as illustrated in Fig. 2 with reference to Fig. 1. Specifically the two carboxylate groups of the aspartate anion were taken as having their respective planes parallel. The calculations were based on the observed bond lengths and angles for the amino acids (Lehmann et al., 1972; Koetzle et al., 1974; Frey et al., 1973; Rao,

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h"H

~ , . . . . i..~j H

Glycine

I

H

oa~..H

~li,~.. i.~,~j H H

---

Serine ~

H

Alonine

i/'

H

. /.0 /

H~CIh~"H H Voline

/

/

i

//

i<;" i i / i ./ i/ ~/ Asportclle

FIG. 2. The structures of the a-amino acid side-groups for glycine, alanine, valine, serine and the aspartite anion.

1973), including neutron diffraction data in which the hydrogen atoms, as well as the other atoms, in the crystalline phase zwitterions were accurately located. Additional slight modifications to the structural parameters were applied in order to secure as much symmetry as possible for the various chemical groups. The simplest of the a-amino acids, glycine ( R = H), while not resolvable into optical isomers, is chiral over the major part of the conformational range spanned by the rotation of its carboxylate group about the bond to the central carbon atom, including ~b = 0 °. Consequently it is included in the investigation as a useful reference for comparison of the effects caused by the more complex side-groups in the other a-amino acids. The total PVES for the five a-amino acids studied are given in Table 1. The calculated value of the PVES is consistently negative in the range - 0 . 8 4 to - 2 . 2 9 x 10 -20 a.u. for the L-enantiomers. Thus remarkably the solvated natural L-enantiomers of alanine, valine, serine and the aspartate anion are stabilized, and energetically preferred, relative to their unnatural mirror-image D-enantiomers. The absolute magnitude of the PVED between the L and D-enantiomers is intrinsically small, of the order 10 -20 a.u. Taken as a free energy difference, such a PVED corresponds to an enantiomeric excess of some 106 L-a-amino acid molecules in one mole of the corresponding racemic mixture in thermodynamic equilibrium at normal terrestrial surface temperatures.

PVED

AND

BIOMOLECULAR TABLE

HOMOCHIRALITY

473

1

The parity-violating energy shift ( Epv) of glycine and the L-enantiomers of alanine, valine, serine and the aspartate anion, each in the conformation favoured in aqueous media Amino acid glycine L-alanine L-valine L-serine L-aspartate

Ept,/]O-20 a.u. - 1.14 - 1.79 -2-29 - 0.84 --"1.46

The effect of side-group R on the total PVES of an amino acid can be visualized as a combination of three processes. Firstly the side-group may be inherently chiral within itself when isolated from the remainder of the amino acid. Consequently it may possess its own intrinsic PVES contribution. Of the five amino acids studied here only the aspartate anion side-group is intrinsically chiral and may contribute to the total PVES in this way, the others having essentially achiral side-groups. Secondly the side-group may be asymmetrically polarized by the remainder of the amino acid, thus imparting a degree of chirality within the side-group and therefore an additional contribution to the total PVES from it. Finally the reverse situation can be envisaged, in which the side-group asymmetrically polarizes the remainder of the amino acid, so causing a variation of its PVES contribution. Both of these latter two polarization processes are active in all five of the a-amino acids reported, thus causing the small variations in the calculated PVES given in Table 1. In view of the consistent stabilization of the L-amino acids studied it appears reasonable to assume that this is a general result, at least for those L-a-amino acids with limited achiral side-group polarizabilities.

5. Protein/Peptide Fragments The L-a-amino acids are commonly found in natural products mainly in the form of proteins and polypeptides. Consequently the calculations were extended to the principal regular conformations of a model peptide structure. The ordered secondary structures of polypeptides derived from a-amino acids, the a-helix and g-sheet, are characterised by the pair of dihedral torsion angles and 0 around the C~-NH and C~-CO bonds respectively (Shulz & Schirmer, 1979) as shown in Fig. 3. An analysis of the main chain dihedral angles of some 2500 L-amino acid residues in the structures of 13 proteins, determined by X-ray crystal diffraction, gives the mean values of the dihedral angle pair (~, ~) as (-76 °, -36 °) for the a-helix structure, and (-100 °, +130 °) for the/3-sheet structure (Levitt, 1976). For the corresponding hypothetical conformations of polypeptides formed from

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0

HJ

I

C

--

R

\/

H

--1

H

| I

FIG. 3. The dihedral torsion angles ~b and ~b in a polypeptide chain for the peptide twist fragment (PTF) and, in enclosing brackets, the corresponding unit (PTU).

D-a-amino acids the signs of the values of the dihedral angles ~b and ~b are simply inverted. A size restriction on the practical running of the G A U S S I A N 82 program limited the calculation of the PVES for the peptide conformations to the small model diamide structure, formylglycinamide, of Fig. 3. This is termed a peptide twist fragment (PTF) since it consists of a portion of a polypeptide, suitably terminated by hydrogen atoms, including a central carbon atom about which the principal twist or torsion of the overall polypeptide secondary structure occurs. The complete PTF molecule itself cannot be considered as a monomeric unit of a polypeptide, however its constituent a-amino acid residue, otherwise termed the peptide twist unit (PTU) and distinguished by square brackets in Fig. 3, is such a unit. The primary structure of the PTF molecule was based upon the standard average bond lengths and angles determined for the polypeptides (Shulz & Schirmer, 1979; Levitt, 1976). In the calculations of the PVES for the a-helix and/3-sheet conformations of the PTF molecule the contributions from all the atoms of the diamide were included. The molecular orbital data of the PTF molecule was then subsequently employed in calculating the PVES for the conformations of the PTU, with the contributions then being restricted to only those atoms of the PTU. This use of the PTF molecular orbital data for the PTU calculations ensures an improved modelling of the electron distribution of a true polypeptide over that obtainable from molecular orbital data restricted solely to the PTU itself. In both sets of calculations the side-group R of the a-amino acid residue was taken as a hydrogen atom, the results of Table 1 indicating the typical sensitivity of PVES to the form of the side-group. With the mean dihedral angles tk and 0/characterizing the secondary structure of an L-polypeptide the PVES of the complete PTF molecule were found to be consistently negative, with Epo = - 0 . 5 5 x 10 -20 a.u. for the a-helix conformation and Epv = -1-07 × 10 -20 a.u. for the /3-sheet conformation. Likewise the PVES of the corresponding PTU were also negative with Epv = - 0 . 3 9 x 10 -20 a.u. for the a-helix and Epv = - 0 . 4 0 x 10 -2o a.u. for the/t-sheet. The implication of the above results is that a polypeptide of the L-series is stabilized with respect to the corresponding D-enantiomer in both the a-helix and/3-sheet

PVED AND BIOMOLECULAR HOMOCHIRALITY

475

conformations. Furthermore this stabilization is due purely to the polypeptide secondary structure, the glycyl amino acid residue of both the PTF and PTU having no intrinsic chiral centre. An L-polypeptide is expected to have a lower energy than the corresponding D-enantiomer by some - 0 . 8 x 10 -20 a.u. for each amino acid residue, although possible cross terms between different peptide residues are, as yet, undetermined. Nonetheless, for a protein composed of some 600 amino acid residues the total PVED would amount to some - 4 8 0 x 10 -20 a.u. in favour of the L-enantiomer, a significant enhancement over that for a single amino acid. 6. A Prebiotic Reaction

Numerous prebiotic reaction mechanisms have been suggested (Cairns-Smith, 1982), of which perhaps the most well known is that of Miller (1957) for the formation of a-amino acids. In the particular Miller mechanism for the production of the fundamental amino acid alanine the most important step, investigated here, is the reaction of the two achiral species, hydrogen cyanide and ethyl-imine, to form the chiral alanine precursor a-amino-propionitrile (APN), thus introducing the first occurrence of chirality in the system. For the purpose of the investigation this prebiotic reaction was taken to proceed by the nucleophillic addition of a cyanide anion to an ethyi-iminium cation as depicted in Fig. 4. The chirality of the product APN is determined by whether the cyanide anion'approaches from above (L-enantiomer) or below (D-enantiomer) the plane of the ethyl-iminium cation in the orientation of Fig. 4. As previously, only the L-form was explicitly considered in the calculations, the L-APN molecule eventually giving L-alanine in the complete Miller mechanism.

N t

N

ER 1 CH~

c NHz

"

H'~'~C~ / --NH z CH3

FIG. 4. The nucleophilic addition o f a cyanide ion to an ethyl-iminium cation to form L-ot-aminopropionitrile, showing the reaction co-ordinate R. Addition from below the molecular plane gives the mirror-image D-enantiomer.

The extent of the passage along the reaction path leading to L-APN is represented by the reaction co-ordinate R, the interatomic distance between the central carbon atom of the ethyl-iminium cation and the carbon atom of the cyanide anion. Determination of the reaction path, and the molecular orbital data for the transient

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species, was achieved by optimization of the geometry of the cyanide/ethyl-iminium system for a series of values of R (Tranter 1985), using the G A U S S I A N 82 program. The variation of the calculated PVES along the reaction path for the formation o f L-APN is graphically illustrated in Fig. 5. It was found that the cyanide anion causes little distortion in the ethyl-iminium cation in the region from co to R ~ 2 - 5 A. Consequently the PVES shows a smooth increase in its positive value from zero at R = oo, for the free achiral reactants, to its maximum value of Epo=+0.23 x 10 -20 a.u. for the rate determining species at R = 2.5 A. 03 0"2

izl

0.1

o

'0

@

0 -0"I -0"2 -0"3

'

'

'

'

'

'

'

'

'

FIG. 5. The parity-violating energy shift (Ep~) along the reaction path for the formation of L-a-aminopropionitrile as a function of the reaction co-ordinate (R).

On proceeding from R = 2 - 5 ,~ to the equilibrium structure, R = 1.531 A, of the product L-APN there is a rapid deformation from approximately planar to tetrahedral geometry about the central carbon atom as its bond to the cyanide carbon atom forms and its double bond to the iminium group transforms to single character. Accompanying this dramatic deformation the PVES rapidly drops to its negative minimum value of Epv = - 0 . 2 0 x 10 -20 a.u. for the equilibrium geometry L-APN. The positive value of the PVES for the rate determining species at R = 2.5 A indicates that L-APN has a slower rate constant for formation, and thus less readily produced, than that of D-APN. Initially this may appear to be the opposite of the situation required if L-alanine is to eventually dominate its D-enantiomer. However careful consideration of the exact reverse reaction equally represented by Fig. 5, in which APN decomposes into its constituent cyanide anion and ethyl-iminium cation, shows that D-APN also decomposes with a faster rate constant than that of L-APN. In combination the forward and reverse reactions, under chemical equilibrium conditions, balance such that the PVES of the equilibrium geometry APN determines the ratio of its L and o-enantiomers. As the PVES of L-APN is at a negative minimum, Epo= -0.20 x 10 -20 a.u., for its equilibrium geometry, L-APN will be in excess over its D-enantiomer under chemical equilibrium conditions, by some 106 molecules per mole of corresponding racemic mixture at ambient temperatures.

PVED

AND

BIOMOLECULAR

HOMOCHIRALITY

477

7. Discussion

Remarkably the results presented here for a series of a-amino acids, peptide fragments and a possible prebiotic reaction consistently indicate that, while small in magnitude the parity-violating energy differences preferentially stabilize the members of the natural L-series with respect to their unnatural mirror-image Denantiomers. The effects of the parity-violating weak interactions on the second major series of chiral biomolecules, the sugars, are still under investigation, but the naturally occurring D-sugars are chemically related to the L-a-amino acids through the conversion of o-glucosamine to L-alanine (Wolfrom et al., 1949). The absolute magnitude of the PVED between enantiomeric molecules is intrinsically small, of the order 10 -2o a . u . (equivalent to --10-~4J mol-~), for small chiral molecules composed of light atoms. Nonetheless the calculated bias in favour of the natural L-series may be capable of providing the initial selection leading to the observed homochiral biochemistry. In order to propagate homochirality from small PVED between enantiomeric species an amplification mechanism or a dynamic metastable system sensitive to small perturbations is required. A number of such kinetic dissymmetry amplification mechanisms have been suggested which exhibit a hypersensitivity to small differences between enantiomers, ensuring the survival of only one (Frank, 1953; Seelig, 1971; Decker, 1974; Fajszi & Czege, 1981; Kondepudi & Nelson, 1983, 1984, 1985). Typically these mechanisms, designed to produce a spontaneous transition from a racemic chemistry to a homochiral alternative, require an open system in which each chiral product autocatalyses its own production from an achiral substrate, and competitively inhibits the propagation of its enantiomer. Such a system remains stable while the input of achiral substrate remains small, producing a racemic output. When the substrate input is increased, a critical point is reached where the racemic process becomes metastable and the system spontaneously resolves itself into a homochiral process, the chirality of which is determined by any systematic chiral bias, such as PVED, moderated by the ever-present random thermal fluctuations. The properties of possible amplification mechanisms have been thoroughly investigated with the aid of bifurcation theory (Kondepudi & Nelson, 1983, 1984, 1985). In particular, it has recently been determined that even a PVED as small as 10-20 a.u. may be sufficient as a selector under conditions relevant to the prebioticbiotic transition (Kondepudi & Nelson, 1985). The determinate selection of the lower-energy homochiral reaction sequence is promoted by the slow increase of substrate input concentration, extended over long time periods. From the PVED between the enantiomers of the a-amino acids, it is estimated that the selection of the L-series may have taken place in a homogeneous lake of volume 4x 10 9 litres (1 km x 1 km x 4 m) during a minimum time of 10 000 years (Kondepudi & Nelson, 1985). Although apparently large volumes and long time periods are required to achieve homochirality such conditions may be expected of the prebiotic era. In conclusion, although there is no absolute proof, the results reported here provide significant evidence that the observed terrestrial homochiral biochemistry may have had its chirality determined by the small parity-violating energy differences

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