Spontaneous Deracemizations.

Spontaneous deracemizations is a challenging, multidisciplinary subject in current chirality research. In the absence of any chiral inductors, an achiral substance or a racemic composition is driven into an enantioenriched or even homochiral state through a selective energy input, e.g., chemical potential, photoirradiation, mechanical grinding, ultrasound waves, thermal gradients, etc. The most prominent examples of such transformations are the Soai reaction and the Viedma deracemization. In this review, we track the most recent developments in this topic and recall that many other deracemizations have been reported for solutions from mesophases to conglomerate crystallizations. A compiled set of simply available achiral organic, inorganic, organometallic, and MOF compounds, yielding conglomerate crystals, should give the impetus to realize new experiments on spontaneous deracemizations. Taking into account thermodynamic constraints, modeling efforts have shown that structural features alone are not sufficient to describe spontaneous deracemizations. As a guideline of this review, particular attention is paid to the physicochemical origin and symmetry requirements of such processes.

Chiral selectivity vs. noise in spontaneous mirror symmetry breaking.

Mirror symmetry breaking bifurcations, that occur in nonlinear chemical systems leading to final chiral states with very large enantiomeric excess, can be exploited as an efficient chiral signal selector for even the smallest chiral polarizations. This effect of the chiral polarization requires the system's capacity for overcoming thermal noise, which is manifested as fluctuating reaction rate constants. Therefore, we investigate the chiral selectivity across a range of tiny parity-violating energy differences (PVED) in the presence of inevitable non-equilibrium temperature fluctuations. We use a stochastic differential equation simulation methodology (Ito process) that serves as a valuable tool in open systems for identifying the thresholds at which the chiral force induces chiral selectivity in the presence of non-equilibrium temperature fluctuations. This approach enables us to include and analyze chiral selectivity in the presence of other types of fluctuations, such as perturbations in the rate of fluid flow into and out of the reactor and in the clamped input concentrations. These concepts may be of practical interest (i.e., spontaneous deracemizations) but are also useful for a better understanding of the general principles governing the emergence of biological homochirality.

Stoichiometric network analysis in reaction networks yielding spontaneous mirror symmetry breaking in a prebiotic atmosphere.

The generation of amino acid homochirality under prebiotic atmosphere conditions is a relevant issue in the study of the origin of life. This research is based on the production of amino acids via Strecker synthesis and how it is adjusted to the Kondepudi-Nelson autocatalytic model. The spontaneous mirror symmetry breaking (SMSB) of the new Kondepudi-Nelson-Strecker model, subject to two modifications (with Limited Enantioselective and Cross Inhibition), and also their combination were studied using the stoichiometric network analysis (SNA). In the calculations, the values obtained from the literature for alanine were considered. A total production of alanine of 7.56 × 109 mol year-1 was determined under prebiotic atmosphere conditions and starting from that value, the reaction rates for the models studied were estimated. Only the model with cross inhibition or achiral dimer formation is driven by stochastic fluctuations during SMSB. The stochastic fluctuation was estimated for a value of 2.619 × 10-15 mol L-1. This perturbation was sufficient to trigger SMSB. Finally, the results of SMSB were used to calculate the entropy production for the cross inhibition model.

The Coordinate Reaction Model: An Obstacle to Interpreting the Emergence of Chemical Complexity.

The way chemical transformations are described by models based on microscopic reversibility does not take into account the irreversibility of natural processes, and therefore, in complex chemical networks working in open systems, misunderstandings may arise about the origin and causes of the stability of non-equilibrium stationary states, and general constraints on evolution in systems that are far from equilibrium. In order to be correctly simulated and understood, the chemical behavior of complex systems requires time-dependent models, otherwise the irreversibility of natural phenomena is overlooked. Micro reversible models based on the reaction-coordinate model are time invariant and are therefore unable to explain the evolution of open dissipative systems. The important points necessary for improving the modeling and simulations of complex chemical systems are: a) understanding the physical potential related to the entropy production rate, which is in general an inexact differential of a state function, and b) the interpretation and application of the so-called general evolution criterion (GEC), which is the general thermodynamic constraint for the evolution of dissipative chemical systems.

Entropic analysis of bistability and the general evolution criterion.

We present a detailed study of the entropy production, the entropy exchange and the entropy balance for the Schlögl model of chemical bi-stability for both the clamped and volumetric open-flow versions. The general evolution criterion (GEC) is validated for the transitions from the unstable to the stable non-equilibrium stationary states. The GEC is the sole theorem governing the temporal behavior of the entropy production in non-equilibrium thermodynamics, and we find no evidence for supporting a "principle" of maximum entropy production. We use stoichiometric network analysis (SNA) to calculate the distribution of the entropy production and the exchange entropy over the elementary flux modes of the clamped and open-flow models, and aim to reveal the underlying mechanisms of dissipation and entropy exchange.

Correction: Spontaneous mirror symmetry breaking: an entropy production survey of the racemate instability and the emergence of stable scalemic stationary states.

Correction for 'Spontaneous mirror symmetry breaking: an entropy production survey of the racemate instability and the emergence of stable scalemic stationary states' by Josep M. Ribó et al., Phys. Chem. Chem. Phys., 2020, 22, 14013-14025, DOI: 10.1039/D0CP02280B.

Does Pressure Break Mirror-Image Symmetry? A Perspective and New Insights.

This paper is aimed at dissecting and discussing the effect of high pressure on chirogenesis, thus unveiling the role of this universal force in astrochemical and primeval Darwinian scenarios. The first part of this contribution revisits the current status and recent experiments, most dealing with crystalline racemates, for which generation of metastable conglomeratic phases would eventually afford spontaneous resolution and hence enantioenriched mixtures. We then provide an in-depth thermodynamic analysis, based on previous studies of non-electrolyte solutions and dense mixtures accounting for the existence of positive excess volume upon mixing, to simulate the mirror symmetry breaking, the evolution of entropy production and dissipation due to enantiomer conversion. Results clearly suggest that mirror symmetry breaking under high pressure may be a genuine phenomenon and that enantioenrichment from initial scalemic mixtures may also take place.

Spontaneous mirror symmetry breaking: an entropy production survey of the racemate instability and the emergence of stable scalemic stationary states.

We study the emergence of both stable and unstable non-equilibrium stationary states (NESS), as well as spontaneous mirror symmetry breaking (SMSB) provoked by the destabilization of the racemic thermodynamic branch, for an enantioselective autocatalytic reaction network in an open flow system, and for a continuous range n of autocatalytic orders. The system possesses a range of double bi-stability and also tri-stability depending on the autocatalytic order. We carry out entropy production and entropy flow calculations, from simulations of ordinary differential equations, stoichiometric network analysis (SNA), and consider a stability analysis of the NESS. The simulations provide a correct description of the relationship between energy state functions, the isothermal dissipated heat, entropy production and entropy flow exchange with the surroundings, and the correct solution of the balance of the entropy currents at the NESS. The validity of the General Evolution Criterion (GEC) is in full agreement with all the dynamic simulations.

Chaotic oscillations, dissipation and mirror symmetry breaking in a chiral catalytic network.

Catalytic reaction networks consist of molecular arrays interconnected by autocatalysis and cross-catalytic pathways among the reactants, and serve as bottom-up models for the design and understanding of molecular evolution and emergent phenomena. An important example of the latter is the emergence of homochirality in biomolecules during chemical evolution. This chiral symmetry breaking is triggered by bistability and bifurcation in networks of chiral replicators. Spontaneous mirror symmetry breaking (SMSB) results from hypercyclic connectivity when the chirality and enantioselectivity of the replicators are taken into account. Heretofore, SMSB has been generally understood as involving chemical transformations yielding scalemic outcomes as non-equilibrium steady states (NESS). Here, in marked contrast, we consider the chaotic regime, in which steady states do not exist. The dissipation, or entropy production, is chaotic as is the exchange entropy. The rate of change of the total system entropy, governed by the entropy balance equation, is also chaotic. Subsequent to the mirror symmetry breaking transition, the time averaged entropy production is minimized in the final chaotic chiral state with respect to the former chaotic racemic state. The chemical forces (i.e., the affinities) evolve in time so as to lower the sum of the entropy production and the exchange entropy, in compliance with the general evolution criterion extended to reaction networks subject to volumetric open flow.

Stoichiometric network analysis of entropy production in chemical reactions.

We use stoichiometric network analysis (SNA) to obtain a flux-based approach for the evaluation and description of the entropy production and exchange for chemical reactions in open systems. For non-equilibrium stationary states (NESS) the production and exchange are expressed as functions over the convex cone of the stationary reaction rates, revealing the reaction pathways and elementary flux modes (EFM) responsible for both entropy production and balance. The analysis of the entropy production of EFMs leads to a unique description of the contribution of the coupling between linear or cyclic reaction network paths, and the fluxes due to the matter exchange of the system with the system's surroundings. Network stoichiometry leads to an independent proof and confirmation of Prigogine's theorem of minimum entropy production for the linear regime of non-equilibrium thermodynamics. Moreover, the non-linear thermodynamic regime allows us to test the validity of the General Evolution Criterion (GEC) for NESS in isothermal chemical networks in mechanical equilibrium.

Open flow non-enzymatic template catalysis and replication.

Template induced replication is the basis of multiplication and reproduction in nature and underlies the importance of gaining a detailed understanding of its mechanisms in terms of chemical reaction networks. We analyze numerically the stationary state solutions for a class of autocatalytic reactions based on reversible template assisted ligation with first and second order catalysis and governed by mass-action kinetics. Chemical thermodynamics leads to constraints on the reaction rate constants which result in very low template yield in systems subject to fixed external concentrations. When however the network is driven out of equilibrium via open flow in a well-mixed reactor, the template yield can be increased significantly for very small fluid flow rates. This can be understood in terms of driven unidirectional pathways, as determined by stoichiometric network analysis.

Stoichiometric network analysis of spontaneous mirror symmetry breaking in chemical reactions.

We apply stoichiometric network analysis (SNA) to study enantioselective chemical reaction schemes, subject to various thermodynamic architectures, which may lead to spontaneous mirror symmetry breaking (SMSB). Stoichiometric matrices are used to calculate extreme currents or fluxes: the vector basis for the convex polyhedral cone of all stationary reaction rates. A major emphasis is given to the constraints that the rate constants must obey and how to express these in terms of the convex parameters and stationary inverse concentrations. We evaluate the corresponding Jacobians in terms of the constrained convex parameters and the inverse stationary concentrations and carry out stability analyses for the steady-state racemic configurations. A geometric visualization of SMSB is proposed, based on the structures of the convex cones, the angles between currents, and the cone's subspaces that result from enforcing the pertinent thermodynamic and chiral constraints.

Necessary conditions for the emergence of homochirality via autocatalytic self-replication.

We analyze a recent proposal for spontaneous mirror symmetry breaking based on the coupling of first-order enantioselective autocatalysis and direct production of the enantiomers that invokes a critical role for intrinsic reaction noise. For isolated systems, the racemic state is the unique stable outcome for both stochastic and deterministic dynamics when the system is in compliance with the constraints dictated by the thermodynamics of chemical reaction processes. In open systems, the racemic outcome also results for both stochastic and deterministic dynamics when driving the autocatalysis unidirectionally by external reagents. Nonracemic states can result in the latter only if the reverse reactions are strictly zero: these are kinetically controlled outcomes for small populations and volumes, and can be simulated by stochastic dynamics. However, the stability of the thermodynamic limit proves that the racemic outcome is the unique stable state for strictly irreversible externally driven autocatalysis. These findings contradict the suggestion that the inhibition requirement of the Frank autocatalytic model for the emergence of homochirality may be relaxed in a noise-induced mechanism.

Competitive exclusion principle in ecology and absolute asymmetric synthesis in chemistry.

The key concepts underlying the Frank model (1953) for spontaneous asymmetric synthesis in chemistry are traced back to the pioneering works of Volterra (1926) and Lotka (1932) on biological species competition. The Lotka-Volterra (L-V) two-species exclusive competition model reduces to the Frank model for the special case of distinguishable but degenerate species (i.e., the enantiomers). The important ecological principle of competitive exclusion, originally derived from the L-V two-competitors model, is a consequence of sufficiently antagonistic interactions between the species competing for limited common resources, or mutual inhibition, as the term is known in the chemical literature on absolute asymmetric synthesis. The L-V and Frank models are described by the same general differential equations, nevertheless a crucial thermodynamic distinction between these models is necessary to correlate ecological selection and chemical selectivity arising from 1) the absence of reversibility in biological transformations, in marked contrast to chemical reactions, and 2) the constraints in chemical scenarios on the reaction rate constants required to fulfill the principle of micro-reversibility.

Absolute asymmetric synthesis in enantioselective autocatalytic reaction networks: theoretical games, speculations on chemical evolution and perhaps a synthetic option.

The Soai reaction and the Viedma deracemization of racemic conglomerate crystal mixtures are experimental pieces of evidence of the ability of enantioselective autocatalytic coupled networks to yield absolute asymmetric synthesis. Thermodynamically open systems or systems with non-uniform energy distributions may lead to chiral final states and, in systems able to come into thermodynamic equilibrium with their surroundings, to kinetically controlled absolute asymmetric synthesis. The understanding of network parameters and of the thermodynamic scenarios that may lead to spontaneous mirror symmetry breaking (SMSB) could assist in the development of new methods for asymmetric synthesis and enantioselective polymerizations (e.g., replicators), and to frame reasonable speculations on the origin of biological homochirality.

Physical Chemistry Models for Chemical Research in the XXth and XXIst Centuries.

Thermodynamic hypotheses and models are the touchstone for chemical results, but the actual models based on time-invariance, which have performed efficiently in the development of chemistry, are nowadays invalid for the interpretation of the behavior of complex systems exhibiting nonlinear kinetics and with matter and energy exchange flows with the surroundings. Such fields of research will necessarily foment and drive the use of thermodynamic models based on the description of irreversibility at the macroscopic level, instead of the current models which are strongly anchored in microreversibility.

Stochastic mirror symmetry breaking: theoretical models and simulation of experiments.

This chapter provides a review of recently elaborated mathematical models for explaining the salient features of two experimental studies selected for their relevance to the problem of stochastic mirror symmetry breaking and amplification. The first experiment modeled treats the phenomena of mirror symmetry breaking via the autocatalytic crystallization of the glycine and α-amino acid system at the air-water interface. The second experiment deals with the lattice-controlled generation of homochiral oligopeptides, which we model based on a kinetic scheme for copolymerization in a closed reaction system. Since the fundamental paradigm of mutual inhibition lies at the core of both these models, we review how the final asymptotic states in the Frank model depend crucially on whether the system is open or closed, and emphasize the importance of temporary chiral excursions, which can and do arise in more complex reaction schemes during their approach to chemical equilibrium in closed systems.

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.