Information, Coding, and Biological Function: The Dynamics of Life.

In the mid-20th century, two new scientific disciplines emerged forcefully: molecular biology and information-communication theory. At the beginning, cross-fertilization was so deep that the term genetic code was universally accepted for describing the meaning of triplets of mRNA (codons) as amino acids. However, today, such synergy has not taken advantage of the vertiginous advances in the two disciplines and presents more challenges than answers. These challenges not only are of great theoretical relevance but also represent unavoidable milestones for next-generation biology: from personalized genetic therapy and diagnosis to Artificial Life to the production of biologically active proteins. Moreover, the matter is intimately connected to a paradigm shift needed in theoretical biology, pioneered a long time ago, that requires combined contributions from disciplines well beyond the biological realm. The use of information as a conceptual metaphor needs to be turned into quantitative and predictive models that can be tested empirically and integrated in a unified view. Successfully achieving these tasks requires a wide multidisciplinary approach, including Artificial Life researchers, to address such an endeavour.

A role for circular code properties in translation.

Circular codes represent a form of coding allowing detection/correction of frame-shift errors. Building on recent theoretical advances on circular codes, we provide evidence that protein coding sequences exhibit in-frame circular code marks, that are absent in introns and are intimately linked to the keto-amino transformation of codon bases. These properties strongly correlate with translation speed, codon influence and protein synthesis levels. Strikingly, circular code marks are absent at the beginning of coding sequences, but stably occur 40 codons after the initiator codon, hinting at the translation elongation process. Finally, we use the lens of circular codes to show that codon influence on translation correlates with the strong-weak dichotomy of the first two bases of the codon. The results can lead to defining new universal tools for sequence indicators and sequence optimization for bioinformatics and biotechnological applications, and can shed light on the molecular mechanisms behind the decoding process.

Chaos and periodicities in a climatic time series of the Iberian Margin.

We analyze the time series of the temperature of the sedimentary core MD01-2443 originating from the Iberian Margin with a duration of 420 kyr. The series has been tested for unit-root and a long term trend is estimated. We identify four significant periodicities together with a low climatic activity every 100 kyr, and these were associated with internal and external forcings. Also, we identify a high-frequency fast component that acts on top of a nonlinear, irreversible slow-changing dynamics. We find the presence of chaos in the climate of the Iberian Margin by means of a neural network asymptotic test on the largest Lyapunov exponent. The analysis suggests that the chaotic dynamics is associated with the fast high-frequency component. We also carry out a statistical analysis of the dimensionality of the attractor. Our results confirm the possibility that periodic behavior and chaos may coexist on different time scales. This could lead to different degrees of predictability in the climate system according to the characteristic time scales and/or phase-space locations.

Chemobrionics: From Self-Assembled Material Architectures to the Origin of Life.

Self-organizing precipitation processes, such as chemical gardens forming biomimetic micro- and nanotubular forms, have the potential to show us new fundamental science to explore, quantify, and understand nonequilibrium physicochemical systems, and shed light on the conditions for life's emergence. The physics and chemistry of these phenomena, due to the assembly of material architectures under a flux of ions, and their exploitation in applications, have recently been termed chemobrionics. Advances in understanding in this area require a combination of expertise in physics, chemistry, mathematical modeling, biology, and nanoengineering, as well as in complex systems and nonlinear and materials sciences, giving rise to this new synergistic discipline of chemobrionics.

Rumer's transformation: A symmetry puzzle standing for half a century.

In 1966, only a few months after the complete elucidation of the standard nuclear genetic code (Kay, 2000), the Russian theoretical physicist Yury Borisovich Rumer uncovered the existence of a particular symmetry (Rumer, 1966): when the keto-amino transformation (also known as Rumer's transformation) is applied to the bases of a codon then the degeneracy of the transformed codon was changed. In particular, if the amino acid associated to the starting codon has degeneracy 4, then the amino acid associated to the transformed codon has degeneracy 1, 2 or 3 (and vice versa). After half a century from this discovery and despite the universality of Rumer's symmetry, little is known about its origin and its possible biological significance. In this article we show that Rumer's symmetry could have originated in an ancestral version of the genetic code, i.e., the pre-early code, and is a natural consequence of the stereo-chemical symmetries of the ancestral synthesis machinery working around such code (Gonzalez et al., 2019). Moreover, the conservation of Rumer's symmetry through evolutionary periods suggests a connection with key biological features. In this respect, intriguing possibilities include those of error detection/correction, control over the synthesis of proteins, and frame maintenance. To a certain extent, such ideas have been explored in the framework of a mathematical model of the genetic code (the non-power model of the genetic code (Gonzalez, 2004; Gonzalez, 2008; Gonzalez et al., 2016), whose definition of dichotomic classes naturally includes Rumer's symmetry (Gonzalez, 2008; Gonzalez et al., 2006, 2008) and the theory of circular codes (Arquès and Michel, 1996; Gonzalez et al., 2011; Fimmel et al., 2015).

DNA as information: at the crossroads between biology, mathematics, physics and chemistry.

On the one hand, biology, chemistry and also physics tell us how the process of translating the genetic information into life could possibly work, but we are still very far from a complete understanding of this process. On the other hand, mathematics and statistics give us methods to describe such natural systems-or parts of them-within a theoretical framework. Also, they provide us with hints and predictions that can be tested at the experimental level. Furthermore, there are peculiar aspects of the management of genetic information that are intimately related to information theory and communication theory. This theme issue is aimed at fostering the discussion on the problem of genetic coding and information through the presentation of different innovative points of view. The aim of the editors is to stimulate discussions and scientific exchange that will lead to new research on why and how life can exist from the point of view of the coding and decoding of genetic information. The present introduction represents the point of view of the editors on the main aspects that could be the subject of future scientific debate.

The non-power model of the genetic code: a paradigm for interpreting genomic information.

In this article, we present a mathematical framework based on redundant (non-power) representations of integer numbers as a paradigm for the interpretation of genomic information. The core of the approach relies on modelling the degeneracy of the genetic code. The model allows one to explain many features and symmetries of the genetic code and to uncover hidden symmetries. Also, it provides us with new tools for the analysis of genomic sequences. We review briefly three main areas: (i) the Euplotid nuclear code, (ii) the vertebrate mitochondrial code, and (iii) the main coding/decoding strategies used in the three domains of life. In every case, we show how the non-power model is a natural unified framework for describing degeneracy and deriving sound biological hypotheses on protein coding. The approach is rooted on number theory and group theory; nevertheless, we have kept the technical level to a minimum by focusing on key concepts and on the biological implications.

Dinucleotide circular codes and bijective transformations.

The presence of circular codes in mRNA coding sequences is postulated to be involved in informational mechanisms aimed at detecting and maintaining the normal reading frame during protein synthesis. Most of the recent research is focused on trinucleotide circular codes. However, also dinucleotide circular codes are important since dinucleotides are ubiquitous in genomes and associated to important biological functions. In this work we adopt the group theoretic approach used for trinucleotide codes in Fimmel et al. (2015) to study dinucleotide circular codes and highlight their symmetry properties. Moreover, we characterize such codes in terms of n-circularity and provide a graph representation that allows to visualize them geometrically. The results establish a theoretical framework for the study of the biological implications of dinucleotide circular codes in genomic sequences.

Circular codes, symmetries and transformations.

Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes.

Genome characterization through dichotomic classes: an analysis of the whole chromosome 1 of A. thaliana.

In this article we show how dichotomic classes, binary variables naturally derived from a new mathematical model of the genetic code, can be used in order to characterize different parts of the genome. In particular, we analyze and compare different parts of whole chromosome 1 of Arabidopsis thaliana: genes, exons, introns, coding sequences (CDS), intergenes, untranslated regions (UTR) and regulatory sequences. In order to accomplish the task we encode each sequence in the 3 possible reading frames according to the definitions of the dichotomic classes (parity, Rumer and hidden). Then, we perform a statistical analysis on the binary sequences. Interestingly, the results show that coding and non-coding sequences have different patterns and proportions of dichotomic classes. This suggests that the frame is important only for coding sequences and that dichotomic classes can be useful to recognize them. Moreover, such patterns seem to be more enhanced in CDS than in exons. Also, we derive an independence test in order to assess whether the percentages observed could be considered as an expression of independent random processes. The results confirm that only genes, exons and CDS seem to possess a dependence structure that distinguishes them from i.i.d sequences. Such informational content is independent from the global proportion of nucleotides of a sequence. The present work confirms that the recent mathematical model of the genetic code is a new paradigm for understanding the management and the organization of genetic information and is an innovative tool for investigating informational aspects of error detection/correction mechanisms acting at the level of DNA replication.

DNA, dichotomic classes and frame synchronization: a quasi-crystal framework.

In this article, we show how a new mathematical model of the genetic code can be exploited for investigating the almost periodic properties of DNA and mRNA protein-coding sequences. We present the main mathematical features of the model and highlight its connections with both number theory and group theory. The group theoretic framework presents interesting analogies with the theory of crystals. Moreover, we exploit the information provided by dichotomic classes, binary variables naturally derived from the mathematical model, in order to build statistical classifiers for retrieving and predicting the normal reading frame used by the ribosome in protein synthesis. The results show that coding sequences possess a local informational structure that can be related to frame synchronization processes. The information for retrieving the normal reading frame, which implies the existence of short-range correlations and almost periodic structures related to the organization of codons, offers an interesting analogy with the properties of quasi-crystals. From a theoretical point of view, our results might contribute to clarifying the relation between biological information and shape in nucleic acids and proteins. Also, from the point of view of applications, we present new promising tools for designing efficient algorithms for frame synchronization, which plays a crucial role in faithful synthesis of proteins.

Strong short-range correlations and dichotomic codon classes in coding DNA sequences.

The study of correlation structures in DNA sequences is of great interest because it allows us to obtain structural and functional information about underlying genetic mechanisms. In this paper we present a study of the correlation structure of protein coding sequences of DNA based on a recently developed mathematical representation of the genetic code. A fundamental consequence of such representation is that codons can be assigned a parity class (odd-even). Such parity can be obtained by means of a nonlinear algorithm acting on the chemical character of the codon bases. In the same setting the Rumer's class can be naturally described and a new dichotomic class, the hidden class, can be defined. Moreover, we show that the set of DNA's base transformations associated to the three dichotomic classes can be put in a compact group-theoretic framework. We use the dichotomic classes as a coding scheme for DNA sequences and study the mutual dependence between such classes. The same analysis is carried out also on the chemical dichotomies of DNA bases. In both cases, the statistical analysis is performed by using an entropy-based dependence metric possessing many desirable properties. We obtain meaningful tests for mutual dependence by using suitable resampling techniques. We find strong short-range correlations between certain combinations of dichotomic codon classes. These results support our previous hypothesis that codon classes might play an active role in the organization of genetic information.

Chaotic phenomena of charged particles in crystal lattices.

In this article, we have applied the methods of chaos theory to channeling phenomena of positive charged particles in crystal lattices. In particular, we studied the transition between two ordered types of motion; i.e., motion parallel to a crystal axis (axial channeling) and to a crystal plane (planar channeling), respectively. The transition between these two regimes turns out to occur through an angular range in which the particle motion is highly disordered and the region of phase space spanned by the particle is much larger than the one swept in the two ordered motions. We have evaluated the maximum Lyapunov exponent with the method put forward by Rosenstein et al. [Physica D 65, 117 (1993)] and by Kantz [Phys. Lett. A 185, 77 (1994)]. Moreover, we estimated the correlation dimension by using the Grassberger-Procaccia method. We found that at the transition the system exhibits a very complex behavior showing an exponential divergence of the trajectories corresponding to a positive Lyapunov exponent and a noninteger value of the correlation dimension. These results turn out to be linked to a physical interpretation. The Lyapunov exponents are in agreement with the model by Akhiezer et al. [Phys. Rep. 203, 289 (1991)], based on the equivalence between the ion motion along the crystal plane described as a "string of strings" and the "kicked" rotator. The nonintegral value of the correlation dimension can be explained by the nonconservation of transverse energy at the transition.

Accuracy rates of US-guided vacuum-assisted breast biopsy.

A prospective study designed to measure the accuracy of mammography (MRx), ultrasound (US), fine-needle aspiration cytology (FNAC) and one of the most recently introduced techniques, vacuum biopsy (VB), in the diagnosis of breast cancer is reported. A sample of 146 breast lesions on 135 patients were examined. The design of the study made it possible to compare MRx, US, FNAC and VB directly, because it excluded several confounding variables. Statistical indicators--sensitivity, specificity, predictive values (PPV and NPV), false-negative and false-positive rates (FN and FP), suspicious plus indeterminate rate and likelihood ratios (LR)--were calculated. The NPV of MRx and US were remarkably high (92.4% and 97.9%, respectively), confirming previous reports. The complete sensitivity of FNAC was 80%, while specificity was 99.1% and LR of positive tests 88.8. The combined score of FNAC, US and MRx resulted in a good increase in complete sensitivity (97.1%), when compared with the results of the single diagnostic tests evaluated separately. The absolute sensitivity of VB was 97.1% and specificity was 100%. In conclusion, considered together, MRx, US and FNAC appear to be reliable diagnostic procedures and, when they are all negative, the possibility of a cancer is extremely low, although it cannot be completely ruled out. The VB test had the highest absolute sensitivity among all the methods compared. Therefore, this technique could be considered conclusive in diagnostically doubtful cases, avoiding open surgical biopsy.