How can quantum mechanics of material evolution be possible?: Symmetry and symmetry-breaking in protobiological evolution

Material self-assembly as a self-organizing process is always accompanied by symmetry-breaking in the material configuration. Self-sequencing of amino acids during their thermal polymerization has lost a certain property of permutation symmetry that was observed in the mixture of free amino acids. The evolutionary precursor state is more symmetrical about its internal material configuration and more degenerate due to the multitude of the indistinguishable individuals. The evolution proceeds in the direction along which the degeneracy in the internal states dissolves owing to the symmetry-breaking originating in material flow equilibrium of open material aggregates. Protobiological information is latent in the material system which is highly symmetrical and highly degenerate in its internal states. Evolution of matter is an endogenous process in which the earlier symmetric property is lost and less degenerate states are approached. Quantum-mechanically, the generation of protobiological information is due to the symmetry-breaking of the Hamiltonian originating in the interaction with the exterior through material flow, in contrast to the Schrödinger equation which preserves a symmetry and the associated invariants.     

Retroviral Oligonucleotide Distributions Correlate with Biased Nucleotide Compositions of Retrovirus Sequences,Suggesting a Duplicative Stepwise Molecular Evolution

A computer-assisted analysis was made of 24 complete nucleotide sequences selected from the vertebrate retroviruses to represent the ten viral groups. The conclusions of this analysis extend and strengthen the previously made hypothesis on the Moloney murine leukemia virus: The evolution of the nucleotide sequence appears to have occurred mainly through at least three overlapping levels of duplication: (1) The distributions of overrepresented (3–6)-mers are consistent with the universal rule of a trend toward TG/CT excess and with the persistence of a certain degree of symmetry between the two strands of DNA. This suggests one or several original tandemly repeated sequences and some inverted duplications. (2) The existence of two general core consensuses at the level of these (3–6)-mers supports the hypothesis of a common evolutionary origin of vertebrate retroviruses. Consensuses more specific to certain sequences are compatible with phylogenetic trees established independently. The consensuses could correspond to intermediary evolutionary stages. (3) Most of the (3–6)-mers with a significantly higher than average frequency appear to be internally repeated (with monomeric or oligomeric internal iterations) and seem to be at least partly the cause of the bias observed by other researchers at the level of retroviral nucleotide composition. They suggest a third evolutionary stage by slippage-like stepwise local duplications. Received: 3 January 1996 / Accepted: 27 March 1996     

Fine structure of the zoospore ofUlothrix belkae with emphasis on the flagellar apparatus

Summary The anterior end of the zoospore ofUlothrix belkae has been examined in detail and is compared toStigeoclonium and other filamentous green algae. The nature of the symmetry of green algal motile cells is discussed and the term, 180° rotational symmetry, is proposed to describe the type of arrangement of anterior end components seen inU. belkae, including the four basal bodies, rootlets and striated fibers. The four microtubular rootlets are cruciately arranged. A striated microtubule-associated component (SMAC) has a periodicity of 6.4 nm and extends with each 2-membered rootlet posteriorly into the cell. One 5-membered rootlet passes very near the eyespot. Phylogeny in green algal motile cells is discussed.     

On the precision and accuracy achieved by Escherichia coli cells at fission about their middle

Length and width of each of the prospective siblings of constricted Escherichia coli cells from different strains and culture conditions were measured from electron micrographs. The data were statistically analyzed to investigate how equally the length and volume of one cell was divided into two. The analysis showed that, for all cultures, bipartition is unbiased or very nearly so, i.e. sibling cells were on the average equally long and large. The precision of bipartition attained by the cells was usually high; it was related to the average cell shape (length/width): slender E. coli cells divided into two less precisely than squat cells. Absolute size, growth rate and strain specificity affected the precision of bipartition only indirectly, i.e. in as much as they influenced cell shape.     

Unimodality,symmetry and the step-state hypothesis of electrophoretic variation in natural populations

Summary The population frequency distributions of electromorphs of polymorphic loci, when ordered by electrophoretic mobility, tend strongly and significantly to be both unimodal and symmetrical. Such distributions are predicted by all step-change models and their generality in published data can be construed as supportive of the step-change hypothesis. On the other hand, unimodality and symmetry might also be due to artifactual unit perception biases that affect the interpretation and reporting of electro-phoretic data. In any case, it appears that perceived electromorphs are highly heterogeneous.This work was supported by PHS Grant RO 1 GM 21283-O1 GEN.     

Models of central pattern generators for quadruped locomotion I. Primary gaits

In this paper we continue the analysis of a network of symmetrically coupled cells modeling central pattern generators for quadruped locomotion proposed by Golubitsky, Stewart, Buono, and Collins. By a cell we mean a system of ordinary differential equations and by a coupled cell system we mean a network of identical cells with coupling terms. We have three main results in this paper. First, we show that the proposed network is the simplest one modeling the common quadruped gaits of walk, trot, and pace. In doing so we prove a general theorem classifying spatio-temporal symmetries of periodic solutions to equivariant systems of differential equations. We also specialize this theorem to coupled cell systems. Second, this paper focuses on primary gaits; that is, gaits that are modeled by output signals from the central pattern generator where each cell emits the same waveform along with exact phase shifts between cells. Our previous work showed that the network is capable of producing six primary gaits. Here, we show that under mild assumptions on the cells and the coupling of the network, primary gaits can be produced from Hopf bifurcation by varying only coupling strengths of the network. Third, we discuss the stability of primary gaits and exhibit these solutions by performing numerical simulations using the dimensionless Morris-Lecar equations for the cell dynamics.     

Symmetry breakage in the vertebrate embryo: When does it happen and how does it work?

Asymmetric development of the vertebrate embryo has fascinated embryologists for over a century. Much has been learned since the asymmetric Nodal signaling cascade in the left lateral plate mesoderm was detected, and began to be unraveled over the past decade or two. When and how symmetry is initially broken, however, has remained a matter of debate. Two essentially mutually exclusive models prevail. Cilia-driven leftward flow of extracellular fluids occurs in mammalian, fish and amphibian embryos. A great deal of experimental evidence indicates that this flow is indeed required for symmetry breaking. An alternative model has argued, however, that flow simply acts as an amplification step for early asymmetric cues generated by ion flux during the first cleavage divisions. In this review we critically evaluate the experimental basis of both models. Although a number of open questions persist, the available evidence is best compatible with flow-based symmetry breakage as the archetypical mode of symmetry breakage.     

The insect centriole: A land of discovery

Centrioles are involved in the formation of cilia and flagella and in the organization of the centrosome, the main microtubule-organizing center of the cell. Since structural and functional centriole aberrations can contribute to several human diseases, these organelles have recently focused the attention of cell biologists. Here, we review data on the insect centrioles, reporting non-canonical aspects of their behaviour, function and architecture. These findings that represent obvious exceptions to the established rule might contribute to advance our understanding in the formation and the function of centrioles.     

From larval bodies to adult body plans: patterning the development of the presumptive adult ectoderm in the sea urchin larva

Echinoderms are unique among bilaterians for their derived, nonbilateral adult body plan. Their radial symmetry emerges from the bilateral larval body plan by the establishment of a new axis, the adult oral–aboral axis, involving local mesoderm–ectoderm interactions. We examine the mechanisms underlying this transition in the direct-developing sea urchin Heliocidaris erythrogramma. Adult ectoderm arises from vestibular ectoderm in the left vegetal quadrant. Inductive signals from the left coelom are required for adult ectodermal development but not for initial vestibule formation. We surgically removed gastrula archenteron, making whole-ectoderm explants, left-, right-, and animal-half ectoderm explants, and recombinants of these explants with left coelom. Vestibule formation was analyzed morphologically and with radioactive in situ hybridization with HeET-1, an ectodermal marker. Whole ectodermal explants in the absence of coelom developed vestibules on the left side or ventrally but not on the right side, indicating that left–right polarity is ectoderm autonomous by the gastrula stage. However, right-half ectodermal explants robustly formed vestibules that went on to form adult structures when recombined with the left coelom, indicating that the right side retains vestibule-forming potential that is normally suppressed by signals from the left-side ectoderm. Animal-half explants formed vestibules only about half the time, demonstrating that animal–vegetal axis determination occurs earlier. However, when combined with the left coelom, animal-half ectoderm always formed a vestibule, indicating that the left coelom can induce vestibule formation. This suggests that although coelomic signals are not required for vestibule formation, they may play a role in coordinating the coelom–vestibule interaction that establishes the adult oral–aboral axis.