Spontaneous Emergence of Homochirality in Noncatalytic Systems

Recycling Frank: Spontaneous emergence of homochirality in noncatalytic systems

Raphae¨l Plasson†‡, Hugues Bersini§, and Auguste Commeyras†

†Organisation Mole´culaire: E´ volution et Mate´riaux Fluore´s, Unite´Mixte de Recherche 5073, CC017, Universite´Montpellier II, Place Eugene Bataillon, 34095 Montpellier Cedex 5, France; and §Institut de Recherches Interdisciplinaires et de De´veloppements en Intelligence Artiﬁcielle, CP194͞6, Universite´Libre de Bruxelles, 50 Avenue Franklin Roosevelt, 1050 Bruxelles, Belgium

Edited by Jack Halpern, University of Chicago, Chicago, IL, and approved October 18, 2004 (received for review July 21, 2004) In this work, we introduce a prebiotically relevant protometabolic We set out to construct such a system, exclusively based on pattern corresponding to an engine of deracemization by using an simple reactions, all realistic from the prebiotic point of view. external energy source. The spontaneous formation of a nonrace- Rather than introducing direct autocatalytic reactions (dubious mic mixture of chiral compounds can be observed in out-of- in a prebiotic environment) autoinduction will be shown to equilibrium systems via a symmetry-breaking phenomenon. This emerge from a network of coupled stereoselective reactions. observation is possible thanks to chirally selective autocatalytic Moreover, as the synthesis of prebiotic material should have reactions (Frank’s model) [Frank, F. C. (1953) Biochim. Biophys. Acta been an important limiting factor, a recycled system based on 11, 459–463]. We show that the use of a Frank-like model in a reversible chemical reactions is considered, rather than the recycled system composed of reversible chemical reactions, rather classical irreversible description. The Frank-based experimen- than the classical irreversible system, allows for the emergence of tations are practically limited to materially closed systems (15, a synergetic autoinduction from simple reactions, without any 17, 18). In the absence of recycling, they can’t reach a real steady autocatalytic or even catalytic reaction. This model is described as state: the evolution of the system stops with the destruction of a theoretical framework, based on the stereoselective reactivity of initial reactants. This absence results in a stochastic behavior preexisting chiral monomeric building blocks (polymerization, leading to a random final enantiomeric excess (16). In a closed epimerization, and depolymerization) maintained out of equilib- system, the accumulation of the final products erodes the CHEMISTRY rium by a continuous energy income, via an activation reaction. It amplification process. Its elimination, for example, thanks to the permits the self-conversion of all monomeric subunits into a single establishment of a product flux by the aperture of the system, chiral conﬁguration. Real prebiotic systems of amino acid deriva- allows us to overcome this limitation (20). The recycling of tives can be described on this basis. They are shown to be able to materials constitutes a natural alternative to this material- spontaneously reach a stable nonracemic state in a few centuries. consuming elimination mechanism, allowing a fully effective In such systems, the presence of epimerization reactions is no more amplification process toward homochirality (21). destructive, but in contrast is the central driving force of the On the basis of these considerations, we describe a dynamic unstabilization of the racemic state. chemical system of reacting chiral monomers, composed of activation, polymerization, epimerization, and depolymerization prebiotic chemistry ͉ protometabolism (APED) reactions between deactivated monomers (L and D), activated monomers (L* and D*), and polymers (Xn, with X he emergence of homochirality is a crucial enigma in the being either L or D, and reacting residue being, by convention, Torigin of life (1): fundamental biomolecules are different represented on the left side). For the sake of simplicity, the from their mirror images and exist only in either the right- polymerization reactions are limited to dimerizations. The po- ␣ handed or left-handed form. For symmetry reasons, the first lymerizations of rates p and p, the depolymerizations of rates ␤ ␥ chiral prebiotic molecules should have been synthesized in equal h and h, and the epimerizations of rates e and e can be ␣ ␤ ␥ amounts of both forms (2), but an initial enantiomeric excess of stereoselective, quantified by the parameters , and , respec- low value can easily exist (3), thanks to statistical fluctuation (4), tively. The activation and deactivation rates are quantified by asymmetry of weak forces (5), or induction by an asymmetric a and b, respectively (see Fig. 1). The total concentration ϭ ϩ ϩ ϩ ϩ ϩ ϩ environment (6–9). The problem thus comes down to under- in residues c [L] [D] [L*] [D*] 2([LL] [DD] ϩ standing how amplification phenomena could take place to [LD] [DL]) is a constant parameter. The APED system can be enhance such initial deviance from symmetry, constituting a real represented as an embedded Frank-like model, with no auto- symmetry breaking toward homochirality. Some explanations catalytic or catalytic reactions (see Fig. 2). The whole system is based on stereoselective polymerization are classically suggested totally recycled and maintained out of equilibrium by the (10, 11). However, the effect is only proportional to the initial continuous activation of monomers. excess and is to be destroyed in the long term by epimerization, If the APED model is very general, it is fully compatible with so that these models are not sufficient as the racemic state the chemistry of amino acids: remains stable (12). Y The polymerization of amino acids can be very stereoselective, True symmetry breaking can occur in an dynamical out-of- favoring the formation of homochiral peptides, namely by equilibrium chemical system, as first introduced by Frank (13), using N-carboxyanhydrides of ␣-amino acids (22, 23). allowing the destabilization of the racemic state. Several exper- Y The activation energy of the epimerization of the N-terminal imental systems corresponding to such a model have been residue of a peptide is much lower than that of all other described (14–18), but as Blackmond (19) recently concluded in residues, either in their free form or embedded in the peptide an analysis about such experimental models, there is still a need of ‘‘other organic transformations that could provide a closer model for how asymmetric amplification in the prebiotic world This paper was submitted directly (Track II) to the PNAS ofﬁce. could have occurred.’’ To be effective, such systems need Abbreviations: APED, activation polymerization, epimerization, and depolymerization; autocatalysis (so that an excess of one configuration favors its NCA, N-carboxyanhydride of ␣-amino acid. own production) and a mechanism capable of destructing the ‡To whom correspondence should be addressed. E-mail: [email protected]. opposite configuration. © 2004 by The National Academy of Sciences of the USA

www.pnas.org͞cgi͞doi͞10.1073͞pnas.0405293101 PNAS ͉ November 30, 2004 ͉ vol. 101 ͉ no. 48 ͉ 16733–16738 Downloaded by guest on October 2, 2021 ␥ ϭ 0, by determining the states where the derivatives of the concentrations of all compounds equal zero. In each case, several fixed points are theoretically possible and may be reached. An absolute condition for the possibility of the fixed point is that all concentration values are positive, which implies for some cases a minimal value of c [i.e., c Ͼ 2a͞(p(1 ϩ a)) or c Ͼ a͞p]. The stability of the fixed points is investigated by the linearization of the equations in the neighborhood of the fixed point. The evolution of the concentrations near a given fixed point is given by:

Ϫ a Ϫ xl Ϫ ␣xd 0 Ϫ yl Ϫ ␣yl 2h 000 0 Ϫ a Ϫ xd Ϫ ␣xl Ϫ ␣yd Ϫ yd 02h 00 a Ϫ xl Ϫ ␣xl Ϫ yl Ϫ ␣yd 00000 f dV Ϫ ␣x a Ϫ x 0 Ϫ y Ϫ ␣y 0000 ϭ d d d l V f dt xl 0 yl 0 Ϫ h 0 e 0 Ϫ ΄ 0 xd 0 yd 0 h 0 e ΅ ␣xd 00␣yl 00Ϫ e 0 0 ␣xl ␣yd 0000Ϫ e with:

l Ϫ lf d Ϫ df l* Ϫ l*f d* Ϫ d*f V f ϭ x ϭ p⅐l f x ϭ p⅐d f y ϭ p⅐l f y ϭ p⅐df ll Ϫ llf ; l * ; d * ; l ; d . ΄dd Ϫ ddf΅ dl Ϫ dlf ld Ϫ ldf Fig. 1. Minimal APED system limited to dimerizations of L and D residues. (Upper) Chemical reactions. (Lower) Reaction network. a, Activation; b, de- l d l d ll dd ld dl l f df l f d f llf ddf ldf dlf ␣ , , *, *, , , , and ( , , * , * , , , , and , activation; p, homochiral polymerization; p, heterochiral polymerization; h, respectively) are the concentrations of L, D, L*, D*, LL, DD, homochiral hydrolysis; ␤h, heterochiral hydrolysis; e, homochiral epimerization; ␥e, heterochiral epimerization. LD, and DL, respectively, at a given time t (in the fixed point). If all of the eigenvalues (or their real part if complex) of the matrix are negative, the considered fixed point V f is asymptot- chain (24). Thus, the D͞L interconversion can be restricted to ically stable. Computer kinetic simulations were performed for the N-terminal residues of peptides, with all other inversion particular cases to verify these analytical results. A fourth-order reactions being insignificant. Runge–Kutta algorithm with adaptive stepsize control was used Y The epimerization reaction can be very stereoselective, favor- with XPPAUT software [version 5.85, written by G. B. Ermentrout ing the formation of the homochiral peptides (25). et al. is free software, distributed under the GNU Public License (www.gnu.org)]. The purpose of this work is to determine whether such a simple system can give rise to dynamic instabilities, so that Systematic Analysis of APED Systems. A program was written in C, homochirality can emerge. Despite the simplicity of this model, based on a fourth-order Runge-Kutta algorithm (26), for the the differential equations set is still complex, as all reactions are automated kinetic simulation of the full APED systems (the coupled. The work was thus performed in three successive steps: source code is available at http:͞͞omemf.univ-montp2.fr͞ an analytical study of a simplified model, a systematic numerical online͞simul.c). Simulations were performed for the case a ϭ study of the whole system, and a numerical application describing h ϭ e ϭ 1sϪ1, c ϭ 2M,andp ϭ 1sϪ1⅐MϪ1, and for all values a more realistic system of amino acid derivatives, based on of 10Ϫ4.5 Յ ␣ Յ 101.5,10Ϫ4.5 Յ ␤ Յ 101.5, and 10Ϫ4.5 Յ ␥ Յ 101.5) literature values for the kinetic rates. by steps of 100.02 on a logarithmic scale. A first excess eeinit ϭ 0.01 Methods was introduced in an initial mixture of L and D. The calculation was performed for a fixed simulated time of reaction, and Local Stability Analysis of Fixed Points. The fixed points are calcu- concentrations were analyzed on the last 10% time, to know ϭ Ϫ1 ␤ ϭ lated from the kinetic equations, in the case b 0s and whether a fixed point is reached or whether the system is unstable (corresponding to an oscillating steady state). The symmetry of the fixed point was determined thanks to the value of the global enantiomeric excess ee ϭ (l ϩ l* ϩ 2ll Ϫ d Ϫ d* Ϫ 2dd)͞c. The system is known to be dead if at the end of the simulation all products but the activated monomers have disappeared.

Results and Discussion Analytical Study. We first reduced the model to the very essential reactions to perform the analytical study on a particular case. Fig. 2. Schematic representations of Frank’s model (A) and the APED model Deactivation is neglected, and the stereoselectivities of depoly- (B). (A) Circled S, synthesis of chiral compounds XL and XD from achiral ␤ ϭ compounds F; circled C, autocatalysis by X and X ; circled M, mutual destruc- merization and epimerization are considered as total (i.e., L D ␥ ϭ 0). This model is obviously extreme and unrealistic, but tion of XL and XD to P. (B) Circled A, activation of L and D to L* and D*; circled P, polymerization from L* and D* to Xn; circled E, epimerization between allows a simple analytical approach of the complete model, polymers; circled D, depolymerization of Xn back to L and D. aiming at the determination of the phenomenology to be ex-

16734 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0405293101 Plasson et al. Downloaded by guest on October 2, 2021 Y In all cases, if the total concentration is too low, no dimers are formed: the only possible state is the dead one (see Fig. 3A). Y If the polymerization favors the formation of homochiral dimers (i.e., ␣ Ͻ 1), the symmetric state is unstable, and the asymmetric state is stable. An initial racemic situation will thus spontaneously evolve to an homochiral situation: a symmetry breaking occurs, where either all L or D residues are spontaneously converted to the opposite form (see Fig. 3B). Y If the polymerization favors the formation of heterochiral dimers, and below a specific critical value (i.e., 1 Ͻ ␣ Ͻ ␣c, ␣c being the critical value of ␣ as a function of c), the symmetric state is stable, and the asymmetric state is unstable. Indepen- dently of the initial conditions, the system will evolve to the racemic state: every initial imbalance is destroyed (see Fig. 3C). Near the critical values of ␣, oscillations can be observed before the racemic state is reached (see Fig. 3D). Y Above the critical value of stereoselectivity (i.e., ␣ Ͼ ␣c) both symmetric and asymmetric states are unstable. As a result, the system oscillates between two opposite values of the enantiomeric excess (see Fig. 3E) and cannot reach any stable fixed point. This case seems quite surprising, but the high values required for ␣ are probably not realistic if applied to a real chemical system. This simple system, although based on noncatalytic reactions, is able to behave similarly as the Frank’s model, with an unstabilization of the racemic state. The autocatalytic reactions (strictly necessary in the Frank’s model) can thus be replaced by CHEMISTRY an autoinduction, stemming from a synergetic action of simple stereoselective reactions.

Systematic Study. Given these results, it appears that the stereoselectivity of polymerization favoring the formation of homochiral dimers (i.e., ␣ Ͻ 1) is absolutely necessary for obtaining a symmetry breaking toward a long-term stable homochirality. To verify whether this observation is specific to this extreme model, we performed a systematic analysis of the complete Fig. 3. The five kinds of behaviors of APED systems. (A–E) Spontaneous model. A computer program has been written to automate the evolution of the enantiomeric excess of several simplified APED systems, kinetic simulations and the analysis of the final state of the calculated for b ϭ 0sϪ1, a ϭ h ϭ e ϭ 1sϪ1, p ϭ 1sϪ1⅐MϪ1, ␤ ϭ ␥ ϭ 0 and ␣ ϭ system as a function of ␣, ␤, and ␥ (see Methods). 0.1, c ϭ 1M(A); ␣ ϭ 0.1, c ϭ 3M(B); ␣ ϭ 1.1, c ϭ 3.2M(C); ␣ ϭ 50, c ϭ 2M(D); Behaviors are roughly similar as in the simple model: the and ␣ ϭ 100, c ϭ 2M(E). (F) Behavior categories of the simplified APED systems. systems can be symmetric, asymmetric, unstable, or dead (see Crosses indicate the position of the A–E system. Solid lines indicate the Fig. 4A). Here again, a stereoselectivity of polymerization separations between dead (d), symmetric (s), asymmetric (a), and unstable (u) favoring the formation of homochiral dimers (␣ Ͻ 1), i.e., a systems. The dotted line represents the separation between monotone and oscillating symmetric systems. ‘‘productive’’ stereoselectivity, is absolutely necessary. A strong opposite, ‘‘counterproductive,’’ stereoselectivity (high values of ␣) makes the system unstable. On top of these observations, a counterintuitive behavior of pected in more general cases. The fixed points can be determined the system occurs if the productive stereoselectivity is too strong from the equations (see Methods). There are three possibilities: (lowest values of ␣). Although a system with a limited stereo-

Y selectivity can reach a quasi-perfect homochirality, only incom- The symmetric state, where all species exists, all enantiomer plete homochirality is obtained with a more stereoselective pairs being in equal concentrations (i.e., this state is totally polymerization: the global enantiomeric excess of the stable racemic). As can be observed, a minimal total concentration fixed point quickly decreases with ␣. The symmetry-breaking is required for fulfilling the existence of all of the compounds. phenomenon is thus only effective for weakly stereoselective Y The asymmetric state, where all residues of one absolute systems. In the example shown in Fig. 4 C and E, the system is configurations have disappeared. This state is totally homo- asymmetric only for 10Ϫ3 Ͻ ␣ Ͻ 1). chiral. Here again, a minimal total concentration is required. The stereoselectivity of depolymerization and epimerization Y The ‘‘dead’’ state, where all concentrations are zero but for the plays a very different role. They both have a similar influence on activated species L* and D*. This state is a dead end, where the system, as shown by the symmetry of the ␣␤␥ diagram. At no reaction can occur. least one of the stereoselectivities is required. Symmetry breaking is favored by the preferential epimerization of heterochiral The stability of these states is investigated by the linearization dimers into homochiral dimers (i.e., ␥ Ͻ 1) and by the prefer- of the equation sets in the neighborhood of the fixed points and ential hydrolysis of homochiral dimers rather than heterochiral the research of the eigenvalues of the corresponding matrix (see dimers (i.e., ␤ Ͻ 1). If one of these two stereoselectivities is Methods). Depending on the values of c and ␣, four steady states counterproductive, the asymmetric system can still be stable if can be identified (the regions of these four behaviors are the other one is sufficiently productive (see Fig. 4 B and D). represented by d, a, s, and u in Fig. 3): The complete APED system is thus still efficient, although

Plasson et al. PNAS ͉ November 30, 2004 ͉ vol. 101 ͉ no. 48 ͉ 16735 Downloaded by guest on October 2, 2021 Fig. 4. Diagram of the APED states as a function of ␣, ␤, and ␥, calculated for b ϭ 0sϪ1, a ϭ h ϭ e ϭ 1sϪ1, p ϭ 1sϪ1⅐MϪ1, and c ϭ 1M.a: Asymmetric system; s: symmetric system; d: dead system; u: unstable system. (A) Complete ␣␤␥ diagram. The dotted axes represents the values of ␣, ␤, and ␥ on a logarithmic scales, from 10Ϫ4 to 101.5, and intersect at ␣ ϭ ␤ ϭ ␥ ϭ 1. (B) ␤␥ Diagram for ␣ ϭ 10Ϫ1 (bilogarithmic scale). (C) ␣␥ Diagram for ␤ ϭ 10Ϫ2 (bilogarithmic scale). (D) Bifurcation diagram for ␣ ϭ 10Ϫ1, representing the enantiomeric excess of the stable fixed point (ԽeefixeԽ) as a function of ␤ ϭ ␥ (logarithmic scale). (E) Bifurcation diagram for ␤ ϭ ␥ ϭ 10Ϫ2, representing ԽeefixeԽ as a function of ␣ (logarithmic scale).

only partial homochirality is stable. It is observed that all three systems can be described as a function of the environmental stereoselectivities of polymerization, epimerization, and depo- conditions, from slow systems with stable peptides, as in lymerization play a crucial role for obtaining a nonracemic Commeyras and coworkers’ model (36), to fast ones with system. A strong collaboration exists between these reactions, short-life peptides, as in Wa¨chtersha¨user and colleagues’ and the autoinduction phenomenon emerges from this synergy. model (33). A simulation was performed from estimated kinetic rates of Real Systems. The preceding model is theoretical, but can be peptides and NCAs reactivity in water, based on previously applied to concrete chemical systems of amino acid derivatives. measured kinetic rates and other literature values. The ratios In a prebiotic point of view, amino acids are known to be between homochiral and heterochiral coupling have been mea- synthesized abiotically in many ways (27–30). However, the sured for several substrates. Values between 1.2 and 5.3 have formation of the first prebiotic peptides is not a trivial problem, been reported (37), corresponding to an average value of 0.35 for as free amino acids are poorly reactive. Some invoked prebiotic ␣. The difference between activation energies of epimerization activations of stable amino acids derivatives rely on the forma- of homochiral and heterochiral dipeptides has been theoretically tion of N-carboxyanhydrides of ␣-amino acids (NCAs) (11, 31), estimated at 3 kJ⅐molϪ1 (25). By supposing that the preexpo- e.g., by the action of nitrogen oxides under mild conditions (32) nential parameter of Arrhenius is roughly equal for both epimer- or carbon monoxide in the presence of (Fe,Ni)S under drastic izations, ␥ can be estimated to: conditions (33). The chemistry of NCAs (34) is of great interest ⌬E Ϫ for building real APED systems: ␥ ϭ e RT Ӎ 0.3 at 300 K. Y They are very reactive amino acids derivatives, which easily ␥ permit the formation of peptides in aqueous solutions (22, 35). Experimental measurements of are still in progress, but initial Y The polymerization of NCAs is stereoselective (22, 23, 36, 37), results tend to confirm this rough value. The rates of polymer- favoring the formation of homochiral peptides. ization (fast) and peptide hydrolysis (slow) are very different in Y This chemistry facilitates the recycling of products, constitut- all conditions. It could be observed that the system is more ing a retroaction loop: peptides are hydrolyzed back to amino effective when this difference is reduced, corresponding to low acids in aqueous solutions; the amino acids’ reactivation into values of pH: the hydrolysis of peptides is enhanced, and the NCAs allows their reintroduction into the peptides. polymerization of peptides is slowed down. The rates of hydrolysis and polymerization of NCAs (37, 38) and the rate of The limiting factor for the loop activity is the slower reaction hydrolysis of peptide (39) were thus taken for acidic conditions, rate, i.e., the depolymerization rate. A wide range of possible corresponding to b ϭ 5.10Ϫ4⅐sϪ1, p ϭ 0.02 sϪ1⅐MϪ1, and h ϭ

16736 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0405293101 Plasson et al. Downloaded by guest on October 2, 2021 racemization of the system when it is isolated, the energetic openness of the system can, in constrast, allow the epimerization to counteract the global racemization, if either the epimerization or the depolymerization is sufficiently stereoselective, favoring the formation and the hydrolysis of homochiral polymers, respectively. This simple model succeeds in fulfilling the two key concepts necessary for the spontaneous emergence of homochirality, as described by Blackmond (19) on the basis of the experimental system developed by Soai et al. (15): Y The synergetic action of epimerization with polymerization and depolymerization allows an emergent autoinduction phenomenon: an excess of L residues favors the inversion of D residues into L ones. Thanks to an activation reaction, this sequence of reactions constitutes a positive retroaction loop in the reaction network, which plays the same role as the direct autocatalysis of the classical Frank’s model. Y Every residue is to be recycled and is likely to be epimerized. Fig. 5. Time evolution of the enantiomeric excess of APED systems based on The suppression of the ‘‘wrong hand’’ residue (strongly re- experimental data, for different concentrations in residues c. Calculated for quired in a system of spontaneous asymmetric synthesis) is Ϫ Ϫ Ϫ Ϫ ⅐ Ϫ Ϫ Ϫ eeini ϭ 0.01; a ϭ 10 8 s 1, b ϭ 5⅐10 4 s 1, p ϭ 2⅐10 2 s 1⅐M 1, ␣ ϭ 0.35, h ϭ 10 7 here inherent to the dynamic of a totally recycled system, Ϫ1 Ϫ7 Ϫ1 s , ␤ ϭ 0.2, e ϭ 10 s , ␥ ϭ 0.3. allowing conversion between residues (i.e., requiring effective epimerization reactions). Ϫ Ϫ 10 7⅐s 1. The epimerization rate of the N-terminal residue of As a result, this model get closer to living systems than classical peptides is of the same order as the hydrolysis rate, and the models, by introducing a protometabolic pattern, i.e., describing difference of activation energy between this epimerization and a cyclic use of organic compounds, fed with external energy flow, CHEMISTRY the one of other residues (either in free form or embedded into rather than the common ‘‘open-flow reactor’’ pattern. The Ϫ a peptide chain) is estimated at Ϸ30 kJ⅐mol 1 (24). Thus, all but relevance of such a pattern in prebiotic conditions is enhanced N-terminal residues can be neglected in epimerization, and e was by the fact that autocatalytic reactions are unnecessary, and that Ϫ Ϫ taken to be equal to h. A slow activation flux a ϭ 10 8 s 1 was epimerization reactions are not drawbacks as often reported introduced. The stereoselectivity of hydrolysis of peptide is (40), but in contrast are the driving force of the stabilization of rarely reported in the literature. An optimum value of 0.2 for ␤ asymmetry. was manually found, corresponding to an hydrolysis favoring the The ‘‘bottom-up’’ approach, developed here, describes the destruction of homochiral peptides, as observed in the theoret- emergence of a network autocatalytic system, rather than a ical study. template autocatalytic system, joining the ‘‘top-down’’ approach In such conditions, the racemic state can still become as developed by Morowitz et al. (41), who have investigated the unstable: as long as the total concentration is sufficiently high, origin of metabolism on the basis of the reductive citric acid stable enantiomeric excess of Ϸ70% can be spontaneously cycle. If the prebiotic origin of a reaction network as complex as reached in a few centuries (see Fig. 5). These conditions are this cycle is questionable, much simpler systems may be relevant globally compatible with the hypothesis of a medium getting (42). Of course, the APED system does not yet constitute a alternatively dried and wet, with an amino acid activation metabolic pattern, but has some of its characteristics. It does not involving NOx compounds (36). The APED model appears to take into account the matter of creation (i.e., the formation of be possible and sensible in such environments, showing that amino acids in the described example), but it describes the use spontaneous prebiotic homochirality can be explained without of external energy to reproduce some properties (here, the invoking any autocatalytic reactions, on the basis of simple absolute configuration of the monomers) and to increase the chemical reactions. complexity of matter (by way of polymerization). An interesting extension to a more complex system is being investigated by Conclusion others, focusing on molecular energetic use, via carboxylic- The APED system is thus a dynamic system that can spontane- phosphoric mixed anhydrides (43). ously evolve to, and remain in, a stable nonracemic state. The model described here constitutes a minimal subset of reactions, We thank J. Reisse (Universite´Libre de Bruxelles), T. Lenaerts (Institut all of them being necessary for reaching symmetry breaking by de Recherches Interdisciplinaires et de De´veloppementsen Intelligence the self-conversion of one of the enantiomers into the other from Artificielle), and R. Pascal and L. Boiteau (Organisation Molećulaire: the racemic state. Consistently with the classical descriptions, a E´volution et Mate´riaux Fluore´s) for helpful advice and discussion and stereoselectivity of polymerization favoring the formation of J.-C. Micheau and D. Lavabre (Interactions Molećulaires et Reáctivite´ Chimique et Photochimique, Toulouse, France) for help during prelim- homochiral polymers is necessary, but was shown to be insuffi- inary work and comments on the manuscript. This work was supported cient. The cooperation between the epimerization of the termi- by the COST D27 European Cooperation in the Field of Scientific and nal residue and the polymer hydrolysis allows the continuous Technical Research program, within the framework of a short-term conversion between L and D residues and the stabilization of the scientific mission completed by R.P. at the Institut de Recherches nonracemic state. If the epimerization obviously tends to the Interdisciplinaires et de De´veloppementsen Intelligence Artificielle.

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