A neutral evolution test derived from a theoretical amino acid substitution model.

A neutral evolution model that explicitly considers codons, amino acids, and the degeneracy of the genetic code is developed. The model is built from nucleotides up to amino acids, and it represents a refinement of the neutral theory of molecular evolution. The model is based on a stochastic process that leads to a stationary probability distribution of amino acids. The latter is used as a neutral test of evolution. We provide some examples for assessing the neutrality test for a small set of protein sequences. The Jukes-Cantor model is generalized to deal with amino acids and it is compared with our neutral model, along with the empirical BLOSUM62 substitution model. The neutral test provides a baseline to which the evolution of any protein can be analyzed, and it clearly helps in discerning putative amino acids with unexpected frequencies that might be under positive or negative selection. Our model and neutral test are as universal as the standard genetic code.

Identity Elements of tRNA as Derived from Information Analysis.

The decipherment of the tRNA's operational code, known as the identity problem, requires the location of the sites in the tRNA structure that are involved in their correct recognition by the corresponding aminoacyl-tRNA synthetase. In this work, we determine the identity elements of each tRNA isoacceptor by means of the variation of information measure from information theory. We show that all isoacceptors exhibit sites associated with some bases of the anticodon. These sites form clusters that are scattered along the tRNA structure. The clusters determine the identity elements of each tRNA. We derive a catalogue of clustered sites for each tRNA that expands previously reported elements.

Phenotypic Graphs and Evolution Unfold the Standard Genetic Code as the Optimal.

In this work, we explicitly consider the evolution of the Standard Genetic Code (SGC) by assuming two evolutionary stages, to wit, the primeval RNY code and two intermediate codes in between. We used network theory and graph theory to measure the connectivity of each phenotypic graph. The connectivity values are compared to the values of the codes under different randomization scenarios. An error-correcting optimal code is one in which the algebraic connectivity is minimized. We show that the SGC is optimal in regard to its robustness and error-tolerance when compared to all random codes under different assumptions.

Symmetrical and Thermodynamic Properties of Phenotypic Graphs of Amino Acids Encoded by the Primeval RNY Code.

The 12 different types of graphs of the 8 amino acids encoded by the presumably primeval RNY code are derived. The symmetry groups of these graphs are analyzed and coincide with the corresponding values of polar requirement for each amino acid. The symmetry groups at the codon level are partially carried over as a group or subgroup at the amino acid level. Measures of centrality of the 12 graphs indicate that all amino acids were equally relevant irrespective of its chronological order of its appearance. The elimination of any amino acid would be strongly selected against and therefore the genetic code at this stage was already frozen.

Symmetrical distributions of aminoacyl-tRNA synthetases during the evolution of the genetic code.

In this work, we formulate the following question: How the distribution of aminoacyl-tRNA synthetases (aaRSs) went from an ancestral bidirectional gene (mirror symmetry) to the symmetrical distribution of aaRSs in a six-dimensional hypercube of the Standard Genetic Code (SGC)? We assume a primeval RNY code, two Extended Genetic RNA codes type 1 and 2, and the SGC. We outline the types of symmetries of the distribution of aaRSs in each code. The symmetry groups of aaRSs in each code are described, until the symmetries of the SGC display a mirror symmetry. Considering both Extended RNA codes the 20 aaRSs were already present before the Last Universal Ancestor. These findings reveal intricacies in the diversification of aaRSs accompanied by the evolution of the genetic code.

The Spike Protein of SARS-CoV-2 Is Adapting Because of Selective Pressures.

The global scale of the COVID-19 pandemic has demonstrated the evolution of SARS-CoV-2 and the clues of adaptation. After two years and two months since the declaration of the pandemic, several variants have emerged and become fixed in the human population thanks to extrinsic selective pressures but also to the inherent mutational capacity of the virus. Here, we applied a neutral substitution evolution test to the spike (S) protein of Omicron's protein and compared it to the others' variant of concern (VOC) neutral evolution. We carried out comparisons among the interactions between the S proteins from the VOCs (Alpha, Beta, Gamma, Delta and Omicron) and the receptor ACE2. The shared amino acids among all the ACE2 binding S proteins remain constant, indicating that these amino acids are essential for the accurate binding to the receptor. The complexes of the RBD for every variant with the receptor were used to identify the amino acids involved in the protein-protein interaction (PPI). The RBD of Omicron establishes 82 contacts, compared to the 74 of the Wuhan original viral protein. Hence, the mean number of contacts per residue is higher, making the contact thermodynamically more stable. The RBDs of the VOCs are similar in sequence and structure; however, Omicron's RBD presents the largest deviation from the structure by 1.11 Å RMSD, caused by a set of mutations near the glycosylation N343. The chemical properties and structure near the glycosylation N343 of the Omicron S protein are different from the original protein, which provoke reduced recognition by the neutralizing antibodies. Our results hint that selective pressures are induced by mass vaccination throughout the world and by the persistence of recurrent infections in immunosuppressed individuals, who did not eliminate the infection and ended up facilitating the selection of viruses whose characteristics are different from the previous VOCs, less pathogenic but with higher transmissibility.

Novel gene signatures for stage classification of the squamous cell carcinoma of the lung.

The squamous cell carcinoma of the lung (SCLC) is one of the most common types of lung cancer. As GLOBOCAN reported in 2018, lung cancer was the first cause of death and new cases by cancer worldwide. Typically, diagnosis is made in the later stages of the disease with few treatment options available. The goal of this work was to find some key components underlying each stage of the disease, to help in the classification of tumor samples, and to increase the available options for experimental assays and molecular targets that could be used in treatment development. We employed two approaches. The first was based in the classic method of differential gene expression analysis, network analysis, and a novel concept known as network gatekeepers. The second approach was using machine learning algorithms. From our combined approach, we identified two sets of genes that could function as a signature to identify each stage of the cancer pathology. We also arrived at a network of 55 nodes, which according to their biological functions, they can be regarded as drivers in this cancer. Although biological experiments are necessary for their validation, we proposed that all these genes could be used for cancer development treatments.

Neutral evolution test of the spike protein of SARS-CoV-2 and its implications in the binding to ACE2.

As the SARS-CoV-2 has spread and the pandemic has dragged on, the virus continued to evolve rapidly resulting in the emergence of new highly transmissible variants that can be of public health concern. The evolutionary mechanisms that drove this rapid diversity are not well understood but neutral evolution should open the first insight. The neutral theory of evolution states that most mutations in the nucleic acid sequences are random and they can be fixed or disappear by purifying selection. Herein, we performed a neutrality test to better understand the selective pressures exerted over SARS-CoV-2 spike protein from homologue proteins of Betacoronavirus, as well as to the spikes from human clinical isolates of the virus. Specifically, Tyr and Asn have higher occurrence rates on the Receptor Binding Domain (RBD) and in the overall sequence of spike proteins of Betacoronavirus, whereas His and Arg have lower occurrence rates. The in vivo evolutionary phenomenon of SARS-CoV-2 shows that Glu, Lys, Phe, and Val have the highest probability of occurrence in the emergent viral particles. Amino acids that have higher occurrence than the expected by the neutral control, are favorable and are fixed in the sequence while the ones that have lower occurrence than expected, influence the stability and/or functionality of the protein. Our results show that most unique mutations either for SARS-CoV-2 or its variants of health concern are under selective pressures, which could be related either to the evasion of the immune system, increasing the virus' fitness or altering protein - protein interactions with host proteins. We explored the consequences of those selected mutations in the structure and protein - protein interaction with the receptor. Altogether all these forces have shaped the spike protein and the continually evolving variants.

Information theory unveils the evolution of tRNA identity elements in the three domains of life.

We determined the identity elements of each tRNA isoacceptor for the three domains of life: Eubacteria, Archaea, and Eukarya. Our analyses encompass the most updated and curated available databases using an information theory approach. We obtained a collection of identity clusters for each of the isoacceptors of the 20 canonical amino acids for the three major domains of life. The identity clusters for all isoacceptors are compared within and among the three domains to determine their pattern of differentiation and to shed light on the evolution of the identity elements.

Anticipation of ventricular tachyarrhythmias by a novel mathematical method: Further insights towards an early warning system in implantable cardioverter defibrillators.

Implantable cardioverter defibrillators (ICD) are the most effective therapy to terminate malignant ventricular arrhythmias (VA) and therefore to prevent sudden cardiac death. Until today, there is no way to predict the onset of such VA. Our aim was to develop a mathematical model that could predict VA in a timely fashion. We analyzed the time series of R-R intervals from 3 groups. Two groups from the Spontaneous Ventricular Tachyarrhythmia Database (v 1.0) were analyzed from a set of 81 pairs of R-R interval time series records from patients, each pair containing one record before the VT episode (Dataset 1A) and one control record which was obtained during the follow up visit (Dataset 1B). A third data set was composed of the R-R interval time series of 54 subjects without a significant arrhythmia heart disease (Dataset 2). We developed a new method to transform a time series into a network for its analysis, the ε-regular graphs. This novel approach transforms a time series into a network which is sensitive to the quantitative properties of the time series, it has a single parameter (ε) to be adjusted, and it can trace long-range correlations. This procedure allows to use graph theory to extract the dynamics of any time series. The average of the difference between the VT and the control record graph degree of each patient, at each time window, reached a global minimum value of -2.12 followed by a drastic increase of the average graph until reaching a local maximum of 5.59. The global minimum and the following local maxima occur at the windows 276 and 393, respectively. This change in the connectivity of the graphs distinguishes two distinct dynamics occurring during the VA, while the states in between the 276 and 393, determine a transitional state. We propose this change in the dynamic of the R-R intervals as a measurable and detectable "early warning" of the VT event, occurring an average of 514.625 seconds (8:30 minutes) before the onset of the VT episode. It is feasible to detect retrospectively early warnings of the VA episode using their corresponding ε-regular graphs, with an average of 8:30 minutes before the ICD terminates the VA event.

The Ancient History of Peptidyl Transferase Center Formation as Told by Conservation and Information Analyses.

The peptidyl transferase center (PTC) is the catalytic center of the ribosome and forms part of the 23S ribosomal RNA. The PTC has been recognized as the earliest ribosomal part and its origins embodied the First Universal Common Ancestor (FUCA). The PTC is frequently assumed to be highly conserved along all living beings. In this work, we posed the following questions: (i) How many 100% conserved bases can be found in the PTC? (ii) Is it possible to identify clusters of informationally linked nucleotides along its sequence? (iii) Can we propose how the PTC was formed? (iv) How does sequence conservation reflect on the secondary and tertiary structures of the PTC? Aiming to answer these questions, all available complete sequences of 23S ribosomal RNA from Bacteria and Archaea deposited on GenBank database were downloaded. Using a sequence bait of 179 bp from the PTC of Thermus termophilus, we performed an optimum pairwise alignment to retrieve the PTC region from 1424 filtered 23S rRNA sequences. These PTC sequences were multiply aligned, and the conserved regions were assigned and observed along the primary, secondary, and tertiary structures. The PTC structure was observed to be more highly conserved close to the adenine located at the catalytical site. Clusters of interrelated, co-evolving nucleotides reinforce previous assumptions that the PTC was formed by the concatenation of proto-tRNAs and important residues responsible for its assembly were identified. The observed sequence variation does not seem to significantly affect the 3D structure of the PTC ribozyme.

On the Uniqueness of the Standard Genetic Code.

In this work, we determine the biological and mathematical properties that are sufficient and necessary to uniquely determine both the primeval RNY (purine-any base-pyrimidine) code and the standard genetic code (SGC). These properties are: the evolution of the SGC from the RNY code; the degeneracy of both codes, and the non-degeneracy of the assignments of aminoacyl-tRNA synthetases (aaRSs) to amino acids; the wobbling property; the consideration that glycine was the first amino acid; the topological and symmetrical properties of both codes.

A unified model of the standard genetic code.

The Rodin-Ohno (RO) and the Delarue models divide the table of the genetic code into two classes of aminoacyl-tRNA synthetases (aaRSs I and II) with recognition from the minor or major groove sides of the tRNA acceptor stem, respectively. These models are asymmetric but they are biologically meaningful. On the other hand, the standard genetic code (SGC) can be derived from the primeval RNY code (R stands for purines, Y for pyrimidines and N any of them). In this work, the RO-model is derived by means of group actions, namely, symmetries represented by automorphisms, assuming that the SGC originated from a primeval RNY code. It turns out that the RO-model is symmetric in a six-dimensional (6D) hypercube. Conversely, using the same automorphisms, we show that the RO-model can lead to the SGC. In addition, the asymmetric Delarue model becomes symmetric by means of quotient group operations. We formulate isometric functions that convert the class aaRS I into the class aaRS II and vice versa. We show that the four polar requirement categories display a symmetrical arrangement in our 6D hypercube. Altogether these results cannot be attained, neither in two nor in three dimensions. We discuss the present unified 6D algebraic model, which is compatible with both the SGC (based upon the primeval RNY code) and the RO-model.

Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids.

Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state.