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.

Gradual Changes of the Protective Effect of Phenols in Virgin Olive Oils Subjected to Storage and Controlled Stress by Mesh Cell Incubation.

The oxidation reactions that take place in virgin olive oil under moderate conditions involved the combined effect of antioxidant and prooxidant compounds. Given the complexity of oxidation processes of multicomponent matrices, there is still a need to develop new methods with a dynamic approach to study the persistence of the compounds with healthy properties. This work studied the joint evolution of them, including phenols and pheophytin a, modeling their tendency during a real storage. The regression equations performed with the total phenol concentration showed that around 2% of the concentration was lost every month. Simultaneously, the progress of oxidation was evaluated by mesh cell incubation and Fourier transform infrared analysis. This method pointed out that, in the presence of light, the prooxidant effect of pigments was able to mask the protective effect of phenols, until the pheophytin a concentration was lower than 1 mg/kg. The antioxidant effect of phenols was less remarkable when the concentration loss was 35% or more.

Steady state of a two-species annihilation process with separated reactants.

We describe the steady state of the annihilation process of a one-dimensional system of two initially separated reactants A and B. The parameters that define the dynamical behavior of the system are the diffusion constant, the reaction rate, and the deposition rate. Depending on the ratio between those parameters, the system exhibits a crossover between a diffusion-limited (DL) regime and a reaction-limited (RL) regime. We found that a key quantity to describe the reaction process in the system is the probability p(x_{A},x_{B}) to find the rightmost A (RMA) particle and the leftmost B (LMB) particle at the positions x_{A} and x_{B}, respectively. The statistical behavior of the system in both regimes is described using the density of particles, the gap length distribution x_{B}-x_{A}, the marginal probabilities p_{A}(x_{A}) and p_{B}(x_{B}), and the reaction kernel. For both regimes, this kernel can be approximated by using p(x_{A},x_{B}). We found an excellent agreement between the numerical and analytical results for all calculated quantities despite the reaction process being quite different in both regimes. In the DL regime, the reaction kernel can be approximated by the probability to find the RMA and LMB particles in adjacent sites. In the RL regime, the kernel depends on the marginal probabilities p_{A}(x_{A}) and p_{B}(x_{B}).

Colloidal model of two-step protocol for epitaxial growth in one dimension.

We explore the application of a two-step growth protocol to a one-dimensional colloidal model. The evolution of the system is described in terms of the time-dependence of both monomer and island densities,N1andN, while its structure is characterized by using distributions of the gap length, the capture zone, the inter-island distance, and the island length. Analytical results obtained from rate equations are compared with these from molecular dynamics simulations. Since the two-step growth protocol deals with nucleation and aggregation processes in two completely separated time regimes, it makes possible to gain better understanding and control on the island formation mechanism than the standard one-step protocol. The predicted features and advantages of the two-step process could be experimentally tested using deposition of colloidal spheres on pattern substrates.

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.

Supporting the Sensory Panel to Grade Virgin Olive Oils: An In-House-Validated Screening Tool by Volatile Fingerprinting and Chemometrics.

The commercial category of virgin olive oil is currently assigned on the basis of chemical-physical and sensory parameters following official methods. Considering the limited number of samples that can be analysed daily by a sensory panel, an instrumental screening tool could be supportive by reducing the assessors' workload and improving their performance. The present work aims to in-house validate a screening strategy consisting of two sequential binary partial least squares-discriminant analysis (PLS-DA) models that was suggested to be successful in a proof-of-concept study. This approach is based on the volatile fraction fingerprint obtained by HS-SPME-GC-MS from more than 300 virgin olive oils from two crop seasons graded by six different sensory panels into extra virgin, virgin or lampante categories. Uncertainty ranges were set for the binary classification models according to sensitivity and specificity by means of receiver operating characteristics (ROC) curves, aiming to identify boundary samples. Thereby, performing the screening approach, only the virgin olive oils classified as uncertain (23.3%) would be assessed by a sensory panel, while the rest would be directly classified into a given commercial category (78.9% of correct classification). The sensory panel's workload would be reduced to less than one-third of the samples. A highly reliable classification of samples would be achieved (84.0%) by combining the proposed screening tool with the reference method (panel test) for the assessment of uncertain samples.

Flash Gas Chromatography in Tandem with Chemometrics: A Rapid Screening Tool for Quality Grades of Virgin Olive Oils.

This research aims to develop a classification model based on untargeted elaboration of volatile fraction fingerprints of virgin olive oils (n = 331) analyzed by flash gas chromatography to predict the commercial category of samples (extra virgin olive oil, EVOO; virgin olive oil, VOO; lampante olive oil, LOO). The raw data related to volatile profiles were considered as independent variables, while the quality grades provided by sensory assessment were defined as a reference parameter. This data matrix was elaborated using the linear technique partial least squares-discriminant analysis (PLS-DA), applying, in sequence, two sequential classification models with two categories (EVOO vs. no-EVOO followed by VOO vs. LOO and LOO vs. no-LOO followed by VOO vs. EVOO). The results from this large set of samples provide satisfactory percentages of correctly classified samples, ranging from 72% to 85%, in external validation. This confirms the reliability of this approach in rapid screening of quality grades and that it represents a valid solution for supporting sensory panels, increasing the efficiency of the controls, and also applicable to the industrial sector.

Alignment and Proficiency of Virgin Olive Oil Sensory Panels: The OLEUM Approach.

A set of 334 commercial virgin olive oil (VOO) samples were evaluated by six sensory panels during the H2020 OLEUM project. Sensory data were elaborated with two main objectives: (i) to classify and characterize samples in order to use them for possible correlations with physical-chemical data and (ii) to monitor and improve the performance of panels. After revision of the IOC guidelines in 2018, this work represents the first published attempt to verify some of the recommended quality control tools to increase harmonization among panels. Specifically, a new "decision tree" scheme was developed, and some IOC quality control procedures were applied. The adoption of these tools allowed for reliable classification of 289 of 334 VOOs; for the remaining 45, misalignments between panels of first (on the category, 21 cases) or second type (on the main perceived defect, 24 cases) occurred. In these cases, a "formative reassessment" was necessary. At the end, 329 of 334 VOOs (98.5%) were classified, thus confirming the effectiveness of this approach to achieve a better proficiency. The panels showed good performance, but the need to adopt new reference materials that are stable and reproducible to improve the panel's skills and agreement also emerged.

Two-step unconventional protocol for epitaxial growth in one dimension with hindered reactions.

We study the effect of hindered aggregation and/or nucleation on the island formation process in a two-step growth protocol. In the proposed model, the attachment of monomers to islands and/or other monomers is hindered by additional energy barriers which decrease the hopping rate of the monomers to the occupied sites of the lattice. For zero and weak barriers, the attachment is limited by diffusion while for strong barriers it is limited by reaction. We describe the time evolution of the system in terms of the monomer and island densities, N_{1} and N. We also calculate the gap length, the capture zone and the island distributions. For all the sets of barriers considered, the results given by the proposed analytical model are compared with those from kinetic Monte Carlo simulations. We found that the behavior of the system depends on the ratio of the nucleation barrier to the aggregation barrier. The two-step growth protocol allows more control and understanding on the island formation mechanism because it intrinsically separates the nucleation and aggregation processes in different time regimes.

Toward a Harmonized and Standardized Protocol for the Determination of Total Hydroxytyrosol and Tyrosol Content in Virgin Olive Oil (VOO). The Pros of a Fit for the Purpose Ultra High Performance Liquid Chromatography (UHPLC) Procedure.

Τoward a harmonized and standardized procedure for the determination of total hydroxytyrosol and tyrosol content in virgin olive oil (VOO), the pros of a recently published in house validated ultra high performance liquid chromatography (UHPLC) protocol are discussed comparatively with those of other procedures that determine directly or indirectly the compounds hosted under the health claim on "olive oil polyphenols" (EC regulation 432/2012). Authentic VOOs were analyzed with five different liquid chromatographic separation protocols and 1H-NMR one in five different laboratories with expertise in VOO phenol analysis within three months. Data comparison indicated differences in absolute values. Method comparison using appropriate tools (Passing-Bablok regression and Bland Altman analyses) for all protocols vs. the UHPLC one indicated slight or statistically significant differences. The results were also discussed in terms of cost effectiveness, detection means, standard requirements and ways to calculate the total hydroxytyrosol and tyrosol content. Findings point out that the in-house validated fit for the purpose UHPLC protocol presents certain pros that should be exploited by the interested parties. These are the simplicity of sample preparation, fast elution time that increase the number of samples analyzed per day and integration of well-resolved peaks with the aid of only two commercially available external standards. Importance of correction factors in the calculations is stressed.

Real time monitoring of the combined effect of chlorophyll content and light filtering packaging on virgin olive oil photo-stability using mesh cell-FTIR spectroscopy.

The present work aimed at examining the combined effect of chlorophyll content and light filtering packaging material on the photo-stability of virgin olive oil (VOO) via mesh cell-FTIR spectroscopy monitoring. Four different VOOs of Koroneiki cultivar differing in total chlorophyll content (∼12-46 mg/kg) were exposed in parallel to direct visible light (6000 lx, 24 °C, 344 h) and FTIR spectra were recorded periodically with or without applying light protection by an industrial filter used for packaging. Findings suggested that the protective role of light filtering material was more evident in the VOO with the lowest total chlorophyll content. Real time monitoring of VOO by mesh cell-FTIR was found to be a useful tool to follow the combined effect of pro-oxidant chlorophylls and the protective light filtering materials on the photo-oxidation process of VOO employing a minute sample amount.

Island size distribution with hindered aggregation.

We study the effect of hindered aggregation on the island formation processes for a one-dimensional model of epitaxial growth with arbitrary nucleus size i. In the proposed model, the attachment of monomers to islands is hindered by an aggregation barrier, ε_{a}, which decreases the hopping rate of monomers to the islands. As ε_{a} increases, the system exhibits a crossover between two different regimes; namely, from diffusion-limited aggregation to attachment-limited aggregation. The island size distribution, P(s), is calculated for different values of ε_{a} by a self-consistent approach involving the nucleation and aggregation capture kernels. The results given by the analytical model are compared with those from kinetic Monte Carlo simulations, finding a close agreement between both sets of data for all considered values of i and ε_{a}. As the aggregation barrier increases, the spatial effect of fluctuations on the density of monomers can be neglected and P(s) smoothly approximates to the limit distribution P(s)=δ_{s,i+1}. In the crossover regime the system features a complex and rich behavior, which can be explained in terms of the characteristic timescales of different microscopic processes.

Fragmentation approach to the point-island model with hindered aggregation: Accessing the barrier energy.

We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length l_{a}. For l_{a}=0 the islands behave as perfect sinks while for l_{a}→∞ they behave as reflecting boundaries. For intermediate values of l_{a}, the system exhibits a crossover between two different kinds of processes, diffusion-limited aggregation and attachment-limited aggregation. We calculate the growth exponents of the density of islands and monomers for the low coverage and aggregation regimes. The capture-zone (CZ) distributions are also calculated for different values of i and l_{a}. In order to obtain a good spatial description of the nucleation process, we propose a fragmentation model, which is based on an approximate description of nucleation inside of the gaps for 1D and the CZs for 2D. In both cases, the nucleation is described by using two different physically rooted probabilities, which are related with the microscopic parameters of the model (i and l_{a}). We test our analytical model with extensive numerical simulations and previously established results. The proposed model describes excellently the statistical behavior of the system for arbitrary values of l_{a} and i=1, 2, and 3.

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.

Interacting steps with finite-range interactions: analytical approximation and numerical results.

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions q on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

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.

Mean-field approximation for spacing distribution functions in classical systems.

We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.