La relation entre codes k-circulaires et codes circulaires

International audienceA code $X$ is $k$-circular if any concatenation of at most $k$ words from $X$, when read on a circle, admits exactly one partition into words from $X$. It is circular if it is $k$-circular for every integer $k$. While it is not a priori clear from the definition, there exists, for every pair ($n$,ℓ), an integer $k$ such that every $k$-circular ℓ-letter code over an alphabet of cardinality n is circular, and we determine the least such integer $k$ for all values of $n$ and ℓ. The $k$-circular codes may represent an important evolutionary step between the circular codes, such as the comma-free codes, and the genetic code.Un code $X$ est $k$-circulaire si toute concaténation d'au plus $k$ mots de $X$, lue de façon circulaire, admet une et une seule partition en mots appartenant à $X$. Il est circulaire s'il est $k$-circulaire pour tout entier $k$. Bien que ce ne soit pas a priori clair à partir de la définition, il existe, pour toute paire ($n$,ℓ), un entier $k$ tel que tout code $k$-circulaire de mots à ℓ lettres sur un alphabet de taille $n$ est circulaire, et nous déterminons la plus petite valeur d'un tel entier $k$ pour toutes les paires ($n$,ℓ). Les codes $k$-circulaires représentent peut-être une importante étape d'évolution entre les codes circulaires, comme les codes comma-free, et le code génétique

An interdisciplinary approach to data management

Many scientific issues involve interdisciplinary approaches that demand scientists with diverse skills and research fields. For the design and fabrication of new materials, this is especially true since new materials with macroscopically observable properties must be proposed based on changes at the molecular level. Research projects of this kind pose particular challenges for efficient execution and documentation, as research data management (RDM) tools usually fit very well to a specific research area, but cannot provide solutions for interdisciplinary topics. In order to guarantee consistent research and its documentation across disciplines, different tools, which may be used in several groups, must be used cooperatively. In the context of the Science Data Center MoMaF, among other things, strategies are being developed to enable research data management across scales. The RDM tools used for this are Chemotion and Kadi4Mat. The systems cover research at the molecular level (chemotion ELN) as well as simulation activities on the meso- and macroscopic scale (Kadi4Mat), and will be extended within the Science Data Center to enable cooperative use of the systems for work across scales. A first use case shows how Chemotion ELN can be used to document necessary parameters at the molecular level, in order to then be able to manage simulations of phase separation processes on their basis in a further step with the help of Kadi4Mat. For this purpose, the procedure and documentation method of already completed projects were first analysed in order to be able to propose a concept for future processes. Chemotion ELN is used in the presented procedure to document molecular descriptions, the performance of polymerization reactions and their outcome, as well as the properties obtained experimentally and from the literature. Kadi4Mat manages and transfers the parameters from the molecular description as input for mesoscopic simulations that describe the phase separation process in a time-dependent manner. Finally, by applying analysis tools on the time-dependent data via Kadi4Mat, macroscopic properties can be derived across scales as a function of the molecular composition

Circular codes in the evolution of the genetic code

Le problème abordé dans cette thèse est de savoir comment retrouver, maintenir et synchroniser la phase de lecture pendant la traduction des gènes en protéines. La traduction est le processus par lequel le ribosome décode l’ARN messager (une séquence de nucléotides {A, C, G,T}) en codons (3 nucléotides) pour créer une protéine. L’ARN messager peut être décodé en trois phases 0, +1 et +2 mais uniquement la phase 0 (phase de lecture) initiée par un ”start” codon code les informations pour synthétiser les protéines. Un code (ensemble de mots) avec la propriété de circularité permet de retrouver la phase de lecture. Un code circulaire, nommé X, formé de 20 trinucléotides a été découvert en 1996 par une analyse statistique des gènes de différentes espèces. Dans ce livre, je présente les nouvelles propriétés des codes circulaires. Sur la base de ces propriétés, je présente une ligne directrice hypothétique qui peut aider à découvrir l'évolution de la synthèse des protéines.The problem that this work addresses is how to retrieve, maintain and synchronize the correct reading frame during the translation process. Translation is the process by which the ribosome decodes the messenger RNA (sequence of nucleotides {A,C,G,T}) as codons (word of 3 nucleotides) to create a specific amino acid chain. Unfortunately, the mRNA can be decoded in three reading frames 0, +1 and +2. Yet, only frame 0 as correct reading frame encodes the Information for the synthesis of proteins. First practical evidence of a genetic model which is able to retrieve the correct reading frame is the so-called X-code. Astonishingly, it turned out that the X-code is a circular code. The advantages of circular genetic codes are incomparable. In this work I introduce new properties. Based on these properties I present a hypothetical guiding line which can help to discover the evolution of protein synthesis

Codes circulaires dans l'évolution du code génétique

The problem that this work addresses is how to retrieve, maintain and synchronize the correct reading frame during the translation process. Translation is the process by which the ribosome decodes the messenger RNA (sequence of nucleotides {A,C,G,T}) as codons (word of 3 nucleotides) to create a specific amino acid chain. Unfortunately, the mRNA can be decoded in three reading frames 0, +1 and +2. Yet, only frame 0 as correct reading frame encodes the Information for the synthesis of proteins. First practical evidence of a genetic model which is able to retrieve the correct reading frame is the so-called X-code. Astonishingly, it turned out that the X-code is a circular code. The advantages of circular genetic codes are incomparable. In this work I introduce new properties. Based on these properties I present a hypothetical guiding line which can help to discover the evolution of protein synthesis.Le problème abordé dans cette thèse est de savoir comment retrouver, maintenir et synchroniser la phase de lecture pendant la traduction des gènes en protéines. La traduction est le processus par lequel le ribosome décode l’ARN messager (une séquence de nucléotides {A, C, G,T}) en codons (3 nucléotides) pour créer une protéine. L’ARN messager peut être décodé en trois phases 0, +1 et +2 mais uniquement la phase 0 (phase de lecture) initiée par un ”start” codon code les informations pour synthétiser les protéines. Un code (ensemble de mots) avec la propriété de circularité permet de retrouver la phase de lecture. Un code circulaire, nommé X, formé de 20 trinucléotides a été découvert en 1996 par une analyse statistique des gènes de différentes espèces. Dans ce livre, je présente les nouvelles propriétés des codes circulaires. Sur la base de ces propriétés, je présente une ligne directrice hypothétique qui peut aider à découvrir l'évolution de la synthèse des protéines

Codes circulaires dans l'évolution du code génétique

The problem that this work addresses is how to retrieve, maintain and synchronize the correct reading frame during the translation process. Translation is the process by which the ribosome decodes the messenger RNA (sequence of nucleotides {A,C,G,T}) as codons (word of 3 nucleotides) to create a specific amino acid chain. Unfortunately, the mRNA can be decoded in three reading frames 0, +1 and +2. Yet, only frame 0 as correct reading frame encodes the Information for the synthesis of proteins. First practical evidence of a genetic model which is able to retrieve the correct reading frame is the so-called X-code. Astonishingly, it turned out that the X-code is a circular code. The advantages of circular genetic codes are incomparable. In this work I introduce new properties. Based on these properties I present a hypothetical guiding line which can help to discover the evolution of protein synthesis.Le problème abordé dans cette thèse est de savoir comment retrouver, maintenir et synchroniser la phase de lecture pendant la traduction des gènes en protéines. La traduction est le processus par lequel le ribosome décode l’ARN messager (une séquence de nucléotides {A, C, G,T}) en codons (3 nucléotides) pour créer une protéine. L’ARN messager peut être décodé en trois phases 0, +1 et +2 mais uniquement la phase 0 (phase de lecture) initiée par un ”start” codon code les informations pour synthétiser les protéines. Un code (ensemble de mots) avec la propriété de circularité permet de retrouver la phase de lecture. Un code circulaire, nommé X, formé de 20 trinucléotides a été découvert en 1996 par une analyse statistique des gènes de différentes espèces. Dans ce livre, je présente les nouvelles propriétés des codes circulaires. Sur la base de ces propriétés, je présente une ligne directrice hypothétique qui peut aider à découvrir l'évolution de la synthèse des protéines

Circular codes in the evolution of the genetic code

The composition of the structure of the genetic code is undoubtedly one of the most challenging questions open in molecular biology. A promising element in solving this question is the evolutionary development of the structure of the genetic code. Therefore, the evolution of the genetic code has increasingly become the focus of the search for medical applications to cure and prevent hereditary diseases. To further promote such research, the main motivation of this dissertation is the theoretical identification of a factor influencing the evolution of the genetic code. The first evolutionary hypothesis not disproved so far was published by Crick in 1968. His frozen accident theory states that the genetic code was generated by chance and has remained frozen ever since. However, most researchers working on the evolution of the genetic code today agree that such an efficient system cannot have appeared spontaneously. Hence, in recent years, new theories have been developed which claim to explain the origin of the genetic code. The most common ones are the stereochemical theory, the adaptive theory, and the co-evolution theory. The influence factor analyzed in this dissertation is derived from the adaptive theory. This theory postulates that evolution aimed at obtaining a code that minimizes errors resulting from mutations. However, we do not claim that other theories such as the stereochemical theory and the co-evolution theory had no influence on the evolution of the genetic code. It is rather a matter of emphasizing properties of the genetic code that can only be assigned to the adaptive theory. Summarized this work introduces properties of the genetic code which address the problems of retrieving, maintaining, and synchronizing the correct reading frame during the translation process. Translation is a subprocess of the protein synthesis. In this process the ribosome decodes the messenger RNA (sequence of nucleotides {A,C,G,T}) as codons (word of 3 nucleotides) to create a specific amino acid chain. Unfortunately, the mRNA can be decoded in three reading frames: 0, +1 and +2. Yet, only frame 0 encodes the correct information needed for the synthesis of proteins. The first practical evidence of a genetic model which can retrieve the correct reading frame is the so-called X-code. This X-code was obtained by Arqùes and Michel in a statistical evaluation of the codons in coding sequences of different species. Astonishingly, the X-code turned out to be a circular code. The advantages of circular genetic codes are incomparable. Such a circular code is a block code, i.e., a code consisting of words of a certain word length, which recognizes a reading frame error. This work introduces new properties of circular codes in general. These included the minimum sequence length to ensure the reading frame, a new classification of circular codes and new hypothetical processes inspired by the circular code theory to ensure the frameshift robustness during the translation process. With these findings, this dissertation presents a hypothetical guiding line which can be a valuable asset to the discovery of the evolution of protein synthesis

Computational Analysis of Genetic Code Variations Optimized for the Robustness against Point Mutations with Wobble-like Effects

It is believed that the codon–amino acid assignments of the standard genetic code (SGC) help to minimize the negative effects caused by point mutations. All possible point mutations of the genetic code can be represented as a weighted graph with weights that correspond to the probabilities of these mutations. The robustness of a code against point mutations can be described then by means of the so-called conductance measure. This paper quantifies the wobble effect, which was investigated previously by applying the weighted graph approach, and seeks optimal weights using an evolutionary optimization algorithm to maximize the code’s robustness. One result of our study is that the robustness of the genetic code is least influenced by mutations in the third position—like with the wobble effect. Moreover, the results clearly demonstrate that point mutations in the first, and even more importantly, in the second base of a codon have a very large influence on the robustness of the genetic code. These results were compared to single nucleotide variants (SNV) in coding sequences which support our findings. Additionally, it was analyzed which structure of a genetic code evolves from random code tables when the robustness is maximized. Our calculations show that the resulting code tables are very close to the standard genetic code. In conclusion, the results illustrate that the robustness against point mutations seems to be an important factor in the evolution of the standard genetic code

La relation entre codes k-circulaires et codes circulaires

A code X is k-circular if any concatenation of at most k words from X, when read on a circle, admits exactly one partition into words from X. It is circular if it is k-circular for every integer k. While it is not a priori clear from the definition, there exists, for every pair (n,ℓ), an integer k such that every k-circular ℓ-letter code over an alphabet of cardinality n is circular, and we determine the least such integer k for all values of n and ℓ. The k-circular codes may represent an important evolutionary step between the circular codes, such as the comma-free codes, and the genetic code.Un code X est k-circulaire si toute concaténation d'au plus k mots de X, lue de façon circulaire, admet une et une seule partition en mots appartenant à X. Il est circulaire s'il est k-circulaire pour tout entier k. Bien que ce ne soit pas a priori clair à partir de la définition, il existe, pour toute paire (n,ℓ), un entier k tel que tout code k-circulaire de mots à ℓ lettres sur un alphabet de taille n est circulaire, et nous déterminons la plus petite valeur d'un tel entier k pour toutes les paires (n,ℓ). Les codes k-circulaires représentent peut-être une importante étape d'évolution entre les codes circulaires, comme les codes comma-free, et le code génétique