Recycling Frank: Spontaneous emergence of homochirality in noncatalytic systems

Chiral symmetry breaking and information accumulation in pre-biological protocell evolution

We study a linear evolutionary model based on the two-dimensional distribution of protocells by total enantiomeric excess and the amount of stored information, which they can pass from generation to generation, and without any mutual inhibition. We show that the evolution of such systems occurs in four distinct stages. The first stage is an exponential growth of the concentration of protocells near the point [Formula: see text] and it should take negligible time on a geological scale. The second stage is a diffusion-like process in both dimensions. This process can also be accompanied by a drift in the direction of increased information passed from generation to generation, provided that the appropriate linear coefficient in the information storage subspace is large enough. The third stage is a rapid symmetry breaking and formation of the species near [Formula: see text] value of enantiomeric excess (assuming a small positive global enantiomeric asymmetry factor). The fourth stage is a relaxation toward a global stationary point, which is a narrow peak located near [Formula: see text] value of enantiomeric excess and some optimal value of the amount of stored information.

Viedma deracemization mechanisms in self-assembly processes

Simulations on an ODE-based model shows that there are many common points between Viedma deracemization and chiral self-assemblies of achiral building blocks towards chiral nanoparticles. Both systems occur in a closed system with energy exchange but no matter exchange with the surroundings and show parallel reversible growth mechanisms which coexist with an irreversible cluster breaking (grinding). The various mechanisms of growth give rise to the formation of polymerization/depolymerization cycles while the consecutive transformation of achiral monomer into chiral cluster results into an indirect enantioselective autocatalysis. Deracemization occurs by the destabilization of the racemic non-equilibrium stationary state likely because of the excess of entropy production generated by the coupling of the reversible cluster growth mechanisms with grinding. Results show that the SMSB bias from the racemic composition occurs already at the oligomeric level of polymerization. Our model goes beyond the scope of the effect of grinding by the stirring of solutions which is thoroughly reported in supramolecular chirality. For instance, some unique characteristics, as those of a SMSB in closed systems, the simultaneous presence of different coupled reversible growth mechanisms, the activation by a depolymerization agent and the reincorporation of oligomers to the polymer growth reactions, could be adapted to replicator selectivity and to the emergence of biological homochirality scenarios.

Step-by-Step Towards Biological Homochirality - from Prebiotic Randomness To Perfect Asymmetry

The history of life's formation and the origin of its stereochemistry are nearly as multifaceted as the life itself. In this review, we focus on analyzing the step-by-step path leading to what we can define as "life" in parallel to what we know about the emergence of enantiomeric imbalance and subsequent transition to full homochirality. We start at the level of assembly of the building blocks of life from inorganic molecules and build up to the polymerization and formation of nucleic acids and peptides. We report and analyze different theories at various stages of this development and try to elucidate the most plausible theory.

Differences in enantiomeric diffusion can lead to selective chiral amplification

A fundamental question associated with chirality is how mixtures containing equal amounts of interconverting enantiomers can spontaneously convert to systems enriched in only one of them. Enantiomers typically have similar chemical properties, but can exhibit distinct reactivity under specific conditions, and these differences can be used to bias the system's composition in favor of one enantiomer. Transport properties are also expected to differ for enantiomers in chiral solvents, but the role of such differences in chiral symmetry breaking has not been clarified yet. In this work, we develop a theoretical framework to show that asymmetry in diffusion properties can trigger a spontaneous and selective symmetry breaking in mixtures of enantiomers. We derive a generic evolution equation for the enantiomeric excess in a chiral solvent. This equation shows that the relative stability of homochiral domains is dictated by the difference of diffusion coefficients of the two enantiomers. Consequently, deracemization toward a specific enantiomeric excess can be achieved when this difference is large enough. These results hold significant implications for our understanding of chiral symmetry breaking.

Linear stability analysis of chemical mechanism, Listanalchem: A tool for the search of spontaneous mirror symmetry breaking

Homochirality, the phenomenon by which one of two virtually identical (non-superimposable mirror images) compounds is favored over the other in the chemistry of life, has been regarded as a requisite for the emergence of all living things on earth. Spontaneous mirror symmetry breaking has been proposed to produce the imbalance. Under this framework, Frank presented, in his foundational article "On spontaneous asymmetric synthesis", a simple chemical reaction network that displays spontaneous symmetry breaking for a specific set of reaction rates. Research has since focused on finding more complex and plausible models, each one with its advantages and disadvantages. Nevertheless, finding reaction rate values that make a model exhibit spontaneous symmetry breaking is a complex task, even for specially crafted models. LInear STability ANALysis of CHEmical Mechanism, Listanalchem, is a method and software for the search for appropriate reaction rates. It includes four different algorithms inspired by the analysis of Frank's network. Two classical algorithms are also included in Listanalchem: the Trace-Determinant plane and the Stoichiometric Network Analysis by Bruce Clarke. Listanalchem reads a chemical reaction network from plain text and runs one or more of the available algorithms according to the user selection. Listanalchem is tested and verified by studying classical, modified, and recent models proposed to explain the origin of biological homochirality.•Listanalchem allows a fast and reliable search for instability behavior in chemical mechanisms that pretend to explain spontaneous mirror symmetry breaking.•Listanalchem contains several model examples, including the most cited in the related literature.•Listanalchem is a tool that tests models that pretend to explain the origin of biological homochirality, helps find errors, and aids in designing new models.

Mathematical Models of Chiral Symmetry-breaking – A Review of General Theories, and Adiabatic Approximations of the APED System

We review the literature surrounding chiral symmetry-breaking in chemical systems, with a focus on understanding the mathematical models underlying these chemical processes. We comment in particular on the toy model of Sandars, Viedma’s crystal grinding systems and the APED model. We include a few new results based on asymptotic analysis of the APED system.

Evolutionary Approach to Biological Homochirality

We study a very simple linear evolutionary model based on distribution of protocells by total enantiomeric excess and without any mutual inhibition and show that such model can produce two species with values of total enantiomeric excess in each of the species approaching $$\pm 1$$ ± 1 when there is a global $$L\leftrightarrow D$$ L ↔ D symmetry. We then consider a scenario when there is a small external global asymmetry factor, like weak interaction, and show that only one of the species remains in such a case, and that is the one, which is more efficient in replication. We perform an estimate of the time necessary to reach homochirality in such a model and show that reasonable assumptions lead to an estimate of around 300 thousand years plus or minus a couple of orders of magnitude. Despite this seemingly large time to reach homochirality, the model is immune to racemization because amino acids in the model follow the lifespan of the protocells rather than the time needed to reach homochirality. We show that not needing mutual inhibition in such evolutionary model is due to the difference in the topology of the spaces in which considered model and many known models of biological homochirality operate. Bifurcation-based models operate in disconnected zero-dimensional space (the space is just two points with enantiomeric excess equal $$-1$$ - 1 and $$1$$ 1 ), whereas considered evolutionary model (in its continuous representation) operates in one-dimensional connected space, that is the whole interval between $$-1$$ - 1 and $$1$$ 1 of total enantiomeric excess. We then proceed with the analysis of the replication process in non-homochiral environment and show that replication errors (the probability to attach an amino acid of wrong chirality) result in a smooth decrease of replication time when total enantiomeric excess of the replicated structure moves away from zero. We show that this decrease in replication time is sufficient for considered model to work.

Biological homochirality and stoichiometric network analysis: Variations on Frank’s model

Biological homochirality is modelled using chemical reaction mechanisms that include autocatalytic and inhibition reactions as well as input and output flows. From the mathematical point of view, the differential equations associated with those mechanisms have to exhibit bistability.  The search for those bifurcations can be carried out using stoichiometric network analysis. This algorithm simplifies the mathematical analysis and can be implemented in a computer programme, which can help us to analyse chemical networks. However, regardless of the reduction to linear polynomials, which is made possible by this algorithm, in some cases, the complexity and length of the polynomials involved make the analysis unfeasible. This problem has been partially solved by extending the stoichiometric matrix with rows that code the duality relations between the different reactions occurring in the network given as input. All these facts allow us to analyse 28 different network models, highlighting the basic requirements needed by a chemical mechanism to have spontaneous mirror symmetry breaking.

Spontaneous chiral symmetry breaking in a random driven chemical system

Living systems have evolved to efficiently consume available energy sources using an elaborate circuitry of chemical reactions which, puzzlingly, bear a strict restriction to asymmetric chiral configurations. While autocatalysis is known to promote such chiral symmetry breaking, whether a similar phenomenon may also be induced in a more general class of configurable chemical systems—via energy exploitation—is a sensible yet underappreciated possibility. This work examines this question within a model of randomly generated complex chemical networks. We show that chiral symmetry breaking may occur spontaneously and generically by harnessing energy sources from external environmental drives. Key to this transition are intrinsic fluctuations of achiral-to-chiral reactions and tight matching of system configurations to the environmental drives, which together amplify and sustain diverged enantiomer distributions. These asymmetric states emerge through steep energetic transitions from the corresponding symmetric states and sharply cluster as highly-dissipating states. The results thus demonstrate a generic mechanism in which energetic drives may give rise to homochirality in an otherwise totally symmetrical environment, and from an early-life perspective, might emerge as a competitive, energy-harvesting advantage.

“A hallmark of living systems is their homochirality, the selection of specific mirror symmetry in their molecules. Here, the authors show that chiral symmetry can be spontaneously broken in complex, random chemical systems via exploitation of environmental energy sources – a possible mechanism for the emergence of homochirality in life.”

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 have 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 the 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 fundamental interactions, 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 the 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: extra-terrestrial 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?). Intense and ongoing theories regarding the emergence of optically pure molecules at different moments of the evolution process towards life, i.e. at the levels of building blocks of Life, of the instructed or functional polymers, or even later at the stage of more elaborated chemical systems, will be critically discussed. The underlying principles and the experimental evidence will be commented for each scenario with particular attention on those leading to the induction and enhancement of enantiomeric excesses in proteinogenic amino acids, natural sugars, and 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.

Effect of configuration-dependent multi-body forces on interconversion kinetics of a chiral tetramer model

We describe a reformulation of the four-site molecular model for chiral phenomena introduced by Latinwo et al. ["Molecular model for chirality phenomena," J. Chem. Phys. 145, 154503 (2016)]. The reformulation includes an additional eight-body force that arises from an explicit configuration-dependent term in the potential energy function, resulting in a coarse-grained energy-conserving force field for molecular dynamics simulations of chirality phenomena. In this model, the coarse-grained interaction energy between two tetramers depends on their respective chiralities and is controlled by a parameter λ, where λ < 0 favors local configurations involving tetramers of opposite chirality and λ > 0 gives energetic preference to configurations involving tetramers of the same chirality. We compute the autocorrelation function for a quantitative chirality metric and demonstrate that the multi-body force modifies the interconversion kinetics such that λ ≠ 0 increases the effective barrier for enantiomer inversion. Our simulations reveal that for λ > 0 and temperatures below a sharply defined threshold value, this effect is dramatic, giving rise to spontaneous chiral symmetry breaking and locking molecules into their chiral identity.

Emergence of homochirality in large molecular systems

The selection of a single molecular handedness, or homochirality across all living matter, is a mystery in the origin of life. Frank's seminal model showed in the '50s how chiral symmetry breaking can occur in nonequilibrium chemical networks. However, an important shortcoming in this classic model is that it considers a small number of species, while there is no reason for the prebiotic system, in which homochirality first appeared, to have had such a simple composition. Furthermore, this model does not provide information on what could have been the size of the molecules involved in this homochiral prebiotic system. Here, we show that large molecular systems are likely to undergo a phase transition toward a homochiral state, as a consequence of the fact that they contain a large number of chiral species. Using chemoinformatics tools, we quantify how abundant chiral species are in the chemical universe of all possible molecules of a given length. Then, we propose that Frank's model should be extended to include a large number of species, in order to possess the transition toward homochirality, as confirmed by numerical simulations. Finally, using random matrix theory, we prove that large nonequilibrium reaction networks possess a generic and robust phase transition toward a homochiral state.

Chiral Symmetry Breaking in Large Peptide Systems

Chiral symmetry breaking in far from equilibrium systems with large number of amino acids and peptides, like a prebiotic Earth, was considered. It was shown that if organic catalysts were abundant, then effective averaging of enantioselectivity would prohibit any symmetry breaking in such systems. It was further argued that non-linear (catalytic) reactions must be very scarce (called the abundance parameter) and catalysts should work on small groups of similar reactions (called the similarity parameter) in order to chiral symmetry breaking have a chance to occur. Models with 20 amino acids and peptide lengths up to three were considered. It was shown that there are preferred ranges of abundance and similarity parameters where the symmetry breaking can occur in the models with catalytic synthesis / catalytic destruction / both catalytic synthesis and catalytic destruction. It was further shown that models with catalytic synthesis and catalytic destruction statistically result in a substantially higher percentage of the models where the symmetry breaking can occur in comparison to the models with just catalytic synthesis or catalytic destruction. It was also shown that when chiral symmetry breaking occurs, then concentrations of some amino acids, which collectively have some mutually beneficial properties, go up, whereas the concentrations of the ones, which don't have such properties, go down. An open source code of the whole system was provided to ensure that the results can be checked, repeated, and extended further if needed.

Chiral Oscillations and Spontaneous Mirror Symmetry Breaking in a Simple Polymerization Model

The origin of biological homochirality—defined as the preference of biological systems for only one enantiomer—has widespread implications in the study of chemical evolution and the origin of life. The activation—polymerization—epimerization—depolymerization (APED) model is a theoretical model originally proposed to describe chiral symmetry breaking in a simple dimerization system. It is known that the model produces chiral and chemical oscillations for certain system parameters, in particular, the preferential formation of heterochiral polymers. In order to investigate the effect of higher oligomers, our model adds trimers, tetramers, and pentamers. We report sustained oscillations of all chemical species and the enantiomeric excess for a wide range of parameter sets as well as the periodic chiral amplification of a small initial enantiomeric excess to a nearly homochiral state.

Computing the Parameter Values for the Emergence of Homochirality in Complex Networks

The goal of our research is the development of algorithmic tools for the analysis of chemical reaction networks proposed as models of biological homochirality. We focus on two algorithmic problems: detecting whether or not a chemical mechanism admits mirror symmetry-breaking; and, given one of those networks as input, sampling the set of racemic steady states that can produce mirror symmetry-breaking. Algorithmic solutions to those two problems will allow us to compute the parameter values for the emergence of homochirality. We found a mathematical criterion for the occurrence of mirror symmetry-breaking. This criterion allows us to compute semialgebraic definitions of the sets of racemic steady states that produce homochirality. Although those semialgebraic definitions can be processed algorithmically, the algorithmic analysis of them becomes unfeasible in most cases, given the nonlinear character of those definitions. We use Clarke’s system of convex coordinates to linearize, as much as possible, those semialgebraic definitions. As a result of this work, we get an efficient algorithm that solves both algorithmic problems for networks containing only one enantiomeric pair and a heuristic algorithm that can be used in the general case, with two or more enantiomeric pairs.

Interactions of Amino Acids and Aminoxazole Derivatives: Cocrystal Formation and Prebiotic Implications Enabled by Computational Analysis

In line with the postulated intermediacy of aminoxazoles derived from small sugars toward the direct assembly of nucleoside precursors, we show here a potential prebiotic scenario where aminoxazolines might have also played further roles as complexing and/or sequestering agents of other primeval blocks, namely amino acids. To this end, a bis-aminoxazoline derivative, generated from dihydroxyacetone and cyanamide, gives rise to stable co-crystal forms with dicarboxylic amino acids (Asp and Glu), while ionic interactions owing to proton transfer are inferred from spectroscopic data in aqueous solution. The structure of a 1:2 aminoxazoline: aspartic acid complex, discussed in detail, was elucidated by X-ray diffractometry. Optimized geometries of such ionic structures with bulk aqueous solvation were assessed by DFT calculations, which disclose preferential arrangements that validate the experimental data. Peripherally, we were able to detect in a few cases amino acid dimerization (i.e. dipeptide formation) after prolonged incubation with the bis-aminoxazole derivative. A mechanistic simulation aided by computation provides some predictive conclusions for future explorations and catalytic design.

Chemical Basis of Biological Homochirality during the Abiotic Evolution Stages on Earth

Spontaneous mirror symmetry breaking (SMSB), a phenomenon leading to non-equilibrium stationary states (NESS) that exhibits biases away from the racemic composition is discussed here in the framework of dissipative reaction networks. Such networks may lead to a metastable racemic non-equilibrium stationary state that transforms into one of two degenerate but stable enantiomeric NESSs. In such a bifurcation scenario, the type of the reaction network, as well the boundary conditions, are similar to those characterizing the currently accepted stages of emergence of replicators and autocatalytic systems. Simple asymmetric inductions by physical chiral forces during previous stages of chemical evolution, for example in astrophysical scenarios, must involve unavoidable racemization processes during the time scales associated with the different stages of chemical evolution. However, residual enantiomeric excesses of such asymmetric inductions suffice to drive the SMSB stochastic distribution of chiral signs into a deterministic distribution. According to these features, we propose that a basic model of the chiral machinery of proto-life would emerge during the formation of proto-cell systems by the convergence of the former enantioselective scenarios.

Insights into Abiotically-Generated Amino Acid Enantiomeric Excesses Found in Meteorites

Biology exhibits homochirality, in that only one of two possible molecular configurations (called enantiomers) is used in both proteins and nucleic acids. The origin of this phenomenon is currently unknown, as nearly all known abiotic mechanisms for generating these compounds result in equal (racemic) mixtures of both enantiomers. However, analyses of primitive meteorites have revealed that a number of amino acids of extraterrestrial origin are present in enantiomeric excess, suggesting that there was an abiotic route to synthesize amino acids in a non-racemic manner. Here we review the amino acid contents of a range of meteorites, describe mechanisms for amino acid formation and their potential to produce amino acid enantiomeric excesses, and identify processes that could have amplified enantiomeric excesses.

Exploring the emergence of complexity using synthetic replicators

A significant number of synthetic systems capable of replicating themselves or entities that are complementary to themselves have appeared in the last 30 years. Building on an understanding of the operation of synthetic replicators in isolation, this field has progressed to examples where catalytic relationships between replicators within the same network and the extant reaction conditions play a role in driving phenomena at the level of the whole system. Systems chemistry has played a pivotal role in the attempts to understand the origin of biological complexity by exploiting the power of synthetic chemistry, in conjunction with the molecular recognition toolkit pioneered by the field of supramolecular chemistry, thereby permitting the bottom-up engineering of increasingly complex reaction networks from simple building blocks. This review describes the advances facilitated by the systems chemistry approach in relating the expression of complex and emergent behaviour in networks of replicators with the connectivity and catalytic relationships inherent within them. These systems, examined within well-stirred batch reactors, represent conceptual and practical frameworks that can then be translated to conditions that permit replicating systems to overcome the fundamental limits imposed on selection processes in networks operating under closed conditions. This shift away from traditional spatially homogeneous reactors towards dynamic and non-equilibrium conditions, such as those provided by reaction-diffusion reaction formats, constitutes a key change that mimics environments within cellular systems, which possess obvious compartmentalisation and inhomogeneity.

Chiral Symmetry Breaking in Peptide Systems During Formation of Life on Earth

Chiral symmetry breaking in complex chemical systems with a large number of amino acids and a large number of similar reactions was considered. It was shown that effective averaging over similar reaction channels may result in very weak effective enantioselectivity of forward reactions, which does not allow most of the known models to result in chiral symmetry breaking during formation of life on Earth. Models with simple and catalytic synthesis of a single amino acid, formation of peptides up to length five, and sedimentation of insoluble pair of substances were considered. It was shown that depending on the model and the values of the parameters, chiral symmetry breaking may occur in up to about 10% out of all possible unique insoluble pair combinations even in the absence of any catalytic synthesis and that minimum total number of amino acids in the pair is 5. If weak enantioselective forward catalytic synthesis of amino acids is present, then the number of possible variants, in which chiral symmetry breaking may occur, increases substantially. It was shown that that the most interesting catalysts have zero or one amino acid of "incorrect" chirality. If the parameters of the model are adjusted in such a way to result in an increase of concentration of longer peptides, then catalysts with two amino acids of incorrect chirality start to appear at peptides of length five. Models of chiral symmetry breaking in the presence of epimerization were considered for peptides up to length three. It was shown that the range of parameters in which chiral symmetry breaking could occur significantly shrinks in comparison to previously considered models with peptides up to length two. An experiment of chiral symmetry breaking was proposed. The experiment consists of a three-step cycle: reversible catalytic synthesis of amino acids, reversible synthesis of peptides, and irreversible sedimentation of insoluble substances.

Stochastic chiral symmetry breaking process besides the deterministic one

In chiral symmetry breaking, populations with initial enantiomeric excess (EE) are probabilistically favored if statistical fluctuation is present, as in nature. Stochastic methods correctly describe chiral symmetry breaking by taking into account the quantitative enantiomeric difference (excess or deficiency) and the statistical fluctuation amplitude, which is inversely proportional to the absolute size of the populations involved. From this, we obtain a law, which indicates that such a favoring probability decreases exponentially [P(EE) = 1/(e^αEE + 1)] with an initial enantiomeric deficiency mediated by statistical fluctuation. Obviously, chiral symmetry breaking equally favors populations without enantiomeric excess [P(0) = 1/2]. However, if deterministic methods are considered, chiral symmetry breaking will strictly favor the population with an initial enantiomeric excess (EE). To study these stochastic chiral symmetry breaking processes the autocatalytic Frank model was considered. Summarizing, our results show that the initial enantiomeric excesses are not entirely responsible for the final state configuration of autocatalytic finite systems.

Emergence of native peptide sequences in prebiotic replication networks

Biopolymer syntheses in living cells are perfected by an elaborate error correction machinery, which was not applicable during polymerization on early Earth. Scientists are consequently striving to identify mechanisms by which functional polymers were selected and further amplified from complex prebiotic mixtures. Here we show the instrumental role of non-enzymatic replication in the enrichment of certain product(s). To this end, we analyzed a complex web of reactions in β-sheet peptide networks, focusing on the formation of specific intermediate compounds and template-assisted replication. Remarkably, we find that the formation of several products in a mixture is not critically harmful, since efficient and selective template-assisted reactions serve as a backbone correction mechanism, namely, for keeping the concentration of the peptide containing the native backbone equal to, or even higher than, the concentrations of the other products. We suggest that these findings may shed light on molecular evolution processes that led to current biology.The synthesis of biopolymers in living cells is perfected by complex machinery, however this was not the case on early Earth. Here the authors show the role of non-enzymatic replication in the enrichment of certain products within prebiotically relevant mixtures.

Origins of life: a problem for physics, a key issues review

The origins of life stands among the great open scientific questions of our time. While a number of proposals exist for possible starting points in the pathway from non-living to living matter, these have so far not achieved states of complexity that are anywhere near that of even the simplest living systems. A key challenge is identifying the properties of living matter that might distinguish living and non-living physical systems such that we might build new life in the lab. This review is geared towards covering major viewpoints on the origin of life for those new to the origin of life field, with a forward look towards considering what it might take for a physical theory that universally explains the phenomenon of life to arise from the seemingly disconnected array of ideas proposed thus far. The hope is that a theory akin to our other theories in fundamental physics might one day emerge to explain the phenomenon of life, and in turn finally permit solving its origins.

Noise-induced symmetry breaking far from equilibrium and the emergence of biological homochirality

The origin of homochirality, the observed single-handedness of biological amino acids and sugars, has long been attributed to autocatalysis, a frequently assumed precursor for early life self-replication. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross-inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here we present a theory for a stochastic individual-level model of autocatalytic prebiotic self-replicators that are maintained out of thermal equilibrium. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states. Moreover, we show that this noise-induced bistability is robust with respect to diffusion of molecules of opposite chirality, and systems of diffusively coupled autocatalytic chemical reactions synchronize their final homochiral states when the self-replication is the dominant production mechanism for the chiral molecules. We conclude that nonequilibrium autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.

Recycling in Asymmetric Catalysis

Cyclic reaction networks consisting of an enantioselective product-forming step and a reverse reaction of the undesired enantiomer back to starting reactant are important for the generation of compounds with high enantiomeric purity. In order to avoid an equilibrium racemic state, a unidirectional cyclic process where product formation and regeneration of starting reactant proceed through different mechanistic pathways is required. Such processes must necessarily include a thermodynamically unfavorable step, since the product of the forward reaction is the reactant of the reverse reaction and vice versa. Thermodynamically uphill processes are ubiquitous to the function of living systems. Such systems gain the required energy by coupling to thermodynamically downhill reactions. In the same way, artificial cyclic reaction networks can be realized in systems open to mass or energy flow, and an out-of equilibrium nonracemic steady state can be maintained as long as the system is supplied with energy. In contrast to a kinetic resolution, a recycling process where the minor enantiomer is converted to starting reactant can result in a quantitative yield, but the enantiomeric purity of the product is limited by the selectivity of the catalysts used for the reactions. On the other hand, in a kinetic resolution, the slowly reacting enantiomer can always be obtained in an enantiomerically pure state, although the yield will suffer. In cyclic reaction systems which use chiral catalysts for both the forward and the reverse processes, a reinforcing effect results, and selectivities higher than those achieved by a single chiral catalyst are observed. A dynamic kinetic resolution can in principle also lead to a quantitative yield, but lacks the reinforcing effect of two chiral catalysts. Most examples of cyclic reaction networks reported in the literature are deracemizations of racemic mixtures, which proceed via oxidation of one enantiomer followed by reduction to the opposite enantiomer. We have developed cyclic reaction networks comprising a carbon-carbon bond formation. In these processes, the product is generated by the addition of a cyanide reagent to a prochiral aldehyde. This is followed by hydrolysis of the minor enantiomer of the product to generate the starting aldehyde. A unidirectional cycle is maintained by coupling to the exergonic transformation of the high potential cyanide reagent to a low potential compound, either a carboxylate or carbon dioxide. The products, which are obtained with high enantiomeric purity, serve as valuable starting materials for a variety of biologically and pharmaceutically active compounds.

Spontaneous Chiral Symmetry Breaking for Finite Systems

Theoretical clues are desirable to help uncover the origin of bio-homochirality in life, as well as the mechanisms for the asymmetric production of functional chiral substances. Here, an open-to-matter reaction network based on a model proposed by Plasson et al. is studied. In the extended model, the statistical fluctuations lead the system to break chiral symmetry autonomously, that is, without any initial enantiomeric excess or external influence. In the stability diagrams, we observe regions of parameter space that correspond to racemic, homochiral, chiral oscillatory, and, to our knowledge, for the first time in a chiral model, chaotic regimes. The dependencies of the final concentrations of chiral substances on the parameters are determined analytically and discussed for both the racemic and homochiral regimes.

Noise-Induced Mechanism for Biological Homochirality of Early Life Self-Replicators

The observed single-handedness of biological amino acids and sugars has long been attributed to autocatalysis. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here, we present a theory for a stochastic individual-level model of autocatalysis due to early life self-replicators. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states, in both well-mixed and spatially extended systems. We conclude that autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.

Diastereoselectivity in prebiotically relevant 5(4H)-oxazolone-mediated peptide couplings

A stereochemical study of a potentially prebiotic peptide-forming reaction was carried out as the first part of a systems chemistry investigation of potential paths for symmetry breaking. Substantial diastereomeric excesses result from a fast epimerization of the 5(4H)-oxazolone intermediate in aqueous solution.

Condensation dynamics of the L-Pro-L-Phe and L-Hyp-L-Phe binary mixtures in solution

We employ the achiral liquid chromatography with diode array, evaporative light scattering and mass spectrometric detection (HPLC-DAD, HPLC-ELSD and LC-MS) to assess structural instability (understood as spontaneous oscillatory chiral conversion and spontaneous oscillatory condensation) of the two pairs of amino acids, L-proline-L-phenylalanine (L-Pro-L-Phe) and L-hydroxyproline-L-phenylalanine (L-Hyp-L-Phe), in aqueous acetonitrile. In our earlier studies, we managed to demonstrate that single amino acids in aqueous and non-aqueous solutions undergo spontaneous oscillatory chiral conversion and oscillatory condensation. We also investigated condensation in the binary L-Pro-L-Hyp mixture in aqueous solution, and proposed a theoretical model to explain the specific dynamics of this process, which involves mutual catalytic effects of the two amino acids. In this study, we demonstrate oscillatory instability with the other two amino acid pairs in the organic-aqueous solution and reflect on the dynamics of condensation in the investigated cases. The choice of L-Pro and L-Hyp is due to their important role as building blocks of collagen, which is omnipresent in the connective tissues of mammals, and largely responsible for tissue architecture and strength. L-Phe is one of the 20 exogenous amino acids and is a building block of the majority of naturally occurring proteins.

Recycling of informational units leads to selection of replicators in a prebiotic soup

Prebiotic chemical reactions would have been greatly aided by a process whereby living materials could have been recycled under conditions of limiting resources. Recombination of RNA fragments is a viable means of recycling but has not been demonstrated. Using systems based on the Azoarcus group I intron ribozyme, computational Monte Carlo studies indicate that a moderate level of recycling activity, spontaneous or catalyzed, leads to the most robust selection scenarios. It is interesting that recycling leads to a threshold effect where a dominant species suddenly jumps to fixation. In conjunction, laboratory studies with the Azoarcus ribozyme corroborate these results, showing that mixtures of scrambled and/or deleteriously mutated molecules can recycle their component fragments to generate fully functional recombinase ribozymes. These studies highlight the importance of recombination and recycling jointly in the advent of living systems.

Amplification of enantiomeric excess, mirror-image symmetry breaking and kinetic proofreading in Soai reaction models with different oligomeric orders

A comprehensive kinetic analysis of three prototypical autocatalytic cycle models based on the absolute asymmetric Soai reaction is presented. The three models, which can give rise to amplification of enantiomeric excess and mirror-image symmetry breaking, vary by their monomeric, dimeric or trimeric order of the assumed catalytic species. Our numerical approach considered the entire chiral combinatorics of the diastereomeric interactions in the models as well as the multiplicity of coupled reversible reactions without applying fast equilibration or quasi-steady state approximations. For the simplest monomeric model, an extensive range of parameters was explored employing a random grid parameter scanning method that revealed the influence of the parameter values on the product distribution, the reaction-time, the attenuation or amplification of enantiomeric excess as well as on the presence or absence of mirror-image symmetry breaking. A symmetry breaking test was imposed on the three models showing that an increase in the catalytic oligomer size from one to three leads to a higher tolerance to poorer chiral recognition between the diastereoisomers and identifies the greater impact of the diastereoisomeric energy difference over an imperfect stereoselectivity in the catalytic step. This robustness is understood as a particular case of so-called kinetic proofreading in asymmetric autocatalysis.

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.

5(4H)-oxazolones as intermediates in the carbodiimide- and cyanamide-promoted peptide activations in aqueous solution

The early days: although considered a species to be avoided in peptide chemistry, the intermediacy of 5(4H)-oxazolones is demonstrated to be essential for the formation of peptides through cyanamide and carbodiimide activation in aqueous solution.

Stochastic mapping of first order reaction networks: a systematic comparison of the stochastic and deterministic kinetic approaches

Stochastic maps are developed and used for first order reaction networks to decide whether the deterministic kinetic approach is appropriate for a certain evaluation problem or the use of the computationally more demanding stochastic approach is inevitable. On these maps, the decision between the two approaches is based on the standard deviation of the expectation of detected variables: when the relative standard deviation is larger than 1%, the use of the stochastic method is necessary. Four different systems are considered as examples: the irreversible first order reaction, the reversible first order reaction, two consecutive irreversible first order reactions, and the unidirectional triangle reaction. Experimental examples are used to illustrate the practical use of the theoretical results. It is shown that the maps do not only depend on particle numbers, but the influence of parameters such as time, rate constants, and the identity of the detected target variable is also an important factor.

Autocatalytic replication and homochirality in biopolymers: is homochirality a requirement of life or a result of it?

A key step in the origin of life is the establishment of autocatalytic cycles controlled by biopolymer catalysts. These catalysts (either ribozymes or proteins) are composed of homochiral monomers. Homochirality in living systems is maintained because biopolymers are asymmetric in their catalysis and synthesize molecules of their own handedness. Asymmetric autocatalysis is also possible with small molecules, as demonstrated by the Soai reaction, but it is rare. As far as we know, single nucleotides and amino acids are not autocatalytic. The observation that organic molecules in meteorites can have an enantiomeric excess of a few percent suggests that the prebiotic mixture may have had a partial chiral bias that was caused by external physical influences. Here, we consider the way that such a partial prebiotic bias would influence the origin of ribozymes in an RNA world scenario. We have previously shown how a transition to a living state can occur in a model for RNA polymerization. Here, we add chirality to the problem by considering simultaneous synthesis and polymerization of left- and right-handed monomers. The two chemical synthesis rates may be equal or unequal, due to physical or chemical effects prior to the origin of life. We determine the stationary states of this reaction system. The nonliving state is racemic, or slightly biased. There are two living states that are almost completely homochiral, whether or not the nonliving state is biased. It is a feature of our model that, for some regions of parameter space, living and nonliving states are both found to be stable under the same conditions. The origin of life therefore involves a stochastic transition between the nonliving and living states. Our model extends previous theories by treating the origin of life and the origin of chirality as aspects of the same model.

Chiral polymerization in open systems from chiral-selective reaction rates

We investigate the possibility that prebiotic homochirality can be achieved exclusively through chiral-selective reaction rate parameters without any other explicit mechanism for chiral bias. Specifically, we examine an open network of polymerization reactions, where the reaction rates can have chiral-selective values. The reactions are neither autocatalytic nor do they contain explicit enantiomeric cross-inhibition terms. We are thus investigating how rare a set of chiral-selective reaction rates needs to be in order to generate a reasonable amount of chiral bias. We quantify our results adopting a statistical approach: varying both the mean value and the rms dispersion of the relevant reaction rates, we show that moderate to high levels of chiral excess can be achieved with fairly small chiral bias, below 10%. Considering the various unknowns related to prebiotic chemical networks in early Earth and the dependence of reaction rates to environmental properties such as temperature and pressure variations, we argue that homochirality could have been achieved from moderate amounts of chiral selectivity in the reaction rates.

Pathways for the formation and evolution of peptides in prebiotic environments

α-Amino acids are easily accessible through abiotic processes and were likely present before the emergence of life. However, the role they could have played in the process remains uncertain. Chemical pathways that could have brought about features of self-organization in a peptide world are considered in this review and discussed in relation with their possible contribution to the origin of life. An overall scheme is proposed with an emphasis on possibilities that may have led to dynamically stable far from equilibrium states. This analysis defines new lines of investigation towards a better understanding of the contribution of the systems chemistry of amino acids and peptides to the emergence of life.