The article is devoted to analysis of emergent properties of the system of binary oppositions in the genetic code ensemble. The epochal model of the double helix of DNA by Watson and Crick showed that the multiple reproduction of genetic information on DNA strands uses the ancient principle "like begets like" based on the simple complementarity in pairs of nucleobases. Each of these pairs is built on the binary opposition "purine-pyrimidine". But the system of DNA n-plet alphabets and genetic coding is much richer in types of binary oppositions, which also have some coding meanings related to this principle. The article contains the results of the application of the author's "method of hierarchy binary stochastics" (HBS-method) to the analysis of the quasi-stochastic organization of binary sequences of hydrogen bonds in genomic single-stranded DNAs. This analysis revealed hidden probability rules related to dichotomous fractal-like probability trees. The relationship between inherited bodily dichotomies in living organisms and the discovered probability dichotomies in information sequences of genomic DNAs is discussed. The encoding properties of molecular binary oppositions in the DNA nucleotide system allows the algorithmic construction of (2n∗2n)-matrices of probabilities of n-plets in these binary sequences, which are matrix representations of 2n-dimensional hyperbolic numbers. Connections of these multidimensional numbers with some inherited physiological phenomena and deep neural networks are noted. A unified algebra-numeric certification of the DNAs of genomes and genes - based on these multidimensional numerical systems - is proposed.

Insights from data analysis of existing cases are important to prevent future outbreaks of coronavirus disease 2019 (COVID-19). Although mathematical models are expected to be useful for this purpose, the adequacy of reproducibility of these models is difficult to confirm because they are based on hypotheses. For example, using the time variation of the parameter of the basic reproduction number for the time variation of complex data on the number of infected persons is a change of expression and does not capture the substance of the problem. We previously showed that the simplest Susceptible, Infected, Recovered (SIR) model alone, without any complex models, exhibits acceptable reproducibility. By clarifying the rationale for this reproducibility, quantifiable characteristics regarding the infection spread, such as the duration of the pandemic and the mechanism of occurrence of several large waves, can be uncovered and this can contribute to countermeasures. Here, we show this method equals the chain reaction equation for infection, allowing the parameters (infection rate, population) of the mathematical models to be extracted from the data. Once a model that reproduces the actual situation is determined, much of the information becomes apparent. As an example, we present three characteristics of the spread of infection effective in controlling COVID-19: the time of onset of infection, the rapidity of the spread, and the time to acquisition of herd immunity. Acquiring this information is likely to increase the predictive accuracy of the model.

Long non-coding RNAs (lncRNA) are emerging as a new class of regulatory RNAs with remarkable potential to be utilized as therapeutic targets against many human diseases. Several genome-wide association studies (GWAS) have catalogued Single Nucleotide Polymorphisms (SNPs) present in the noncoding regions of the genome from where lncRNAs originate. In this study, we have selected 67 lncRNAs with GWAS-tagged SNPs and have also investigated their role in affecting the local secondary structures. Majority of the SNPs lead to changes in the secondary structure of lncRNAs to a different extent by altering the base pairing patterns. These structural changes in lncRNA are also manifested in form of alteration in the binding site for RNA binding proteins (RBPs) along with affecting their binding efficacies. Ultimately, these structural modifications may influence the transcriptional and post-transcriptional pathways of these RNAs, leading to the causation of diseases. Hence, it is important to understand the possible underlying mechanism of RBPs in association with GWAS-tagged SNPs in human diseases.

Organismal evolution displays complex dynamics in phase and scale which seem to trend towards increasing biocomplexity and diversity. For over a century, such amazing dynamics have been cleverly explained by the apparently straightforward mechanism of natural selection: all diversification, including speciation, results from the gradual accumulation of small beneficial or near-neutral alterations over long timescales. However, although this has been widely accepted, natural selection makes a crucial assumption that has not yet been validated. Specifically, the informational relationship between small microevolutionary alterations and large macroevolutionary changes in natural selection is unclear. To address the macroevolution-microevolution relationship, it is crucial to incorporate the concept of organic codes and particularly the "karyotype code" which defines macroevolutionary changes. This concept piece examines the karyotype from the perspective of two-phased evolution and four key components of information management. It offers insight into how the karyotype creates and preserves information that defines the scale and phase of macroevolution and, by extension, microevolution. We briefly describe the relationship between the karyotype code, the genetic code, and other organic codes in the context of generating evolutionary novelties in macroevolution and imposing constraints on them as biological routines in microevolution. Our analyses suggest that karyotype coding preserves many organic codes by providing system-level inheritance, and similar analyses are needed to classify and prioritize a large number of different organic codes based on the phases and scales of evolution. Finally, the importance of natural information self-creation is briefly discussed, leading to a call to integrate information and time into the relationship between matter and energy.

Modeling our causal intuition can contribute to understanding our behavior. In this paper, we introduce a causal induction model called proportion of assumed-to-be rare instances (pARIs) and examine its adaptive properties. We employ the two-stage theory of causal induction proposed by Hattori and Oaksford in 2007, which divides causal induction into two stages: first, observed events are sifted and likely candidates are extracted; second, each of them is verified through intervention. Here, we focus on the first stage. We conducted a meta-analysis and computer simulations in a similar way to Hattori and Oaksford (2007) but with some corrections and improvements. We added two experiments and excluded one in our reconstructed meta-analysis and augmented the simulations by correcting two problems. Our meta-analysis results show that pARIs outperforms more than 40 existing models in terms of data fit from human causal induction experiments while being simpler. Additionally, our simulation results show that pARIs outperforms DFH in terms of population covariation detection, especially under small sample sizes and rarity of events. Overall, pARIs qualifies as one of the best models for the first stage of causal induction. These findings may enable a deeper understanding of our cognitive biases. The first stage can now be considered a causal discovery stage where the topology of causal models is to be hypothesized.

To propose a mathematical model of consciousness and will, we first simulated the inverted qualia with a toy model of a neural network. As a result, we confirmed that there can be an inverted qualia on the neural network. In other words, the qualia were individual-dependent and considered difficult as an indicator of consciousness and will. To solve that difficulty, we introduce a probability space and a random variable into a set of qualia and define a human language for events. Based on this idea of human language, consciousness and will are modeled. In this proposal, future actions are randomly selected from the comparison between "recognition of events" by external observation and past episodic memory, and the actual "recognition of actions" is regarded as the occurrence of consciousness. The basic formula is also derived. This proposal is compared with other past philosophical discussions.

The Nye-Tinker-Barber model is a classical convection–diffusion model for nutrient uptake by plant roots in cylindrical coordinates and has one nonlinear left Robin boundary condition with Michaelis–Menten function of concentration. First the Michaelis–Menten function is fitted into a function of time by numerical concentration at root surface from difference scheme, and then the Laplace and numerical inverse Laplace transforms — Zakian inversion method are taken to obtain the approximate analytical solution. Compared with other solutions made by difference scheme, Stehfest inversion method and previous analytical methods, it is found that the analytical solution obtained by Laplace and Zakian inversion transforms has higher accuracy and computation efficiency. This analytical method can be extended to other nutrient uptake models with Michaelis–Menten function.

Root growth and their interactions can provide valuable information for the development of asynchronous logic systems. Here, maize root behavior due to positive gravitropism and nutritropism is evaluated as three-inputs-three-outputs logical gates. Using plant roots as the element for unconventional computing, the Boolean functions of each root tropism were constructed through arithmetic-logical operations. One gravity gate (rGG) and two nutrient gates (rNG1 and rNG2) were fabricated using additive manufacturing. The rGG platform was oriented with roots directly pulled down by gravity which computes (x, y, z) = (xz + yz, x + ȳz+yz̄, xy + yz), whereas specific output channels in rNG1 and rNG2 were fertigated with high phosphorus concentration resulting in (x, y, z) = (x + y + z, xy + xz, xyz) for rNG1 and (x, y, z) = (xyz, xȳz+xyz̄, x + y + z) for rNG2. For rGG, rNG1, and rNG2, the symbols x, y, and z pertain to "root presence" in the related channel, whereas top bar on the symbols indicates "root absence". Anatomical traits of roots were evaluated to assess possible differences in vascular tissues due to gravitropic and nutritropic responses. Overall, maize primary roots showed prominent positive gravitropism and nutritropism, and the roots that were most attracted by gravitational or nutritional stimuli showed an increase in the diameter of phloem and xylem. The logic exhibited by roots was dependent on the gravitropic and nutritropic stimuli to which they were exposed in the different logic gates. The responsiveness of maize roots to environmental stimuli such as gravity and nutrients provided valuable information to be used in computational bioelectronics.

We consider the risk of a disease caused by the presence within the genome of one deleterious mutation or two interacting mutations. For an individual, the probability of being mutated/doubly mutated can be estimated by knowing the phenotype of the other members in the family pedigree. We study the performance of this process as a function of the size, the shape of the family tree and the parameters of the model. We carry out simulations using the parameters pertaining to breast/ovarian cancer in BRCA-mutated families.

Robert Rosen defines organisms as natural systems closed to efficient causation, and proposes the (M, R) system as a model for them. He argues that the study of this formal system provides an understanding of living beings that cannot be obtained from conventional biology. However, he recognizes that answering specific questions about specific organisms requires identifying his relational concepts with specific characteristics of individual biological systems. Therefore, to apply the proposed model to biological research, it is necessary to recover the material systems through a process of realization of the formal system. The description of the cell as a realization of the (M, R) system has been notoriously problematic to date. This article posits a cell model based on the functional organization of cellular biochemical processes, and on Rosen's construction of the replication function. Then, based on the proposed model, the meaning of the replication function is discussed and the (M, R) system is analyzed as a theory of life.

In systems biology, models play a crucial role in understanding studied systems. There are many modelling approaches, among which rewriting systems provide a framework for describing systems on a mechanistic level. Describing biochemical processes often requires incorporating knowledge on an abstract level to simplify the system description or substitute the missing details. For this purpose, we present regulation mechanisms, an extension of this formalism with additional controls on the rewriting process. We introduce several regulation mechanisms and apply them to a rule-based language, a notation suitable for modelling biological phenomena. Finally, we demonstrate the usage of such regulations on several case studies from the biochemical domain.

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.

Perception of numerousness, i.e. number of items in a set, is an important cognitive ability, which is present in several animal taxa. In spite of obvious differences in neuroanatomy, insects, fishes, reptiles, birds, and mammals all possess a "number sense". Furthermore, information regarding numbers can belong to different sensory modalities: animals can estimate a number of visual items, a number of tones, or a number of their own movements. Given both the heterogeneity of stimuli and of the brains processing these stimuli, it is hard to imagine that number cognition can be traced back to the same evolutionary conserved neural pathway. However, neurons that selectively respond to the number of stimuli have been described in higher-order integration brain centres both in primates and in birds, two evolutionary distant groups. Although most probably not of the same evolutionary origin, these number neurons share remarkable similarities in their response properties. Instead of homology, this similarity might result from computational advantages of the underlying coding mechanism. This means that one might expect numerousness information to undergo similar steps of neural processing even in evolutionary distant neural pathways. Following this logic, in this review we summarize our current knowledge of how numerousness is processed in the brain from sensory input to coding of abstract information in the higher-order integration centres. We also propose a list of key open questions that might promote future research on number cognition.

In this article, we introduce the new mathematical concept of circular mixed sets of words over an arbitrary finite alphabet. These circular mixed sets may not be codes in the classical sense and hence allow a higher amount of information to be encoded. After describing their basic properties, we generalize a recent graph theoretical approach for circularity and apply it to distinguish codes from sets (i.e. non-codes). Moreover, several methods are given to construct circular mixed sets. Finally, this approach allows us to propose a new evolution model of the present genetic code that could have evolved from a dinucleotide world to a trinucleotide world via circular mixed sets of dinucleotides and trinucleotides.

The universal phenomenon of evolution consists of change after change in flow configuration in a time direction that is perceptible to the observer. This reality clashes with the doctrine of precise optima, minima, and maxima, now rigidly in place because of calculus and computational simulations of all kinds of flowing and changing configurations. With two dissimilar examples, access on an area (a human settlement) and along a line (animal locomotion), it is shown that even a 1-percent imperfection in performance is accompanied by a sizable bandwidth of freedom to hit the 'target', that is, an easily accessible design with close to perfect performance. The evolutionary designs reveal the physics behind the phenomenon of diminishing returns in the vicinity of the mathematical optimum. In evolution what works is kept.

Proteinoids, or thermal proteins, are inorganic entities formed by heating amino acids to their melting point and commencing polymerisation to form polymeric chains. Typically, their diameters range from 1μm to 10μm. Some amino acids incorporated into proteinoid chains are more hydrophobic than others, leading proteinoids to cluster together when they are present in aqueous solutions at specific concentrations, allowing them to grow into microspheres. The peculiar structure of proteinoids composed of linked amino acids endows them with unique properties, including action-potential like spiking of electrical potential. These unique properties make ensembles of proteinoid microspheres a promising substrate for designing future artificial brains and unconventional computing devices. To evaluate a potential of proteinoid microspheres for unconventional electronic devices we measure and analyse the data-transfer capacities of proteinoid microspheres. In experimental laboratory conditions we demonstrate that the transfer function of proteinoids microspheres is a nontrivial phenomenon, which might be due to the wide range of proteinoid shapes, sizes, and structures.

Inspired in a coenzyme-like behavior, an alternative mechanism to induce homochirality within a small vesicle is proposed. The system includes six different chemical species: an achiral substrate A, the enantiomeric forms L and D, a coenzyme E and two intermediate catalytic forms LE and DE. Whereas the coenzyme and the intermediate catalytic forms are trapped within the vesicle, the substrate and the two enantiomeric forms are able to diffuse selectively across the vesicle boundary. Instead of using autocatalysis, the production of new enantiomers includes two different steps, the production of intermediate catalytic species (LE, DE) and the catalytic production of new enantiomers from the substrate. Using a suitable parameterization, we found that the chiral evolution of the system is highly dependent on the total amount of coenzyme within the vesicle, regardless of whether the surrounding membrane is permeable or not. However, the existence of large flows from the outside can destabilize the homochiral state inside the vesicle. In general, homochiral states tend to arise when the amount of coenzyme is quite low, a value that can vary according to the parametrization. On the other hand, the system tends to decrease the enantiomeric excess when the coenzyme levels are high enough. In general, the appearance of homochirality is conditioned by stochastic fluctuations in coenzyme levels within the vesicle, an effect that is gradually amplified throughout the entire process of enantiomer synthesis.