Quentin Sallembien
email: quentin.sallembien.2017@enscbp.fr

Laurent Bouteiller

Jeanne Crassous
email: jeanne.crassous@univ-rennes1.fr

Matthieu Raynal
email: matthieu.raynal@sorbonne-universite.fr

Possible Chemical and Physical Scenarios Towards Biological Homochirality

The single chirality of biological molecules in terrestrial biology raises more questions than certitudes about its origin. The emergence of biological homochirality (BH) and its connection with the appearance of Life has elicited a large number of theories related to the generation, amplification and preservation of a chiral bias in molecules of Life under prebiotically relevant conditions. However, a global scenario is still lacking. Here, the possibility of inducing a significant chiral bias "from scratch", i.e. in absence of pre-existing enantiomerically-enriched chemical species, will be considered first. It includes phenomena that are inherent to the nature of matter itself, such as the infinitesimal energy difference between enantiomers as a result of violation of parity in certain interactions within nucleus of atoms, and physicochemical processes related to interactions between chiral organic molecules and physical fields, polarized particles, polarized spins and chiral surfaces. The spontaneous emergence of chirality in absence of detectable chiral physical and chemical sources has recently undergone significant advances thanks to the deracemization of conglomerates through Viedma ripening and asymmetric auto-catalysis with the Soai reaction. All these phenomena are commonly discussed as plausible sources of asymmetry under prebiotic conditions and are potentially accountable for the primeval chiral bias in molecules of Life. Then, several scenarios will be discussed that are aimed to reflect the different debates about the emergence of BH: extraterrestrial or terrestrial origin (where?), nature of the mechanisms leading to the propagation and enhancement of the primeval chiral bias (how?) and temporal sequence between chemical homochirality, BH and Life emergence (when ?). The last point encompasses various theories setting the emergence of optically pure molecules at the stage of building blocks of Life, of instructed/functional polymers or later. The underlying principles and the experimental evidences will be commented for each scenario with a particular attention on those leading to the induction and enhancement of enantiomeric excesses in proteinogenic amino acids, natural sugars, their intermediates or derivatives. The aim of this review is to propose an updated and timely synopsis in order to stimulate new efforts in this interdisciplinary field.

Dedicated

to the memory of Sandra Pizzarello (1933-2021) 7

Chirality is found at all scales in matter, from elementary particles to cucumber tendrils, 8 from screws to spiral galaxies, in living and inert systems. 9 It is also an everyday concern in industry (e.g. pharma, agribusiness, cosmetics) 10-14 as well as in fundamental research (visible in countless conferences encompassing not only chemistry, physics, and biology but also economy and arts). 15 Homochirality of Life refers to the fact that Nature has chosen a specific handedness. Homochirality is a fascinating aspect of terrestrial biology: All living systems are composed of L-amino acids and D-sugars & to such an elevated extent that the occurrence of the molecules of Life with different configurations (e.g. D-amino acids) is seen as a curiosity. 16

Clearly, the perfect level of selectivity reached by evolution and preserved along billion years, is out of reach for currently ARTICLE

Introduction

In 1884, Lord Kelvin used the word chirality, -derived from the Proto-Indo-European *ǵʰesr-through the Ancient Greek χείρ (kheír), that both mean 'hand'-and gave the following definition: "an object is chiral if and only if it is not superimposable on its mirror image".

1 Additionally, chirality can be described based on symmetry aspects: an object is chiral if it possesses no symmetry elements of the second kind (i.e. if it is devoid of any improper axis of rotation). [START_REF] Mislow | Topics in Stereochemistry[END_REF] Whilst the manifestation of chirality at the macroscopic scale sparked human's curiosity from antiquity, its observation at the molecular and sub-atomic levels is relatively recent. In the 19 th -century, advances made in optics, 3 crystallography 4 and chemistry 5 paved the way to the scientific study of molecular chirality (named 'molecular dissymmetry' by Louis Pasteur) 6 which soon after manifested itself in a variety of studied phenomena. The term "chirality" took additionally almost 80 years to be introduced in chemistry by Kurt Mislow (1962). stereochemical imperative. 17 As a matter of example, D-sugars are building blocks of helically-shaped DNA and RNA macromolecules, which store genetic information and encode the synthesis of proteins through the ligation of their constituting amino acids. Glucose monomers in glycogen, starch and cellulose also have a D configuration. This suggests that chirality, structure, and functions of these biomacromolecules are intimately related.

18

In 1857, Louis Pasteur revealed the dramatic difference in the fermentation rate of the two tartaric acid enantiomers with a yeast microorganism, thus uncovering biological enantioselectivity. [19][20][21] Pasteur was convinced that chirality was a manifestation of Life, and unsuccessfully looked for the link between physical forces ruling out the Cosmos and the molecular dissymmetry observed in natural products. In 1886, the Italian chemist Arnaldo Piutti 22 succeeded to isolate (R)asparagine, mirror-image of the tasteless amino-acid (S)asparagine, and found that it was intensely sweet. 23 These discoveries refer to the link between the handedness of chiral substances and their biological properties but does not explain the origin of biological homochirality (BH). Despite an extensive literature, the emergence of BH remains a conundrum. The key points of this intricate topic can be summarized as: how, when and where did single chirality appear and eventually lead to the emergence of Life (Figure 1). [START_REF] Zubay | Origins of Life on the Earth and in the Cosmos[END_REF][START_REF] Ruiz-Mirazo | [END_REF][47][48] Along this line, the question of the creation of the original chiral bias appears critical (box "how?" in Figure 1). Huge efforts have been dedicated to decipher which processes may lead to the generation of a chiral bias without the action of pre-existing enantiomerically-enriched chemical species, that is without using the commonly employed routes in stereoselective synthesis. The creation of a chiral bias "from scratch", often referred to as absolute asymmetric synthesis 30,31,49,50 and spontaneous deracemization, 41,51,52 actually encompasses a large variety of phenomena. Here, a distinction can be made between chiral biases that: (i) are inherent to the nature of matter itself, (ii) originate from the interaction of molecules with physical fields, particles, spins or surfaces, or (iii) emerge from the mutual interaction between molecules (Figure 1). The first category (i) corresponds to the fact that a racemate deviates infinitesimally from its ideal equimolar composition deterministically, i.e. in direction of the same enantiomer for a given racemate, as a result of parity violation in certain interactions within nuclei. 53,54 The second category (ii) refers to natural physical fields (gravitational, magnetic, electric), light and their combinations, which under certain conditions constitute truly chiral fields, 30 but also to a range of inherently chiral sources such as chiral light and polarized particles (mostly electrons), polarized electron spins, vortices, or surfaces. [START_REF] Bonner | [END_REF] The third category (iii) encompasses processes that lead to the spontaneous emergence of chirality in absence of detectable chiral physical and chemical sources, upon destabilization of the racemic state and stabilization of a scalemic or homochiral state. Such spontaneous mirror symmetry breaking (SMSB) phenomena 40 involve interactions between molecules through auto-catalytic processes which under far-from-equilibrium conditions may lead to the emergence of enantiopure molecules. The topic has recently undergone significant progress thanks to numerous theoretical models and experimental validations, namely the deracemization of conglomerates through Viedma ripening 55 and the asymmetric auto-catalysis with the Soai reaction. 56 Importantly, the plausibility of the aforementioned chirality induction processes in the context of BH will depend on several parameters such as: the extent of asymmetric induction they may provide, their mode of action, i.e. if they are unidirectional (deterministic towards a single enantiomer) or bidirectional (leading to either type of enantiomers), their relevance according to prebiotic conditions present on Earth 4 billion years ago, the scope of molecules it could be applied to, and their validation by experimental evidences. The first three parts of this review will provide an updated version of phenomena i-iii that are commonly discussed as plausible sources of asymmetry under prebiotic conditions and can thus Please do not adjust margins Please do not adjust margins be potentially accountable for the primeval chiral bias in molecules of Life. However, uncovering plausible mechanisms towards the emergence of a chiral bias is not enough per se for elucidating the origin of BH. Additional fundamental challenges such as the extra-terrestrial or terrestrial origin of molecule of Life precursors (box "where ?" in Figure 1), the mechanism(s) for the propagation and enhancement of the original chiral bias (box "how 2?" in Figure 1) and the chemical/biological pathways leading to functional bio-relevant molecules are key aspects to propose a credible scenario. The detection of amino acids and sugars with preferred L and D configuration, respectively, on carbonaceous meteorites 57 instigated further research for determining plausible mechanisms for the production of chiral molecules in interstellar environment and their subsequent enantiomeric enrichment. 58,59 Alternatively, hydrothermal vents in primeval Oceans constitute an example of reaction domains often evoked for prebiotic chemistry which may also include potential sources of asymmetry such as high-speed microvortices. 60 Some mechanisms are known for increasing an existing e.e., such as the selfdisproportionation of enantiomers (SDE), 61 non-linear effects in asymmetric catalysis, 62,63 and stereoselective polymerization. 64 Noteworthy in the present context, these processes may be applied to increase the optical purity of prebiotically relevant molecules. However, a general amplification scheme which is valid for all molecules of Life is lacking.

The temporal sequence between chemical homochirality, BH and Life emergence is another intricate point (box "when?" in Figure 1). Tentative explanations try to build-up either abiotic theories considering that single chirality is created before the living systems or biotic theories suggesting that Life preceded homochirality. [START_REF] Bonner | [END_REF] Purely abiotic theories refer to reactions or physicochemical processes involving low-molecular weight organic molecules presumably present in the prebiotic soup. 38,65 From a different angle, polymerization of activated building blocks is also discussed as a possible stage for the induction/enhancement of chirality, 64 even though prebiotic mechanisms towards these essential-to-Life macromolecules remain highly elusive. [START_REF] Zubay | Origins of Life on the Earth and in the Cosmos[END_REF][START_REF] Ruiz-Mirazo | [END_REF][47][48] In the fourth part of this review, we will propose an update of the most plausible chemical and physical scenarios towards BH, with an emphasis on the underlying principles and the experimental evidences, showing merits and limitations of each mechanism. Notably, relevant experimental investigations conducted with building blocks of Life: proteinogenic amino acids, natural sugars, their intermediates or derivatives, will be commented in regards of the different scenarios.

Ultimately, the aim of this literature review is to familiarize the novice with research dealing with BH, and to propose to the expert an updated and timely synopsis of this interdisciplinary field.

Parity Violation (PV) and Parity-Violating Energy Difference (PVED)

"Videmus nunc per speculum in aenigmate," (Holy Bible, I Cor. XIII, 12) which can be translated into "At present, we see indistinctly, as in a mirror" refers to the intuition that a mirror reflection is a distorted representation of the reality. The perception of the different nature of mirror-image objects is also found in the modern literature. In his famous novel "Through the Looking-Glass" by Lewis Caroll Alice raises important questions: 'How would you like to live in Lookingglass House, Kitty? I wonder if they'd give you milk in there? Perhaps Looking-glass milk isn't good to drink…" These sentences refer to the intuition that a mirror reflection is a distorted representation of the reality. The perception of the different nature of mirror-image objects is also found in the modern literature.

9,24

The Universe is constituted of elementary particles which interact through fundamental forces, namely the electromagnetic, strong, weak, and gravitational forces. Until the mid-20 th century, fundamental interactions were thought to equally operate in a physical system and its image built through space inversion. Indeed, these laws were assumed by physicists to be conserved under the parity operator P (which transforms the spatial coordinates x,y,z into -x,-y,-z), i.e. parityeven. However, in 1956, Lee and Yang highlighted that parity was only conserved for strong and electromagnetic forces, and proposed experiments to test it for weak interactions. 66 A few months later, Wu experimentally demonstrated that the parity symmetry is indeed broken in weak forces (which are hereby parity-odd), 67 by showing that the transformation of unstable 60

Co nuclei into 60 Ni, through the  --decay of a neutron into a proton, emit electrons of only left-handedness. In fact, solely left-handed electrons were emitted since W + and W -bosons (abbreviated as W ± bosons), which mediate the weak chargedcurrent interactions, only couple with left-handed particles.

Right-handed particles are not affected by weak interactions carried by W ± bosons and consequently, neutrinos, that are only generated by processes mediated by W ± bosons, are all left-handed in the universe. 68 The weak neutral current interactions, mediated by the Z 0 boson (sometimes called Z forces), are without charge exchange and, just like the charged ones, violate the parity symmetry. [69][70][71][72][START_REF] Di Lella | 60 Years of CERN Experiments and Discoveries[END_REF] Thus, all weak interactions, carried by W ± or Z 0 bosons, break the fundamental parity symmetry. Parity violation has been observed in nuclear 67 and atomic Physics. [START_REF] Bouchiat | [END_REF][75][76][77] In consequence, the contribution of the Z force between the nuclei and electrons produces an energy shift between the two enantiomers of a chiral molecule. The lowerenergy enantiomer would thus be present in slight excess in an equilibrium mixture; this imbalance may provide a clue to the origin of biomolecular homochirality, i.e. why chiral molecules usually occur in a single enantiomeric form in nature. Such a tiny parity violation energy difference (PVED of about 10 -17 kT at 300 K) should be measurable by any absorption spectroscopy provided that ultra-high resolution is reached. 128,129 Whether PVED could have provided a sufficient bias for the emergence of BH likely depends on the related amplification mechanism, a point that will be discussed into more details in part 3.

Chiral fields

Physical fields, polarized particles, polarized spins and surfaces are commonly discussed as potential chiral inducers of enantiomeric excesses in organic molecules. The aim of this part is to present selected chiral fields along with experimental observations which are relevant in the context of elucidating BH.

Physical fields a True and False Chirality

Chirality's definitions based on symmetry arguments are adequate for stationary objects, but not when motion comes into play. To address the potential chiral discriminating nature of physical fields, Barron defined true and false chirality as follows: the "true chirality is shown by systems existing in two distinct enantiomeric states that are interconverted by space inversion (P), but not by time reversal (T) combined with any proper spatial rotation (R  )". 130 Along this line, a stationary and a translating rotating cone are prototypical representations of false and true chirality, respectively (Figure 2a). Cones help to better visualize the true chiral nature of vortices, but the concept is actually valid for any translating spinning objects, e.g. photons and electrons. 85,131 All experimental attempts to produce any chiral bias using a static uniform magnetic or electric field, or unpolarized light failed and this can be explained by the non-chiral nature of these fields. 30,31,49 In addition, the parallel or antiparallel combination of static uniform magnetic and electric fields constitute another example of false chirality (Figure 2b).

Figure 2 Distinction between "true" and "false" chirality by considering the effect of parity (P) and time (T) reversal on spinning cones (a) and aligned magnetic and electric fields (b). Figure 2a is reprinted from reference 41 with permission from American Chemical Society. Figure 2b is adapted from reference 30 with permission from American Chemical Society.

Importantly, only when interacting with a truly chiral system the energy of enantiomeric probes can be different (corresponding to diastereomeric situations), while no loss of degeneration in energy levels can happen in a falsely chiral system; however, asymmetry could be obtained for processes out of thermodynamic equilibrium. 30,31 Based on these definitions, truly chiral forces may lift the degeneracy of enantiomers and induce enantioselection in a reaction system reaching its stationary state, while an influence of false Please do not adjust margins

Please do not adjust margins chirality is only possible for kinetically controlled reaction outputs, since in this case the enantiomers remain strictly degenerate and only the breakdown of the reaction path microreversibility occurs. 41 Furthermore, the extent of chiral induction that can be achieved by a chiral physical field is intimately related to the nature of its interaction with matter, i.e. with prebiotically relevant organic molecules in the context of BH. A few examples of physical fields for absolute asymmetric synthesis are mentioned in the next paragraphs.

b Magnetochiral effects

A light beam of arbitrary polarization (with k as wavevector) propagating parallel to a static magnetic field (B) also possesses true chirality (k•B), exploited by the magneto-chiral dichroism (MChD, Figure 3a). 132 MChD was first observed by Rikken and Raupach in 1997 for a chiral europium(III) complex, and was further extended to other metal compounds and a few aggregates of organic molecules. [132][133][134][135][136] Photoresolution of Δ-and Λ-chromium(III) tris(oxalato) complexes thanks to magnetochiral anisotropy was accomplished in 2000 by the same authors, 137 with an enantioenrichment proportional to the magnetic field, e.e./B being equal to 1 × 10 -5 T -1 (Figure 4b). Whilst mechanical interactions of chiral objects with their environment is well established at the macroscale, the ability of these interactions to mediate the separation of molecular enantiomers remains largely under-explored.

139

A few experimental reports indicate that fluid flows can discriminate not only large chiral objects, [140][141][142] but also helical bacteria, 143 colloidal particles, 144 and supramolecular aggregates. 145,146 It has been indeed found that vortices, being induced by stirring, microfluidics or temperature gradients, are capable of controlling the handedness of supramolecular helical assemblies. 60,[145][146][147][148][149][150][151][152][153][154][155][156][157][158][159] Laminar vortices have been recently

employed as the single chiral discriminating source for the emergence of homochiral supramolecular gels in milliseconds. 60 High speed vortices have been evoked as potential sources of asymmetry present in hydrothermal vents, presumed key reaction sites for the generation of prebiotic molecules. However, the propensity of shear flow to prevent the Brownian motion and allow for the discrimination of small molecules remain to be demonstrated. Grzybowski and co-workers showed that s-shaped µm-size particles located at the oil/air interface parallel to the shear plane migrate to different positions in a Couette cell. 160 The proposed chiral drift mechanism may in principle allow the separation of smaller chiral objects, with size on the order of Please do not adjust margins Please do not adjust margins the ten of nanometres. In 2015, a new molecular parameter called hydrodynamic chirality was introduced to characterize the coupling of rotational motion of a chiral molecule to its translational motion and quantify the direction and velocity of such motion. 138 The concept concerns the possibility to control the motion of chiral molecules by orienting and aligning their dipole moment with the electric field position leading to their rotation. The so-called molecular propeller effect allows enantiomers of two binaphthyl derivatives, upon exposition to rotating electric fields (REF), to propel in opposite directions, leading to a local enrichment of up to 60% e.e. (Figure 4). It would be essential to probe interactions of vortices, shear flows and rotating physical fields with biologically relevant molecules in order to uncover whether it could have played a role in the emergence of a chiral bias on early Earth.

d Combined action of gravity, magnetic field and rotation Micali et al. demonstrated in 2012 that the combination of gravity, magnetic field and rotation can be used to direct the handedness of supramolecular helices generated upon assembly of an achiral porphyrin monomer (TPPS 3 , Figure 5).

161

It was presumed that the enantiomeric excess generated at the onset of the aggregation was amplified by autocatalytic growth of the particles during the elongation step. The observed chirality is correlated to the relative orientation of the angular momentum and the effective gravity, the direction of the former being set by clockwise or anticlockwise rotation. The role of the magnetic field is fundamentally different to that in MChD effect (2.1 a) since its direction does not influence the sign of the chiral bias. Its role is to provide tunable magnetic levitation force and alignment of the supramolecular assemblies. These results therefore seem to validate experimentally the prediction by Barron that falsely chiral influence may lead to absolute asymmetric synthesis after enhancement of an initial chiral bias created under farfrom-equilibrium conditions. 130 According to the authors, control experiments performed in absence of magnetic field discard macroscopic hydrodynamic chiral flow, i.e. a true chiral force (see 2.1 c), as the driving force for chirality induction; a point that has been recently disputed by other authors.

41

Whatever the true of false nature of the combined action of gravity, magnetic field and rotation, its potential connection to BH is hard to conceive at this stage.

e Through plasma-triggered chemical reactions Plasma, produced by the impact of extra-terrestrial objects on Earth, has been investigated as a potential source of asymmetry. Price and Furukawa teams reported, in 2013 and 2015, respectively, that nucleobases and/or proteinogenic amino acids were formed under conditions which presumably reproduced the conditions of impact of celestial bodies on primitive Earth. 162,163 When shocked with a steel projectile fired at high velocities in a light gas gun, ice mixtures made of NH 4 OH, CO 2 and CH 3 OH, were found to produce equal amounts of (R)-and (S)-alanine, -aminoisobutyric acid and isovaline as well as their precursors.

162 Importantly, only the impact shock is responsible for the formation of amino-acids because post-shot heating is not sufficient. A richer variety of organic molecules, including nucleobases, was obtained by shocking ammonium bicarbonate solution under nitrogen (representative of the Hadean ocean and its atmosphere) with various metallic projectiles (as simplified meteorite materials). 163 The production of amino-acids is correlated to the concentration of ammonium bicarbonate concentration, acting as the C1-source. The attained pressure and temperature (up to 60 GPa and thousands Kelvin) allowed chemical reactions to proceed, as well as racemization as evidenced later, 164 but were not enough to trigger plasma processes. A meteorite impact was reproduced in the laboratory by Wurz and co-workers in 2016, 165 by firing projectiles of pure C synthetic diamond to a multilayer target consisting of ammonium nitrate, graphite and steel. The impact generated a pressure of 170 GPa and a temperature of 3 to 4 × 10 4 K, enough to form a plasma torch, through the interaction between the projectile and target materials and their subsequent atomization and ionization. The most striking result is certainly the formation of 13 C-enriched alanine which is claimed to be obtained with e.e. values ranging from 7 to 25%. The exact source of asymmetry is uncertain: the far-fromequilibrium nature of the plasma-triggered reactions and the presence of spontaneously generated electromagnetic fields in the reactive plasma torch may have led to the observed chiral biases. 166 This first report of an impact-produced enantioenrichment needs to be confirmed experimentally and supported theoretically.

Polarized radiations and spins a Circularly Polarized Light (CPL)

A long time before the discussions on the true or false chiral nature of physical fields, Le Bel and van't Hoff already proposed, at the end of the nineteenth century, to use circularly polarized light, a truly chiral electromagnetic wave existing in two enantiomorphic forms (i.e. the left-and righthanded CPL), as chiral bias to induce enantiomeric excess. 31,[167][168][169] Cotton strengthened this idea in 1895, 170-172 when he reported the circular dichroism (CD) of an aqueous solution of potassium chromium(III) tartrate. in the absorption region of an optically active material, as well the spectroscopic method that measures it. 173,174 Enantiomers absorbing CPL of one handedness constitute non-degenerated diastereoisomeric systems, based on the interaction between two distinct chiral influences, one chemical and the other physical. Thus, one state of this system is energetically favoured, and one enantiomer preferentially absorbs CPL of one polarization state (l-or r-CPL).

The dimensionless Kuhn anisotropy (or dissymmetry) factor g allows to quantitatively describe the chiroptical response of enantiomers (Equation 1). The Kuhn anisotropy factor is expressed by the ratio between the difference in molar extinction coefficients of l-CPL and r-CPL (Δε), and the global molar extinction coefficient (ε), where and are the molar extinction coefficients for left-and right-handed CPL, respectively.

175 It ranges from -2 to +2, for a total absorption of right-and left-handed CPL, respectively, and is wavelengthdependent. Enantiomers have equal but opposite g values, corresponding to their preferential absorption of one CPL handedness.

(1)

The preferential excitation of one over the other enantiomer in presence of CPL allows the emergence of a chiral imbalance from a racemate (by asymmetric photoresolution or photolysis) or from rapidly interconverting chiral conformations (by asymmetric photosynthesis).

176-178

Asymmetric photolysis is based on the irreversible photochemical consumption of one enantiomer at a higher rate, within a racemic mixture which does not racemize during the process (Figure 6a). In most cases, the (enantio-enriched) photo products are not identified. Thereby, the enantioenrichment comes from the accumulation of the slowly reacting enantiomer. It depends both on the unequal molar extinction coefficients (ε R and ε S ) for CPL of the (R)-and (S)enantiomers, governing the different rate constants, as well as the extent of reaction ξ. Asymmetric photoresolution occurs within a mixture of enantiomers that interconvert in their excited states (Figure 6b). Since the reverse reactions, from the excited to the ground states, should not be enantiodifferentiating, the deviation from the racemic mixture is only due to the difference of extinction coefficients (ε R and ε S ). CH 3 OH and NH 3 at 80 K with CPL centred at 187 nm, which led to the formation of alanine with an e.e. of 1.34 ± 0.40%. 204 The same team also studied the effect of CPL on regular ice analogues or organic residues coming from their irradiation in order to mimic the different stages of asymmetric induction in interstellar ices. 205 Sixteen amino acids were identified, and five of them (including alanine and valine) were analysed by enantioselective two-dimensional gas chromatography, GC×GC, 206 coupled to TOF mass spectrometry, to show enantioenrichments up to 2.54 ± 0.28% e.e. Optical activities likely originated from the asymmetric photolysis of the amino acids initially formed as racemates. Advantageously, all five amino acids exhibited e.e. of identical sign for a given polarization and wavelength, suggesting that irradiation by CPL could constitute a general route towards amino acids with a single chirality. Even though the chiral biases generated upon CPL irradiation are modest, these values can be significantly amplified through different physicochemical processes, notably those including autocatalytic pathways (see parts 3 and 4).

b Spin-polarized particles

In the cosmic scenario, it is believed that the action of polarized quantum radiation in space, such as circularly polarized photons or spin-polarized particles, may have induced asymmetric conditions in the primitive interstellar media resulting in terrestrial bioorganic homochirality. In particular, nuclear-decay-or cosmic-ray-derived leptons (i.e. electrons, muons, and neutrinos) in nature have a specified helicity, that is, they have a spin angular momentum polarized parallel or antiparallel to their kinetic momentum due to parity violations (PV) in the weak interaction (part 1). Of the leptons, electrons are one of the most universally present particles in ordinary materials. Spin-polarized electrons in nature are emitted with  -decay from radioactive nuclear particles derived from PV involving the weak nuclear interaction and spin-polarized positrons (the anti-particle of electrons) from  + decay. In  -/ + -decay, with the weak interaction, the spin angular momentum vectors of electron/positron are perfectly polarized as antiparallel/parallel to the vector direction of the kinetic momentum.

In this meaning, spin-polarized Please do not adjust margins

Please do not adjust margins electrons/positrons are "chiral radiation", as well as are muons and neutrinos, which will be mentioned below. It is expected that the spin-polarized leptons will induce reactions different from those triggered by CPL. For example,  -decay from 60 Co is accompanied by circularly polarized gamma-rays.

207

Similarly, spin-polarized muon irradiation has the potential to induce novel types of optical activities different from those of polarized photon and spin-polarized electron irradiation. Single-handed polarized particles produced by supernovae explosions may thus interact with molecules in the proto-solar clouds. [START_REF] Tsarev | [END_REF][208][209][210]207 Left-handed electrons generated by  -decay impinge on matter to form a polarized electromagnetic radiation through bremsstrahlung. At the end of fifties, Vester and Ulbricht suggested that these circularly-polarized "Bremsstrahlen" photons can induce and direct asymmetric processes towards a single direction upon interaction with organic molecules. 107,211 From the sixties to the eighties, 212-220 many experimental attempts to show the validity of the "V-U hypothesis", generally by photolysis of amino acids in presence of a number of -emitting radionuclides or through selfirradiation of 14 C-labeled amino acids, only led to poorly conclusive results. [START_REF] Bonner | [END_REF]221,222 During the same period, the direct effect of high-energy spin-polarized particles (electrons, protons, positrons and muons) have been probed for the selective destruction of one amino acid enantiomer in a racemate, but without further success as reviewed by Bonner. [START_REF] Bonner | [END_REF]54 More recent investigations by the international collaboration RAMBAS (RAdiation Mechanism of Biomolecular ASymmetry) claimed minute e.es. (up to 0.005%) upon irradiation of various amino acid racemates with (natural) lefthanded electrons.

223,224

Other fundamental particles have been proposed to play a key role in the emergence of BH. 207,209,225 Amongst them, electron antineutrinos have received particular attention, through the Supernova Neutrino Amino Acid Processing (SNAAP) model.

226-

228 Electron antineutrinos are emitted after a supernova explosion, to cool the nascent neutron star, and, by a similar reasoning to that applied with neutrinos, they are all righthanded. According to the SNAAP scenario, right-handed electron antineutrinos generated in the vicinity of neutron stars with strong magnetic and electric fields were presumed to selectively transform 14 N into 14 C, and this process depended on whether the spin of the 14 N was aligned or antialigned with that of the antineutrinos. Calculations predicted enantiomeric excesses for amino acids from 0.02% to a few percent, and a preferential enrichment in (S)-amino acids. No experimental evidences have been reported to date in favour of a deterministic scenario for the generation of a chiral bias in prebiotic molecules.

c Chirality Induced Spin Selectivity (CISS)

An electron in helical roto-translational motion with spin-orbit coupling (i.e. translating in a "ballistic" motion with its spin projection parallel or antiparallel to the direction of propagation) can be regarded as chiral, existing as two possible enantiomers, corresponding to the α and β spin configurations, which do not coincide upon space and time inversion. Such peculiar "chiral actor" is the object of spintronics, the fascinating field of modern physics which deals with the active manipulation of spin degrees of freedom of charge carriers. 230 The interaction between polarized spins of secondary electrons (SEs) and chiral molecules leads to chirality induced spin selectivity (CISS), a recently reported phenomenon.

In 2008, Rosenberg et al.

231 irradiated adsorbed molecules of (R)-2-butanol or (S)-2-butanol on a magnetized iron substrate with low-energy SEs (10-15% of spin polarization) and measured a difference of about ten percent in the rate of CO bond cleavage of the enantiomers. Extrapolations of the experimental results suggested that an e.e. of 25% would be obtained after photolysis of the racemate at 98.6% of conversion. Importantly, the different rates in the photolysis of the 2-butanol enantiomers depend on the spin polarization of the SE, showing the first example of CISS. [232][233][234] Later, SEs with a higher degree of spin polarization (60%) were found to dissociate Cl from epichlorohydrin (Epi) with a quantum yield 16% greater for the S form. 229 To achieve this, electrons are produced by X-ray irradiation of a gold substrate and spinfiltered by a self-assembled overlayer of DNA before they reach the adlayer of Epi (Figure 8). Please do not adjust margins Please do not adjust margins substrate and the adsorbed molecule (circled in blue and red) is favoured when the two spins are antiparallel leading to the preferential adsorption of one enantiomer over the other. Reprinted from reference 235 with permission from the American Association for the Advancement of Science In 2018, Banerjee-Ghosh et al. showed that a magnetic field perpendicular to a ferromagnetic (FM) substrate can generate enantioselective adsorption of polyalanine, ds-DNA and cysteine.

235 One enantiomer was found to be more rapidly adsorbed on the surface depending on the magnetization direction (Figure 9). The effect is not attributed to the magnetic field per se but to the exchange interaction between the adsorbed molecules and surface electrons spins, i.e. CISS. Enantioselective crystallization of initially racemic mixtures of asparagine, glutamic acid, and threonine, known to crystallize as conglomerates, was also observed on a ferromagnetic substrate surface (Ni(120 nm)/Au(10 nm)). 230 The racemic mixtures were crystallized from aqueous solution on the ferromagnetic surfaces in the presence of two magnets, one pointing north and the other south, located at different sites of the surface. A clear enantioselective effect was observed in the formation of an excess of d-or l-crystals, depending on the direction of the magnetization orientation.

In 2020, the CISS effect was successfully applied to several asymmetric chemical processes, SEs acting as chiral reagents.

236 Spin-polarized electrons, produced by a magnetized Ni/Au substrate coated with an achiral selfassembled monolayer (SAM) of carboxyl-terminated alkanethiols [HS-(CH 2 ) x-1 -COO -], caused an enantiospecific association of 1-amino-2-propanol enantiomers, leading to an e.e. of 20% in the reactive medium. The enantioselective electro-reduction of (1R/1S)-10-camphorsulfonic acid (CSA) into isoborneol was also governed by the spin orientation of SEs, injected through an electrode, with an e.e. of about 11.5% after the electrolysis of 80% of the initial amount of CSA. Electrochirogenesis links CISS process to biological homochirality through several theories, all based on an initial bias stemming from spin polarized electrons. 232,237 Strong fields and radiations of neutron stars could align ferrous magnetic domains in interstellar dust particles, and produce spin-polarized electrons, able to create an enantiomeric excess into adsorbed chiral molecules. One enantiomer from a racemate in a cosmic cloud would merely accrete on a magnetized domain in an enantioselective manner as well.

Alternatively, magnetic minerals of the prebiotic world, like pyrite (FeS 2 ) or greigite (Fe 3 S 4 ), might serve as an electrode in the asymmetric electrosynthesis of amino acids or purines, or as spin-filter in the presence of an external magnetic field, e.g. in hydrothermal vents.

Chiral surfaces a Inorganic minerals and clays

Chiral surfaces constitute unequivocal true asymmetry sources that are widespread over the Earth surface under the form of various minerals, -quartz, calcite, gypsum, and some clays notably. The implication of chiral surfaces in the context of BH has been debated [START_REF] Bonner | [END_REF][238][239][240][241][242] along two main axes: (i) the preferential adsorption of prebiotically relevant molecules, and (ii) the potential unequal distribution of left-handed and right-handed surfaces for a given mineral or clay on the Earth surface.

Selective adsorption is generally the consequence of reversible and preferential diastereomeric interactions between the chiral surface and one of the enantiomers, 239 commonly described by the simple three-point model. But this model, assuming that only one enantiomer can present three groups that match three active positions of the chiral surface, 243 fails to fully explain chiral recognition which are the fruit of more subtle interactions. 244 In the second part of the XX th century, a large number of studies have focused on demonstrating chiral interactions between biological molecules and inorganic mineral surfaces. Quartz is the only common mineral which is composed of enantiomorphic crystals. Right-handed (d-quartz) and lefthanded (l-quartz) can be separated (similarly to the tartaric acid salts of the famous Pasteur experiment) and investigated independently in adsorption studies of organic molecules. The process of separation is made somewhat difficult by the presence of "Brazilian twins" (also called chiral or optical twins), 242 which might bias the interpretation of the experiments. Bonner et al. in 1974 245,246 measured the differential adsorption of alanine derivatives defined as % adsorbed on d-quartz -% adsorbed on l-quartz. These authors reported on the small but significant 1.4 ± 0.4% preferential adsorption of (R)-alanine over d-quartz and (S)-alanine over lquartz, respectively. A more precise evaluation of the selectivity with radiolabelled (RS)-alanine hydrochloride led to higher levels of differential adsorption between l-quartz and dquartz (up to 20%). 247 The hydrochloride salt of alanine isopropyl ester was also found to be adsorbed enantiospecifically from its chloroform solution leading to chiral enrichment varying between 1.5 and 12.4%.

248

Furuyama and co-workers also found preferential adsorption of (S)-alanine and (S)-alanine hydrochloride over l-quartz from their ethanol solutions. 249,250 Anhydrous conditions are required to get sufficient adsorption of the organic molecules onto -quartz crystals which, according to Bonner, discards quartz as a suitable mineral for the deracemization of building blocks of Life. 251 According to Hazen and Scholl,239 the fact that these studies have been conducted on powdered quartz crystals (i.e. polycrystalline quartz) have hampered a precise determination of the mechanism and magnitude of adsorption on specific surfaces of -quartz. Some of the faces of quartz crystals likely display opposite chiral preferences which may have reduced the experimentally-reported chiral selectivity. Moreover, chiral indices of the commonest crystal growth surfaces of quartz, as established by Downs and Hazen, are relatively low (or zero), suggesting that potential of enantiodiscrimination of organic molecules by quartz is weak in overall. 252 Quantum-mechanical studies using density functional theories (DFT) have also been performed to probe the enantiospecific adsorption of various amino acids on hydroxylated quartz surfaces. [253][254][255][256] In short, the computed differences in the adsorption energies of the enantiomers are modest (on the order of 2 kcal.mol -1 at best) but strongly depend on the nature of amino acids and quartz surfaces. A

Please do not adjust margins

Please do not adjust margins 261 reported that (S)-aspartic acid adsorbs preferentially on the face of calcite, whereas (R)-aspartic acid adsorbs preferentially on the face. An e.e. value on the order of 0.5% on average was measured for the adsorbed aspartic acid molecules. No selectivity was observed on a centric surface that served as control. The experiments were conducted with aqueous solutions of (rac)-aspartic acid and selectivity was greater on crystals with terraced surface textures, presumably because enantiomers concentrated along step-like linear growth features. The calculated chiral indices of the (214) scalenohedral face of calcite was found to be the highest amongst 14 surfaces selected from various minerals (calcite, diopside, quartz, orthoclase) and face-centred cubic (FCC) metals. 252 In contrast, DFT studies revealed negligible difference in adsorption energies of enantiomers (< 1 kcal.mol -1

) of alanine on the face of calcite because alanine cannot establish three points of contact on the surface. 262 Conversely, it is well established that amino acids modify the crystal growth of calcite crystals in a selective manner leading to asymmetric morphologies, e.g. upon crystallization 263,264 or electrodeposition (Figure 10a). 259 Vaterite helicoids, produced by crystallization of CaCO 3 in presence of non-racemic mixtures of aspartic acid, were found to be single-handed (Figure 10b). 260 Enantiomeric ratio are identical in the helicoids and in solution, i.e. incorporation of aspartic acid in valerite displays no chiral amplification effect. Asymmetric growth was also observed for various organic substances with gypsum, another mineral with a centrosymmetric crystal structure.

265

As expected, asymmetric morphologies produced from amino acid enantiomers are mirror image (Figure 10). Clay minerals, which for some of them display high specific surface area, adsorption and catalytic properties, are often invoked as potential promoters of the transformation of prebiotic molecules. Amongst the large variety of clays, serpentine and montmorillonite were likely the dominant ones on Earth prior to Life's origin. Please do not adjust margins

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Ribó and co-workers proposed that chiral surfaces could have been involved in the chiral enrichment of prebiotic molecules on carbonaceous chondrites present on meteorites. 284 In their scenario, mirror symmetry breaking during the formation of planetesimal bodies and comets may have led to a bias in the distribution of chiral fractures, screw distortions or step-kink chiral centres on the surfaces of these inorganic matrices. This in turn would have led to a bias in the adsorption of organic compounds. Their study was motivated by the fact that the enantiomeric excesses measured for organic molecules vary according to their location on the meteorite surface. 285 Their measurement of the optical activity of three meteorite samples by circular birefringence (CB) indeed revealed a slight bias towards negative CB values for the Murchinson meteorite.

The optically active areas are attributed to serpentines and other poorly identified phyllosilicate phases, whose formation may have occurred concomitantly to organic matter. The implication of inorganic minerals in biasing the chirality of prebiotic molecules remains uncertain given that no strong asymmetric adsorption values have been reported to date and that certain minerals were even found to promote the racemization of amino acids 286 and secondary alcohols. b Organic crystals Organic crystals may have also played a role in biasing the chirality of prebiotic chemical mixtures. Along this line, glycine appears as the most plausible candidate given its probable dominance over more complex molecules in the prebiotic soup.

-Glycine crystallizes from water into a centrosymmetric form.

In the 1980s, Lahav, Leiserowitch and co-workers demonstrated that amino acids were occluded to the basal faces (010 and ) of glycine crystals with exquisite selectivity. [289][290][291] For example, when a racemic mixture of leucine (1-2% wt/wt of glycine) was crystallized with glycine at an air/water interface, (R)-Leu was incorporated only into those floating glycine crystals whose (010) faces were exposed to the water solution, while (S)-Leu was incorporated only into the crystals with exposed ( faces. This results into the nearly perfect resolution (97-98% e.e.) of Leu enantiomers. In presence of a small amount of an enantiopure amino-acid (e.g. (S)-Leu), all crystals of Gly exposed the same face to the water solution leading to one enantiomer of a racemate being occluded in glycine crystals while the other remains in solution. These striking observations led the same authors to propose a scenario in which the crystallization of supersaturated solutions of glycine in presence of amino-acid racemates would have led to the spontaneous resolution of all amino acids (Figure 11). This can be considered as a "by chance" mechanism in which one of the enantiotopic face (010) would have been exposed preferentially to the solution in absence of any chiral bias. From then, the solution, enriched into (S)-amino acids, enforces all glycine crystals to expose their (010) faces to water, eventually leading to all (R)-amino acids being occluded in glycine crystals. A somewhat related strategy was disclosed in 2010 by Soai and co-workers.

292 Dehydration of centrosymmetric crystals of cytosine monohydrate yielded enantio-enriched anhydrous cytosine chiral crystals when only one of two enantiotopic faces of the crystal was put into direct contact with the hot plate. Enrichment was also observed if the dehydration was performed under reduced pressure but with a surprising inversion of the configuration of the chiral crystal relatively to thermal dehydration. 293 Rearrangement of the hydrogen bond network during the transition between the centrosymmetric and chiral forms of the cytosine crystals is likely at the origin of this selective process. Reactions occurring at the enantiotopic surface of an achiral compound also yields enantio-enriched compounds whose optical purity can be enhanced by SMSB processes.

294,295 c Metal surfaces

The last two decades have seen the emergence of chiral metal surfaces displaying high adsorption enantioselectivities. 239,244,296 The choice between metal surfaces can be oriented based on computational predictions of their enantiospecificity as reported recently for a variety of α-amino acids on Ag/Cu/Pd/Pt(531) surfaces. 297 Mechanisms leading to specific adsorptions on chiral metal surfaces can be Please do not adjust margins

Please do not adjust margins well established. As a matter of example, the decomposition of tartaric acid, enantiospecifically adsorbed on Cu(651) S surfaces, follows non-linear kinetics, suggesting autocatalysis. 298 Likewise, adsorption of scalemic mixtures of aspartic acid onto an achiral Cu(111) surface occurs with amplification of the chirality, i.e. the e.e. of the adsorbed enantiomers of the surface is largely higher than the e.e. of enantiomers in the gas phase. 299 This effect, which presents some similarity to non-linear effects observed in asymmetric catalysis, 62 is related to the formation of homochiral adsorbate clusters. Auto-catalysis and chiral amplification are two key requirements for spontaneous mirror symmetry breaking (Part 3) and consequently such mechanistic studies on chiral metal surfaces may reveal important pathways towards homochirality. 300

Spontaneous Mirror-Symmetry Breaking (SMSB)

Definition, models and the Soai reaction

Spontaneous mirror-symmetry breaking (SMSB) phenomenon is the process that leads to the preferential formation of one chiral state over its enantiomeric form in absence of a detectable chiral bias or enantiomeric imbalance. As defined by Ribó and co-workers, SMSB concerns the transformation of "metastable racemic non-equilibrium stationary states (NESS) into one of two degenerate but stable enantiomeric NESSs".

301 Despite this definition being in somewhat contradiction with the textbook statement that enantiomers need the presence of a chiral bias to be distinguished, it was recognized a long time ago that SMSB can emerge from reactions involving asymmetric self-replication or auto-catalysis. The connection between SMSB and BH is appealing, [START_REF] Morozov | [END_REF]40,51,[301][302][303][304][305][306][307][308] since SMSB is the unique physicochemical process that allows for the emergence and retention of enantiopurity from scratch. It is also intriguing to note that the competitive chiral reaction networks that might give rise to SMSB could exhibit replication, dissipation and compartmentalization, 301,309 i.e.

fundamental functions of living systems. Systems able to lead to SMSB consist of enantioselective autocatalytic reaction networks, described through models dealing with either the transformation of achiral to chiral compounds, or the deracemization of racemic mixtures. 301 As early as 1953, Frank described a theoretical model dealing with the former case. According to Frank model, SMSB emerges from a system involving homochiral self-replication (one enantiomer of the chiral product accelerates its own formation) and heterochiral inhibition (the replication of the other product enantiomer is prevented). 303 It is now wellrecognized that the Soai reaction, 56 an auto-catalytic asymmetric process (Figure 12a), disclosed 42 years later, 310 is an experimental validation of the Frank model. The reaction between pyrimidine-5-carbaldehyde and diisopropyl zinc (two achiral reagents) is strongly accelerated by their zinc alkoxy product, which is found to be enantiopure (>99% e.e.) after a few cycles of reaction/addition of reagents (Figure 12b andc). [310][311][312] Kinetic models based on the stochastic formation of homochiral and heterochiral dimers [313][314][315] of the zinc alkoxy product provide good fits of the kinetic profile even though the involvement of higher species has gained more evidence recently. [316][317][318][319][320][321][322][323][324] In this model, homochiral dimers serve as auto-catalyst for the formation of the same enantiomer of the product whilst heterochiral dimers are inactive and sequester the minor enantiomer, a Frank model-like inhibition mechanism. A hallmark of the Soai reaction is that direction of the autocatalysis is dictated by extremely weak chiral perturbations: quartz, cryptochiral molecules, circularly polarized light, chiral isotopomers amongst others (Figure 12b). 312 In addition, the apparent outcome of the Soai reaction performed in absence of detectable chiral species is stochastic as expected for a truly SMSB process (Figure 12c). [325][326][327][328][329][330][331][332][333] On the one hand, the Soai reaction offers a credible mechanistic scenario from which homochiral biomolecules at the origin of Life would have been created on a deterministic manner through a SMSB process coupled to an infinitesimal chiral bias (vide infra). This bias would have survived from a larger one despite significant erosion through racemization processes. On the other hand, the Soai reaction is more the exception than the rule in the chemical space explored up to date. [334][335][336][337][338][339][340][341][342] The exergonic and irreversible nature of the organozinc addition reaction are key for pushing the system far-from-equilibrium and for the generation and preservation of the homochiral state. On the contrary, it is assumed that prebiotic chemical reactions would have been only weakly exergonic, i.e. their products would have been more prone to racemization or to side reactions occurring in solution. 37,46,301 Many other models of spontaneous emergence of homochirality in far-from-equilibrium systems have been proposed in the literature. 301 In the absence of any chiral influence, the obtained metastable NESS are exposed to statistical fluctuations, and evolve towards scalemic or homochiral NESSs, as long as the systems are farfrom-equilibrium. It is important to note that in absence of these boundary conditions, systems will be able to equilibrate with their surrounding and the deviation from the racemic state will be lost, e.g. racemization would occur under classically employed reaction workups operated in solution. 41,352 This is probably the main reason why a single SMSB process has been identified to date for a reaction performed in solution (the Soai reaction). On the contrary, SMSB processes have been observed more frequently in crystals (vide infra) or in supramolecular assemblies, 353 i.e.

processes involving phase transition. Asymmetric reactions performed with catalytic single-handed supramolecular assemblies obtained through a SMSB process were found to yield enantio-enriched products whose configuration is left to chance. 157,354 SMSB processes leading to homochiral crystals as the final state appear particularly relevant in the context of BH and will thus be discussed separately in the following section.

Homochirality by crystallization

Havinga postulated that just one enantiomorph can be obtained upon a gentle cooling of a racemate solution: i) when the crystal nucleation is rare and the growth is rapid and, ii) when fast inversion of configuration occurs in solution (i.e. racemization). Under these circumstances, only monomers with matching chirality to the primary nuclei crystallize leading to SMSB. 55,355 Havinga reported in 1954 a set of experiments aimed at demonstrating his hypothesis with N,N,N- allylethylmethylanilinium iodide -an organic molecule which crystallizes as a conglomerate from chloroform (Figure 13).

355

Fourteen supersaturated solutions were gently heated in sealed tubes, then stored at 0°C to give crystals which were in 12 cases inexplicably more dextrorotatory (measurement of optical activity by dissolution in water, where racemization is not observed). Seven other supersaturated solutions were carefully filtered before cooling to 0°C, but no crystallization occurred after one year. Crystallization occurred upon further cooling: three crystalline products with no optical activity were obtained, while the four other ones showed a small optical activity ([α] D = +0.2°; +0.7°; -0.5°; -3.0°). More successful examples of preferential crystallization of one enantiomer appeared in the literature notably with tri-o-thymotide, 356 and 1,1'-binaphthyl. 357,358 In the latter case, the distribution of specific rotations recorded for several independent experiments is centred to zero. Sodium chlorate (NaClO 3 ) crystallizes by evaporation of water into a conglomerate (P2 1 3 space group). [359][360][361] Preferential crystallization of one of the crystal enantiomorph over the other was already reported by Kipping and Pope in 1898.

362,363

From static (i.e. non-stirred) solution, NaClO 3 crystallization seems to undergo an uncertain resolution, similar to Havinga findings with the aforementioned quaternary ammonium salt. However, a statistically significant bias in favour of d-crystals was invariably observed, likely due to the presence of biocontaminants. 364 Interestingly, Kondepudi et al. showed revealed that the maximum degree of supersaturation is solely reached once, when the first primary nucleation occurs. At this stage, the magnetic stirring bar breaks up the first nucleated crystal into small fragments that have the same chirality than the 'Eve crystal', and act as secondary nucleation centres whence crystals grow (Figure 14). This constitutes a SMSB process coupling homochiral self-replication plus inhibition through the supersaturation drop during secondary nucleation, precluding new primary nucleation and the formation of crystals of the mirror-image form. 307 This deracemization strategy was also successfully applied to 4,4'dimethyl-chalcone, 370 and 1,1'-binaphthyl (from its melt).

371 In 2005, Viedma reported that solid-to-solid deracemization of NaClO 3 proceeded from its saturated solution by abrasive grinding with glass beads. 373 Complete homochirality with bimodal distribution is reached after several hours or days.

374

The process can also be triggered by replacing grinding with ultrasound, 375 turbulent flow, 376 or temperature variations. 376,377 Although this deracemization process is easy to implement, the mechanism by which SMSB emerges is an ongoing highly topical question that falls outside the scope of this review. 40,41,378-381 Viedma ripening was exploited for deracemization of conglomerate-forming achiral or chiral compounds (Figure 15). 55,382 The latter can be formed in situ by a reaction involving a prochiral substrate. For example, Vlieg et al. coupled an attrition-enhanced deracemization process with a reversible organic reaction (an aza-Michael reaction) between prochiral substrates under achiral conditions to produce an enantiopure amine. 383 In a recent review, Buhse and coworkers identified a range of conglomerate-forming molecules that can be potentially deracemized by Viedma ripening. 41 Viedma ripening also proves to be successful with molecules crystallizing as racemic compounds at the condition that conglomerate form is energetically accessible. 384 Furthermore, a promising mechanochemical method to transform racemic compounds of amino acids into their corresponding conglomerates has been recently found. were desymmetrized by Viedma ripening with DBU (1,8diazabicyclo [5.4.0]undec-7-ene) as the racemization catalyst. Successful deracemization was also achieved with amino acid precursors such as -aminonitriles, 394-396 -iminonitriles, 397 Nsuccinopyridine 398 and thiohydantoins. 399 The first three classes of compounds could be obtained directly from prochiral precursors by coupling synthetic reactions and Viedma ripening. In the preceding examples, the direction of SMSB process is selected by biasing the initial racemic mixtures in favour of one enantiomer or by seeding the crystallization with chiral chemical additives. In the next sections, we will consider the possibility to drive the SMSB process towards a deterministic outcome by means of PVED, physical fields, polarized particles, and chiral surfaces, i.e. the sources of asymmetry depicted in Part 2 of this review.

Deterministic SMSB processes a Parity violation coupled to SMSB

In the 1980s, Kondepudi and Nelson, constructed stochastic models of a Frank-type autocatalytic network which allowed them to probe the sensitivity of the SMSB process to very weak chiral influences. 304,[400][401][402] Their estimated energy values for biasing the SMSB process into a single direction was in the range of PVED values calculated for biomolecules. Despite the competition with the bias originated from random fluctuations (as underlined later by Lente), 126 it appears possible that such a very weak "asymmetric factor can drive the system to a preferred asymmetric state with high probability". 307 Recently, -10 -15 kJ/mol). This means that the two experimentally SMSB processes reported to date are not sensitive enough to detect any influence of PVED and questions the existence of an ultra-sensitive auto-catalytic process, as the one described by Kondepudi and Nelson. The possibility to bias crystallization processes with chiral particles emitted by radionuclides was probed by several groups as summarized in the reviews of Bonner. This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins (+) and (-)-NaClO 3 crystals, largely biased in favour of (+) crystals. 405 It was presumed that spin polarized electrons produced chiral nucleating sites, albeit chiral contaminants cannot be excluded.

b Chiral surfaces coupled to SMSB

The extreme sensitivity of the Soai reaction to chiral perturbations is not restricted to soluble chiral species. The effect of chiral additives on crystallization processes, in which the additive inhibits one of the enantiomer growth thereby enriching the solid phase with the opposite enantiomer is well established as "the rule of reversal".

412,413

In the realm of the Viedma ripening, Noorduin et al. discovered in 2020 a way of propagating homochirality between -iminonitriles, possible intermediates in the Strecker synthesis of -amino acids. 414 These authors demonstrated that an enantiopure additive (1-20 mol%) induces an initial enantio-imbalance, which is then amplified by Viedma ripening up to a complete mirror-symmetry breaking. In contrast to the "rule of reversal", the additive favours the formation of the product with identical configuration. The additive is actually incorporated in a thermodynamically controlled way into the bulk crystal lattice of the crystallized product of the same configuration, i.e. a solid solution is formed enantiospecifically.

c CPL coupled to SMSB

Coupling CPL-induced enantioenrichment and amplification of chirality has been recognized as a valuable method to induce a preferred chirality to a range of assemblies and polymers. 182,183,354,415,416 On the contrary, the implementation of CPL as a trigger to direct auto-catalytic processes towards enantiopure small organic molecules has been scarcely investigated.

CPL was successfully used in the realm of the Soai reaction to direct its outcome, either by using a chiroptical switchable additive, or by asymmetric photolysis of a racemic substrate. In 2004, Soai et al. illuminated during 48h a photoresolvable chiral olefin with l-or r-CPL, and mixed it with the reactants of the Soai reaction to afford (S)-or (R)-5-pyrimidyl alkanol, respectively, in e.e. higher than 90%. 417 In 2005, the photolyzate of a pyrimidyl alkanol racemate acted as an asymmetric catalyst for its own formation reaching e.e. greater than 99.5%. 418 The enantiomeric excess of the photolyzate was below the detection level of chiral HPLC instrument but was amplified thanks to the SMSB process.

In 2009, Vlieg et al. coupled CPL with Viedma ripening to achieve complete and deterministic mirror-symmetry breaking.

419 Previous investigation revealed that the deracemization by attrition of the Schiff base of phenylglycine amide (rac-1, Figure 16a) always occurred in the same direction, the (R)-enantiomer, as a probable result of minute levels of chiral impurities.

372 CPL was envisaged as potent chiral physical field to overcome this chiral interference. Irradiation of solid-liquid mixtures of rac-1 indeed led to complete deracemization, the direction of which was directly correlated to the circular polarization of light. Control experiments indicated that the direction of the SMSB process is controlled by a non-identified chiral photoproduct generated upon irradiation of (rac)-1 by CPL. This photoproduct (S* or R* in Figure 16b) then serves as an enantioselective crystal-growth inhibitor which mediates the deracemization process towards the other enantiomer (Figure 16b). In the context of BH, this work highlights that asymmetric photosynthesis by CPL is a potent mechanism that can be exploited to direct deracemization processes when coupled to an amplification phenomenon.

Theories for the emergence of BH

Physical fields, CPL, polarized particles, polarized spins, chiral surfaces and SMSB processes have been presented as potential candidates for the emergence of chiral biases in prebiotic molecules. Their main properties are summarized in Table 1. The plausibility of the occurrence of these biases under the conditions of the primordial universe have also been evoked for certain physical fields (such as CPL or CISS). However, it is important to provide a more global overview of the current theories that tentatively explain the following Please do not adjust margins Please do not adjust margins puzzling questions: where, when and how did the molecules of Life reach a homochiral state? At which point of this undoubtedly intricate process did Life emerge?

Terrestrial or Extra-Terrestrial Origin of BH?

The enigma of the emergence of BH might potentially be solved by finding the location of the initial chiral bias, might it be on Earth or elsewhere in the universe. The 'panspermia'

ARTICLE

Please do not adjust margins Please do not adjust margins 197,198,199 (f) Recently, spin-polarized SE through the CISS effect have been implemented as chiral reagents with relatively high e.e. values (up to a ten percent) reached for a set of reactions. 236 (g) The standard deviation for 1 mole of chiral molecules is of 1.9 × 10 11 . 126 na: not applicable.

ARTICLE

Please do not adjust margins Please do not adjust margins hypothesis, 424 for which living organisms were transplanted to Earth from another solar system, sparked interest into an extra-terrestrial origin of BH, but the fact that such a high level of chemical and biological evolution was present on celestial objects have not been supported by any scientific evidence.

44

Accordingly, terrestrial and extra-terrestrial scenarios for the original chiral bias in prebiotic molecules will be considered in the following. a Terrestrial origin of BH A range of chiral influences have been evoked for the induction of a deterministic bias to primordial molecules generated on Earth. Enantiospecific adsorptions or asymmetric syntheses on the surface of abundant minerals have long been debated in the context of BH [START_REF] Bonner | [END_REF][238][239][240][241][242] since no significant bias of one enantiomorphic crystal or surface over the other has been measured when counting is averaged over several locations on Earth. 257,258 Prior calculations supporting PVED at the origin of excess of l-quartz over d-quartz 114,425 or favouring the A-form of kaolinite 426 are thus contradicted by these observations. Abyssal hydrothermal vents during the Hadean/Eo-Archaean eon are argued as the most plausible regions for the formation of primordial organic molecules on the early Earth. 427 Temperature gradients may have offered the different conditions for the coupled autocatalytic reactions and clays may have acted as catalytic sites. 347 However, chiral inductors in these geochemically reactive habitats are hypothetical, even though vortices 60 or CISS occurring at the surfaces of greigite have been mentioned recently.

CPL and

MChD are not potent asymmetric forces on Earth as a result of low levels of circular polarization detected for the former and small anisotropic factors of the latter. [429][430][431] PVED is an appealing "intrinsic" chiral polarization of matter but its implication in the emergence of BH is questionable (Part 1).

126

Alternatively, theories suggesting that BH emerged from scratch, i.e. without any involvement of the chiral discriminating sources mentioned in Part 1-2 and SMSB processes (Part 3), have been evoked in the literature since a long time, 420 and variant versions appeared sporadically.

Herein, these mechanisms are named as "random" or "by chance" and are based on probabilistic grounds only (Table 1).

The prevalent form comes from the fact that a racemate is very unlikely made of exactly equal amounts of enantiomers, due to natural fluctuations described statistically like coin tossing. 126,432 One mole of chiral molecules actually exhibits a standard deviation of 1.9 × 10 11

. Putting into relation this statistical variation and putative strong chiral amplification mechanisms and evolutionary pressures, Siegel suggested that homochirality is an imperative of molecular evolution. 17 However, the probability to get both homochirality and Life emerging from statistical fluctuations at the molecular scale appears very unlikely. [START_REF] Tsarev | [END_REF]59,433 SMSB phenomena may amplify statistical fluctuations up to homochiral state, yet the direction of process for multiple occurrences will be left to chance in absence of a chiral inducer (Part 3). Other theories suggested that homochirality emerges during the formation of biopolymers "by chance", as a consequence of the limited number of sequences that can be possibly contained in a reasonable amount of macromolecules (see 4.3). 17,421,422 Finally, kinetic processes have also been mentioned in which a given chemical event would have occurred to a larger extent for one enantiomer over the other under achiral conditions (see one possible physicochemical scenario in Figure 11).

Hazen notably argued that nucleation processes governing auto-catalytic events occurring at the surface of crystals are rare and thus a kinetic bias can emerge from an initially unbiased set of prebiotic racemic molecules. 239 However, to stray from "geocentrism" is still worthwhile; another plausible scenario is the exogenous delivery on Earth of enantio-enriched molecules relevant for the appearance of Life. The body of evidence grew from the characterization of organic molecules, especially amino acids and sugars, and their respective optical purity, in meteorites, 59 comets, and laboratory-simulated interstellar ices.

434

The 100-kg Murchison's meteorite that fell to Australia in 1969 is generally considered as the standard reference for extraterrestrial organic matter (Figure 17a). 435 In fifty years, analyses of its composition revealed more than ninety α, β, γ and δ-isomers of C 2 to C 9 amino acids, diamino acids, and dicarboxylic acids as well as numerous polyols including sugars (ribose, 436 a building block of RNA), sugar acids and alcohols, but also α-hydroxycarboxylic acids, 437 and deoxy acids.

434

Unequal amounts of enantiomers were also found with a quasi-exclusively predominance for (S)-amino acids To complete these analyses of the difficult-to-access outer space, laboratory experiments have been conducted by reproducing the plausible physicochemical conditions present on astrophysical ices (Figure 17b). 444 Natural ones are formed in interstellar clouds, 445,446 These molecules were obtained with no significant bias from the ideal racemic composition which supports their abiotic origin. 444 However, when similar experiments are conducted under CPL irradiation, amino acids are generated with significant biases towards one enantiomer as described in 2.2a.

204,205

The occurrence of CPL-driven photochirogenesis on interstellar dust grains was supported by the detection of near-infrared light with significant circular polarization degrees (up to 22%), 457 in parsec-sized star-forming regions, such as massive molecular clouds. [458][459][460][461][462][463][464] Cosmic circularly polarized photons arise from synchrotron radiations emitted by neutron stars, remnants of supernovae explosions, 35 through bremsstrahlung, dichroic scattering and/or light extinction (along lined up grains). 465 In addition, although it was not directly observed due to dust shielding, models predicted the generation of vacuum ultraviolet (VUV) and UV-CPL under these conditions, 459 i.e. spectral regions of light absorbed by amino acids and sugars. Photolysis by broad band and optically impure CPL is expected to yield lower enantioenrichments than those obtained experimentally by monochromatic and quasiperfect circularly polarized synchrotron radiation (see 2.2a).

198 However, a broad band CPL is still capable of inducing chiral bias by photolysis of an initially abiotic racemic mixture of aliphatic -amino acids as previously debated.

466,467

Likewise, CPL in the UV range will produce a wide range of amino acids with a bias towards the (S) enantiomer, 195 including -dialkyl amino acids.

468 l-and r-CPL produced by a neutron star are equally emitted in vast conical domains in the space above and below its equator. [START_REF] Tsarev | [END_REF] However, appealing hypotheses were formulated against the apparent contradiction that amino acids have always been found as predominantly (S) on several celestial bodies, 59 and the fact that CPL is expected to be portioned into left-and right-handed contributions in equal abundance within the outer space. In the 1980s, Bonner and Rubenstein proposed a detailed scenario in which the solar system, revolving around the centre of our galaxy, had repeatedly traversed a molecular cloud and accumulated enantioenriched incoming grains. 430,469 The same authors assumed that this enantioenrichment would come from asymmetric photolysis induced by synchrotron CPL emitted by a neutron star at the stage of planets formation. Later, Meierhenrich remarked in addition that, in molecular clouds, regions of homogeneous CPL polarization can exceed the expected size of a protostellar disk -or of our solar system, 458,470 allowing a unidirectional enantioenrichment within our solar system, including comets. [START_REF] Meierhenrich | Amino acids and the asymmetry of life: caught in the act of formation[END_REF] A solid scenario towards BH thus involves CPL as a source of chiral induction for biorelevant candidates, through photochemical processes on the surface of dust grains, and delivery of the enantio-enriched compounds on primitive Earth by direct grain accretion or by impact 471 of larger objects (Figure 18). The high enantiomeric excesses detected for (S)-isovaline in certain stones of the Murchison's meteorite (up to 15.2±0.2%) suggested that CPL alone cannot be at the origin of this enantioenrichment.

285

The broad distribution of e.es. (0-15.2%) and the abundance ratios of isovaline relatively to other amino acids also point to (S)-isovaline (and probably other amino acids) being formed through multiple synthetic processes that occurred during the chemical evolution of the meteorite. 440 Finally, based on the anisotropic spectra, 188 it is highly plausible that other physiochemical processes, e.g. racemization coupled to phase transitions or coupled nonequilibrium/equilibrium processes, 378,475 have led to a change in the ratio of enantiomers initially generated by UV-CPL. 59 In addition, a serious limitation of the CPL-based scenario shown in Figure 18 is the fact that significant enantiomeric excesses can only be reached at high conversion, i.e. by decomposition of most of the organic matter (see equation 2 in 2.2a). Even though there is a solid foundation for CPL being involved as an initial inducer of chiral bias in extra-terrestrial organic molecules, chiral influences other than CPL cannot be excluded. Induction and enhancement of optical purities by physicochemical processes occurring at the surface of meteorites and potentially involving water and the lithic environment have been evoked but have not been assessed experimentally.

285 Asymmetric photoreactions 431 induced by MChD can also be envisaged notably in neutron stars environment, of tremendous magnetic fields ( 108 -10 12 T) and synchrotron radiations.

35,476

Spin-polarized electrons (SPEs), another potential source of asymmetry, can potentially be produced upon ionizing irradiation of ferrous magnetic domains present in interstellar dust particles, aligned by the enormous magnetic fields produced by a neutron star. One enantiomer from a racemate in a cosmic cloud could adsorb enantiospecifically on the magnetized dust particle. In addition, meteorites contain magnetic metallic centres that can act as asymmetric reaction sites upon generation of SPEs.

Finally, polarized particles such as antineutrinos (SNAAP model 226-228 ) have been proposed as a deterministic source of asymmetry, at work in the outer space. Radioracemization must potentially be considered as a jeopardizing factor in that specific context. [START_REF] Bonner | [END_REF]477,478 Further experiments are needed to probe whether these chiral influences may have played a role in the enantiomeric imbalances detected in celestial bodies.

Purely abiotic scenarios

Emergences of Life and biomolecular homochirality must be tightly linked, [START_REF] Ruiz-Mirazo | [END_REF]479,480 but in such a way that needs to be cleared up. As recalled recently by Glavin, homochirality by itself cannot be considered as a biosignature. 59 Non proteinogenic amino acids are predominantly (S) and abiotic physicochemical processes can lead to enantio-enriched molecules. However, it has been widely substantiated that polymers of Life (proteins, DNA, RNA) as well as lipids need to be enantiopure to be functional. Considering the NASA definition of Life, "a self-sustaining chemical system capable of Darwinian evolution", 481 and the "widespread presence of ribonucleic acid (RNA) cofactors and catalysts in today′s terran This journal is © The Royal Society of Chemistry 20xx

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Please do not adjust margins biosphere", 482 a strong hypothesis for the origin of Darwinian evolution and Life is "the abiotic formation of long-chained RNA polymers" with selfreplication ability. 309 Current theories differ by placing the emergence of homochirality at different times of the chemical and biological evolutions leading to Life. Regarding on whether homochirality happens before or after the appearance of Life discriminates between purely abiotic and biotic theories, respectively (Figure 19). In between these two extreme cases, homochirality could have emerged during the formation of primordial polymers and/or their evolution towards more elaborated macromolecules. a Enantiomeric cross-inhibition The puzzling question regarding primeval functional polymers is whether they form from enantiopure, enantio-enriched, racemic or achiral building blocks. A theory that has found great support in the chemical community was that homochirality was already present at the stage of the primordial soup, i.e. that the building blocks of Life were enantiopure. Proponents of the purely abiotic origin of homochirality mostly refer to the inefficiency of polymerization reactions when conducted from mixtures of enantiomers. More precisely, the term enantiomeric crossinhibition was coined to describe experiments for which the rate of the polymerization reaction and/or the length of the polymers were significantly reduced when non-enantiopure mixtures were used instead of enantiopure ones. [START_REF] Meierhenrich | Amino acids and the asymmetry of life: caught in the act of formation[END_REF][START_REF] Bonner | [END_REF] Seminal studies were conducted by oligo-or polymerizing -amino acid N-carboxy-anhydrides (NCAs) in presence of various initiators. Idelson and Blout observed in 1958 that (R)-glutamate-NCA added to reaction mixture of (S)-glutamate-NCA led to a significant shortening of the resulting polypeptides, inferring that (R)-glutamate provoked the chain termination of (S)glutamate oligomers. 483 Lundberg and Doty also observed that the rate of polymerization of (R)/(S) mixtures of a glutamate-NCA and the mean chain length reached at the end of the polymerization were decreased relatively to that of pure (R)-or (S)-glutamate-NCA. 485,486 Similar studies for oligonucleotides were performed with an enantiopure template to replicate activated complementary nucleotides. Joyce et al. showed in 1984 that the guanosine oligomerization, directed by a poly-D-cytosine template, was inhibited when conducted with a racemic mixture of activated mononucleotides. 484 The L residues are predominantly located at the chain-end of the oligomers, acting as chain terminators, thus decreasing the yield in oligo-D-guanosine (Figure 20). A

Please do not adjust margins Please do not adjust margins similar conclusion was reached by Goldanskii and Kuz'min upon studying the dependence of the length of enantiopure oligonucleotides on the chiral composition of the reactive monomers. 429 Interpolation of their experimental results with a mathematical model led to the conclusion that the length of potent replicators will dramatically be reduced in presence of enantiomeric mixtures reaching a value of 10 monomer units at best for a racemic medium. Finally, the oligomerization of activated racemic guanosine was also inhibited on DNA and PNA templates. 487 The latter being achiral, it suggests that enantiomeric cross-inhibition is intrinsic to the oligomerization process involving complementary nucleobases. b Propagation and enhancement of the primeval chiral bias Studies demonstrating enantiomeric cross-inhibition during polymerization reactions have led the proponents of purely abiotic origin of BH to propose several scenarios for the formation building blocks of Life in an enantiopure form. In this regards, racemization appears as a redoubtable opponent considering that harsh conditions -intense volcanism, asteroid bombardment and scorching heat 488,489 -prevailed between the Earth formation, 4.5 billion years ago, and the appearance of Life, 3.5 billion years ago at the latest. 490,491 At that time, deracemization inevitably suffered from its nemesis, racemization, which may take place in days or less in hot alkaline aqueous medium. 35,301,492-494 Several scenarios have considered that initial enantiomeric imbalances have probably been decreased by racemization but not eliminated. Abiotic theories thus rely on processes that would be able to amplify tiny enantiomeric excesses (likely << 1% e.e.) up to homochiral state. Intermolecular interactions cause enantiomer and racemate to have different physicochemical properties and this can be exploited to enrich a scalemic material into one enantiomer under strictly achiral conditions. This phenomenon of self-disproportionation of the enantiomers (SDE) is not rare for organic molecules and may occur through a wide range of physicochemical processes.

61

SDE with molecules of Life such as amino acids and sugars is often discussed in the framework of the emergence of BH. SDE often occurs during crystallization as a consequence of the different solubility between racemic and enantiopure crystals, and its implementation to amino acids was exemplified by Morowitz as early as 1969. 495 It was confirmed later that a range of amino acids displays high eutectic e.e. values which allows very high e.e. values to be present in solution, even from moderately biased enantiomeric mixtures. 496 Serine is the most striking example since a virtually enantiopure solution (> 99% e.e.) is obtained at 25°C under solid-liquid equilibrium conditions starting from a 1% e.e. mixture only.

497

Enantioenrichment was also reported for various amino acids after consecutive evaporations of their aqueous solutions 498 or preferential kinetic dissolution of their enantiopure crystals.

499

Interestingly, the eutectic e.e. values can be increased for certain amino acids by addition of simple achiral molecules such as carboxylic acids. 500 DL-Cytidine, DL-adenosine and DLuridine also form racemic crystals and their scalemic mixture can thus be enriched towards the D enantiomer in the same way at the condition that the amount of water is small enough that the solution is saturated in both D and DL. 501 SDE of amino acids does not occur solely during crystallization; 502 e.g.

sublimation of near-racemic samples of serine yields a sublimate which is highly enriched in the major enantiomer.

503 Amplification of e.e. by sublimation has also been reported for other scalemic mixtures of amino acids, [504][505][506] or for a racemate mixed with a non-volatile optically pure amino acid. 507 Alternatively, amino acids were enantio-enriched by simple dissolution/precipitation of their phosphorylated derivatives in water.

508

Figure 21

Selected catalytic reactions involving amino acids and sugars, and leading to the enantioenrichment of prebiotically relevant molecules.

It is likely that prebiotic chemistry have linked amino acids, sugars and lipids in a way that remains to be determined.

Merging the organocatalytic properties of amino acids with the aforementioned SDE phenomenon offers a pathway towards enantiopure sugars. 509 The aldol reaction between 2chlorobenzaldehyde and acetone was found to exhibit a strongly positive non-linear effect, i.e. the e.e. in the aldol product is drastically higher than that expected from the optical purity of the engaged amino acid catalyst. 497 Again, the effect was particularly strong with serine since nearly racemic serine (1% e.e.) and enantiopure serine provided the aldol product with the same enantioselectivity (ca. 43% e.e., Figure 21, (1)). Enamine catalysis in water was employed to prepare glyceraldehyde, the probable synthon towards ribose and This journal is © The Royal Society of Chemistry 20xx

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Please do not adjust margins other sugars, by reacting glycolaldehyde and formaldehyde in presence of various enantiopure amino acids. It was found that all (S)-amino acids, except (S)-proline, provided glyceraldehyde with a predominant R configuration (up to 20% e.e. with (S)glutamic acid, Figure 21, ( 2)). 65,510 This result coupled to SDE furnished a small fraction of glyceraldehyde with 84% e.e. Enantio-enriched tetrose and pentose sugars are also produced by means of aldol reactions catalysed by amino acids and peptides in aqueous buffer solutions, albeit in modest yields.

503-505

The influence of -amino acids on the synthesis of RNA precursors was also probed. Along this line, Blackmond and coworkers reported that ribo-and arabino-amino oxazolines were enantio-enriched towards the expected D configuration when 2-aminooxazole and (RS)-glyceraldehyde were reacted in presence of (S)-proline (Figure 21, ( 3)). 514 When coupled with the SDE of the reacting proline (1% e.e.) and of the enantioenriched product (20-80% e.e.), the reaction yielded enantiopure crystals of ribo-amino-oxazoline. (S)-proline does not act as a mere catalyst in this reaction but rather traps the (S)-enantiomer of glyceraldehyde, thus accomplishing a formal resolution of the racemic starting material. The latter reaction can also be exploited in the opposite way to resolve a racemic mixture of proline in presence of enantiopure glyceraldehyde (Figure 21, ( 4)). This dual substrate/reactant behaviour motivated the same group to test the possibility of synthetizing enantio-enriched amino acids with D-sugars. The hydrolysis of 2-benzyl -amino nitrile yielded the corresponding -amino amide (precursor of phenylalanine) with various e.e. values and configurations depending on the nature of the sugars. 515 Notably, D-ribose provided the product with 70% e.e. biased in favour of unnatural (R)-configuration (Figure 21, ( 5)). This result, which is apparently contradictory with such process being involved in the primordial synthesis of amino acids, was solved by finding that the mixture of four Dpentoses actually favoured the natural (S) amino acid precursor. This result suggests an unanticipated role of prebiotically relevant pentoses such as D-lyxose in mediating the emergence of amino acid mixtures with a biased (S) configuration.

How the building blocks of proteins, nucleic acids and lipids would have interacted between each other before the emergence of Life is a subject of intense debate.

Homochirality through polymerization

Purely abiotic theory is based on the argument that enantiomeric cross-inhibition will ineluctably impede the formation of potent replicators. However, the fact that chemical processes may follow dramatically different mechanisms depending on the conditions has been overlooked. Likewise, stereoselective and non-selective polymerization reactions which allow regular and random arrangements of the monomer enantiomers along the polymer backbone, respectively, are ubiquitous in polymer science, and cross-inhibition is likely to be the exception rather than the norm.

526,527

a Stereoselective polymerization or ligation Along this line, experimental efforts have been devoted to demonstrate the preferential formation of isotactic over heterochiral macromolecules for reactions initiated with racemic mixture of amino acids. An additional objective of Please do not adjust margins

Please do not adjust margins these studies was to demonstrate the emergence of homochiral oligomers, of a sufficient size to sustain a secondary structure. It is indeed well established that the helical configuration present in peptides tends to improve further the stereoselectivity of the polymerization process, through preferential helical growth. 485,528 Goldberg studied the ligation of enantiopure amino esters, dipeptides and tripeptides (derived from alanine, aspartic acid and glycine) to racemic mixtures of activated alanine or aspartic acid amino esters in DMF and found a modest but significant bias towards the formation of homochiral peptides in the majority of cases. 529 More recent investigations by the group of Luisi on the polymerization of racemic -amino acid NCAs of leucine (Leu), isoleucine (Ile), tryptophan (Trp) and glutamic acid (Glu) in buffered aqueous solution also indicated a slight bias towards homochiral sequences. 530 Excess factors, calculated relatively to a stereorandom polymerization process, were higher for the longer oligomers. 531 In the case of Leu, the presence of ()-quartz as 1:1 mixture of the d and l enantiomorphs was found to improve the stereoselectivity of the polymerization process thanks to the selective adsorption of the more regular homochiral peptides on the quartz surface. 532 The combination of ()-quartz and a reaction mixture biased in favour of one of the amino-acid enantiomer (20% e.e.) was necessary to get homochiral sequences as the major component of the peptide stereoisomers. 533 The length of peptides reached under these conditions remains limited (n<10) which lets the question of how long and well-structured homochiral peptides sequences emerged from the prebiotic soup unanswered. One possibility is that their formation was triggered by a ribozyme, i.e. that the construction of functional and catalytic RNAs preceded the generation of peptides and proteins.

516

Synthetic chemistry aimed at mimicking prebiotic conditions for the synthesis of RNA oligomers has provided some support along this direction. Oligomers of up to 55 nucleotides can be synthetized by successive elongation of a decanucleotide with enantiopure nucleotides on Na + -montmorillonite.

288

Subsequent experiments have then been conducted directly from racemic mixtures of activated mononucleotides in order to probe the possibility of generating homochiral RNA oligomers, again with Na + -montmorillonite. Activated racemic adenosine oligomerized with comparable efficiency to enantiopure D-monomers discarding significant enantiomeric cross-inhibition. 534 The distribution of oligomer stereoisomers (up to 8 units) appeared to be biased in favour of homochiral sequences. Deeper investigation of these reactions confirmed important and modest chiral selection in the oligomerization of activated adenosine [535][536][537] and uridine, respectively. 537 Cooligomerization reaction of activated adenosine and uridine exhibited greater efficiency (up to 74% homochiral selectivity for the trimers) compared with the separate reactions of enantiomeric activated monomers. 538 Again, the length of Replication provided an advantage for achieving stereoselectivity at the condition that reactivity of chirally mismatched combinations are disfavoured relative to homochiral ones. A 32-residue peptide replicator was designed to probe the relationship between homochirality and selfreplication.

539 Electrophilic and nucleophilic 16-residue peptide fragments of the same handedness were preferentially ligated, even in the presence of their enantiomers (ca. 70% of diastereomeric excess was reached when peptide fragments E L , E D , N E , and N D were engaged, Figure 22). The replicator entails a stereoselective autocatalytic cycle, for which all bimolecular steps are faster for matched versus unmatched pairs of substrate enantiomers, thanks to self-recognition driven by hydrophobic interactions. 542 The process is very sensitive to the optical purity of the substrates, fragments embedding a single (S)/(R) amino acid substitution lacked significant auto-catalytic properties. On the contrary, This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins stereochemical mismatches were tolerated in the replicator: single mutated templates were able to couple homochiral fragments, a process referred to as "dynamic stereochemical editing".

Templating also appeared to be crucial for promoting the oligomerization of nucleotides in a stereoselective way. The complementarity between nucleobase pairs was exploited to achieve homochiral sequences of pyranosyl-RNA. 421 Activated homochiral tetramers containing hemi self-complementary base sequences (pr(GCCG)-2'3'cyclophosphate, pr= pyranosylribo) yielded relatively long oligomers (a ten of units) under mild conditions. Heterochiral tetramers (e.g. DDDL, DDLD, DLDD stereoisomers) were found to be poorly reactive under the same conditions. Importantly, the oligomerization of the homochiral tetramer was only slightly affected when conducted in the presence of heterochiral tetramers. These results raised the possibility that a similar experiment performed with the whole set of stereoisomers would have generated "predominantly homochiral" (L) and (D) sequences libraries of relatively long p-RNA oligomers. The studies with replicating peptides or auto-oligomerizing pyranosyl tetramers undoubtedly yield peptides and RNA oligomers that are both longer and optically purer than in the aforementioned reactions (part 4.2) involving activated monomers. Further work is needed to delineate whether these elaborated molecular frameworks could have emerged from the prebiotic soup.

Replication in the aforementioned systems stems from the stereoselective non-covalent interactions established between products and substrates. Stereoselectivity in the aggregation of non-enantiopure chemical species is a key mechanism for the emergence of homochirality in the various states of matter. 543 The formation of homochiral versus heterochiral aggregates with different macroscopic properties led to enantioenrichment of scalemic mixtures through SDE as discussed in 4.2. Alternatively, homochiral aggregates might serve as templates at the nanoscale. In this context, the ability of serine (Ser) to form preferentially octamers when ionized from its enantiopure form is intriguing. 544 Moreover, (S)-Ser in these octamers can be substituted enantiospecifically by prebiotic molecules (notably D-sugars) 545 suggesting an important role of this amino acid in prebiotic chemistry. However, the preference for homochiral clusters is strong but not absolute and other clusters form when the ionization is conducted from racemic Ser, 546,547 making the implication of serine clusters in the emergence of homochiral polymers or aggregates doubtful. Lahav and co-workers investigated into details the correlation between aggregation and reactivity of amphiphilic activated racemic -amino acids. 548 These authors found that the stereoselectivity of the oligomerization reaction is strongly enhanced under conditions for which -sheet aggregates are initially present 549 or emerge during the reaction process.

550-

552 These supramolecular aggregates serve as templates in the propagation step of chain elongation leading to long peptides and co-peptides with a significant bias towards homochirality. Large enhancement of the homochiral content was detected, notably for the oligomerization of rac-Val NCA in presence of 5% of an initiator (Figure 23). 551 Racemic mixtures of isotactic peptides are desymmetrized by adding chiral initiators 551 or by biasing the initial enantiomer composition. 553,554 The interplay between aggregation and reactivity might have played a key role for the emergence of primeval replicators. b Heterochiral polymers DNA and RNA duplexes as well as protein secondary and tertiary structures are usually destabilized by incorporating chiral mismatches, i.e. by substituting the biological enantiomer by its antipode. As a consequence, heterochiral polymers, which can hardly be avoided from reactions initiated by racemic or quasi racemic mixtures of enantiomers, are mainly considered in the literature as hurdles for the emergence of biological systems. Several authors have nevertheless considered that these polymers could have formed at some point of the chemical evolution process towards potent biological polymers. This is notably based on the observation that the extent of destabilization of heterochiral versus homochiral macromolecules depends on a variety of factors, including the nature, number, location, and environment of the substitutions; 555 e.g. certain D to L mutations are tolerated in DNA duplexes. 556 Moreover, simulations recently suggested that "demi-chiral" proteins, which contain 1:1 ratio of (R) and (S) -amino acids, even though less stable than their homochiral analogues, exhibit racemic membranes, i.e. composed of lipid antipodes, were found to be of comparable stability than homochiral ones.

521

Several scenarios towards BH involve non-homochiral polymers as possible intermediates towards potent replicators.

Joyce proposed a three-phase process towards the formation of genetic material assuming the formation of flexible polymers, constructed from achiral or prochiral acyclic nucleoside analogues, as intermediates towards RNA and finally DNA. 541 It was presumed that ribose-free monomers would be more easily accessed from the prebiotic soup than ribose ones and that the conformational flexibility of these polymers would work against enantiomeric cross-inhibition.

Other simplified structures, relatively to RNA, have been proposed by others. 558 However, the molecular structures of the proposed building blocks is still complex relatively to what is expected to be readily generated from the prebiotic soup. Davis hypothesized a set of more realistic polymers that could have emerged from very simple building blocks such as formaldehyde, -substituted ketones, aldehydes, alkenes, amino-acids or -hydroxy acids. 422 Polymers with random arrangement of (R) and (S) stereogenic centres are expected to be replicated through recognition of their chiral sequence. Such chiral encoding 559 might allow the emergence of replicators with specific catalytic properties. If one considers that the large number of possible sequences exceeds the number of molecules present in a reasonably sized sample of these chiral informational polymers, then their mixture will not constitute a perfect racemate since certain heterochiral polymers will lack their enantiomers. This argument of the emergence of homochirality or of a chiral bias "by chance" mechanism through the polymerization of a racemic mixture was also put forward previously by Eschenmoser 421 and

Siegel. 17 This concept has been sporadically probed notably through the template-controlled copolymerization of the racemic mixtures of two different activated amino acids.

560-562

However, in absence of any chiral bias, it is more likely that this mixture will yield informational polymers with pseudo enantiomeric like structures rather than the idealized chirally uniform polymers (see part 4.4). Finally, Davis also considered that pairing and replication between heterochiral polymers could operate through interaction between their helical structures, rather than on their individual stereogenic centres (Figure 24). 422 On this specific point, it should be emphasized that the helical conformation adopted by the main chain of certain types of polymers can be "amplified", i.e. that single handed fragments may form even if composed of nonenantiopure building blocks.

563

For example, synthetic polymers embedding a modestly biased racemic mixture of enantiomers adopt a single-handed helical conformation thanks to the so-called "majority-rules" effect. [564][565][566] This phenomenon might have helped to enhance the helicity of the primeval heterochiral polymers relatively to the optical purity of their feeding monomers.

c. Theoretical models of polymerization

Several theoretical models accounting for the homochiral polymerization of a molecule in the racemic state, i.e. mimicking a prebiotic polymerization process, were developed by means of kinetic or probabilistic approaches. As early as 1966, Yamagata proposed that stereoselective polymerization coupled with different activation energies between reactive stereoisomers will "accumulate" the slight difference in energies between their composing enantiomers (assumed to originate from PVED) to eventually favour the formation of a single homochiral polymer. Sandars). 64,575 Hochberg considered in addition a closed chemical system (i.e. the total mass of matter is kept constant) which allows polymers to grow towards a finite length (see reaction scheme in Figure 25). 64 Starting from an infinitesimal e.e. bias (e.e. %), the model shows the emergence of homochiral polymers in an absolute but temporary manner. The reversibility of this SMSB process was expected for an open system. Ma and co-workers recently published a probabilistic approach which is presumed to better reproduce the emergence of the primeval RNA replicators and ribozymes in the RNA World. 576 The D-nucleotide and L-nucleotide precursors are set to racemize to account for the behaviour of glyceraldehyde under prebiotic conditions; and the polynucleotide synthesis is surface-or template-mediated. The emergence of RNA polymers with RNA replicase or nucleotide synthase properties during the course of the simulation led to amplification of the initial chiral bias. Finally, several models show that cross-inhibition is not a necessary condition for the emergence of homochirality in polymerization processes. Higgs and co-workers considered all polymerization steps to be random (i.e. occurring with the same rate constant) whatever the nature of condensed monomers and that a fraction of homochiral polymers catalyzes the formation of the monomer enantiomers in an enantiospecific manner. 577 The simulation yielded homochiral polymers (of both antipodes) even from a pure racemate under conditions which favour the catalyzed over non-catalyzed synthesis of the monomers. These polymers are referred as "chiral living polymers" as the result of their auto-catalytic properties. Hochberg modified its previous kinetic reaction scheme drastically by suppressing cross-inhibition (polymerization operates through a stereoselective and cooperative mechanism only), and by allowing fragmentation and fusion of the homochiral polymer chains. 578 The process of fragmentation is irreversible for the longest chains, mimicking a mechanical breakage. This breakage represents an external energy input to the system. This binary chain fusion mechanism is necessary to achieve SMSB in this simulation from infinitesimal chiral bias (e.e. %). These models should stimulate the quest of polymerization pathways which include stereoselective ligation, enantioselective synthesis of the monomers, replication and cross-replication, i.e. hallmarks of an ideal stereoselective polymerization process.

Purely biotic scenarios

In the previous two sections, the emergence of BH was dated at the level of prebiotic building blocks of Life (for purely abiotic theories) or at the stage of the primeval replicators, i.e. at the early or advanced stages of the chemical evolution, respectively. In most theories, an initial chiral bias was amplified yielding either prebiotic molecules or replicators as single enantiomers. Others hypothesized that homochiral replicators and then Life emerged from unbiased racemic mixtures by chance, basing their rationale on probabilistic grounds. 17,421,559,577 In 1957, Fox, 579 Rush 580 and Wald 581 held a different view and independently emitted the hypothesis that BH is an inevitable consequence of the evolution of the living matter. [START_REF] Bonner | [END_REF] Wald notably reasoned that, since polymers made of homochiral monomers likely propagate faster, are longer and have stronger secondary structures (e.g. helices), it must have provided sufficient criteria to the chiral selection of amino acids thanks to the formation of their polymers in ad hoc conditions. This statement was indeed confirmed notably by experiments showing that stereoselective polymerization is enhanced when oligomers adopt a -helix conformation.

485,528

However, Wald went a step further by supposing that homochiral polymers of both handedness would have been generated under the supposedly symmetric external forces present on prebiotic Earth and that primordial Life would have originated under the form of two populations of organisms, enantiomers of each other. From then, the natural forces of evolution led certain organisms to be superior to their enantiomorphic neighbours leading to Life in a single form, as we know it today. The purely biotic theory of emergence of BH thanks to biological evolution, instead of chemical evolution for abiotic theories, was accompanied with large scepticism in the literature even though the arguments of Wald were

Please do not adjust margins Please do not adjust margins developed later on by others [START_REF] Bonner | [END_REF] and notably by Ageno (sexual reproduction naturally resolves enantiomeric populations), 582 and Kuhn (the stronger enantiomeric form of Life survived in the "struggle"). 583 More recently, Green and Jain summarized the Wald theory into the catchy formula "Two Runners, One Tripped", 584 and called for deeper investigation on routes towards racemic mixtures of biologically relevant polymers. The Wald theory by its essence has been difficult to assess experimentally. On the one side, (R)-amino acids when found in mammals are often related to destructive and toxic effects suggesting a lack of complementary with the current biological machinery in which (S)-amino acids are ultra-predominating.

On the other side, (R)-amino acids have been detected in the cell wall peptidoglycan layer of bacteria 585 and in various peptides of bacteria, archaea, and eukaryotes. 16 (R)-amino acids in these various living systems have an unknown origin.

Certain proponents of the purely biotic theories suggest that the small but general occurrence of (R)-amino acids in nowadays living organisms can be a relic of a time in which mirror-image living systems were "struggling". Likewise, to rationalize the aforementioned "lipid divide", it has been proposed that the LUCA of bacteria and archaea could have embedded a heterochiral lipid membrane, i.e. a membrane containing two sorts of lipid with opposite configurations.

521

Several studies also probed the possibility to prepare a biological system containing the enantiomers of the molecules of Life as we know it today. L-polynucleotides and (R)polypeptides were synthesized; and expectedly they exhibited chiral substrate specificity and biochemical properties that mirrored those of their natural counterparts. [586][587][588] In a recent example, Liu, Zhu and co-workers showed that a synthesized 174-residue (R)-polypeptide catalyzes the template-directed polymerization of L-DNA and its transcription into L-RNA. 587 It was also demonstrated that the synthesized and natural DNA polymerase systems operate without any cross-inhibition when mixed together in presence of a racemic mixture of the constituents required for the reaction (D-and L primers, D-and L-templates and D-and L-dNTPs). From these impressive results, it is easy to imagine how mirror-image ribozymes would have worked independently in the early evolution times of primeval living systems. One puzzling question concerns the feasibility for a biopolymer to synthesize its mirror-image. This has been addressed elegantly by the group of Joyce which demonstrated very recently the possibility for a RNA polymerase ribozyme to catalyze the templated synthesis of RNA oligomers of the opposite configuration. 589 The D-RNA ribozyme was selected, through 16 rounds of selective amplification away from a random sequence, for its ability to catalyze the ligation of two L-RNA substrates on a L-RNA template. The D-RNA ribozyme exhibited sufficient activity to generate full-length copies of its enantiomer through the template-assisted ligation of 11 oligonucleotides. A variant of this cross-chiral enzyme was able to assemble a two-fragment form of a former version of the ribozyme from a mixture of trinucleotide building blocks. 590 Again, no inhibition was detected when the ribozyme enantiomers were put together with the racemic substrates and templates (Figure 26). In the hypothesis of a RNA world, it is intriguing to consider the possibility of a primordial ribozyme with cross-catalytic polymerization activities. In such a case, one can consider the possibility that enantiomeric ribozymes would have existed concomitantly and that evolutionary innovation would have favoured the systems based on D-RNA and (S)polypeptides leading to the exclusive form of BH present on Earth nowadays. Finally, a strongly convincing evidence for the standpoint of the purely biotic theories would be the discovery in sediments of primitive forms of Life based on a molecular machinery entirely composed of (R)-amino acids and L-nucleic acids.

Conclusions and Perspectives of Biological Homochirality Studies

Questions accumulated while considering all the possible origins of the initial enantiomeric imbalance that have ultimately led to biological homochirality. When some hypothesize a reason behind its emergence (such as for informational entropic reasons, resulting in evolutionary advantages towards more specific and complex functionalities), [START_REF] Morozov | [END_REF]350 others wonder whether it is reasonable to reconstruct a chronology 3.5 billion years later. 37 Many are circumspect in front of the pile-up of scenarios and assert that the solution is likely not expected in a near future (due to the difficulty to do all required control experiments, and fully understand the theoretical background of the putative selection mechanism). 53 In parallel, the existence, and the extent, of a putative link between the different configurations of biologically-relevant amino acids and sugars also remain unsolved, 591 and only Goldanskii and Kuz'min studied the This journal is © The Royal Society of Chemistry 20xx

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429 Nevertheless, great progress has been made recently for a better perception of this long-standing enigma. The scenario involving circularly polarized light as a chiral bias inducer is more and more convincing thanks to operational and analytical improvements. Increasingly accurate computational studies supply precious information, notably about SMSB processes, chiral surfaces, and other truly chiral influences. Asymmetric autocatalytic systems and deracemization processes have also undoubtedly grown in interest (notably thanks to the discoveries of the Soai reaction and the Viedma ripening). Space missions are also an opportunity: to study in situ organic matter, its conditions of transformations, and possible associated enantio-enrichment; to elucidate the solar system origin and its history; and maybe, to find traces of chemicals with "unnatural" configurations in celestial bodies, what could indicate that the chiral selection of terrestrial BH could be a mere coincidence.

The current state-of-the-art indicates that further experimental investigations of the possible effect of other sources of asymmetry are needed. Photochirogenesis is attractive in many respects: CPL has been detected in space, e.es. have been measured for several prebiotic molecules found on meteorites or generated in laboratory-reproduced interstellar ices. However, this detailed postulated scenario still faces pitfalls related to the variable sources of extraterrestrial CPL, the requirement of finely-tuned illumination conditions (almost full extent of reaction at the right place and moment of the evolutionary stages), and the unknown mechanism leading to the amplification of the original chiral biases. Strong calls to organic chemists are thus necessary, to discover new asymmetric autocatalytic reactions, maybe through the investigation of complex and large chemical systems, 592 that can meet the criteria of primordial conditions. 40,41,302,312 Anyway, the quest of the biological homochirality origin is fruitful in many aspects. The first concerns one consequence of the asymmetry of Life: the contemporary challenge of synthesizing enantiopure bioactive molecules. Indeed, many synthetic efforts are directed towards the generation of optically-pure molecules, to avoid potential side effects of racemic mixtures due to the enantioselectivity of biological receptors. These endeavors can undoubtedly draw inspiration from the range of deracemization and chirality induction processes conducted in connection with biological homochirality. One example is the Viedma ripening, which allows the preparation of enantiopure molecules displaying potent therapeutic activities. 55,593 Other efforts are devoted to the building-up of sophisticated experiments and pushing their measurement limits to be able to detect tiny enantiomeric excesses, thus strongly contributing to important improvements in scientific instrumentation and acquiring fundamental knowledge at the interface between chemistry, physics, and biology. Overall, this joint endeavor at the frontier of many fields is also beneficial to material sciences notably for the elaboration of biomimetic materials and emerging chiral materials.

594,595

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The French Agence Nationale de la Recherche is acknowledged for funding the project AbsoluCat (ANR-17-CE07-0002) to MR. The GDR 3712 Chirafun from Centre National de la recherche Scientifique (CNRS) is acknowledged for allowing a collaborative network between partners involved in this review. J.C. warmly thanks Dr. Benoît Darquié from the Laboratoire de Physique des Lasers (Université Sorbonne Paris Nord) for fruitful discussions and precious advice.

Notes and references

& Proteinogenic amino acids and natural sugars are usually mentioned as L-amino acids and D-sugars according to the descriptors introduced by Emil Fischer. It is worth noting that the natural L-cysteine is (R) using the Cahn-Ingold-Prelog system, due to the sulfur atom in the side chain which changes the priority sequence. In the present review, (R)/(S) and D/L descriptors will be used for amino acids and sugars, respectively, as commonly employed in the literature dealing with BH. This journal is © The Royal Society of Chemistry 20xx

Figure 1

 1 Figure 1 Schematic representation of the questions and potential answers which are fundamentally related to the conundrum of the origin of the homochirality of Life. The review is divided into 4 parts as indicated in the scheme. PVED: Parity-Violating Energy Difference. SMSB: Spontaneous Mirror Symmetry Breaking.

78 - 81

 7881 Over the past decades, various experiments have been proposed to observe parity violation in chiral molecules, including measurements of PV frequency shifts in NMR spectroscopy, the strength of finer calculations, and Lente 126,127 asserted that a PVED of around 10 -13 J/mol causes an excess of only 6 × 10 6 molecules in one mole (against 1.9 × 10 11 for the standard deviation). In reply, MacDermott claimed, by means of a new generation of PVED computations, that the enantiomeric excess of four gaseous amino acids found in the Murchison meteorite (in the solid state) could originate from their PVED.

Figure 3 a

 3 Figure 3 a) Schematic representation of MChD for a racemate of a metal complex: the unpolarised light is preferentially absorbed by the  versus  enantiomers. Reprinted from ref 136 with permission from Wiley-VCH. b) Photoresolution of the chromium(III) tris(oxalato) complex. Plot of the e.e. after irradiation with unpolarised light for 25 min at = 695.5 nm, as a function of magnetic field, with an irradiation direction k, either parallel or perpendicular to the magnetic field. Reprinted from reference 137 with permission from Nature publishing group. c Mechanical chiral interactions

Figure 5

 5 Figure 5 Control of the handedness of TPPS3 helical assemblies by the relative orientation of the angular momentum of the rotation (L) and the effective gravity (Geff). TPPS3: tris-(4-sulfonatophenyl)phenyl porphyrin. Reprinted from reference 161 with permission from Nature publishing group.

Figure 6

 6 Figure 6 Simplified kinetic schemes for asymmetric (a) photolysis, (b) photoresolution and (c) photosynthesis with CPL. S R and SS are substrate enantiomers and SR* and SS* are their photoexcited states. PR and PS are the products generated from the respective photoexcited states. The thick line represents the preferential absorption of CPL by one of the enantiomers. [SS]>[SR] for asymmetric photolysis and photoresolution processes whilst [PR]>[PS] for asymmetric photosynthesis.

Figure 7

 7 Figure 7 Anisotropy spectra (thick lines, left ordinate) of isotropic amorphous (R)alanine (red) and (S)-alanine (blue), in the VUV and UV spectral region. Dashed lines represent the enantiomeric excess (right ordinate) that can be induced by photolysis of rac-alanine with either left-(in red) or right-(in blue) circularly polarized light at ξ= 0.9999. Positive e.e. value corresponds to scalemic mixture biased in favour of (S)-alanine. Note that enantiomeric excesses are calculated from Equation (2). Reprinted from reference 192 with permission from Wiley-VCH.

Figure 8

 8 Figure 8 Enantioselective dissociation of epichlorohydrin by spin polarized SEs. Red (black) arrows indicate the electron's spin (motion direction, respectively). Reprinted from reference 229 with permission from Wiley-VCH.

Figure 9

 9 Figure 9Scheme of the enantiospecific interaction triggered by chiral-induced spin selectivity. Enantiomers are sketched as opposite green helices, electrons as orange spheres with straight arrows indicating their spin orientation, which can be reversed for surface electrons by changing the magnetization direction. In contact with the perpendicularly magnetized FM surface, molecular electrons are redistributed to form a dipole, the spin orientation at each pole depending on the chiral potentials of enantiomers. The interaction between the FM

258 Figure 10

 25810 Figure 10 Asymmetric morphologies of CaCO3-based crystals induced by enantiopure amino acids. a) Scanning electron micrographs (SEM) of calcite crystals obtained by electrodeposition from calcium bicarbonate in the presence of magnesium and (S)-aspartic acid (left), and (R)-aspartic acid (right). Reproduced from reference 259 with permission from American Chemical Society. b) SEM images of vaterite helicoids obtained by crystallization in presence of non-racemic solutions (40% e.e.) biased in favour of (S)-aspartic acid (left) and (R)-aspartic acid. Reproduced from reference 260 with permission from Nature publishing group. Calcite (CaCO 3 ), as the most abundant marine mineral in the Archaean era, has potentially played an important role in the formation of prebiotic molecules relevant to Life. The trigonal scalenohedral crystal form of calcite displays chiral faces which can yield chiral selectivity. In 2001, Hazen et al. 261 reported

  287However, evidences exist that minerals could have served as hosts and catalysts for prebiotic reactions, including the polymerization of nucleotides.288 In addition, minute chiral biases provided by inorganic minerals could have driven SMSB processes into a deterministic outcome (Part 3).

Figure 11

 11 Figure 11 Resolution of amino acid enantiomers following a "by chance" mechanism including enantioselective occlusion into achiral crystals of glycine. Adapted from references 290 and 289 with permission from American Chemical Society and Nature publishing group, respectively

Figure 12 a

 12 Figure 12 a) General scheme for an auto-catalysed asymmetric reaction. b) Soai reaction performed in the presence of detected chirality, leading to highly enantio-enriched alcohol with the same configuration in successive experiments (deterministic SMSB). c) Soai reaction performed in absence of detected chirality, leading to highly enantio-enriched alcohol with a bimodal distribution of the configurations in successive experiments (stochastic SMSB). c) Adapted from reference 311 with permission from D. Reidel Publishing Co.

  [343][344][345] Most of them are derived from the Frank model but do not include any mutual inhibition This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins reaction. The limited enantioselective (LES) model 306,346 assumes that both the asymmetric auto-catalysis (similar to the homochiral self-replication in the Frank model) and the non-enantioselective auto-catalysis (the accelerated formation of both enantiomers of the product) can co-exist. SMSB emerges if these two autocatalytic processes are: i) individually compartmentalized within regions experiencing different temperature, 347,348 or ii) are driven by a constant concentration of external reagents. 349 Required conditions for SMSB through LES model could have been present in deep ocean hydrothermal plumes. Likewise, a chemical scenario has been proposed for LES based on coupled Strecker-type reactions for amino acid synthesis and degradation which have been postulated to be accelerated by a heterogeneous catalytic support such as phyllosilicates. 349 However, the LES model has found no experimental evidence up to date. Models for enantioselective hypercyclic replicators were recently disclosed in which the inhibition reaction in the Frank model has been replaced by mutual cross-catalytic processes occurring between families of coupled replicators. 350,351 These models support a scenario in which the combination of SMSB, formation of the first (coupled) self-replicators and the emergence of their functions would have led to BH. 301 This intriguing concept may foster experimental investigations of SMSB processes in polymerization/depolymerization reactions. Imposed boundary conditions for SMSB involve "either systems open to matter exchange, or closed systems unable to equilibrate energy with their surroundings".

  Figure 13Enantiomeric preferential crystallization of N,N,Nallylethylmethylanilinium iodide as described by Havinga. Fast racemization in solution supplies the growing crystal with the appropriate enantiomer. Reprinted from reference55 with permission from the Royal Society of Chemistry.

Figure 14

 14 Figure 14Primary nucleation of an enantiopure 'Eve crystal' of random chirality, slightly amplified by growing under static conditions (top, Havinga-like), or strongly amplified by secondary nucleation thanks to magnetic stirring (bottom, Kondepudi-like). Reprinted from reference55 with permission from the Royal Society of Chemistry.

Figure 15

 15 Figure 15 Schematic representation of Viedma ripening and solution-solid equilibria of an intrinsically achiral molecule (a) and a chiral molecule undergoing solution-phase racemization (b). The racemic mixture can result from chemical reaction involving prochiral starting materials (c). Adapted from references 356 and 382 with permission from the Royal Society of Chemistry and the American Chemical Society, respectively.

312

  Enantio-enriched or enantiopure pyrimidine alcohol was generated with determined configuration when the autocatalytic reaction was initiated with chiral crystals, such as (of the heterogeneous reaction steps that provide the initial enantiomer bias remains to be determined. 300

Figure 16 a

 16 Figure 16 a) Molecular structure of rac-1. b) CPL-controlled complete attritionenhanced deracemization of rac-1. (S) and (R) are the enantiomers of rac-1 and S* and R* are chiral photoproducts formed upon CPL irradiation of rac-1. Reprinted from reference 419 with permission from Nature publishing group.

Figure 17 a

 17 Figure 17 a) A fragment of the meteorite landed in Murchison, Australia, in 1969, and exhibited at the National Museum of Natural History (Washington). b) Scheme of the preparation of interstellar ice analogues. A mixture of primitive gas molecules is deposited and irradiated under vacuum on a cooled window. Composition and thickness are monitored by infrared spectroscopy. Reprinted from reference 434 with permission from MDPI.indubitably lead to a better determination of the composition of extra-terrestrial organic matter. The fact that major enantiomers of extra-terrestrial amino acids and sugar derivatives have the same configuration as the building blocks of Life constitutes a promising set of results. To complete these analyses of the difficult-to-access outer space, laboratory experiments have been conducted by reproducing the plausible physicochemical conditions present on astrophysical ices (Figure17b).444 Natural ones are formed

Figure 18

 18 Figure 18 CPL-based scenario for the emergence of BH following the seeding of the early Earth with extra-terrestrial enantio-enriched organic molecules. Adapted from reference 474 with permission from Wiley-VCH.

Figure 19

 19 Figure 19 Possible connections between the emergences of Life and homochirality at the different stages of the chemical and biological evolutions. Possible mechanisms leading to homochirality are indicated below each of the three main scenarios. Some of these mechanisms imply an initial chiral bias which can be of terrestrial or extra-terrestrial origins as discussed in 4.1. LUCA = Last Universal Cellular Ancestor.

Figure 20

 20 Figure 20 HPLC traces of the condensation reactions of activated guanosine mononucleotides performed in presence of a complementary poly-D-cytosine template. Reaction performed with D (top) and L (bottom) activated guanosine mononucleotides. The numbers labelling the peaks correspond to the lengths of the corresponding oligo(G)s. Reprinted from reference 484 with permission from Nature publishing group.

Figure 22

 22 Figure 22 Top: schematic representation of the stereoselective replication of peptide residues with the same handedness. Below: diastereomeric excess (de) as a function of time. de (%)= [(T LL +T DD )-(T LD +T DL )]/T total . Adapted from reference 539 with permission from Nature publishing group. oligomers detected in these experiments is far below the estimated number of nucleotides necessary to instigate chemical evolution. 540 This questions the plausibility of RNA as the primeval informational polymer. Joyce and co-workers evoked the possibility of a more flexible chiral polymer based on acyclic nucleoside analogues as an ancestor of the more rigid furanose-based replicators but this hypothesis has not been probed experimentally. 541

Figure 23

 23 Figure 23 Stereoselective polymerization of rac-Val N-carboxyanhydride in presence of 5 mol% (square) or 25 mol% (diamond) of n-butylamine as initiator. Homochiral enhancement is calculated relatively to a binomial distribution of the stereoisomers. Reprinted from reference 551 with permission from Wiley-VCH.

Figure 25

 25 Figure 25 Hochberg model for chiral polymerization in closed systems. N= maximum chain length of the polymer, f= fidelity of the feedback mechanism, Q and P are the total concentrations of left-handed and right-handed polymers, respectively.  (-), k (k-), kaa (k - aa), kbb (k bb), kba (k ba), kab (k ab) denote the forward (reverse) reaction rate constants. Adapted from reference 64 with permission from the Royal Society of Chemistry.

  Finally, even though not specifically designed for a polymerization process, a recent model by Ribó and Hochberg show how homochiral replicators could emerge from two or more catalytically coupled asymmetric replicators, again with no need of the inclusion of a heterochiral inhibition reaction. 350 Six homochiral replicators emerge from their simulation by means of an open flow reactor incorporating six achiral precursors and replicators in low initial concentrations and minute chiral biases (e.e.

Figure 26

 26 Figure 26 Cross-chiral ligation: the templated ligation of two oligonucleotides (shown in blue, B: biotin) is catalyzed by a RNA enzyme of the opposite handedness (open rectangle: primers, N30: optimized nucleotide (nt) sequence). The D and L substrates are labelled with either fluoresceine (green) or borondipyrromethene (red), respectively. No enantiomeric cross-inhibition is observed when the racemic substrates, enzymes, and templates are mixed together. Adapted from reference 589 wih permission from Nature publishing group.

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  While the total concentration in enantiomers (C R + C S ) is constant during the photoresolution, the photostationary state (p ss ) is reached after a prolonged irradiation irrespective of the initial enantiomeric composition.

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	induced by asymmetric photolysis can be approximated as
	Equation 2:	188
			(2)
	where ξ is the extent of reaction.
	In 1974, the asymmetric photodecomposition of racemic
	camphor reported by Kagan et al. reached 20% e.e. at 99%
	completion, a long-lasting record in this domain.	189 Three years
	later, Norden	190 and Bonner et al. 191 independently showed
	that enantioselective photolysis by UV-CPL was a viable source
	of symmetry-breaking for amino acids, by inducing e.e. up to
	2% in aqueous solutions of alanine and glutamic acid,	191 or
	0.2% with leucine. 190 Leucine was then intensively studied
	thanks to a high anisotropy factor in the UV region.	192 The e.e.
	was increased up to 1.3% in 2001 (ξ = 0.55) by Inoue et al. by
	exploiting the pH-dependence of the g value.	193,194 Since the
	early 2000s, Meierhenrich et al. got closer to astrophysically
	relevant conditions by irradiating samples in the solid state
	with synchrotron vacuum ultraviolet (VUV)-CPL (below 200 nm). It made it possible to avoid the water absorption in the VUV, and allowed to reach electronic transitions having higher anisotropy factors (Figure 7). 195 In 2005, a solid racemate of leucine was reported to reach 2.6% of e.e. after illumination with r-CPL at 182 nm (ξ not reported). 196 More recently, the same team improved the selectivity of the photolysis process thanks to amorphous samples of finely-tuned thickness, providing e.es. of 5.2 ± 0.5% and 4.2 ± 0.2% for leucine, 197 and alanine, 198,199 respectively. A similar enantioenrichment was reached in 2014 with gaseous photoionized alanine, 200 which constitutes an appealing result taking into account the detection of interstellar gases such as propylene oxide 201 and glycine 202 in star-forming regions. Important studies in the context of BH reported the direct formation of enantio-enriched amino acids generated from simple chemical precursors, when illuminated with CPL. Takano et al. showed in 2007 that eleven amino acids could be generated upon CPL irradiation of macromolecular compounds, originating from proton-irradiated gaseous mixtures of CO, NH 3 and H 2 O. 203 Small e.es., +0.44 ± 0.31% and -0.65 ± 0.23%, were detected for alanine upon irradiation with r-and l-CPL, respectively. Nuevo et al. irradiated interstellar ice analogues composed of H 2 O, 13	177 In absence of side reactions, the p ss is reached for ε R C R = ε S C S , which allows to determine e.e. pss , e.e. at the photostationary state, as being equal to (C R -C S )/(C R + C S )= g/2. Asymmetric photosynthesis or asymmetric fixation produces an enantio-enriched product by preferentially reacting one enantiomer of a substrate undergoing fast racemization (Figure 6c). Under these conditions, the (R)/(S) ratio of the product is equal to the excitation ratio ε R /ε S , and the e.e. of the photoproduct is thus equal to g/2. The chiral bias which can be reached in asymmetric photosynthesis and photoresolution processes is thus related to the g value of enantiomers, whereas the e.e. in asymmetric photolysis is influenced by both g and ξ values. The first CPL-induced asymmetric partial resolution dates back to 1968 thanks to Stevenson and Verdieck, who worked with octahedral oxalato complexes of chromium(III). 179 Asymmetric photoresolution was further investigated for small organic molecules, 180,181 macromolecules 182 and supramolecular assemblies. 183 A number of functional groups such as overcrowded alkene, azobenzene, diarylethene, α,β-unsaturated ketone or fulgide were specifically-designed to 58 enhance the efficiency of the photoresolution process. Kagan et al. pioneered the field of asymmetric photosynthesis with CPL in 1971, through examining hexahelicene
			photocyclization in the presence of iodine	184 . The following
			year, Calvin et al. reported e.e. up to 2% for an octahelicene
			produced under similar conditions.	185 Enantioenrichment by
			photoresolution and photosynthesis with CPL is limited in
			scope, since it requires molecules with high g values to be
			detected, and in intensity, since it is limited to g/2.
			Since its discovery by Kuhn et al. ninety years ago,	186,187
			through the enantioselective decomposition of ethyl-α-
			bromopropionate and N,N-dimethyl-α-azidopropionamide, the
			asymmetric photolysis of racemates has attracted a lot of
			interest. In the common case of two competitive pseudo-first
			order photolytic reactions with unequal rate constants, k S and
			k R , for the (S) and (R) enantiomers, respectively, and if the
			anisotropies are close to zero, the enantiomeric excess
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Table 1

 1 Potential sources of asymmetry and "by chance" mechanisms for the emergence of a chiral bias in prebiotic and biologically-relevant molecules. kJ/mol.53 (b) However, experimental results are not conclusive (see part 2.2b). (c) e.e.MChD= gMChD/2 with gMChD≈ (gNCD × gMCD)/2. NCD: Natural Circular Dichroism. MCD: Magnetic Circular Dichroism. For the resolution of Cr complexes, 137 e.e= k × B with k= 10 -5 T -1 at = 695.5 nm. (d) The minute chiral induction is amplified upon aggregation leading to homochiral helical assemblies.423 (e) For photolysis, e.e. depends both on g and the extent of reaction (see equation 2 and the text in part 2.2a). Up to a few e.e. percent have been observed experimentally.

	Type	Truly/ Falsely chiral	Direction	Extent of induction		Scope	Importance in the context of BH	Selected references
	PV	Truly	Unidirectional, deterministic, (+) or (-) for a given molecule	Minute	a		Any chiral molecules	PVED: theo. calculations (natural) polarized particles: asymmetric destruction of racemates b	52, 53, 124
	MChD	Truly	Bidirectional, (+) or (-) depending on the relative orientation of light and magnetic field	Minute	c		Chiral molecules with high gNCD and gMCD values	Proceed with unpolarised light	137
	Aligned magnetic field, gravity and rotation	Falsely	momentum and effective gravity Bidirectional, (+) or (-) depending on the relative orientation of angular	Minute	d		Large supramolecular aggregates	Ubiquitous natural physical fields	161
	Vortices	Truly	Bidirectional, (+) or (-) depending on the direction of the vortices	Minute	d		Large objects or aggregates	Ubiquitous natural physical field (pot. present in hydrothermal vents)	149, 158
	CPL	Truly	Bidirectional, (+) or (-) depending on the direction of CPL	Low to Moderate e	Chiral molecules with high gNCD values	Asymmetric destruction of racemates	58
	Spin-polarized electrons (CISS effect)	Truly	Bidirectional, (+) or (-) depending on the polarization	Low to high	f	Any chiral molecules	racemate, asymmetric synthesis Enantioselective adsorption/crystallization of	233
	Chiral surfaces	Truly	Bidirectional, (+) or (-) depending on surface chirality	Low to excellent	Any adsorbed chiral molecules	Enantioselective adsorption of racemates	237, 243
	SMSB (crystallization)	na	Bidirectional, stochastic distribution of (+) or (-) for repeated processes	Low to excellent	Conglomerate-forming molecules	Resolution of racemates	54, 367
	SMSB (asymmetric auto-catalysis)	na	Bidirectional, stochastic distribution of (+) or (-) for repeated processes	Low to excellent	Soai reaction	to be demonstrated	312
	Chance mechanisms	na	Bidirectional, stochastic distribution of (+) or (-) for repeated processes	Minute	g		Any chiral molecules	to be demonstrated	17, 412-414
	(a)

  on the surface of dust grains from which condensates a gaseous mixture of carbon, nitrogen and oxygen-based molecules (e.g. H 2 O, CH 3 OH, CH 4 , NH 3 , CO 2 ),

					447
	under the influence of very low temperature (5-15 K) 448 and
	pressure. Subsequent photochemical processes in this mantle
	of frost are assumed to lead to complex molecules.	449 Since
	collapsing clouds gave birth to our solar system through the
	aggregation of dust grains,	450 studies of their composition
	receive a keen interest to broaden our knowledge about the
	prebiotic environment. Experiments on simulated interstellar
	ices support the formation of many proteinaceous amino
	acids,	451,452 and building blocks of RNA and DNA such as
	sugars,	453 like ribose	454 and deoxyribose,	455 as well as
	nucleobases (adenine, cytosine, uracil and thymine for
	example).

456

  Sandars model was modified in different ways by several groups[570][571][572][573][574] to integrate more realistic parameters such as the possibility for polymers of all lengths to act catalytically in the breakdown of the achiral substrate into chiral monomers (instead of solely polymers of length N in the model of

			124 the
	unrealistic condition of perfect stereoselectivity has been
	pointed out.	567 Yamagata later developed a probabilistic model
	which (i) favours ligations between monomers of the same
	chirality without discarding chirally mismatched combinations,
	(ii) gives an advantage of bonding between L monomers (again
	thanks to PVED) and (iii) allows racemization of the monomers
	and reversible polymerization. Homochirality in that case
	appears to develop much more slowly than the growth of
	polymers.	568 This conceptual approach neglects enantiomeric
	cross-inhibition and relies on the difference in reactivity
	between enantiomers which has not been observed
	experimentally. The kinetic model developed by Sandars	569 in
	2003 received deeper attention as it revealed some intriguing
	features of homochiral polymerization processes. The model is
	based on the following specific elements: (i) chiral monomers
	are produced from an achiral substrate, (ii) cross-inhibition is
	assumed to stop polymerization, (iii) polymers of a certain
	length N catalyses the formation of the enantiomers in an
	enantiospecific fashion (similarly to a nucleotide synthetase
	ribozyme), and (iv) the system operates with a continuous
	supply of substrate and a withhold of polymers of length N (i.e.
	the system is open). By introducing a slight difference in the
	initial concentration values of the (R) and (S) enantiomers,
	bifurcation	304 readily occurs, i.e. homochiral polymers of a

108 Amongst other criticisms, single enantiomer are formed. The required conditions are sufficiently high values of the kinetic constants associated with enantioselective production of the enantiomers and crossinhibition. This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins

The

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44,54Kondepudi-like crystallization of NaClO 3 in presence of  particles from a 39 Sr

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W. Thomson, Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light, Cambridge Univ. Press. Warehouse,

Acknowledgements

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Author Contributions

QS selected the scope of the review, made the first critical analysis of the literature and wrote the first draft of the review. JC modified parts 1 and 2 according to her expertise to the domains of chiral physical fields and parity violation. MR re-organized the review into its current form and extended parts 3 and 4. All authors were involved in the revision and proof-checking of the successive versions of the review.

Conflicts of interest

There are no conflicts to declare.