I analysed the similarity gradient observed in protein families - of phylogenetically deep fundamental traits - of bacteria and archaea, ranging from cases such as the core of the DNA replication apparatus where there is no sequence similarity between the proteins involved, to cases in which, as in the translation initiation factors, only some proteins involved would be homologs, to cases such as for aminoacyl-tRNA synthetases in which most of the proteins involved would be homologs. This pattern of similarity between bacteria and archaea would seem to be a very clear indication of a transitional evolutionary stage that preceded both the Last Bacterial Common Ancestor and the Last Archaeal Common Ancestor, i.e. progenotic stages. Indeed, this similarity pattern would seem to exemplify an ongoing transition as all the evolutionary phases would be represented in it. Instead, in the cellular stage it is expected that these evolutionary phases should have already been overcome, i.e. completed, and therefore no longer detectable. In fact, if we had really been in the presence of the prokaryotic stage then we should not have observed this similarity pattern in proteins involved in defining the ancestral characters of bacteria and archaea, as the completion of the different cellular structures should have required a very low number of proteins to be late evolved in lineages leading to bacteria and archaea. Indeed, the already reached state of the Prokaryote would have determined complete cellular structures therefore a total absence of proteins to evolve independently in the two main phyletic lineages and able to complete the evolution of a particular character already evidently in a definitive state, which, on the other hand, does not appear to have been the case. All this would have prevented the formation of this pattern of similarity which instead would appear to be real. In conclusion, the existence of this pattern of similarity observed in the families of homologous proteins of bacteria and archaea would imply the absence of the evolutionary stage of the Prokaryote and consequently a progenotic status to be assigned to the LUCA. Indeed, the LUCA stage would have been a stage of evolutionary transition because it is belatedly marked by the presence of all the different evolutionary phases, evidently more easily interpretable within the definition of progenote than that of genote precisely because they are inherent in an evolutionary transition and not to an evolution that has already been achieved. Finally, I discuss the importance of these arguments for the polyphyletic origin of proteins.

Nature possesses inherent mechanisms for error detection and correction during the translation of genetic information, as demonstrated by the discovery of a self-complementary circular C3-code called X0 in various organisms such as bacteria, eukaryotes, plasmids, and viruses (Arquès and Michel, 1996; Michel, 2015, 2017). Since then, extensive research has focused on circular codes, which are believed to be remnants of ancient comma-free codes. These codes can be regarded as an additional genetic code specifically optimized for detecting and preserving the proper reading frame in protein-coding sequences. A study by Fimmel et al. in 2014 identified that a total of 216 maximal self-complementary C3-codes can be grouped into 27 equivalence classes with eight codes in each class. In this work, we study how the 27 equivalence classes are related to each other. While the codes in each equivalence class obtained by Fimmel et al. in 2014 are permutations of each other, i.e. one code can be obtained from the other by applying a permutation of the bases, it has not been clear how the equvalence classes are connected. We show that there is an ordering of the equivalence classes such that one gets from one class to the next one by substituting only one pair of codon/anticodon in the corresponding codes, i.e. the corresponding codes have a maximal intersection of 18 codons. To perform this analysis, we define two graphs, G216 and G27, whose vertices are, respectively, all 216 maximal self-complementary C3-codes and 27 equivalence classes. Several properties of the graphs are obtained. Most surprisingly, it turns out that G27 contains Hamiltonian paths of length 27. This fact ultimately leads to a representation of the set of all 216 maximal self-complementary C3-codes as a kind of spider web. Finally, we define dinucleotide cuts of such codes by projecting each codon to its first two bases and show that the paths of lengths 27 in G216 can even be chosen so that all the codes contain a special subset of dinucleotides defined by Rumer's roots. These observations raise a lot of new questions about the biological function of such structures.

Virtually every biological system is governed by complex relations among its components. Identifying such relations requires a rigorous or heuristics-based search for patterns among variables/features of a system. Various algorithms have been developed to identify two-dimensional (involving two variables) patterns employing correlation, covariation, mutual information, etc. It seems obvious, however, that comprehensive descriptions of complex biological systems need also to include more complicated multivariable relations, which can only be described using patterns that simultaneously embrace 3, 4, and more variables. The goal of this manuscript is to (a) introduce a novel type of associations (multivariable Boolean patterns) that can be manifested between features of complex systems but cannot be identified (described) by traditional pair-vise metrics; (b) propose patterns classification method, and (c) provide a novel definition of the pattern's strength (pattern's score) able to accommodate heterogeneous multi-omics data. To demonstrate the presence of such patterns, we performed a search for all possible 2-, 3-, and 4-dimensional patterns in historical data from the Human Microbiome Project (15 body sites) and collection of H. pylori genomes associated with gastric ulcers, gastritis, and duodenal ulcers. In all datasets under consideration, we were able to identify hundreds of statistically significant multivariable patterns. These results suggest that such patterns can be common in microbial genomics/microbiomics systems.

In Microbiology it is often assumed that growth rate is maximal. This may be taken to suggest that the dependence of the growth rate on every enzyme activity is at the top of an inverse-parabolic function, i.e. that all flux control coefficients should equal zero. This might seem to imply that the sum of these flux control coefficients equals zero. According to the summation law of Metabolic Control Analysis (MCA) the sum of flux control coefficients should equal 1 however. And in Flux Balance Analysis (FBA) catabolism is often limited by a hard bound, causing catabolism to fully control the fluxes, again in apparent contrast with a flux control coefficient of zero. Here we resolve these paradoxes (apparent contradictions) in an analysis that uses the 'Edinburgh pathway', the 'Amsterdam pathway', as well as a generic metabolic network providing the building blocks or Gibbs energy for microbial growth. We review and show that (i) optimization depends on so-called enzyme control coefficients rather than the 'catalytic control coefficients' of MCA's summation law, (ii) when optimization occurs at fixed total protein, the former differ from the latter to the extent that they may all become equal to zero in the optimum state, (iii) in more realistic scenarios of optimization where catalytically inert biomass is compensating or maintenance metabolism is taken into consideration, the optimum enzyme concentrations should not be expected to equal those that maximize the specific growth rate, (iv) optimization may be in terms of yield rather than specific growth rate, which resolves the paradox because the sum of catalytic control coefficients on yield equals 0, (v) FBA effectively maximizes growth yield, and for yield the summation law states 0 rather than 1, thereby removing the paradox, (vi) furthermore, FBA then comes more often to a 'hard optimum' defined by a maximum catabolic flux and a catabolic-enzyme control coefficient of 1. The trade-off between maintenance metabolism and growth is highlighted as worthy of further analysis.