Celia Blanco

Chiral polymerization: symmetry breaking and entropy production in closed systems

We solve numerically a kinetic model of chiral polymerization in systems closed to matter and energy flow, paying special attention to its ability to amplify the small initial enantiomeric excesses due to the internal and unavoidable statistical fluctuations. The reaction steps are assumed to be reversible, implying a thermodynamic constraint among some of the rate constants. Absolute asymmetric synthesis is achieved in this scheme. The system can persist for long times in quasi-stationary chiral asymmetric states before racemizing. Strong inhibition leads to long-period chiral oscillations in the enantiomeric excesses of the longest homopolymer chains. We also calculate the entropy production σ per unit volume and show that σ increases to a peak value either before or in the vicinity of the chiral symmetry breaking transition.

Spontaneous Emergence of Chirality in the Limited Enantioselectivity Model: Autocatalytic Cycle Driven by an External Reagent

The model of limited enantioselectivity (LES) in closed systems, and under experimental conditions able to achieve chemical equilibrium, can give rise to neither spontaneous mirror symmetry breaking (SMSB) nor kinetic chiral amplifications. However, it has been recently shown that it is able to lead to SMSB, as a stationary final state, in thermodynamic scenarios involving nonuniform temperature distributions and for compartmentalized separation between the two autocatalytic reactions. Herein, it is demonstrated how SMSB may occur in LES in a cyclic network with uniform temperature distribution if the reverse reaction of the nonenantioselective autocatalysis, which gives limited inhibition on the racemic mixture, is driven by an external reagent, that is, in conditions that keep the system out of chemical equilibrium. The exact stability analysis of the racemic and chiral final outcomes and the study of the reaction parameters leading to SMSB are resolved analytically. Numerical simulations, using chemical kinetics equations, show that SMSB may occur for chemically reasonable parameters. Numerical simulations on SMSB are also presented for speculative, but reasonable, scenarios implying reactions common in amino acid chemistry.

Mirror symmetry breaking with limited enantioselective autocatalysis and temperature gradients: a stability survey

We analyze limited enantioselective (LES) autocatalysis in a temperature gradient and with internal flow/recycling of hot and cold material. Microreversibility forbids broken mirror symmetry for LES in the presence of a temperature gradient alone. This symmetry can be broken however when the auto-catalysis and limited enantioselective catalysis are each localized within the regions of low and high temperature, respectively. This scheme has been recently proposed as a plausible model for spontaneous emergence of chirality in abyssal hydrothermal vents. Regions in chemical parameter space are mapped out in which the racemic state is unstable and bifurcates to chiral solutions.

The Viedma Deracemization of Racemic Conglomerate Mixtures as a Paradigm of Spontaneous Mirror Symmetry Breaking in Aggregation and Polymerization

Simulations of a chemical kinetics model, based on the free-energy relationships of classical primary nucleation theory, show that the deracemization phenomenon in systems of achiral or fast racemizing compounds yielding enantiopure crystals as the more stable solid phase is a true spontaneous mirror symmetry breaking process (SMSB). That is, the achievement of a stationary chiral state is more stable than the racemic one. The model translates the free-energy relationships determined by the existence of a critical size cluster to a chemical kinetics model, in which the consideration of forward and backward reaction rate constants avoids the misuse of network parameters that violate thermodynamic constraints (microreversibility principle), which would lead to apparent in silico SMSB. The model provides qualitative agreement for deracemizations by mechanical attrition of visible crystals, as well as for those obtained under temperature gradients. The analysis of the effect of the system parameters to obtain a SMSB scenario shows that the network possesses the principal characteristics of SMSB networks: 1) an enantioselective autocatalytic stage, corresponding to the non-linear kinetics of enantioselective (homochiral) cluster-to-cluster growth, and 2) the mutual inhibition step originating in the backward flow of chiral clusters towards smaller achiral clusters, or even to a racemizing monomer. The application of such a SMSB kinetic model to enantioselective polymerizations and to chiral biopolymers is discussed.

Spontaneous Mirror Symmetry Breaking in the Limited Enantioselective Autocatalysis Model: Abyssal Hydrothermal Vents as Scenario for the Emergence of Chirality in Prebiotic Chemistry

The emergence of chirality in enantioselective autocatalysis for compounds unable to transform according to the Frank-like reaction network is discussed with respect to the controversial limited enantioselectivity (LES) model composed of coupled enantioselective and non-enantioselective autocatalyses. The LES model cannot lead to spontaneous mirror symmetry breaking (SMSB) either in closed systems with a homogeneous temperature distribution or in closed systems with a stationary non-uniform temperature distribution. However, simulations of chemical kinetics in a two-compartment model demonstrate that SMSB may occur if both autocatalytic reactions are spatially separated at different temperatures in different compartments but coupled under the action of a continuous internal flow. In such conditions, the system can evolve, for certain reaction and system parameters, toward a chiral stationary state; that is, the system is able to reach a bifurcation point leading to SMSB. Numerical simulations in which reasonable chemical parameters have been used suggest that an adequate scenario for such a SMSB would be that of abyssal hydrothermal vents, by virtue of the typical temperature gradients found there and the role of inorganic solids mediating chemical reactions in an enzyme-like role.

Temporary mirror symmetry breaking and chiral excursions in open and closed systems

The reversible Frank model is capable of amplifying the initial small statistical deviations from the idealized racemic composition. This temporary amplification can be interpreted as a chiral excursion in a dynamic phase space. It is well known that if the system is open to matter and energy exchange, a permanently chiral state can be reached asymptotically, while the final state is necessarily racemic if the system is closed. In this work, we combine phase space analysis, stability analysis and numerical simulations to study the initial chiral excursions and determine how they depend on whether the system is open, semi-open or closed.

Chiral and chemical oscillations in a simple dimerization model.

We consider the APED model (activation-polymerization-epimerization-depolymerization) for describing the emergence of chiral solutions within a non-catalytic framework for chiral polymerization. The minimal APED model for dimerization can lead to the spontaneous appearance of chiral oscillations and we describe in detail the nature of these oscillations in the enantiomeric excess, which are the consequence of oscillations of the concentrations of the associated chemical species.

Induced mirror symmetry breaking via template-controlled copolymerization: theoretical insights

A chemical equilibrium model of template-controlled copolymerization is presented for describing the outcome of the experimental induced desymmetrization scenarios recently proposed by Lahav and co-workers.

Models for mirror symmetry breaking via β-sheet-controlled copolymerization: (i) mass balance and (ii) probabilistic treatment.

Experimental mechanisms that yield the growth of homochiral copolymers over their heterochiral counterparts have been advocated by Lahav and co-workers. These chiral amplification mechanisms proceed through racemic β-sheet-controlled polymerization operative in both surface crystallites as well as in solution. We develop two complementary theoretical models for these template-induced desymmetrization processes leading to multicomponent homochiral copolymers. First, assuming reversible β-sheet formation, the equilibrium between the free monomer pool and the polymer strand within the template is assumed. This yields coupled nonlinear mass balance equations whose solutions are used to calculate enantiomeric excesses and average lengths of the homochiral chains formed. The second approach is a probabilistic treatment based on random polymerization. The occlusion probabilities depend on the polymerization activation energies for each monomer species and are proportional to the concentrations of the monomers in solution in the constant pool approximation. The monomer occlusion probabilities are represented geometrically in terms of unit simplexes from which conditions for maximizing or minimizing the likelihood for mirror symmetry breaking can be determined.

Chiral symmetry breaking via crystallization of the glycine and α-amino acid system: a mathematical model

We introduce and numerically solve a mathematical model of the experimentally established mechanisms responsible for the symmetry breaking transition observed in the chiral crystallization experiments reported by I. Weissbuch, L. Addadi, L. Leiserowitz and M. Lahav, J. Am. Chem. Soc., 1988, 110, 561-567. The mathematical model is based on five basic processes: (1) the formation of achiral glycine clusters in solution, (2) the nucleation of oriented glycine crystals at the air/water interface in the presence of hydrophobic amino acids, (3) a kinetic orienting effect which inhibits crystal growth, (4) the enantioselective occlusion of the amino acids from solution, and (5) the growth of oriented host glycine crystals at the interface. We translate these processes into differential rate equations. We first study the model with the orienting process (2) without (3) and then combine both allowing us to make detailed comparisons of both orienting effects which actually act in unison in the experiment. Numerical results indicate that the model can yield a high percentage orientation of the mixed crystals at the interface and the consequent resolution of the initially racemic mixture of amino acids in solution. The model thus leads to separation of enantiomeric territories, the generation and amplification of optical activity by enantioselective occlusion of chiral additives through chiral surfaces of glycine crystals.