We propose a kind of novel topological quantum state of semimetals in a quasi-one-dimensional (1D) crystals BaMX3 (M = V, Nb or Ta; X = S or Se) family by using symmetry analysis and first principles calculation. We find that in BaVS3 the valence and conduction bands are degenerate in the kz = π/c plane (c is the lattice constant alongẑ axis) of the Brillouin Zone (BZ). These nodal points form a node-surface and they are protected by a nonsymmorphic crystal symmetry consisting of a two-fold rotation about theẑ axis and a half-translation along the sameẑ axis. The band degeneracy in the node-surface is lifted in BaTaS3 by including strong spin-orbit coupling (SOC) of Ta. The node-surface is reduced into 1D node-lines along the high-symmetry paths kx = 0 and kx = ± √ 3ky on the kz = π/c plane. These node-lines are robust against SOC and guaranteed by the symmetries of P 63/mmc space group. These node-line states are entirely different from previous proposals which are based on the accidental band touchings. We also propose a useful material design for realizing topological node-surface and node-line semimetals.
Many complex networks such as computer and social networks exhibit modular structures, where links between nodes are much denser within modules than between modules. It is widely believed that cellular networks are also modular, reflecting the relative independence and coherence of different functional units in a cell. While many authors have claimed that observations from the yeast protein–protein interaction (PPI) network support the above hypothesis, the observed structural modularity may be an artifact because the current PPI data include interactions inferred from protein complexes through approaches that create modules (e.g., assigning pairwise interactions among all proteins in a complex). Here we analyze the yeast PPI network including protein complexes (PIC network) and excluding complexes (PEC network). We find that both PIC and PEC networks show a significantly greater structural modularity than that of randomly rewired networks. Nonetheless, there is little evidence that the structural modules correspond to functional units, particularly in the PEC network. More disturbingly, there is no evolutionary conservation among yeast, fly, and nematode modules at either the whole-module or protein-pair level. Neither is there a correlation between the evolutionary or phylogenetic conservation of a protein and the extent of its participation in various modules. Using computer simulation, we demonstrate that a higher-than-expected modularity can arise during network growth through a simple model of gene duplication, without natural selection for modularity. Taken together, our results suggest the intriguing possibility that the structural modules in the PPI network originated as an evolutionary byproduct without biological significance.
One of the few commonly believed principles of molecular evolution is that functionally more important genes (or DNA sequences) evolve more slowly than less important ones. This principle is widely used by molecular biologists in daily practice. However, recent genomic analysis of a diverse array of organisms found only weak, negative correlations between the evolutionary rate of a gene and its functional importance, typically measured under a single benign lab condition. A frequently suggested cause of the above finding is that gene importance determined in the lab differs from that in an organism's natural environment. Here, we test this hypothesis in yeast using gene importance values experimentally determined in 418 lab conditions or computationally predicted for 10,000 nutritional conditions. In no single condition or combination of conditions did we find a much stronger negative correlation, which is explainable by our subsequent finding that always-essential (enzyme) genes do not evolve significantly more slowly than sometimes-essential or always-nonessential ones. Furthermore, we verified that functional density, approximated by the fraction of amino acid sites within protein domains, is uncorrelated with gene importance. Thus, neither the lab-nature mismatch nor a potentially biased among-gene distribution of functional density explains the observed weakness of the correlation between gene importance and evolutionary rate. We conclude that the weakness is factual, rather than artifactual. In addition to being weakened by population genetic reasons, the correlation is likely to have been further weakened by the presence of multiple nontrivial rate determinants that are independent from gene importance. These findings notwithstanding, we show that the principle of slower evolution of more important genes does have some predictive power when genes with vastly different evolutionary rates are compared, explaining why the principle can be practically useful despite the weakness of the correlation.
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