Mirror symmetry breaking in biochemical evolution.

The problem of origination of molecular asymmetry in biochemical evolution is discussed. The theoretical analysis shows that chiral purity of biomolecules has the biological significance for self-reproduction of organisms. The models of spontaneous symmetry-breaking in molecular systems are given. The aspects of various stages of biochemical evolution associated with the development of chiral polarization are analysed.     

Spontaneous symmetry breaking in genome evolution

The quest for evolutionary mechanisms providing separation between the coding (exons) and noncoding (introns) parts of genomic DNA remains an important focus of genetics. This work combines an analysis of the most recent achievements of genomics and fundamental concepts of random processes to provide a novel point of view on genome evolution. Exon sizes in sequenced genomes show a lognormal distribution typical of a random Kolmogoroff fractioning process. This implies that the process of intron incretion may be independent of exon size, and therefore could be dependent on intron-exon boundaries. All genomes examined have two distinctive classes of exons, each with different evolutionary histories. In the framework proposed in this article, these two classes of exons can be derived from a hypothetical ancestral genome by (spontaneous) symmetry breaking. We note that one of these exon classes comprises mostly alternatively spliced exons.     

Ecological symmetry breaking can favour the evolution of altruism in an action-response game

The evolution of altruistic behaviour is studied in a simple action-response game with a tunable degree of conflict of interest. It is shown that for the continuous, mixed-medium approach no stable polymorphism favours altruism. Ecological dynamics are explored with the addition of a spatial dimension and a local energy variable. A continuous spatial model with finite local range does not introduce any substantial difference in the results with respect to the level of altruism. However, the model illustrates how ecological coupling may lead to the formation of stable spatial patterns in the form of discrete and isolated clusters of players as a consequence of inverse density dependence. A discrete, individual-based model is built in which local interactions are also modelled as occurring within a finite neighbourhood of each individual and spatial positions are not restricted as in lattice models. This model shows substantially different results. A high level of altruism is observed for low (but positive) degrees of conflict and this level decreases linearly for higher degrees of conflict. The evolution of altruism is explained by studying the broken symmetries introduced by the spatial clusters themselves, mainly between their central and peripheral regions which, in combination with the discrete and the stochastic nature of the model, result in the stabilization of strategies in which players behave altruistically towards the same type. As a consequence of the activity of the players, energy resources at the centre of an altruistic cluster are very depleted; so much so that, for low conflict, fitter non-altruistic mutants may initially invade only to become locally extinct due to their less efficient use of energy as their numbers increase. In peripheral regions invader may subsist; however, for geometrical reasons long-lasting genealogies tend to originate only at the centre of a cluster.     

Cytoskeletal symmetry breaking in animal cells

Symmetry breaking is a crucial step in structure formation and function of all cells, necessary for cell movement, cell division, and polarity establishment. Although the mechanisms of symmetry breaking are diverse, they often share common characteristics. Here we review examples of nematic, polar, and chiral cytoskeletal symmetry breaking in animal cells, and analogous processes in simplified reconstituted systems. We discuss the origins of symmetry breaking, which can arise spontaneously, or involve amplification of a pre-existing external or internal bias to the whole cell level. The underlying mechanisms often involve both chemical and mechanical processes that cooperate to break symmetry in a robust manner, and typically depend on the shape, size, or properties of the cell’s boundary.     

Visualizing the breaking of symmetry

Axon specification is a hallmark of neuron polarization. Although several models have been proposed, few studies have provided clues about polarization events in real time. Using time-lapse imaging, a recent study described visualizing symmetry-breaking events during this process.     

Emergence of symmetry breaking in fucoid zygotes

Fucoid zygotes are model cells for the study of symmetry breaking in plants. After fertilization, their initial spherical symmetry reduces to an axial symmetry, even in the absence of any external cue. This indicates that zygotes have an intrinsic ability to break symmetry in a way that is solely dependent on their internal biochemical and/or biophysical state. In our opinion, symmetry breaking is a self-organized process. It arises around the fucoid zygotes from the ion dynamics through channels (voltage-dependent calcium channels and a potassium leak) and outside the membrane (electrodiffusion owing to slower calcium diffusion compared with potassium). The robustness of this self-organized process and its lability ensure its relevance in plants where symmetry breaking is correlated with transcellular ion currents.     

Entropy production in chiral symmetry breaking transitions

It is now well known that nonequilibrium chemical systems may reach conditions that spontaneously generate chiral asymmetry. One can find a host of model reactions that exhibit such behavior in the literature. Among these, models based on one originally devised by Frank have been studied extensively. Though the kinetic aspects of such model reactions have been discussed in great detail, the behavior of entropy in such systems is rarely discussed. In this article, the rate of entropy production per unit volume, sigma, in a modified Frank model is discussed. It is shown that the slope of sigma changes at the point at which the asymmetric states appear, behavior similar to that observed in second-order phase transitions.     

Spontaneous chiral symmetry breaking in early molecular networks

Background  

An important facet of early biological evolution is the selection of chiral enantiomers for molecules such as amino acids and sugars. The origin of this symmetry breaking is a long-standing question in molecular evolution. Previous models addressing this question include particular kinetic properties such as autocatalysis or negative cross catalysis.     

Morphological and chiral symmetry breaking in reaction-diffusion systems

Morphological and chiral symmetry breaking in reaction-diffusion systems is considered on the basis of the theory of imperfect codimension-two bifurcations. A new type of pattern selection with two triggers is elucidated: (1) morphologically asymmetric structures displaying optical activity can probably be originated from initially racemic and homogeneous conditions when chiral interaction, having the characteristic strength delta (such as electroweak interaction and circularly polarized light) as well as external field, having the characteristic strength eta (such as gravitational field and electrostatic field) are considered; (2) the selective sensitivity of molecular chirality and morphological asymmetry is omicron(delta 1/3) and omicron(eta 1/3), respectively; the sensitivity of mode-mode interaction between chiral polarization and concentration vector is omicron(delta 2/3) or omicron(eta 2/3), respectively. The relation of these conclusions to the life problem is discussed briefly.     

Cracking up: symmetry breaking in cellular systems

The shape of animal cells is, to a large extent, determined by the cortical actin network that underlies the cell membrane. Because of the presence of myosin motors, the actin cortex is under tension, and local relaxation of this tension can result in cortical flows that lead to deformation and polarization of the cell. Cortex relaxation is often regulated by polarizing signals, but the cortex can also rupture and relax spontaneously. A similar tension-induced polarization is observed in actin gels growing around beads, and we propose that a common mechanism governs actin gel rupture in both systems.     

Scaffold-mediated symmetry breaking by Cdc42p

Cell polarization generally occurs along a single well-defined axis that is frequently determined by environmental cues such as chemoattractant gradients or cell-cell contacts, but polarization can also occur spontaneously in the apparent absence of such cues, through a process called symmetry breaking. In Saccharomyces cerevisiae, cells are born with positional landmarks that mark the poles of the cell and guide subsequent polarization and bud emergence to those sites, but cells lacking such landmarks polarize towards a random cortical site and proliferate normally. The landmarks employ a Ras-family GTPase, Rsr1p, to communicate with the conserved Rho-family GTPase Cdc42p, which is itself polarized and essential for cytoskeletal polarization. We found that yeast Cdc42p was effectively polarized to a single random cortical site even in the combined absence of landmarks, microtubules and microfilaments. Among a panel of Cdc42p effectors and interacting proteins, we found that the scaffold protein Bem1p was uniquely required for this symmetry-breaking behaviour. Moreover, polarization was dependent on GTP hydrolysis by Cdc42p, suggesting that assembly of a polarization site involves cycling of Cdc42p between GTP- and GDP-bound forms, rather than functioning as a simple on/off switch.     

Polarized growth in fungi: symmetry breaking and hyphal formation

Cell shape is a critical determinant for function. The baker's yeast Saccharomyces cerevisiae changes shape in response to its environment, growing by budding in rich nutrients, forming invasive pseudohyphal filaments in nutrient poor conditions and pear shaped shmoos for growth towards a partner during mating. The human opportunistic pathogen Candida albicans can switch from budding to hyphal growth, in response to numerous environmental stimuli to colonize and invade its host. Hyphal growth, typical of filamentous fungi, is not observed in S. cerevisiae. A number of internal cues regulate when and where yeast cells break symmetry leading to polarized growth and ultimately distinct cell shapes. This review discusses how cells break symmetry using the yeast S. cerevisiae paradigm and how polarized growth is initiated and maintained to result in dramatic morphological changes during C. albicans hyphal growth.     

Robust neuronal symmetry breaking by Ras-triggered local positive feedback

Neuronal polarity is initiated by a symmetry-breaking event whereby one out of multiple minor neurites undergoes rapid outgrowth and becomes the axon [1]. Axon formation is regulated by phosphatidylinositol 3-kinase (PI3K)-related signaling elements [2-10] that drive local actin [11] and microtubule reorganization [3, 12], but the upstream signaling circuit that causes symmetry breaking and guarantees the formation of a single axon is not known. Here, we use live FRET imaging in hippocampal neurons and show that the activity of the small GTPase HRas, an upstream regulator of PI3K, markedly increases in the nascent axonal growth cone upon symmetry breaking. This local increase in HRas activity results from a positive feedback loop between HRas and PI3K, locally reinforced by vesicular transport of HRas to the axonal growth cone. Recruitment of HRas to the axonal growth cone is paralleled by a decrease in HRas concentration in the remaining neurites, suggesting that competition for a limited pool of HRas guarantees that only one axon forms. Mathematical modeling demonstrates that local positive feedback between HRas and PI3K, coupled to recruitment of a limited pool of HRas, generates robust symmetry breaking and formation of a single axon in the absence of extrinsic spatial cues.     

Informational symmetry breaking between proteins and nucleic acids.

Anti-symmetry of the information-processing mechanisms between proteins and nucleic acids is generalized to informational symmetry breaking between a genetic polymer and an anti-genetic polymer so as not to depend on particular chemical species. In a genetic polymer, e.g. nucleic acids, any sequence can form a closed double-stranded structure with a specific partner sequence. On the other hand, in an anti-genetic polymer, e.g. proteins, a chain could fold to an open multi-stranded structure and reinterpretation of the genetic information through slides or shifts between stacked strands could be induced by external perturbations. The possibility of the informational symmetry breaking by hierarchical organization of a single chemical species, i.e. polypeptides as a genetic polymer and nucleic acids as an anti-genetic polymer, is examined. The informational functions of genetic polymers and anti-genetic polymers in a complex mixture of macromolecules are characterized.     

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.