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Spontaneous Emergence of Homochirality in Noncatalytic Systems

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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 linear- ization 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 epimeriza- tion; ␥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.
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