Lipid Aggregates Inducing Symmetry Breaking in Prebiotic Polymerisations

It is a long-standing and still open problem to determine the origin of biomolecular homochirality, and many scenarios have been suggested. Amphiphilic molecules are renowned for their capability to reorganize themselves in a variety of different morphologies and topologies, and for their capability to partition chemicals in well defined domains. Here a possible role for amphiphilic molecules inducing symmetry breaking is suggested in the framework of the research on origin of life.     

Symmetry Breaking on Density in Escaping Ants: Experiment and Alarm Pheromone Model

The symmetry breaking observed in nature is fascinating. This symmetry breaking is observed in both human crowds and ant colonies. In such cases, when escaping from a closed space with two symmetrically located exits, one exit is used more often than the other. Group size and density have been reported as having no significant impact on symmetry breaking, and the alignment rule has been used to model symmetry breaking. Density usually plays important roles in collective behavior. However, density is not well-studied in symmetry breaking, which forms the major basis of this paper. The experiment described in this paper on an ant colony displays an increase then decrease of symmetry breaking versus ant density. This result suggests that a Vicsek-like model with an alignment rule may not be the correct model for escaping ants. Based on biological facts that ants use pheromones to communicate, rather than seeing how other individuals move, we propose a simple yet effective alarm pheromone model. The model results agree well with the experimental outcomes. As a measure, this paper redefines symmetry breaking as the collective asymmetry by deducing the random fluctuations. This research indicates that ants deposit and respond to the alarm pheromone, and the accumulation of this biased information sharing leads to symmetry breaking, which suggests true fundamental rules of collective escape behavior in ants.     

Dissipative structures and amplification of enantiomeric excess (an experimental point of view)

Various mathematical models have been proposed to account for the origin of chiral molecules in biological systems. Most of these models invoke non-linear phenomena, and are based on the general concept of dissipative structures. These theoretical models define the fundamental criteria which must be obeyed by the experimental systems that we have investigated. Our initial approach to this problem was an extensive search of the literature data in order to select a few systems or experimental situations which would satisfy the criteria defined by the theoretical models. For these reasons, we carried out a study of the possibility of stereospecific autocatalysis in the asymmetric polymerisation of benzofuran. Similarly, the formation of spatial dissipative structures by coupling of a transport process with an interfacial reaction was investigated as a simple experimental example of symmetry breaking.     

Establishment of vertebrate left-right asymmetry

The generation of morphological, such as left-right, asymmetry during development is an integral part of the establishment of a body plan. Until recently, the molecular basis of left-right asymmetry was a mystery, but studies indicate that Nodal and the Lefty proteins, transforming growth factor-beta-related molecules, have a central role in generating asymmetric signals. Although the initial mechanism of symmetry breaking remains unknown, developmental biologists are beginning to analyse the pathway that leads to left-right asymmetry establishment and maintenance.     

Parity violation and chiral symmetry breaking of a racemic mixture

The chiral symmetry breaking of a racemic mixture by the parity violating weak interaction is considered. Particular attention is given to a mechanism recently proposed by Mason and Tranter whereby the weak neutral current interaction in chiral molecules leads to the differential absorption of unpolarized light by D vs. L enantiomers. After extending the usual theory of optical activity to include weak neutral currents, it is found that for spin-allowed transitions in typical organic molecules the weak photoabsorption asymmetry is much smaller than the value obtained using the reasoning of Mason and Tranter. Upon making a comparison with other mechanisms, it is concluded that differential radiolysis by beta electrons is likely to produce the largest symmetry breaking effect by the weak interaction.     

The mechanical behaviour of cell membranes as a possible physical origin of cell polarity

The mechanical behaviour of a closed layered membrane enclosing a structureless interior is considered. The shape of such an object in flaccid conditions is determined theoretically by assuming that it corresponds to the minimum value of the membrane bending energy. The symmetry breaking properties of this system are revealed. It is suggested that a continuous transition from an axisymmetrical shape involving mirror symmetry with regard to the equatorial plane of the object to the shape with polar asymmetry could be the primary event in establishing cell polarity.     

Asymmetries of nature and the origin of biomolecular handedness

New developments in the problem of the origin of the asymmetry of the living systems are reviewed. The time of the appearance of the asymmetry was very probably during the chemical evolution. The asymmetry of weak interaction is still considered small to be the cause of chiral purity. New sources of asymmetry should also be considered, like the one proposed by Gilat.     

Broken symmetry between RNA enantiomers in a crystal lattice

Explaining the origin of the homochirality of biological molecules requires a mechanism of disrupting the natural equilibrium between enantiomers and amplifying the initial imbalance to significant levels. Authors of existing models have sought an explanation in the parity-breaking weak nuclear force, in some selectively acting external factor, or in random fluctuations that subsequently became amplified by an autocatalytic process. We have obtained crystals in which l- and d-enantiomers of short RNA duplexes assemble in an asymmetric manner. These enantiomers make different lattice contacts and have different exposures to water and metal ions present in the crystal. Apparently, asymmetry between enantiomers can arise upon their mutual interactions and then propagate via crystallization. Asymmetric racemic compounds are worth considering as possible factors in symmetry breaking and enantioenrichment that took place in the early biosphere.     

Space Asymmetry as a Possible Global Feature

A series of reports in the literature indicated symmetry breaking in assemblies of chiral molecules of opposite handedness. These unexpected observations could be accounted for as being generated by the “parity violation” of the nuclear weak force, combined with an autocatalytic amplification process. However, in many such cases, in particular of chiral fluids, this putative mechanism is far from providing a reasonable explanation for such discrimination. In this article it is suggested that space may have deviated a priori from absolute symmetry, a possibility which complies with observations in atoms and molecules and may even be implicated in the asymmetrical configuration of spiral galaxies. Space asymmetry can be extrapolated to a difference between the relative statistical weights of the “right” versus the “left” directions with respect to Euclidian coordinates or, analogously, to a difference between the clockwise and anticlockwise orientations in polar coordinates. The difference in weights of these directions in space is estimated to be around 1%, based on the differences observed in density values of chiral fluids and chiral crystals of NaClO₃. The implied asymmetry of time, as the conjugated fourth dimension, suggests a similar difference in magnitude of the time coordinate in a right‐handed versus left‐handed space, which is feasible for experimental verification. Chirality 25:308–311, 2013. © 2013 Wiley Periodicals, Inc.     

A Sequential Scenario for the Origin of Biological Chirality

A sequential model is proposed regarding the origin of biological chirality. Three major stages are presumed: a symmetry breaking (prebiotic chiral disruption in enantiomeric mixtures of monomers), a chiral amplification (prebiotic increase of the chiral character of the monomers affected first by the symmetry breaking), and a chiral expansion (proto biological increase of the chiral character and spread of the chirality to molecules which were less affected by prebiotic chiralizations). As a symmetry-breaking mechanism, the model proposed by Deutsch (1991) is used, which involves a dissymmetric exposure of amino acids (AA) to ultraviolet circularly polarized light (UV-CPL) on evaporative seashores. It is presumed that the chiral amplification, up to a protobiologic significance, was influenced by a periodic overlapping of two abiotic events, a synchronization between tidal-based hydrous–anhydrous cycles, and littoral asymmetric photolysis cycles. This long-term astronomic asymmetry acted around 3.8–4.2 billion years ago and was unique to the Earth in our solar system. It is also presumed that the abiotic symmetry breaking is heterogenous, that only a few l-AAs were used in the beginning, and that the chirality expanded later to all 20 AAs based on a coevolutionary strategy of the genetic code and on a physiological relationship between AAs. In this scenario the d-chirality of pentoses in polynucleotides was attributed to both d-pentose/l-AA relationships and to a structural evolution. Received: 10 May 1996 / Accepted: 13 August 1996     

Remarks on origins of biomolecular asymmetry

A simple criterion for mirror symmetry breaking in a non-linear chemical system is presented. The selection effect of external asymmetric agents in the process of generation and amplification of biomolecular asymmetry is studied. It is pointed out that this effect will play an important role at bifurcation point, but when the asymmetry of a system has been amplified to a certain extent, a weak asymmetric agent will no longer be able to change the chirality of the system.     

Strategies to establish left/right asymmetry in vertebrates and invertebrates

Left/right (L/R) asymmetry is essential during embryonic development for organ positioning, looping and handed morphogenesis. A major goal in the field is to understand how embryos initially determine their left and right hand sides, a process known as symmetry breaking. A number of recent studies on several vertebrate and invertebrate model organisms have provided a more complex view on how L/R asymmetry is established, revealing an apparent partition between deuterostomes and protostomes. In deuterostomes, nodal cilia represent a conserved symmetry-breaking process; nevertheless, growing evidence shows the existence of pre-cilia L/R asymmetries involving active ion flows. In protostomes like snails and Drosophila, symmetry breaking relies on different mechanisms, involving, in particular, the actin cytoskeleton and associated molecular motors.     

Viewing and Inducing Symmetry Breaking at the Single‐Molecule Limit

Symmetry breaking by photons, electrons, and molecular interactions lies at the heart of many important problems as varied as the origin of homochiral life to enantioselective drug production. Herein we report a system in which symmetry breaking can be induced and measured in situ at the single‐molecule level using scanning tunneling microscopy. We demonstrate that electrical excitation of a prochiral molecule on an achiral surface produces large enantiomeric excesses in the chiral adsorbed state of up to 39%. The degree of symmetry breaking was monitored as a function of scanning probe tip state, and the results revealed that enantiomeric excesses are correlated with the intrinsic chirality in scanning probe tips themselves, as evidenced by height differences between single molecule enantiomers. While this work has consequences for the study of two‐dimensional chirality, more importantly, it offers a new method for interrogating the coupling of photons, electrons, and combinations of physical fields to achiral starting systems in a reproducible manner. This will allow the mechanism of chirality transfer to be studied in a system in which enantiomeric excesses are quantified accurately by counting individual molecules. Chirality 24:1051–1054, 2012. © 2012 Wiley Periodicals, Inc.     

Starlings can categorize symmetry differences in dot displays

Fluctuating asymmetry is an estimate of developmental stability and, in some cases, the asymmetry of morphological traits can reflect aspects of individual fitness. As asymmetry can be a marker for fitness, it has been proposed that organisms could use morphological asymmetry as a direct visual cue during inter- and intraspecific encounters. Despite some experimental evidence to support this prediction, the perceptual abilities of animals to detect and respond to symmetry differences have been largely overlooked. Studying the ability of animals to perceive symmetry and factors that affect this ability are crucial to assessing whether fluctuating asymmetry could be used as a visual cue in nature. In this study, we investigated the ability of wild-caught European starlings Sturnus vulgaris to learn to discriminate symmetry from asymmetry in random dot patterns through operant learning experiments. The birds did not possess a spontaneous preference for either symmetry or asymmetry. The birds learned a symmetry preference, although the learning process took longer than that previously reported for pigeons Columba livia and was more error prone. After being trained to discriminate symmetry differences in random dot patterns, birds successfully transferred their symmetry discrimination abilities to a set of novel stimuli that they had not previously seen. This indicates that starlings can form a mental categorization of visual stimuli on the basis of a somewhat generalized symmetry phenomenon. We discuss these findings in relation to the probability that birds use fluctuating asymmetry as a visual cue.     

Mathematical Analysis of Spontaneous Emergence of Cell Polarity

Cell polarization, in which intracellular substances are asymmetrically distributed, enables cells to carry out specialized functions. While cell polarity is often induced by intracellular or extracellular spatial cues, spontaneous polarization (the so-called symmetry breaking) may also occur in the absence of spatial cues. Many computational models have been used to investigate the mechanisms of symmetry breaking, and it was proved that spontaneous polarization occurs when the lateral diffusion of inactive signaling molecules is much faster than that of active signaling molecules. This conclusion leaves an important question of how, as observed in many biological systems, cell polarity emerges when active and inactive membrane-bound molecules diffuse at similar rates while cycling between cytoplasm and membrane takes place. The recent studies of Rätz and Röger showed that, when the cytosolic and membrane diffusion are very different, spontaneous polarization is possible even if the membrane-bound species diffuse at the same rate. In this paper, we formulate a two-equation non-local reaction-diffusion model with general forms of positive feedback. We apply Turing stability analysis to identify parameter conditions for achieving cell polarization. Our results show that spontaneous polarization can be achieved within some parameter ranges even when active and inactive signaling molecules diffuse at similar rates. In addition, different forms of positive feedback are explored to show that a non-local molecule-mediated feedback is important for sharping the localization as well as giving rise to fast dynamics to achieve robust polarization.     

Left‐right asymmetry in the light of TOR: An update on what we know so far

The internal left‐right (LR) asymmetry is a characteristic that exists throughout the animal kingdom from roundworms over flies and fish to mammals. Cilia, which are antenna‐like structures protruding into the extracellular space, are involved in establishing LR asymmetry during early development. Humans who suffer from dysfunctional cilia often develop conditions such as heterotaxy, where internal organs appear to be placed randomly. As a consequence to this failure in asymmetry development, serious complications such as congenital heart defects (CHD) occur. The mammalian (or mechanistic) target of rapamycin (mTOR) pathway has recently emerged as an important regulator regarding symmetry breaking. The mTOR pathway governs fundamental processes such as protein translation or metabolism. Its activity can be transduced by two complexes, which are called TORC1 and TORC2, respectively. So far, only TORC1 has been implicated with asymmetry development and appears to require very precise regulation. A number of recent papers provided evidence that dysregulated TORC1 results in alterations of motile cilia and asymmetry defects. In here, we give an update on what we know so far of mTORC1 in LR asymmetry development.     

The Trail Less Traveled: Individual Decision-Making and Its Effect on Group Behavior

Social insect colonies are complex systems in which the interactions of many individuals lead to colony-level collective behaviors such as foraging. However, the emergent properties of collective behaviors may not necessarily be adaptive. Here, we examine symmetry breaking, an emergent pattern exhibited by some social insects that can lead colonies to focus their foraging effort on only one of several available food patches. Symmetry breaking has been reported to occur in several ant species. However, it is not clear whether it arises as an unavoidable epiphenomenon of pheromone recruitment, or whether it is an adaptive behavior that can be controlled through modification of the individual behavior of workers. In this paper, we used a simulation model to test how symmetry breaking is affected by the degree of non-linearity of recruitment, the specific mechanism used by individuals to choose between patches, patch size, and forager number. The model shows that foraging intensity on different trails becomes increasingly asymmetric as the recruitment response of individuals varies from linear to highly non-linear, supporting the predictions of previous work. Surprisingly, we also found that the direction of the relationship between forager number (i.e., colony size) and asymmetry varied depending on the specific details of the decision rule used by individuals. Limiting the size of the resource produced a damping effect on asymmetry, but only at high forager numbers. Variation in the rule used by individual ants to choose trails is a likely mechanism that could cause variation among the foraging behaviors of species, and is a behavior upon which selection could act.     

Systems biology of symmetry breaking during neuronal polarity formation

Polarization, in which a single axon and multiple dendrites are formed, is crucial for neuronal functions, and symmetry breaking is the initial step of this process. Accumulating studies have revealed a number of molecules that act asymmetrically in neurons, and thereby regulate neuronal polarity. Thus, one of the major goals of current research is to understand how asymmetric signals are generated during the symmetry-breaking step. Current models of neuronal symmetry breaking generally involve "local activation" for induction of axon outgrowth and "global inhibition" to suppress formation of multiple axons and can be categorized into "one-takes-all" and "activator-inhibitor" models. Both types of model incorporate a positive feedback loop to execute local activation, but differ in the manner of global inhibition. Quantitative experimentation combined with computational modeling is a powerful strategy in systems biology, and analyses in this direction have begun to yield a more profound understanding of how neurons break their symmetry during polarity formation.     

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.

     

Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry

Background

Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry.

Results

We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis.

Conclusions

The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.