Homochirality: a prerequisite or consequence of life?
aa r X i v : . [ q - b i o . B M ] D ec Chapter 4
Homochirality: a prerequisite orconsequence of life?
Axel Brandenburg
Abstract
Many of the building blocks of life such as amino acids and nu-cleotides are chiral, i.e., different from their mirror image. Contemporarylife selects and synthesizes only one of two possible handednesses. Chiralmolecules also tend to be optically active and rotate polarized light in aleft-handed sense for many proteins and in a right-handed sense for manynucleotides and sugars. In an abiotic environment, however, there are usuallyequally many left- and right-handed molecules, so we talk about a racemicmixture. If homochirality was a prerequisite of life, there must have beenphysical or chemical circumstances that led to the selection of a certain pref-erence. Conversely, if it was a consequence of life, we must identify possiblepathways for accomplishing a transition from a racemic to a homochiral chem-istry. There has been significant progress on both approaches. One of the fourelementary forces of nature, the weak force, responsible for the decay of freeneutrons, for example, does give rise to a preference for chemical reactionsbetween molecules of a certain chirality, but the effect is very small comparedto that of random fluctuations that are always present. On the other hand,amino acids from certain meteorites suggest a preference for the left-handedamino acids – at least for some of them – although the question of contamina-tion is not fully ruled out. This could be explained by polarized light, whichcan give rise to a selection of a net handedness of biomolecules, but the effectis again small. Depending on the mechanism that is responsible for generatingpolarized light, either both signs or only one sign of polarization are possible.After a detailed discussion of these ideas and the observational evidence, we Nordita, KTH Royal Institute of Technology and Stockholm University, Stockholm, Swe-den Department of Astronomy, AlbaNova University Center, Stockholm, Sweden McWilliams Center for Cosmology, Carnegie Mellon University, Pittsburgh, PA 15213,USACorrespondence: Nordita, Roslagstullsbacken 23, SE-10691 Stockholm, Swedene-mail: [email protected] , Tel: +46 8 5537 8707, mobile: +46 73 270 4376 http://orcid.org/0000-0002-7304-021X also review alternative ideas where homochirality of any handedness couldemerge as a consequence of the first polymerization events of nucleotides inan emerging RNA world. In those proposals, autocatalysis was thought to bea crucial ingredient, but recent studies show that this is not necessarily thecase. Also, the effect of enantiomeric cross inhibition, the termination of poly-merization with monomers of the opposite chirality, may not be detrimental,as was originally thought, but it may instead be beneficial. There are indeedmechanisms that can produce full homochirality through the combination ofboth autocatalysis and enantiomeric cross inhibition. These mechanisms arenot limited to nucleotides, but can also occur for peptides, as a precursor tothe RNA world. The question of homochirality is, in this sense, intimately tiedto the origin of life. Future Mars missions may be able to detect biomoleculesof extant or extinct life. We will therefore also discuss possible experimentalsetups for determining the chirality of primitive life forms in situ on Mars.
Key words:
DNA polymerization, enantiomeric cross-inhibition, origin ofhomochirality. Revision: 1.79
The occurrence of handedness in biology is not uncommon. The differencebetween our left and right hands is the most obvious occurrence in the macro-scopic world. In ancient Greek, the word χǫιρ means hand, which explainsthe origin of the word chirality. Also some trees exhibit a preference for aleft-handed swirl and others for a right-handed swirl. Snails are another suchexample. In the microscopic world, the biological significance of a preferredhandedness was discovered by Pasteur (1853) by analyzing the effect of tar-taric acid on polarized light.Polarization is a property of transversal waves when the wave shows os-cillations perpendicular to the direction of propagation. This is different forsound waves that are longitudinal. Unpolarized light consists of a superposi-tion of waves with all the different polarization orientations of the wave plane.Using a polarizer, which is an optical filter with maximum transmission fora particular wave plane, one can determine the orientation of polarization. Itturns out that natural sugar in solution has the property of rotating the planeof polarization of polarized light in the right-handed sense, so they are calleddextrorotatory, denoted by (+), while many amino acids in solution rotatepolarized light in the left-handed sense, denoted by ( − ). Pasteur (1853) alsoinspected the shapes of crystals of tartaric acid under the microscope andfound upon separating them that the two rotate polarized light in oppositesenses.Handedness of biomolecules is primarily a consequence of the tetrahedralshape of the of carbon compounds; see Figure 4.1. If each of the four bonds of Homochirality: a prerequisite or consequence of life? 3
Fig. 4.1
An amino acid that is chiral whenever the residue R is different fromH. For example, when R = CH , we have alanine, but when R = H, themolecule is glycine, which is the same as its mirror image, i.e., it is achiral. (Source: https://chem.libretexts.org/@api/deki/files/19089/molecule.png?revision=1 ) the carbon atom connect to a different group, its three dimensional structurewould be different from that of its mirror image. In the case of complexmolecules, there can be several carbon atoms that cause a violation of mirrorsymmetry. Those carbon atoms are then called chiral centers. In the case oftartaric acid (Figure 4.2), there are two chiral centers. There is then also thepossibility that only one of the two chiral centers is different. That version iscalled meso-tartaric acid and it is achiral, i.e., it is mirrorsymmetric.There is no immediate connection between the handedness of molecules(Figure 4.2) and the handedness hidden in the structure of a crystal (Fig-ure 4.3). In fact, the association of a given chiral structure with left or rightrelies on some convention. This also explains that there is nothing strange inhaving right-handed sugars in our DNA and left-handed amino acids in ourproteins. Nevertheless, the very fact that something can occur in two possibleforms that are mirror images of one another is non-trivial and requires someunderlying structure that can also be subdivided into two opposite mirrorimages of each other. It is therefore plausible that one of the two handed-nesses of the l -tartaric acid molecule crystallizes into macroscopic structuresof one form, and the d -tartaric acid into its mirror image (Derewenda, 2008).In the molecular context, these two forms are called enantiomers. We must emphasize that the terminology in terms of levorotatory and dextrorotatory isquite different from that in terms of d and l . Levorotatory/dextrorotatory is the physicalproperty for a compound to induce the rotation of polarized light to the left/right. Thisproperty is abbreviated ( − )/(+). By contrast, l / d refers to a structural property of amolecule to denote its handedness, that is solely based on conventions. This conventiononly applies to specific biomolecules, including amino acids and sugars. This conventionhas been taken in such a way that all biogenic sugars are d , and all biogenic amino acidsare l . There is yet another terminology in which R and S refer to a structural propertydenoting the handedness of a given chiral carbon in a molecule. This is also based on aconvention, which applies to any chiral organic compound. This convention has been takenin such a way that any chiral carbon can be assigned uniquely an R or S handednessgiven a precise set of rules and is thus a drastically different convention from l / d . Forexample, biogenic l -alanine is dextrorotatory (+) and its chiral carbon is of configuration Axel Brandenburg Fig. 4.2
Dextrorotatory (left) and levorotatory (right) tartaric acid. Adapted from Sevin(2015).
Fig. 4.3
Original drawing from Pasteur’s publication (Pasteur, 1922) showing dextroro-tatory (left, denoted Fig. 1) and levorotatory (right, denoted Fig. 4) tartaric acid. Adaptedfrom Sevin (2015).
Interestingly, already back then, Pasteur made the statement that theoccurrence of handedness is a demarcating property between living and non-living matter; see Goldanskii & Kuz’min (1989). Particularly important isPasteur’s discovery of 1857 that certain unidentified microorganisms had aconsiderable preference consuming (+)-tartaric acid over ( − )-tartaric acid;see the review articles by Gal (2008) and especially Sevin (2015). The con-nection between a preferred handedness of biomolecules and living matterwas reinforced in a number of subsequent papers. The first important onewas by Frank (1953), who started his paper by saying “I am informed by mycolleague Professor W. Moore that there is still widely believed to be a prob-lem of explaining the original asymmetric synthesis giving rise to the generaloptical activity of the chemical substances of living matter.” He then pro-posed a model, which contained two key ingredients for producing a system- S; biogenic l -serine is levorotatory ( − ) and its chiral carbon is of configuration S; biogenic l -cysteine is dextrorotatory (+) and its chiral carbon is of configuration R. Regardingsugars, d -glucose is dextrorotatory and d -fructose is levorotatory. Note also that commontable sugar (sucrose, i.e., a d -glucose– d -fructose dimer) is dextrorotatory. If one hydrolyzesit, one obtains a 1:1 mixture of d -glucose: l -fructose, corresponding to a mixture that islevorotatory, and thus its common name of “inverted sugar”. Homochirality: a prerequisite or consequence of life? 5 Fig. 4.4
Circular polarization measurements of the star-forming region OMC-1 in theOrion constellation. Note that the circular polarization is predominantly positive in thebulk of the molecular cloud. Courtesy of Bailey et al. (1998). atic handedness: autocatalysis and mutual antagonism. Autocatalysis meansmaking more of itself. This is of course a governing principle of biology, butit is meant here to be used at the molecular level during polymerization, i.e.,when long chains of shorter monomers are being assembled into a long macro-molecule. When each building block of the polymer has the same chirality,one says that it is isotactic. Mutual antagonism, on the other hand, can beinterpreted as the tendency for a monomer of the wrong handedness to spoilthe polymerization, so that the polymer would no longer be isotactic.The basic principle discovered by Frank has been governing many of theideas reflected in subsequent work in the field of homochirality. One suchexample was the work of Fajszi & Cz´eg´e (1981), who also proposed a math-ematical model closely related to that of Frank. However, there are variousother clues to the question of homochirality on Earth. One is that there ishandedness in one of the four basic forces in nature, the weak force. We ex-plain the details below, but this discovery implies that certain properties ofa chiral molecule, for example the dissociation energy, can be different forthe two enantiomers. The energy difference is usually a very small fraction– below 10 − of the energy of the molecule itself; see Bonner (2000) for areview. Because of the smallness, it is not obvious that this alone can be re-sponsible for achieving full homochirality. Thus, it is generally believed thatsome amplification mechanism is always needed.An interesting astrobiological connection emerges when considering circu-larly polarized light from astrophysical sources. This is light where the polar-ization plane rotates with time or position. Star-forming regions in the Orionconstellation have been found to emit circularly polarized light preferentiallyin only one of two possible senses; see Bailey et al. (1998); Bailey (2001); seeFigure 4.4 for an image of circular polarization in the Orion molecular cloud(OMC). This is interesting because different enantiomers can dissociate or Axel Brandenburg degrade differently under the influence of circularly polarized light. There isfurther support for this line of thought in that the chirality of amino acids inspace, for example in meteorites, is found to show a slight preference for thelevorotatory ones.We mentioned already that the connection between chirality and the originof life goes back to an early suggestion by Pasteur. Another connection toastrobiology arises when considering origins of life on other worlds. We willreturn to this at the end when we discuss possible ways of assessing the realityof extinct or extant life on Mars.
We mentioned already that the connection between the origin of homochi-rality and the origin of life has been suspected since the early work of Pas-teur. This connection became more concrete with an important discoveryof Joyce et al. (1984). He performed experiments with polynucleotide tem-plates, which facilitate polymerization with the complementary monomers ofthe same handedness. It was thought that polynucleotide templates of one handedness would di-rect the pairing with monomers of the same handedness and therefore favorthe selection of nucleotides of the same chirality. Joyce et al. (1984) performedexperiments with polymers of dextrorotatory ( d ) cytosine (C) nucleobases,poly(C d ), that are expected to pair with guanosine (G) mono-nucleotides toform short strands, oligo(G d ), along the poly(C d ). This was indeed the caseand led to the formation of up to 20 base pairs if the solution contained onlymonomers that are also dextrorotatory; see Figure 4.5a. By contrast, whenthe solution contained only levorotatory monomers, no polycondensation oc-curred; see Figure 4.5b.This was also expected, because base pairs with opposite handednessdo not fit together. The surprise came when using a racemic mixture of d and Lmono-nucleotides. A racemic mixture would indeed be expected un-der prebiotic conditions. However, in that case there was no significantpolycondensation—not even with the d mononucleotides; see Figure 4.5c.Thus, the idea of using template-directed polycondensation to select only oneof two handednesses did not work out. This phenomenon, which is known asenantiomeric cross inhibition, turned therefore out to be a major problem forthe RNA world (Gilbert, 1986), unless there was a reason to expect that onlymonomers of one handedness would be around. Joyce et al. (1984) wrote that“this inhibition raises an important problem for many theories of the origin Instead of polymerization, one sometimes talks about polycondensation to emphasize thefact that polymerization implies the removal of water in the reaction. Homochirality: a prerequisite or consequence of life? 7
Fig. 4.5
Chromatograms from the work of Joyce et al. (1984) showing template-directedpolycondensation of oligo(G d ) on poly(C d ) templates with d mononucleotide (left panel), Lmononucleotide (middle panel), and a racemic mixture of d and Lmononucleotide (rightpanel). of life”. Bonner (1991) credited Gol’danskii and Kuz’min in saying “that abiogenic scenario for the origin of chiral purity was not viable even in prin-ciple, since without preexisting chiral purity the selfreplication characteristicof living matter could not occur.” This is where the discovery of the weakforce comes into play. It provides a reason why one particular handednessmight be preferred. This will be discussed next. At the atomic level, there is the strong and the weak force. They are two ofthe four fundamental forces in nature: gravity, the electromagnetic force, theweak force, and the strong force; see the early review by Ulbricht (1975) inthe astrobiological context. The weak force is still rather strong comparedwith gravity (10 times stronger than gravity), but weak compared with theelectromagnetic force (10 times weaker). The weak force is responsible forthe decay of free neutrons, whose half-time is only about 10 minutes. Theneutron (n) decays then into a proton (p) and an electron (e). This, as well asthe reverse process (electron capture), occur also in the nuclei of atoms, forexample in the decay of radioactive potassium-40 into calcium-40 and argon-40, where the half-time is 1 .
25 Gyr. While there is significant astrobiologicalsignificance in this, for example for dating rocks, we are here concerned withthe fact that the electrons from the decay of neutrons are always left-handed. Measuring the argon inclusions in solidified rocks is the basis for determining the age ofrocks. The potassium-40 isotope constitutes only 0.01% of naturally occurring potassium.Its half-time is 1 .
25 Gyr, making it ideal for geochronology. The two decay reactions are K −→ Ca : n → p + e + ¯ ν e ( β decay) , (4.1) K −→ Ar : p + e → n + ν e (electron capture) . (4.2)The latter reaction is responsible for the argon in the atmospheres of Earth and Mars. Axel Brandenburg Fig. 4.6
Illustration of lepton helicity. The momentum p is a polar vector, while the spin S is an axial vector, so their dot product is a pseudoscalar, so it changes its sign wheninspected in a mirror. The electron from the beta decay of a neutron has p · S < left-handed . This means that the spin of the electron is anti-aligned with its momentum;see Figure 4.6. At low energies, however, the spin can flip relative to themomentum, so the handedness of electrons is predominantly a high energyphenomenon.The fact that electrons produced by β decay are chiral is remarkable,because it means that our physical world is, at least in some respects, dif-ferent from its mirror image. This goes back to a remarkable discovery byLee & Yang (1956), which earned them the Nobel Prize in Physics of 1957“for their penetrating investigation of the so-called parity laws which has ledto important discoveries regarding the elementary particles.”The connection between the chirality of electrons and that of biomoleculesis not immediately evident. There are two different ways of establishinga connection between the handedness imposed by the electroweak forceand the handedness in the biomolecules. One is through the fact that thebremsstrahlung emission from chiral electrons rotating around magneticfield lines is circularly polarized with a sense of polarization that dependson the chirality of the electrons. This implies that the sense of polariza-tion from bremsstrahlung is always negative and that this radiation de-stroys preferentially right-handed amino acids through photolysis. This wasfound by Goldhaber et al. (1957) and McVoy (1957) in back-to-back pa-pers in the Physical Review almost immediately after the influential paperby Lee & Yang (1956). If the idea that circularly polarized light can affectthe stability and selection of biomolecules is to make any sense, one shouldbe able to discover polarized light in nature. Interestingly, star-forming re-gions of OMC-1 in the Orion constellation have indeed been found to emitright-handed circularly polarized light (Bailey et al., 1998), supporting thisbasic idea; see Bailey (2001) for a discussion of the astrobiological impli-cations. However, the circular polarization observed by Bailey et al. (1998)occurred at near-infrared wavelengths and is not related to the mechanism ofGoldhaber et al. (1957) and McVoy (1957), who considered circularly polar-ized bremsstrahlung. Bailey et al. (1998) argued that the observed circularpolarization is caused by Mie scattering of unpolarized light, but this mech- Homochirality: a prerequisite or consequence of life? 9 anism is unrelated to the weak force. It is therefore conceivable that alsoleft-handed circularly polarized light could have been produced in the oppo-site direction.Instead of relying on starlight, there is yet another possibility. Muons,like electrons, belong to the group of fermions that tend to have a certainhandedness. Muons are about 200 times more massive than electrons andcan therefore be more effective in producing strongly circularly polarizedradiation. Muons occur in the cosmic radiation on Earth. They are only pro-duced when an energetic cosmic particle hits the Earth’s atmosphere andproduces a muon shower. For this reason, the muons in the cosmic radi-ation can play a significant role in affecting the chirality of biomoleculesGlobus & Blandford (2020). Unlike the observed circular polarization fromthe OMC-1 in the Orion constellation, the sense of circular polarization fromthis mechanism is connected with the weak force and therefore, just like inthe case of bremsstrahlung, only one of the two senses are possible, givingrise to the preferential destruction of right-handed amino acids.There is another completely different connection between biomolecules andthe weak force. Quantum-mechanical calculations have shown that the disso-ciation energies for d and Lmolecules are slightly different (Hegstrom, 1984;Hegstrom et al., 1980; Mason & Tranter, 1984). Therefore, the d and Laminoacids in a racemic mixture will degrade at different rates, which leads to anexcess of Lamino acids. Amino acids have been found in some meteorites (Engel & Macko, 1997).Two particular meteorites are often discussed in connection with the enan-tiomeric excess of amino acids: the Murray and the Murchison meteorites(Pizzarello & Cronin, 2000). Those are carbonaceous chondrites, which meansthat they are carbon-rich. They are also rich in organics, as was superficiallyevidenced by the smell reported by initial eyewitnesses of the Murchisonmeteorite. Interestingly, Table 1.5 of Rothery et al. (2008) lists 18 differentamino acids that have been found not only in the Murchison meteorite, butalso in the Miller–Urey experiment (Miller, 1953). Twelve of them are notfound in proteins on Earth. This is interesting, because it suggests that thoseamino acids were indeed originally present in the meteorite and could nothave come from contamination by life after the meteorite landed on Earth.Those amino acids that are found on Earth include glycine, alanine, valine,proline, aspartic acid, and glutamic acidThe sense of the enantiomeric excess is the same in the two meteorites,corresponding to levorotatory amino acids, but the amount is different(Pizzarello & Cronin, 2000). In addition, there is the possibility that theenantiomeric excess may be caused by terrestrial contamination (Bada, 1995).
But, as emphasized above, this would only apply to the six amino acids thatare also found on Earth. In particular, those amino acids that have the clear-est enantiomeric excess are also those that are most vulnerable to contamina-tion; see Ehrenfreund et al. (2001) for a discussion of terrestrial contaminantsin connection with the carbonaceous chondrites Orgueil and Ivuna. They areof the type CI (I for Ivuna) and are extremely fragile and therefore suscep-tible to terrestrial weathering. In Orgueil, alanine was found to be racemicand was argued to be abiotic in origin (Ehrenfreund et al., 2001). They couldnot, however, support the suggestion of terrestrial contamination with cor-responding soil samples. Incidently, the Orgueil meteorite is also known fora famous contamination hoax; see Anders et al. (1964), who discusses thepaper by Cloez (1864) claiming the existence of life on the meteoritic parentbody a few weeks after Pasteur’s famous lecture to the French Academy onthe spontaneous generation of life.Among the possible causes for the enantiomeric excess of meteoritic aminoacids, there is the aforementioned effect of circularly polarized starlight. Cir-cularly polarized ultraviolet light could have preferentially destroyed one ofthe two chiralities through photolysis (Zeldovich et al., 1977). The exper-iments of Bonner et al. (1981) with a d Lmixture of leucine showed thatright-handed circular polarized light leads to a preferential destruction of d leucine, while left-handed circular polarized leads to a preferential destruc-tion of Lleucine; see also (Meierhenrich & Thiemann, 2004) for recent ex-periments. To explain the systematic Lexcess of amino acids on Earth, onewould need the protosolar nebula to be irradiated by right-handed polarizedlight. Indeed, the star-forming region OMC-1 has been found to emit right-handed circularly polarized light, supporting this basic idea (Bailey et al.,1998; Bailey, 2001; Boyd et al., 2018). However, as discussed above, also left-handed circularly polarized light could have been produced in the oppositedirection. Therefore, any systematic Lexcess of amino acids caused by thismechanism would have been by chance.The enantiomeric excess found in some amino acids is at most around 1–2%. This would be too small to avoid the problem reported by Joyce et al.(1984). So, even if there is an external effect producing a systematic enan-tiomeric excess, we always need an amplification mechanism. Therefore, wediscuss next the Frank mechanism and move then to some variants of itthat avoid either autocatalysis or enantiomeric cross inhibition. We begin byexplaining first the basic idea. The essence of the mechanism of Frank (1953) is the combination of twoingredients operating in a substrate: catalysis of molecules for their own pro-duction and “anticatalysis” that corresponds to some antagonism or delete-
Homochirality: a prerequisite or consequence of life? 11
Fig. 4.7
Sketch showing the effect of enantiomeric cross inhibition only. Red and bluebars indicate opposite enantiomers, with the blue one being initially in the majority byone “unit”, the separation between subsequent bars. The gray columns indicate the totalamounts, which is 5 units for the column with blue bars and 4 units for the column withred bars. In the end, in step 4, only one unit of the enantiomer marked with blue barssurvives. rious effect. He even talks about “poisoning” one of the two enantiomers outof existence. In fact, he called his simple mathematical model a “life model”,suggesting already back then that he was thinking of them as being processesacting at the moment when the first life emerged.The essence of Frank’s model is perhaps best explained graphically. Forthis purpose, it is most instructive to begin with the deleterious effect byassuming that an equal amount of d and Lenantiomers eliminate each otherin each reaction step. This is illustrated in Figure 4.7, where we indicate theamount of d enantiomers with blue bars and the amount of Lenantiomerswith red bars.We see that, in the end, only d is left (see the blue bars), but the amountis very small, namely just as big as the initial difference by which one of thetwo enantiomers exceeded the other. This is why we also need autocatalysis.Autocatalysis is a process that is not enantioselective, i.e., it works the sameway for the d and Lenantiomers. This is demonstrated by stretching out thecolumns by a factor such that the highest column always retains the originalheight; see Figure 4.8. It is instructive to quantify here the enantiomericexcess (e.e.) as the ratio of the difference to the sum of the concentrations ofright- and left-handed compounds, i.e.,e.e. = [ D ] − [ L ][ D ] + [ L ] (4.3)At each each, the value of e.e. in Figs. 4.7 and 4.8 is the same: 1 / (5+4) = 1 / / (4 + 3) = 1 /
7, 1 / (3 + 2) = 1 /
5, 1 / (2 + 1) = 1 /
3, and finally1 / Fig. 4.8
Similar to Figure 4.7, but in each reaction step, the separations between sub-sequent bars has been stretched by a certain factor such that the column with the bluebars retains the same height. The stretching emulates the effect of autocatalysis. In theend, again only the enantiomers marked with blue bars survive, but now, because of thestretching, the amount is no longer small. tiomeric cross inhibition. It was clear from Frank’s work that, as long as bothreactions, autocatalysis and antagonism, remain active, the racemic state isunstable and there will be a bifurcation into a chiral state with an excess ofeither d or Lenantiomers; see also Sandars (2005), where enantiomeric crossinhibition was no longer regarded as a problem, but as an essential ingredientin achieving full homochirality.In the Frank mechanism, there must be at least a very small initial imbal-ance which will then be amplified. However, this is not a problem because,even if we tried to construct a purely racemic mixture in the laboratory, therewill always remain a tiny imbalance. This is just for the same reasons thatin a cup of blueberries we will hardly ever have exactly the same numbertwice. Given that the racemic state is unstable, the enantiomeric excess, as de-fined in Eq. (4.3), will grow exponentially in time and it does therefore notmatter how small the initial imbalance in the concentrations of d and Lwas.To demonstrate this more clearly, we use here a figure of Brandenburg et al.(2007), who considered the model of Plasson et al. (2004), which we discusslater in more detail in Section 4.10. This model also has the property thatthe racemic state is unstable and that the system evolves toward one of thetwo homochiral states.In the following, we discuss an ensemble of solutions of the model ofPlasson et al. (2004) with different realizations or initial states, which con-sisted of a racemic mixture of equally many d and Lenantiomers. Figure 4.9shows that one always obtains a fully homochiral state, but in about 50% ofthe cases (or in 50% of the realizations of the same experiment), one obtains If you take a cup of blueberries, for example, the exact number varies between 65and 70 ( ), so we mustalways expect there to be a small imbalance in the number if we say we have an equal amount of d and Lenantiomers. Mathematically, this imbalance grows with the squareroot of the number of molecules (or blueberries) and would be about ± for onemole with N = 6 × molecules (or ± / √N = 10 − in one mole (or 12% for 65 blueberries). Homochirality: a prerequisite or consequence of life? 13 Fig. 4.9
Probability distribution of the initial enantiomeric excess (e.e.) for racemic mix-tures with 10 and 10 molecules together with the resulting evolution of e.e., both inlogarithmic and linear representations. The dashed lines give a gaussian fit to the distri-bution function. Adapted from Brandenburg et al. (2007). eventually a state with either just d enantiomers, and in the other 50% ofthe cases or realizations, one with only Lenantiomers. When we talk aboutdifferent cases or realizations, we must realize that the genesis of life on Earthis just one such realization. Another one may have occurred on Mars, or inthe atmosphere of Venus, or elsewhere in the Galaxy. Of course, there is alsothe possibility of multiple geneses on Earth alone, with certain lifeforms be-ing either completely or partially wiped out (Davies & Lineweaver, 2005).The latter case may be particularly interesting in models where we allow forchemical evolution in models with spatial extent, which will also be discussedlater in Section 4.9. Unlike the process of enantiomeric cross inhibition, where we have referredto the experiments of Joyce et al. (1984), the actual evidence for auto-catalysis is poor. In fact, there is only the classical reaction of Soai et al.(1995) that exhibits autocatalysis and can lead to a finite enantiomeric ex-cess; see Gehring et al. (2010) and Athavale et al. (2020) for more recentwork clarifying the implications of the Soai reaction. However, the basicidea of autocatalysis remains plausible, especially since the discovery by
Guerrier-Takada & Altman (1984) and Cech (1986) that RNA molecules canexhibit autocatalytic functionality. This was a very important discovery thatearned Sidney Altman and Thomas R. Cech the Nobel Prize in Chemistry in1989 “for their discovery of catalytic properties of RNA.” It is this mechanismthat is at the heart of the idea of an RNA world (Gilbert, 1986).It is important to realize that the existing evidence for autocatalysis isirrelevant from an astrobiological viewpoint. This is particularly clear in viewof the fact that the Soai reaction requires zinc alkoxides as an additionalcrucial catalyst. Those compounds are not generally believed to play a roleon the early Earth.Autocatalysis in the sense of making more of itself is obviously a basicprinciple of life, but this is already at a rather complex and not at the levelof individual molecules. It is therefore possible that autocatalysis does notplay a significant role and that it is rather the process of network catalysis(Plasson, 2015), i.e., the combined action of different molecules that lead tothe desired appearance of what is in the end equivalent to autocatalysis. Wewill return to this in Section 4.10, when we discuss a particular sequenceof reactions that, in the end, have the effect of autocatalysis, even thoughautocatalysis is not present in any individual reaction.
In the beginning of this review, we have discussed extensively the possibilityof a systematic bias resulting eventually from the fact that the weak forceintroduces a preference of one of two handednesses through one or severalpossible effects. Those would always favor Lamino acids and d sugars. Onthe other hand, we have now seen that the Frank mechanism can result infull homochirality of either chirality. Does this mean that the bias introducedby the weak force is unimportant? Maybe not quite. It depends on how strongthe external influence is in comparison with the speed of autocatalysis, whichdetermines the rate of the instability. This was first discussed in the workof Kondepudi & Nelson (1983, 1985) in papers that appeared just at thetime as that of Joyce et al. (1984), but, at the time, neither of those authorsmentioned the work of Frank.The paper by Kondepudi & Nelson (1983, 1985) was in principle quitegeneral and therefore applicable to other symmetry breaking instabilities. Inessence, the effect of the bias is that it makes the bifurcation asymmetric.A symmetric bifurcation is one where the enantiomeric excess (positive ornegative) departs away from strictly zero as some bifurcation parameter in-creases. Sandars (2003) identified this bifurcation parameter with the fidelityof the autocatalytic process, which measures the probability with which thecatalytic process does indeed facilitate the polymerization with monomers ofthe same chirality instead of the opposite one. The fidelity f is unity (zero) Homochirality: a prerequisite or consequence of life? 15
Fig. 4.10
Bifurcation diagrams showing a slight preference for positive enantiomericexcess (e.e., here denoted by η ). The left panel has been adapted from Brandenburg et al.(2005), where the bifurcation begins for a fidelity f that is clearly below the otherwisecritical value of f = 0 .
5. (The dashed line denotes the unstable solution.) The right panelhas been adapted from Brandenburg (2019), who considered a stochastic model where f = 0 . when the autocatalytic process always (never) produces polymerization withthe same handedness.In Figure 4.10 we show a bifurcation diagram from the work of Brandenburg et al.(2005), where we see that for all values of the fidelity f , the solution withpositive enantiomeric excess ( η ) is stable. For η > ∼ .
5, the solution withnegative η is also stable, but to reach this solution, the initial fluctuationsmust be large enough. The complete bifurcation diagram also contains an un-stable solution, which corresponds to the watershed between the two stablebranches. In the left hand plot of Figure 4.10, it is shown as a dashed line.Similar diagrams have also appeared in the works of Kondepudi & Nelson(1983) and later in the review of Avetisov et al. (1991). Looking at the chromatographs of Joyce et al. (1984), we see that the ul-timate goal is to assemble long polymers. For this reason, Sandars (2003)developed a polymerization model for d and Lnucleotides, where he also al-lowed for enantiomeric cross inhibition. In his model, monomers of the d and Lforms are being produced at rates, Q D and Q L , respectively, that are pro-portional to same reaction rate k C and the concentration of some substrate[ S ], i.e., Q D = k C [ S ] n (1 + f ) C D + (1 − f ) C L + C D o , (4.4) Q L = k C [ S ] n (1 + f ) C L + (1 − f ) C D + C L o , (4.5) where 0 ≤ f ≤ C L and C D are parameters describing theglobal handedness of the system [the concentrations of the longest possi-ble chains of left- and right-handed polymers for Sandars (2003) and quan-tities proportional to the masses of all polymers of the d and Lforms forBrandenburg et al. (2005)]. These parameters are introduced in such a waythat for f > Q D increases with C D , and Q L increases with C L . The parameters C D and C L allow for the possibilityof non-catalytic production of left- and right-handed monomers. They canbe different from zero when there is an external bias or external influence.When C D = C L = 0, Eqs. (4.4) and (4.5) show that Q D = k C [ S ] C D and Q L = k C [ S ] C L when f = 1, while Q D = Q L = k C [ S ]( C D + C L ) / f = 0.Sandars (2003) assumed that the catalytic effect depends on the concen-trations of the longest possible chains of left and right handed polymers.Brandenburg et al. (2005) adopted a similar model, but assumed that C D and C L to be proportional to the masses of all polymers of the d and Lforms,respectively. This allowed them to extend the model to much longer polymerswithout needing to wait for the longest one to appear before autocatalysisbecame possible at all.The full set of reactions included in the model of Sandars (2003) is (for n ≥ L n + L k S −→ L n +1 , (4.6) L n + D k I −→ L n D , (4.7) L + L n D k S −→ L n +1 D , (4.8) D + L n D k I −→ D L n D , (4.9)where k S and k I are suitably chosen reaction rates for symmetric autocatal-ysis and (non-symmetric) inhibition, respectively. For all four equations wehave the complementary reactions obtained by exchanging L ⇄ D . The poly-merization starts from a large but limited set of monomers that all begin todevelop longer polymers. Because the number of monomers was limited, thetheoretically obtained chromatograms show a characteristic wave-like motionwith increasing time; see Figure 4.11.Particularly important is of course the case where monomers of both chiral-ities exist. In that case, the result depends on the fidelity of the autocatalyticreactions; see Figure 4.12 for such a result. We see that longer polymers canonly be produced when the fidelity is relatively high. The lack of sufficientfidelity therefore explains the limited length of polymers found in the workof Joyce et al. (1984). Homochirality: a prerequisite or consequence of life? 17
Fig. 4.11
Normalized concentration [ L n ] versus n showing a wave-like evolution of aninitial Gaussian profile (solid line). All later times are shown as dashed lines, except for thelast time, which is shown as a long-dashed line. Adapted from Brandenburg et al. (2005). Fig. 4.12 [ L n ] (left) and [ L n D ] (right) of equilibrium solutions for different values of f .For f = 1 we have [ L n D ] = 0, which cannot be seen in the logarithmic representation.Adapted from Brandenburg et al. (2005). In all the chemical reactions discussed so far, the assumption was made thatthe system is well mixed. This means that the concentrations [ D n ], [ D n L ], etc,are the same everywhere. On larger length scales, this assumption must even-tually break down. Even on the scale of alkaline hydrothermal vents, wheremany scientists place the origin of life (Russell, 2006) the relevant chemical re-actions would take place within small semiporous cells. It is then conceivablethat similar reactions take place in neighboring compartments that would beformed by the sulfurous precipitants from these vents. Russell (2006) drawshere an analysis to the chemical gardens that would allow for a growing arrangement of new compartments, which could act as primitive cells andwould, in principle, allow for Darwinian evolution as these chemical reactionspropagate from one layer of compartments to the next; see also Russell et al.(2014) and Barge et al. (2017, 2019) for more recent developments. In eachof these compartments, strong spatial gradients and 10 -fold concentrationenhancements can be achieved through thermal convective flows when theaspect ratio of the compartment is sufficiently large (Baaske et al., 2007).This setup can also lead to oscillations, which can locally lead to exponen-tial replication of nuclei acids, analogous to the polymerase chain reaction(Braun & Libchaber, 2002).In the scenario described above, we can no longer talk about a well mixedsystem. Therefore, the concentrations must be regarded as function not onlyof time, but also of space. Because the chemistry in neighboring compart-ments is loosely coupled by diffusion terms, there would be spatio-temporalevolution. In that case, the chemical reaction equations attain a spatial diffu-sion term. The resulting system of equations is usually referred to as reaction–diffusion equations. Such models, but for only one instead of several species,have frequently been employed in modeling the dynamics of diseases such asthe black death (Noble, 1974) or rabies (K¨all´en et al., 1985; Murray et al.,1986). It has also been used to model the spreading of the novel coronavirus,where the total number of cases was found to follow a quadratic or piecewisequadratic growth behavior (Brandenburg, 2020).To address the question of homochirality in an extended system, Brandenburg & Multam¨aki(2004) employed a similar approach, but with two or multiple species. Mul-tiple species occur when we invoke polymers of different length and com-position of different species for the d and Lforms. They found that a givenspecies tends to spread through front propagation. It turned out that, oncetwo populations of opposite chirality meet, the front can no longer propagateand the evolution comes to a halt. This result was first obtained in a one-dimensional model, where the concentrations of d and l depend on just onespatial coordinate x and on time t . The result is shown in Figure 4.13, for theevolution of short polymers. These are all regarded as separate species. Theinitial condition consists of a small number of monomers of the Lform at oneposition (at x/λ = − . λ is the length of the domain)and a three times larger number of monomers of the d form at another po-sition (at x/λ = +0 . x position. We see that in both positions, longer polymersare produced, indicated by the yellow-reddish colors. The initially threefoldlarger number of d monomers is insignificant, because the growth is exponen-tially fast soon saturates at the same level as that for the Lmonomers, whenthe polymers have reached their maximum size. At the same time, polymersof the same handedness can still be produced by diffusion to the neighbor-ing positions. This leads to a propagation front. However, when polymers ofopposite chirality emerge at neighboring positions, the front stops (here at Homochirality: a prerequisite or consequence of life? 19
Fig. 4.13
Color scale plots of [ D n ] and [ L n ] after 0 . x and polymer length n . In 0 < x/λ < .
25, only d polymers exist (left) and no Lpolymers at all (right), while in − . < x/λ < x ≈ d and Lmolecules around a circular front, then the numberof molecules on the inner front is would be one less than the number ofmolecules on the outer front; see Figure 4.16 for an illustration. To understand why the difference in the number of molecules between the outer and innercircles is always just three, let us imagine the molecules being represented by little discsof radius r on the periphery of a circle of radius R . The circumferences of the outer andinner peripheries are 2 π ( R ± r ) = 2 πR ± πr for the upper and lower signs, respectively. Thedifference is therefore 2 πr ≈ d , where d = 2 r is the diameter of each disc. The differencein the number of discs is there for three.0 Axel Brandenburg Fig. 4.14
Left : Fractional concentration of one chirality versus position ( x and y ) atfour different times t , normalized by the diffusivity κ per total surface area λ , so tκ/λ isnondimensional. In this numerical simulation, κ/ ( λ λ ) = 2 × − , and the resolution was1024 mesh points. The number of disconnected regions decreases from 4 in the first plotto 3, 2, and 1. Right : Evolution of enantiomeric excess η for the model shown in the left.The inset shows the normalized slope. Note the four distinct regimes with progressivelydecreasing slope. Adapted from Brandenburg & Multam¨aki (2004). Fig. 4.15
Left : Shrinking of an initially large patch of molecules of the d form surroundedby molecules of the Lform. Right : The resulting enantiomeric excess (e.e.) versus time t ,scaled with the activation rate a , so at is nondimensional. Note that it was initially positive,but reaches later complete homochirality with η = − We said already in Section 4.6 that autocatalysis may not be a particularlyevident process on the early Earth. For that reason, Plasson et al. (2004)devised a completely different mechanism that they advertised as “recyclingFrank”. It is based on the combination of the following four important reac-
Homochirality: a prerequisite or consequence of life? 21
Fig. 4.16
Sketch illustrating that densely packed discs inside the periphery of a circlediffer in their number from those outside the periphery by just 3. This result is independentof the total number; compare the left and right illustrations with 60 and 120 discs, respec-tively. As time goes on, pairs of red and blue discs get eliminated and the circle shrinks,because the number of discs inside the periphery is slightly smaller (by three) than thenumber of discs outside the periphery. The smallness of the difference in the numbers onthe inner and outer peripheries is the reason for the shrinking of the circle slowing down. tions: activation (A), polymerization (P), epimerization (E), and depolymer-ization (D). So the resulting model is also referred to as the APED model. Avariant of this model was studied by Konstantinov & Konstantinova (2018).It is important to emphasize that there is no explicit autocatalytic reaction.However, the combined sequence of reactions (Brandenburg et al., 2007) D + L a −→ D ∗ + L p −→ DL e −→ LL h −→ L + L, (4.10) L + D a −→ L ∗ + D p −→ LD e −→ DD h −→ D + D. (4.11)does effectively result in an autocatalytic reaction, but it is not a directone. First of all, it requires an activation step, indicated by asterisk, a poly-merization step (with the rate constant p ), an epimerization step (with therate constant e ), and finally a depolymerization step (with the rate constant h ). Because the autocatalysis in indirect, this sequence of steps can there-fore be regarded as a simple example of a network catalysis (Plasson, 2015;Hochberg et al., 2017). During the last decade, there has been some increased interest in the roleof fluctuations; see a recent review by Walker (2017). Fluctuations can play important roles in diluted systems, in which the number of molecules is small.In such case, rate equations no longer provide a suitable description of therelevant kinetics when the system is dilute and reactions are rare (Gillespie,1977; Toxvaerd, 2014). In that case, a stochastic approach must be adopted.This may be relevant to the work of Toxvaerd (2013), where homochiral-ity has been found without apparent autocatalysis or enantiomeric cross-inhibition. Instead of solving rate equations, as discussed in the previoussections, one solves stochastic equations. This means that at each reactionstep, the state of the system changes, but with a reaction that is taken todepend on chance with a certain probability. The system is then described byvector q = ( n A , n D , n L ), where n A denotes the numbers of achiral moleculesand n D and n L denotes the number of molecules of the d and Lforms, re-spectively. In the model of Brandenburg (2019), seven different reactions wereconsidered, each with a certain probability. Not all those seven reactions needto be possible in a certain experiment, so the probability for some reactionscan be zero. Applying a single reaction step with enantiomeric cross inhibitionimplies ( n A , n D , n L ) k × −→ ( n A + 2 , n D − , n L − , (4.12)i.e., the numbers of D and L get reduced by one, and that of A increases bytwo. We can also include spontaneous deracemization reactions, i.e.,( n A , n D , n L ) k + −→ ( n A − , n D + 1 , n L ) , (4.13)( n A , n D , n L ) k + −→ ( n A − , n D , n L + 1) . (4.14)To model different reaction rates, the different reactions must happen withdifferent probabilities. This is done by taking at each reaction step a randomnumber between zero and one. Suppose we want to model enantiomeric crossinhibition together with spontaneous deracemization, then the probabilitythat the first reaction happens is proportional to k × , and the probability thatone of the other two reactions in Eqs. (4.14) and (4.14) occurs is proportionalto k + /
2. If we also allow for the possibility that nothing happens (probabilityproportional to k ), then our scheme with q → q + ∆ q is as follows:if 0 ≤ r < r ≡ k × then ∆ q = (2 , − , − , (4.15)if r ≤ r < r ≡ r + k + / ∆ q = ( − , , , (4.16)if r ≤ r < r ≡ r + k + / ∆ q = ( − , , , (4.17)if r ≤ r < ∆ q = (no reaction) . (4.18)Note that k × + k + + k = 1 is here assumed. This particular experimentwas referred to as experiment III in Brandenburg (2019), where k = 0 wasassumed. As he varied k × , k + was assumed to vary correspondingly suchthat k + = 1 − k × . The results of this experiment are similar to those withspontaneous deracemization replaced by autocatalysis, which is referred to as Homochirality: a prerequisite or consequence of life? 23
Fig. 4.17
Bifurcation diagrams of h| η |i (black) and h A i (red) for N = 3000 (solid lines)and N = 300 (dotted lines) as a function of parameters for models I, II, III, and IV.Adapted from Brandenburg (2019). experiment I in Figure 4.17. Here, the autocatalysis rate is varied such that k C = 1 − k × . This is the standard Frank model, but for a diluted system, whilemodel III is close to that of Sugimori et al. (2008, 2009), who were the firstto find a transition to full homochirality even without autocatalysis. Next,in experiment II, there is autocatalysis, but no enantiomeric cross inhibitionand just spontaneous racemization instead. This type of model was first con-sidered by Jafarpour et al. (2015, 2017). The transition to full homochiralitywas originally though impossible in such a model (Stich et al., 2016).In a comparative study, all these processes were studied within a singleunified model. In Figure 4.17 we show the results of the four different ex-periments. We mentioned already experiments I–III. In experiment IV, bycomparison, there is just racemization and deracemization, but neither auto-catalysis nor enantiomeric cross inhibition. In that case, the average of themodulus of the enantiomeric excess, h| η |i , no longer reaches unity, but levelsoff at about 0 . k + > ∼ .
4. We also see from the red lines that the achiralcompounds ( A ) get depleted in favor of producing chiral ones either of the d or the Lform. Back in 1976, when the Viking I and II landers visited the Chryse Planitiaand Utopia Planitia regions, respectively, many of the things we now knowabout Mars were still unclear. In particular, the existence of water on Marswas still very much an open question. Nevertheless, one was relatively opti-mistic at the time. Both landers came with advanced experiments on board tolook for life. One of the experiments, the Labeled Release (LR) experiment,was actually successful (Levin & Straat, 1976, 1977), but another experimentnever detected any organics, which was decisive enough to conclude that nolife was detected after all (Klein et al., 1976).The idea behind the LR experiment is simple: take Martian soil, mix it withwater and organics as nutrients, and see whether a metabolic reaction occursthat decomposes the nutrients and produces a gaseous waste product, for ex-ample methane or carbon dioxide; see the recent account by Levin & Straat(2016), where detailed tests with various terrestrial soils were presented. Thecarbon atoms of the nutrients were labelled with carbon-14 isotopes, a tech-nique commonly used in medicine, which allows one to trace those labeledcarbon atoms by their radioactivity. To identify the gaseous waste product,one simply measured the level of radioactivity. Control experiments withsterilized soil showed that only fresh Martian soil produced a reaction. TheViking laboratories were flexible enough to perform additional experimentswith lower sterilization temperatures. The critical temperature below whichno sterilization occurred was found to be around 50 ◦ . Those temperatureswould appear reasonable for Martian cryophiles, but are generally too lowfor sterilization on Earth. The experiment was tested in various deserts onEarth and it was able to detect metabolism at measurable levels.It is only since 2012 that organics were detected on the Martian surface bythe Curiosity rover; see Voosen (2018) for a popular account. We also knowthat organics get quickly destroyed by perchlorates, in particular KClO ,which were discovered on the Martian surface by the Phoenix lander in 2008(Hecht et al., 2009). Such processes could potentially result in reactions foundwith the LR experiment (Quinn et al., 2005), but it remains puzzling whya critical sterilization temperature of 50 ◦ was found, and not much higher,for example. Thus, while an explanation in terms of abiotic processes hasnot been fully conclusive (Valdivia-Silva, 2012), the explanation that life wasactually detected might seem more straightforward (Levin & Straat, 2016).However, as already noted by Carl Sagan, “the more extraordinary the claim,the more extraordinarily well-tested the evidence must be. The person makingthe extraordinary claim has the burden of proving to the experts at largethat his or her belief has more validity than the one almost everyone elseaccepts.” In any case, it seems justified to repeat this experiment to clarify Homochirality: a prerequisite or consequence of life? 25
Fig. 4.18
Metabolic consumption of d -glucose (filled symbols) and L-glucose (opensymbols) and by (1) Saccharomyces cerevisiae , (2)
Penicilium expansum , (3)
E. coli , (4)
Micrococcus luteus , (5)
Natronobacterium sp. , and (6)
Halostagnicola sp.
Adapted fromSun et al. (2009). the phenomenon that the Viking landers discovered back in 1976; see alsothe recent paper by Carrier et al. (2020).Given that the experiment is relatively simple and can detect life underharsh conditions on Earth, it would be interesting to repeat some variantsof it in the future. One such variant would be to allow for the detection of handedness. This would constitute a more conclusive signature of life thanjust the discovery of some metabolism. Such an experiment can be done byusing chiral nutrients, which goes back to the old findings of Pasteur of 1857that certain microorganisms had a preference for consuming (+)-tartaric acidover ( − )-tartaric acid; see the reviews by Gal (2008) and Sevin (2015).In Figure 4.18 we show the result of recent experiments by Sun et al. (2009)using different types of eukarya, bacteria, and archaea, which were giveneither d sugars or Lsugars. In most of the cases there was a clear preferencein the microbes taking up the naturally occurring d sugars compared with thesynthetically produced Lsugars. Subsequent work showed that the specificityfor some microbes is low and that some of those can use sugars of the oppositechirality also (Moazeni et al., 2010). Although the dependence on the type ofnutrients has not yet been studied in detail, it may be important to allow fora broad range of different ones in an attempt to account for such ambiguities. Louis Pasteur was well ahead of his time when he identified the biologicalrole of chirality in living matter. Particular remarkable is his realization that,during fermentation, the metabolic uptake of nutrients of opposite chiralitiesis different. To understand why this experiment was not put in the contextof extraterrestrial life detection, we have to realize that in those years, itwas not uncommon to think of extraterrestrial life on Mars. When the as-tronomer Herschel (1784) discovered seasons on Mars, he wrote in his paperin the Philosophical Transactions of the Royal Society that this “planet has aconsiderable but moderate atmosphere so that its inhabitants probably enjoya situation in many respects similar to ours.” So, not just the existence oflife, but the existence of intelligent of life on Mars was commonly expected.This only changed in 1964, when Mariner 4 returned the first flyby picturesof Mars, which suggested that any life there would probably only be of mi-crobial nature. But that Vikings 1 and 2 would not even find any organicson Mars was such a shock to many that the search for life in the Universeappeared fairly hopeless, and Mars exploration was put on hold for the nexttwo decades. This all changed since the turn of the century with the discoveryof extremophiles on Earth and the realization that terrestrial life has existedsince the time that stable continents existed. Gradually, with the conclusivedetection of water on Mars, the search for extinct or extant life on Marsrestarted, and Pasteur’s discovery of different metabolic uptakes of d and Lnutrients may finally turn into an actual Martian experiment. As shownby Sun et al. (2009), this property can be used to detect the presence of ho-mochirality through in situ experiments. Homochirality can also be detectedthrough remote sensing by looking for circular polarization. This approachhas been persued by Patty et al. (2019), who found negative or left-handed Homochirality: a prerequisite or consequence of life? 27 circularly polarized light emitted from terrestrial plant life at about 680 nm;see also Avnir (2021) for a recent review. To what extent this technique canbe used as a biomarker still needs to be seen, but it is amazing to see oncemore how Pasteur’s early discoveries have shaped some important aspects ofastrobiology.While homochirality remains a property that is strongly associated withlife—or at least some chemical process that keeps the system far fromequilibrium—it is not clear whether we should expect it to have the sameor the opposite handedness as an Earth (Bada, 1996). To answer this ques-tion, one would need to have more realistic models with meaningful estimatesfor the concentrations of suitable chemicals in some protocells. This wouldallow for an estimate of the level of fluctuations in relation to the strengthsof the small but systematic effects resulting from the weak force. It wouldbe the only way of guaranteeing that each genesis of life always producesthe same chirality. But for now, we should be satisfied if one could find (andunderstand) any type of an extraterrestrial metabolic process that works dif-ferently for nutrients of d and Lforms. Thus, the discussed possibilities wouldneed to be put on a quantitatively meaningfully basis. And if it is not life, itcertainly is interesting enough to deserve serious attention! Acknowledgements
I am grateful to the two referees for many useful comments and suggestionsthat have led to improvements of the manuscript. In particular, I wish toacknowledge Rapha¨el’s clarifications on the differences in the terminology interms of levorotatory and dextrorotatory on the one hand and that in termsof d and Lon the other. This work was supported in part through the SwedishResearch Council, grant 2019-04234. I acknowledge the allocation of comput-ing resources provided by the Swedish National Allocations Committee atthe Center for Parallel Computers at the Royal Institute of Technology inStockholm. References
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