Spontaneous mirror symmetry breaking and origin of biological homochirality

Circularly Polarized Luminescence From Spontaneous Symmetry Breaking in a Bimetallic Eu-Al Complex

The emergence of optically active functional compounds through spontaneous chiral symmetry breaking is a rare but intriguing phenomenon with relevance of both practical and fundamental interest. Here we show that a racemic Eu-Al compound, bearing only non-chiral ligands, forms a conglomerate upon crystallization. Single crystals of the compound are electronic circular dichroism (ECD) and circularly polarized luminescence (CPL) active. Moreover, we found that a significant enantiomeric excess (50%) of either enantiomer is present in each crystallization batch (non-racemic conglomerate). Such spontaneous symmetry breaking leads not only to optically active single enantiomorph crystals but to an overall solid bulk with significant ECD and CPL.

Methyl side-groups control the Ia3̄d phase in core-non-symmetric aryloyl-hydrazine-based molecules

Control of the formation of liquid crystalline Ia3̄d gyroid phases and their nanostructures is critical to advance materials chemistry based on the structural feature of three-dimensional helical networks. Here, we present that introducing methyl side-group(s) and slight non-symmetry into aryloyl-hydrazine-based molecules is unexpectedly crucial for their formation and can be a new design strategy through tuning intermolecular interactions: the two chemical modifications in the core portion of the chain-core-chain type molecules effectively lower and extend the Ia3̄d phase temperature ranges with the increased twist angle between neighboring molecules along the network. The detailed analyses of the aggregation structure revealed the change in the core assembly mode from the double-layered core mode of the mother molecule (without methyl groups) to the single-layered core mode. Such changes are explained in terms of modified intermolecular interactions in those phases employing quantum chemical calculations.

Fundamental constraints to the logic of living systems

It has been argued that the historical nature of evolution makes it a highly path-dependent process. Under this view, the outcome of evolutionary dynamics could have resulted in organisms with different forms and functions. At the same time, there is ample evidence that convergence and constraints strongly limit the domain of the potential design principles that evolution can achieve. Are these limitations relevant in shaping the fabric of the possible? Here, we argue that fundamental constraints are associated with the logic of living matter. We illustrate this idea by considering the thermodynamic properties of living systems, the linear nature of molecular information, the cellular nature of the building blocks of life, multicellularity and development, the threshold nature of computations in cognitive systems and the discrete nature of the architecture of ecosystems. In all these examples, we present available evidence and suggest potential avenues towards a well-defined theoretical formulation.

Symmetry-Breaking and Symmetry-Retaining Morphological Evolution of the Single Crystals of Cyclodextrin Metal-Organic Frameworks

The morphological symmetry-retaining and symmetry-breaking of single crystals of the γ-cyclodextrin metal-organic framework have been achieved via introducing lower symmetric β-cyclodextrins and α-cyclodextrins, respectively. β-cyclodextrins led to a morphological evolution with retained symmetry from cubic to rhombic dodecahedra, while α-cyclodextrins resulted in the original cubic crystal missing a vertex angle presenting symmetry-breaking behavior. The crystal structures of rhombic dodecahedra and angle-deficient crystals were confirmed through X-ray crystallography, and the mechanisms underlying the morphological transformation evolution were further analyzed. Our work not only provides a rare case realizing two different paths of morphological evolution in one system, but also encourages future efforts towards the evolution of artificial crystal systems in a natural way.

Molecular Ratchets and Kinetic Asymmetry: Giving Chemistry Direction

Over the last two decades ratchet mechanisms have transformed the understanding and design of stochastic molecular systems-biological, chemical and physical-in a move away from the mechanical macroscopic analogies that dominated thinking regarding molecular dynamics in the 1990s and early 2000s (e.g. pistons, springs, etc), to the more scale-relevant concepts that underpin out-of-equilibrium research in the molecular sciences today. Ratcheting has established molecular nanotechnology as a research frontier for energy transduction and metabolism, and has enabled the reverse engineering of biomolecular machinery, delivering insights into how molecules 'walk' and track-based synthesisers operate, how the acceleration of chemical reactions enables energy to be transduced by catalysts (both motor proteins and synthetic catalysts), and how dynamic systems can be driven away from equilibrium through catalysis. The recognition of molecular ratchet mechanisms in biology, and their invention in synthetic systems, is proving significant in areas as diverse as supramolecular chemistry, systems chemistry, dynamic covalent chemistry, DNA nanotechnology, polymer and materials science, molecular biology, heterogeneous catalysis, endergonic synthesis, the origin of life, and many other branches of chemical science. Put simply, ratchet mechanisms give chemistry direction. Kinetic asymmetry, the key feature of ratcheting, is the dynamic counterpart of structural asymmetry (i.e. chirality). Given the ubiquity of ratchet mechanisms in endergonic chemical processes in biology, and their significance for behaviour and function from systems to synthesis, it is surely just as fundamentally important. This Review charts the recognition, invention and development of molecular ratchets, focussing particularly on the role for which they were originally envisaged in chemistry, as design elements for molecular machinery. Different kinetically asymmetric systems are compared, and the consequences of their dynamic behaviour discussed. These archetypal examples demonstrate how chemical systems can be driven inexorably away from equilibrium, rather than relax towards it.

Variations in activation energy and nuclei size during nucleation explain chiral symmetry breaking

We show that variations in enantiomer nuclei size and activation energy during the nucleation stage of crystallization are responsible for the chiral symmetry breaking resulting in excess of one of the possible enantiomers with respect to the other. By understanding the crystallisation process as a non-equilibrium self-assembly process, we quantify the enantiomeric excess through the probability distribution of the nuclei size and activation energy variations which are obtained from the free energy involved in the nucleation stage of crystallisation. We validate our theory by comparing it to Kondepudi et al. previous experimental work on sodium chlorate crystallisation. The results demonstrate that the self-assembly of enantiomeric crystals provides an explanation for chiral symmetry breaking. These findings could have practical applications for improving the production of enantiopure drugs in the pharmaceutical industry, as well as for enhancing our understanding of the origins of life since enantiomeric amino acids and monosaccharides are the building blocks of life.

The protometabolic nature of prebiotic chemistry

The field of prebiotic chemistry has been dedicated over decades to finding abiotic routes towards the molecular components of life. There is nowadays a handful of prebiotically plausible scenarios that enable the laboratory synthesis of most amino acids, fatty acids, simple sugars, nucleotides and core metabolites of extant living organisms. The major bottleneck then seems to be the self-organization of those building blocks into systems that can self-sustain. The purpose of this tutorial review is having a close look, guided by experimental research, into the main synthetic pathways of prebiotic chemistry, suggesting how they could be wired through common intermediates and catalytic cycles, as well as how recursively changing conditions could help them engage in self-organized and dissipative networks/assemblies (i.e., systems that consume chemical or physical energy from their environment to maintain their internal organization in a dynamic steady state out of equilibrium). In the article we also pay attention to the implications of this view for the emergence of homochirality. The revealed connectivity between those prebiotic routes should constitute the basis for a robust research program towards the bottom-up implementation of protometabolic systems, taken as a central part of the origins-of-life problem. In addition, this approach should foster further exploration of control mechanisms to tame the combinatorial explosion that typically occurs in mixtures of various reactive precursors, thus regulating the functional integration of their respective chemistries into self-sustaining protocellular assemblies.

A Complex Reaction Network Model for Spontaneous Mirror Symmetry Breaking in Viedma Deracemizations

Attrition-enhanced chiral symmetry breaking in crystals, known as Viedma deracemization, is a promising method for converting racemic solid phases into enantiomerically pure ones under non-equilibrium conditions. However, many aspects of this process remain unclear. In this study, we present a new investigation into Viedma deracemization using a comprehensive kinetic rate equation continuous model based on classical primary nucleation theory, crystal growth, and Ostwald ripening. Our approach employs a fully microreversible kinetic scheme with a size-dependent solubility following the Gibbs-Thomson rule. To validate our model, we use data from a real NaClO3 deracemization experiment. After parametrization, the model shows spontaneous mirror symmetry breaking (SMSB) under grinding. Additionally, we identify a bifurcation scenario with a lower and upper limit of the grinding intensity that leads to deracemization, including a minimum deracemization time within this window. Furthermore, this model uncovers that SMSB is caused by multiple instances of concealed high-order autocatalysis. Our findings provide new insights into attrition-enhanced deracemization and its potential applications in chiral molecule synthesis and understanding biological homochirality.

Conditions for the origin of homochirality in primordial catalytic reaction networks

We study the generation of homochirality in a general chemical model (based on the homogeneous, fully connected Smoluchowski aggregation-fragmentation model) that obeys thermodynamics and can be easily mapped onto known origin of life models (e.g. autocatalytic sets, hypercycles, etc.), with essential aspects of origin of life modeling taken into consideration. Using a combination of theoretical modeling and numerical simulations, we look for minimal conditions for which our general chemical model exhibits spontaneous mirror symmetry breaking. We show that our model spontaneously breaks mirror symmetry in various catalytic configurations that only involve a small number of catalyzed reactions and nothing else. Of particular importance is that mirror symmetry breaking occurs in our model without the need for single-step autocatalytis or mutual inhibition, which may be of relevance for prebiotic chemistry.

Chiral conformity emerges from the least-time free energy consumption

The prevalence of chirally pure biological polymers is often assumed to stem from some slight preference for one chiral form at the origin of life. Likewise, the predominance of matter over antimatter is presumed to follow from some subtle bias for matter at the dawn of the universe. However, rather than being imposed from the start, handedness standards in societies emerged to make things work. Since work is the universal measure of transferred energy, it is reasoned that standards at all scales and scopes emerge to consume free energy. Free energy minimization, equal to entropy maximization, turns out to be the second law of thermodynamics when derived from statistical physics of open systems. This many-body theory is based on the atomistic axiom that everything comprises the same fundamental elements known as quanta of action; hence, everything follows the same law. According to the thermodynamic principle, the flows of energy naturally select standard structures over less-fit functional forms to consume free energy in the least time. Thermodynamics making no distinction between animate and inanimate renders the question of life's handedness meaningless and deems the search for an intrinsic difference between matter and antimatter pointless.

Magnetic Circular Dichroism in Archean Stratospheric Oxygen: Enantiomeric Excess of Amino Acids Produced in Volcanic Plumes

While there is consensus that Archean atmosphere was anoxic with O2 pressure, p(O2) <10-6 PAL (present atmospheric level) at sea-level, evidence suggests that p(O2) at stratospheric altitudes of 10-50 km was orders of magnitude higher, a result of photodissociation of CO2 by UVC sunlight and incomplete mixing of O2 with other gases. Molecular O2 is paramagnetic due to triplet ground state. Magnetic circular dichroism (MCD) by stratospheric O2 is examined in earth's magnetic field and shows maximum circular polarization │(I+ - I-)│ at altitude of 15-30 km (I+/I- is intensity of left/right circularly polarized light). While (I+ - I-)/(I+ + I-) is small (~10-10), it is an unexplored source of enantiomeric excess (EE) by asymmetric photolysis of amino acid precursors produced in volcanic eruptions. The precursors reside in stratosphere for periods of over a year due to relative absence of vertical transport. Due to negligible thermal gradient across equator, they are trapped in the hemisphere where they are produced, with interhemispheric exchange time of over a year. The precursors diffuse through altitudes of maximum circular polarization before getting hydrolyzed on ground to amino acids. Enantiomeric excess of ~10-12 is calculated for precursors and amino acids. While small, this EE is orders of magnitude higher than predicted (~10-18) by parity violating energy differences (PVED) and could be the seed for growth of biological homochirality. Preferential crystallization (PC) is described as a plausible mechanism for amplification of solution EE of some amino acids from 10-12 to 10-2, for period of several days.

Chiral symmetry breaking induced by energy dissipation

Spontaneous chiral symmetry breaking is observed in a wide variety of systems on very different scales, from the subatomic to the cosmological. Despite its generality and importance for a large number of applications, its origin is still a matter of debate. It has been shown that the existence of a difference between the energies of the intermediate states of optical enantiomers leads to disparate production rates and thus to symmetry breaking. However, it is still unclear why this occurs. We measured for the first time the optical rotation angle of NaClO₃ enantiomeric crystals in solution during their formation and found that the amount of energy needed to induce the enantiomeric excess is exactly the same as the energy dissipated per mole of solid salt calculated from the entropy production obtained from the proposed model. The irreversible nature of the process leading to entropy production thus explains the chiral symmetry breaking in the salt crystals studied. The proposed method could be used to explain the formation of self-organised structures generated by self-assembly of enantiomers arising from chiral symmetry breaking, such as those emerging in the production of advanced materials and synthetic biological tissues.

Real-time Observation of Macroscopic Helical Morphologies under Optical Microscope: A Curious Case of π-π Stacking Driven Molecular Self-assembly of an Organic Gelator Devoid of Hydrogen Bonding

Supramolecular assemblies such as tubules/helix/double helix/helical tape etc. are usually submicron objects preventing direct observation under optical microscope. Chiral-pure form of these assemblies is important for potential applications. Herein, we report a rare phenomenon wherein a DMSO gel of a simple terpyridine derivative [(4-CNPhe)4PyTerp] produced macroscopic helical morphologies (μm length scale) which could be observed under optical microscope, formation of which could be monitored by optical videography, stable enough to withstand acidic vapour, robust enough to display reversible gel↔sol in response to acidic and ammonia vapour and sturdy enough to be maneuvered with a needle. These properties appeared to be unique to the title compound as the other related derivatives failed to display such assembly structures. SXRD and MD simulation studies suggested that weak interactions (π-π stacking) played a crucial role in the self-assembly process.

Fundamental Cause of Bio-Chirality: Space-Time Symmetry—Concept Review

The search for fundamental determinants of bio-molecular chirality is a hot topic in biology, clarifying the meaning of evolution and the enigma of life’s origin. The question of origin may be resolved assuming that non-biological and biological entities obey nature’s universal laws grounded on space-time symmetry (STS) and space-time relativity (SPR). The fabric of STS is our review’s primary subject. This symmetry, encompassing the behavior of elementary particles and galaxy structure, imposes its fundamental laws on all hierarchical levels of the biological world. From the perspective of STS, objects across spatial scales may be classified as chiral or achiral concerning a specific space-related symmetry transformation: mirror reflection. The chiral object is not identical (i.e., not superimposable) to its mirror image. In geometry, distinguish two kinds of chiral objects. The first one does not have any reflective symmetry elements (a point or plane of symmetry) but may have rotational symmetry axes (dissymmetry). The second one does not have any symmetry elements (asymmetry). As the form symmetry deficiency, Chirality is the critical structural feature of natural systems, including sub-atomic particles and living matter. According to the Standard Model (SM) theory and String Theory (StrT), elementary particles associated with the four fundamental forces of nature determine the existence of micro- and galaxy scales of nature. Therefore, the inheritance of molecular symmetry from the symmetry of elementary particles indicates a bi-directional (internal [(micro-scale) and external (galaxy sale)] causal pathway of prevalent bio-chirality. We assume that the laws of the physical world impact the biological matter’s appearance through both extremities of spatial dimensions. The extended network of multi-disciplinary experimental evidence supports this hypothesis. However, many experimental results are derived and interpreted based on the narrow-view prerogative and highly specific terminology. The current review promotes a holistic approach to experimental results in two fast-developing, seemingly unrelated, divergent branches of STS and biological chirality. The generalized view on the origin of prevalent bio-molecular chirality is necessary for understanding the link between a diverse range of biological events. The chain of chirality transfer links ribosomal protein synthesis, cell morphology, and neuronal signaling with the laterality of cognitive functions.

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.

Symmetry Breaking by Consecutive Amplification: Efficient Paths to Homochirality

To understand chiral symmetry breaking on the molecular level, we developed a method to efficiently investigate reaction kinetics of single molecules. The model systems include autocatalysis as well as a reaction cascade to gain further insight into the prebiotic origin of homochirality. The simulated reactions start with a substrate and only a single catalyst molecule, and the occurrence of symmetry breaking was examined for its degree of dependence on randomness. The results demonstrate that interlocking processes, which e.g., form catalysts, autocatalytic systems, or reaction cascades that build on each other and lead to a kinetic acceleration, can very well amplify a statistically occurring symmetry breaking. These results suggest a promising direction for the experimental implementation and identification of such processes, which could have led to a shift out of thermodynamic equilibrium in the emergence of life.

Frontiers in Prebiotic Chemistry and Early Earth Environments

The Prebiotic Chemistry and Early Earth Environments (PCE₃) Consortium is a community of researchers seeking to understand the origins of life on Earth and in the universe. PCE₃ is one of five Research Coordination Networks (RCNs) within NASA’s Astrobiology Program. Here we report on the inaugural PCE₃ workshop, intended to cross-pollinate, transfer information, promote cooperation, break down disciplinary barriers, identify new directions, and foster collaborations. This workshop, entitled, “Building a New Foundation”, was designed to propagate current knowledge, identify possibilities for multidisciplinary collaboration, and ultimately define paths for future collaborations. Presentations addressed the likely conditions on early Earth in ways that could be incorporated into prebiotic chemistry experiments and conceptual models to improve their plausibility and accuracy. Additionally, the discussions that followed among workshop participants helped to identify within each subdiscipline particularly impactful new research directions. At its core, the foundational knowledge base presented in this workshop should underpin future workshops and enable collaborations that bridge the many disciplines that are part of PCE₃.

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 Emergence of Transient Chirality in Closed, Reversible Frank-like Deterministic Models

To explore abiotic theories related to the origin of biomolecular homochirality, we analyze two entirely reversible kinetic models composed of an enantioselective autocatalysis with limited stereoselectivity that is coupled to an enantiomeric mutual inhibition (Frank-like models). The two models differ in their autocatalytic steps in respect to the formation of monomer species in one model and of dimer species in the other. While fully reversible and running in a closed system, spontaneous mirror symmetry breaking (SMSB) gives rise to transient chiral excursions, even when starting from a strictly achiral situation. Before the SMSB, the two models differ in the main dissipative processes. At the SMSB, the entropy production rate reaches its maximum in both models. Here it is the enantioselective autocatalysis with retention of the winner enantiomer that dominates. During the terminal phase, the enantioselective autocatalysis with inversion prevails, while the entropy production rate vanishes, thus fulfilling the conditions of microscopic reversibility. SMSB does not occur if the autocatalytic rate constant is too strong or too weak. However, when the autocatalysis is relatively weak, the temporary chiral excursions last for long periods of time and could be the starting point of a cascade of asymmetric reactions. The realism of such Frank-like models is discussed from the viewpoint of their relevance to prebiotic chemistry.

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.”

Stochastic Emergence of Two Distinct Self-Replicators from a Dynamic Combinatorial Library

Unraveling how chemistry can give rise to biology is one of the greatest challenges of contemporary science. Achieving life-like properties in chemical systems is therefore a popular topic of research. Synthetic chemical systems are usually deterministic: the outcome is determined by the experimental conditions. In contrast, many phenomena that occur in nature are not deterministic but caused by random fluctuations (stochastic). Here, we report on how, from a mixture of two synthetic molecules, two different self-replicators emerge in a stochastic fashion. Under the same experimental conditions, the two self-replicators are formed in various ratios over several repeats of the experiment. We show that this variation is caused by a stochastic nucleation process and that this stochasticity is more pronounced close to a phase boundary. While stochastic nucleation processes are common in crystal growth and chiral symmetry breaking, it is unprecedented for systems of synthetic self-replicators.

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.

Symmetry of Post-Translational Modifications in a Human Enzyme

Paraoxonase 2 (PON2) is a member of a small family of human lactonases. Recently, post-translational modifications (PTMs) of PON2 were highlighted, one of which involved the modulation of the enzyme activity. Furthermore, two important single nucleotide polymorphisms (SNPs) involved in type 2 diabetes and its consequences, were found to modulate the enzyme activity as well. The position on the PON2 structural model of both residues corresponding to SNPs and PTMs suggested a symmetry of the molecule. By sequence and structure superposition we were able to confirm this finding. The result will be discussed in light of the evolution of symmetry in biological molecules and their function.

Hierarchical self-assembly into chiral nanostructures

One basic principle regulating self-assembly is associated with the asymmetry of constituent building blocks or packing models. Using asymmetry to manipulate molecular-level devices and hierarchical functional materials is a promising topic in materials sciences and supramolecular chemistry. Here, exemplified by recent major achievements in chiral hierarchical self-assembly, we show how chirality may be utilized in the design, construction and evolution of highly ordered and complex chiral nanostructures. We focus on how unique functions can be developed by the exploitation of chiral nanostructures instead of single basic units. Our perspective on the future prospects of chiral nanostructures via the hierarchical self-assembly strategy is also discussed.

Spontaneous mirror symmetry breaking in reaction–diffusion systems: ambivalent role of the achiral precursor

Reaction–diffusion simulations reveal that the achiral substrate concentration may play an ambivalent role in spontaneous mirror symmetry breaking.

Chiral symmetry conservation principle

We show a chiral symmetry conservation principle based on chemical kinetics using stochastic results. Suppose the chiral symmetry conservation is evoked, and our universe can be considered globally asymmetric. In that case, there are at least two mirrored asymmetric universes if all the chiral properties are strongly correlated. However, if the chiral correlations are weak or nonexistent, there are possibly Many-(Chiral-Symmetry)-Worlds. Alternatively, if our universe is only locally asymmetric, there could be a single universe with segregated chiral regions. The possible mechanisms of the primordial chiral symmetry breaking can only be found if the chiral symmetry is not truly conserved by assuming the initial racemic conditions. In that case, our universe is asymmetric and could be alone. On the other hand, if the chiral symmetry is conserved, there is no chance of finding the primordial chiral symmetry breaking. Based on this conservation (or not), it is possible to infer two opposite hypotheses, where two general scenarios about the chiral universes are possible.

Absolute Asymmetric Catalysis, from Concept to Experiment: A Narrative

The generally accepted hypothesis to explain the origin of biological homochirality (that is to say, the fact that proteinogenic amino acids are left-handed, and carbohydrates right-handed, in all living beings) is to assume, in the course of prebiotic chemical evolution, the appearance of an initial enantiomeric excess in a set of chiral molecular entities by spontaneous mirror-symmetry breaking (SMSB), together with suitable amplification and replication mechanisms that overcome the thermodynamic drive to racemization. However, the achievement of SMSB in chemical reactions taking place in solution requires highly specific reaction networks showing nonlinear dynamics based on enantioselective autocatalysis, and examples of its experimental realization are very rare. On the other hand, emergence of net supramolecular chirality by SMSB in the self-assembly of achiral molecules has been seen to occur in several instances, and the chirality sign of the resulting supramolecular system can be controlled by the action of macroscopic chiral forces. These considerations led us to propose a new mechanism for the generation of net chirality in molecular systems, in which the SMSB takes place in the formation of chiral supramolecular dissipative structures from achiral monomers, leading to asymmetric imbalances in their composition that are subsequently transferred to a standard enantioselective catalytic reaction, dodging in this way the highly limiting requirement of finding suitable reactions in solution that show enantio­selective autocatalysis. We propose the name ‘absolute asymmetric catalysis’ for this approach, in which an achiral monomer is converted into a nonracemic chiral aggregate that is generated with SMSB and that is catalytically active.

Our aim in this Account is to present a step-by-step narrative of the conceptual and experimental development of this hitherto unregarded, but prebiotically plausible, mechanism for the emergence of net chirality in molecular reactions.

1 Introduction: The Origin of Biological Homochirality and Spontaneous Mirror-Symmetry Breaking

2 Experimental Chemical Models for Spontaneous Mirror-Symmetry Breaking: The Soai Reaction and Beyond

3 Spontaneous Mirror-Symmetry Breaking in Supramolecular Chemistry: Plenty of Room at the Top

4 Absolute Asymmetric Catalysis: An Alternative Mechanism for the Emergence of Net Chirality in Molecular Systems

5 Experimental Realization of Top-Down Chirality Transfer to the

Molecular Level

6 Conclusions and Outlook

Symmetry breaking meets multisite modification

Multisite modification is a basic way of conferring functionality to proteins and a key component of post-translational modification networks. Additional interest in multisite modification stems from its capability of acting as complex information processors. In this paper, we connect two seemingly disparate themes: symmetry and multisite modification. We examine different classes of random modification networks of substrates involving separate or common enzymes. We demonstrate that under different instances of symmetry of the modification network (invoked explicitly or implicitly and discussed in the literature), the biochemistry of multisite modification can lead to the symmetry being broken. This is shown computationally and consolidated analytically, revealing parameter regions where this can (and in fact does) happen, and characteristics of the symmetry-broken state. We discuss the relevance of these results in situations where exact symmetry is not present. Overall, through our study we show how symmetry breaking (i) can confer new capabilities to protein networks, including concentration robustness of different combinations of species (in conjunction with multiple steady states); (ii) could have been the basis for ordering of multisite modification, which is widely observed in cells; (iii) can significantly impact information processing in multisite modification and in cell signalling networks/pathways where multisite modification is present; and (iv) can be a fruitful new angle for engineering in synthetic biology and chemistry. All in all, the emerging conceptual synthesis provides a new vantage point for the elucidation and the engineering of molecular systems at the junction of chemical and biological systems.

Proteins help our cells perform the chemical reactions necessary for life. Once proteins are made, they can also be modified in different ways. This can simply change their activity, or otherwise make them better suited for their specific jobs within the cell. Biological ‘catalysts’ called enzymes carry out protein modifications by reversibly adding (or removing) chemical groups, such as phosphate groups.

‘Multisite modifications’ occur when a protein has two or more modifications in different areas, which can be added randomly or in a specific sequence. The combination of all the modifications attached to a protein acts like a chemical barcode and confers a specific function to the protein.

Modification networks add levels of complexity above individual proteins. These encompass not only the proteins in a cell or tissue, but also the different enzymes that can modify them, and how they all interact with each other. Although our knowledge of these networks is substantial, basic aspects, such as how the ordering of multisite modification systems emerges, is still not well understood.

Using a simple set of multisite modifications, Ramesh and Krishnan set out to study the potential mechanisms allowing the creation of order in this context. Symmetry is a pervasive theme across the sciences. In biology, symmetry and how it may be broken, is important to understand, for example, how organism develop. Ramesh and Krishnan used the perspective of symmetry in protein networks to uncover the origins of ordering.

First, mathematical models of simple modification networks were created based on their basic descriptions. This system centred on proteins that could have phosphate modifications at two possible sites. The network was ‘symmetric’, meaning that the rate of different sets of chemical reactions was identical, as were the amounts of all the enzymes involved.

Dissecting the simulated network using a variety of mathematical approaches showed that its initial symmetry could break, giving rise to sets of ordered multisite modifications. Breaking symmetry did not require any additional features or factors; the basic chemical ‘ingredients’ of protein modification were all that was needed. The prism of symmetry also revealed other aspects of these multisite modification networks, such as robustness and oscillations.

This study sheds new light on the mechanism behind ordering of protein modifications. In the future, Ramesh and Krishnan hope that this approach can be applied to the study of not just proteins but also a wider range of biochemical networks.

Handed Mirror Symmetry Breaking at the Photo-Excited State of π-Conjugated Rotamers in Solutions

The quest to decode the evolution of homochirality of life on earth has stimulated research at the molecular level. In this study, handed mirror symmetry breaking, and molecular parity violation hypotheses of systematically designed π-conjugated rotamers possessing anthracene and bianthracene core were evinced via circularly polarized luminescence (CPL) and circular dichroism (CD). The CPL signals were found to exhibit a (−)-sign, and a handed dissymmetry ratio, which increased with viscosity of achiral solvents depending on the rotation barrier of rotamers. The time-resolved photoluminescence spectroscopy and quantum efficiency measurement of these luminophores in selected solvents reinforced the hypothesis of a viscosity-induced consistent increase of the (−)-sign handed CPL signals.

Resonance in Chirogenesis and Photochirogenesis: Colloidal Polymers Meet Chiral Optofluidics

Metastable colloids made of crystalline and/or non-crystalline matters render abilities of photonic resonators susceptible to chiral chemical and circularly polarized light sources. By assuming that μm-size colloids and co-colloids consisting of π- and/or σ-conjugated polymers dispersed into an optofluidic medium are artificial models of open-flow, non-equilibrium coacervates, we showcase experimentally resonance effects in chirogenesis and photochirogenesis, revealed by gigantic boosted chiroptical signals as circular dichroism (CD), optical rotation dispersion, circularly polarized luminescence (CPL), and CPL excitation (CPLE) spectral datasets. The resonance in chirogenesis occurs at very specific refractive indices (RIs) of the surrounding medium. The chirogenesis is susceptible to the nature of the optically active optofluidic medium. Moreover, upon an excitation-wavelength-dependent circularly polarized (CP) light source, a fully controlled absolute photochirogenesis, which includes all chiroptical generation, inversion, erase, switching, and short-/long-lived memories, is possible when the colloidal non-photochromic and photochromic polymers are dispersed in an achiral optofluidic medium with a tuned RI. The hand of the CP light source is not a determining factor for the product chirality. These results are associated with my experience concerning amphiphilic polymerizable colloids, in which, four decades ago, allowed proposing a perspective that colloids are connectable to light, polymers, helix, coacervates, and panspermia hypotheses, nuclear physics, biology, radioisotopes, homochirality question, first life, and cosmology.

Strong Enantiomeric Preference on the Macroion-Counterion Interaction Induced by Weakly Associated Chiral Counterions

The role of chiral counterions on the attraction and self-assembly of chiral Pd₁₂L₂₄ metal organic cages (MOCs) with NO₃^- being the original counterion is studied by laser light scattering and isothermal titration calorimetry. Nitrates can trigger the self-assembly of macrocationic Pd₁₂L₂₄ into hollow spherical blackberry-type supramolecular structures via counterion-mediated attraction. Although chiral counteranions, such as N-(tert-butoxycarbonyl)-alanine (Boc-Ala), have weaker interaction with the MOCs compared to NO₃^-, they can induce different assembly behaviors between two enantiomeric MOCs by inhibiting the MOC-nitrate binding and weakening the interaction between them. The d-counterions are capable of selectively suppressing and slowing down the assembly of l-MOCs and also considerably decreasing their assembly size due to the much weaker MOC-nitrate interaction. The same scenario is observed for l-counterions when interacting with the d-MOCs. This study unveils the role of weakly associated chiral counterions on the central chiral macroions, especially their supramolecular structure formation, and provides additional evidence on the mechanism of the homochirality phenomenon.

Mirror Symmetry Breaking in Liquids and Their Impact on the Development of Homochirality in Abiogenesis: Emerging Proto-RNA as Source of Biochirality?

Recent progress in mirror symmetry breaking and chirality amplification in isotropic liquids and liquid crystalline cubic phases of achiral molecule is reviewed and discussed with respect to its implications for the hypothesis of emergence of biological chirality. It is shown that mirror symmetry breaking takes place in fluid systems where homochiral interactions are preferred over heterochiral and a dynamic network structure leads to chirality synchronization if the enantiomerization barrier is sufficiently low, i.e., that racemization drives the development of uniform chirality. Local mirror symmetry breaking leads to conglomerate formation. Total mirror symmetry breaking requires either a proper phase transitions kinetics or minor chiral fields, leading to stochastic and deterministic homochirality, respectively, associated with an extreme chirality amplification power close to the bifurcation point. These mirror symmetry broken liquids are thermodynamically stable states and considered as possible systems in which uniform biochirality could have emerged. A model is hypothesized, which assumes the emergence of uniform chirality by chirality synchronization in dynamic “helical network fluids” followed by polymerization, fixing the chirality and leading to proto-RNA formation in a single process.

Phase transitions of heliconical smectic-C and heliconical nematic phases in banana-shaped liquid crystals

A mean-field theory is introduced to describe heliconical nematic (N_{TB}), heliconical smectic-C (S_{m}C_{TB}), and biaxial heliconical smectic-C (S_{m}C_{TB,b}) phases with mirror symmetry breaking. We extend our previous theories of the N_{TB} phase to the heliconical smectic-C phases, by taking into account one-dimensional spatial ordering of smectic layers. The calculated phase diagrams on the temperature-alkyl chain length plane show a rich variety of phase transitions: first- and second-order N_{TB}-S_{m}C_{TB} transitions, etc., including tricritical, tetracritical, and multicritical points. Our theory is qualitatively consistent with an experimental phase diagram.

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.

Chemistry of Abiotic Nucleotide Synthesis

The chemistry of abiotic nucleotide synthesis of RNA and DNA in the context of their prebiotic origins on early earth is a continuing challenge. How did (or how can) the nucleotides form and assemble from the small molecule inventories and under conditions that prevailed on early earth 3.5-4 billion years ago? This review provides a background and up-to-date progress that will allow the reader to judge where the field stands currently and what remains to be achieved. We start with a brief primer on the biological synthesis of nucleotides, followed by an extensive focus on the prebiotic formation of the components of nucleotides-either via the synthesis of ribose and the canonical nucleobases and then joining them together or by building both the conjoined sugar and nucleobase, part-by-part-toward the ultimate goal of forming RNA and DNA by polymerization. The review will emphasize that there are-and will continue to be-many more questions than answers from the synthetic, mechanistic, and analytical perspectives. We wrap up the review with a cautionary note in this context about coming to conclusions as to whether the problem of chemistry of prebiotic nucleotide synthesis has been solved.

The origin of biological homochirality along with the origin of life

How homochirality concerning biopolymers (DNA/RNA/proteins) could have originally occurred (i.e., arisen from a non-life chemical world, which tended to be chirality-symmetric) is a long-standing scientific puzzle. For many years, people have focused on exploring plausible physic-chemical mechanisms that may have led to prebiotic environments biased to one chiral type of monomers (e.g., D-nucleotides against L-nucleotides; L-amino-acids against D-amino-acids)–which should have then assembled into corresponding polymers with homochirality, but as yet have achieved no convincing advance. Here we show, by computer simulation–with a model based on the RNA world scenario, that the biased-chirality may have been established at polymer level instead, just deriving from a racemic mixture of monomers (i.e., equally with the two chiral types). In other words, the results suggest that the homochirality may have originated along with the advent of biopolymers during the origin of life, rather than somehow at the level of monomers before the origin of life.

People have long been curious about the fact that central molecules in the living world (biopolymers), i.e., nucleic acids and proteins, are asymmetric in chirality (handedness), but as the relevant background, the chemical world is symmetric in chirality. Now that life should have originated from a prebiotic non-life background, how could this dissymmetry have occurred? Previous studies in this area focused their efforts on how the chirality-symmetry may have been broken at the monomer level (i.e., nucleotides or amino acids), but have achieved little advance over decades of years. Here we demonstrate, by in silico simulation, that instead, the required chirality-deviation may have been established along with the emergence of biopolymers at the beginning stage in the origin of life–just deriving from a chirality-symmetric monomer pool. The process is actually not only an issue of chemistry but also an issue involving evolution–thus previously difficult to reveal by pure lab work in this area. By modelling the evolutionary process, the present computer simulation study provides significant clues for experiments in future.

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

Stability of non-equilibrium stationary states and spontaneous mirror symmetry breaking, provoked by the destabilization of the racemic thermodynamic branch, is studied for enantioselective autocatalysis in an open flow system, and for a continuous range n of autocatalytic orders.

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

The entropy production per unit volume in the chaotic regime of a chiral hypercycle in an open-flow reactor.

The role of sugar-backbone heterogeneity and chimeras in the simultaneous emergence of RNA and DNA

Hypotheses of the origins of RNA and DNA are generally centred on the prebiotic synthesis of a pristine system (pre-RNA or RNA), which gives rise to its descendent. However, a lack of specificity in the synthesis of genetic polymers would probably result in chimeric sequences; the roles and fate of such sequences are unknown. Here, we show that chimeras, exemplified by mixed threose nucleic acid (TNA)-RNA and RNA-DNA oligonucleotides, preferentially bind to, and act as templates for, homogeneous TNA, RNA and DNA ligands. The chimeric templates can act as a catalyst that mediates the ligation of oligomers to give homogeneous backbone sequences, and the regeneration of the chimeric templates potentiates a scenario for a possible cross-catalytic cycle with amplification. This process provides a proof-of-principle demonstration of a heterogeneity-to-homogeneity scenario and also gives credence to the idea that DNA could appear concurrently with RNA, instead of being its later descendent.

Symmetry Breaking in Self-Assembled Nanoassemblies

The origin of biological homochirality, e.g., life selects the L-amino acids and D-sugar as molecular component, still remains a big mystery. It is suggested that mirror symmetry breaking plays an important role. Recent researches show that symmetry breaking can also occur at a supramolecular level, where the non-covalent bond was crucial. In these systems, equal or unequal amount of the enantiomeric nanoassemblies could be formed from achiral molecules. In this paper, we presented a brief overview regarding the symmetry breaking from dispersed system to gels, solids, and at interfaces. Then we discuss the rational manipulation of supramolecular chirality on how to induce and control the homochirality in the self-assembly system. Those physical control methods, such as Viedma ripening, hydrodynamic macro- and micro-vortex, superchiral light, and the combination of these technologies, are specifically discussed. It is hoped that the symmetry breaking at a supramolecular level could provide useful insights into the understanding of natural homochirality and further designing as well as controlling of functional chiral materials.

Entropic Analysis of Mirror Symmetry Breaking in Chiral Hypercycles

Replicators are fundamental to the origin of life and evolvability. Biology exhibits homochirality: only one of two enantiomers is used in proteins and nucleic acids. Thermodynamic studies of chemical replicators able to lead to homochirality shed valuable light on the origin of homochirality and life in conformity with the underlying mechanisms and constraints. In line with this framework, enantioselective hypercyclic replicators may lead to spontaneous mirror symmetry breaking (SMSB) without the need for additional heterochiral inhibition reactions, which can be an obstacle for the emergence of evolutionary selection properties. We analyze the entropy production of a two-replicator system subject to homochiral cross-catalysis which can undergo SMSB in an open-flow reactor. The entropy exchange with the environment is provided by the input and output matter flows, and is essential for balancing the entropy production at the non-equilibrium stationary states. The partial entropy contributions, associated with the individual elementary flux modes, as defined by stoichiometric network analysis (SNA), describe how the system's internal currents evolve, maintaining the balance between entropy production and exchange, while minimizing the entropy production after the symmetry breaking transition. We validate the General Evolution Criterion, stating that the change in the chemical affinities proceeds in a way as to lower the value of the entropy production.

Symmetry breaking and functional incompleteness in biological systems

Symmetry-based explanations using symmetry breaking (SB) as the key explanatory tool have complemented and replaced traditional causal explanations in various domains of physics. The process of spontaneous SB is now a mainstay of contemporary explanatory accounts of large chunks of condensed-matter physics, quantum field theory, nonlinear dynamics, cosmology, and other disciplines. A wide range of empirical research into various phenomena related to symmetries and SB across biological scales has accumulated as well. Led by these results, we identify and explain some common features of the emergence, propagation, and cascading of SB-induced layers across the biosphere. These features are predicated on the thermodynamic openness and intrinsic functional incompleteness of the systems at stake and have not been systematically analyzed from a general philosophical and methodological perspective. We also consider possible continuity of SB across the physical and biological world and discuss the connection between Darwinism and SB-based analysis of the biosphere and its history.

Spontaneous mirror-symmetry breaking coupled to top-bottom chirality transfer: from porphyrin self-assembly to scalemic Diels–Alder adducts

This report shows how the net supramolecular chirality that emerged by spontaneous mirror-symmetry breaking (SMSB) at the mesoscale level can be transferred towards asymmetric solution chemistry.

Stoichiometric network analysis of entropy production in chemical reactions

SNA extreme currents allow for the evaluation and understanding of entropy production of NESS in open system reaction networks.