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Along with a strict determinism of early embryogenesis in most living organisms, some of them exhibit variability of cell fates and developmental pathways. Here we discuss the phenomena of determinism and variability of developmental pathways, defining its dependence upon cell potency, cell sensitivity to the external signals and cell signaling. We propose a set of conjectures on the phenomenon of variability of developmental pathways, and denote a difference between a normal (local) variability, leading to an invariant final structure (e.g., embryo shape), and fundamental one, which is a switching between different developmental pathways, leading to different possible structures. For illustrating our conjectures, we analyzed early developmental stages of plant embryos with different levels of variability of morphogenesis pathways, and provide a set of computational experiments by Morphogenesis Software.

The notions of positional information and positional value describe the role of cell position in cell development and pattern formation. Despite their frequent usage in literature, their definitions are blurry, and are interpreted differently by different researchers. Through reflection on previous definitions and usage, and analysis of related experiments, we propose three clear and verifiable criteria for positional information/value. Then we reviewed literature on molecular mechanisms of cell development and pattern formation, to search for a possible molecular basis of positional information/value, including those used in theoretical models. We conclude that although morphogen gradients and cell-to-cell contacts are involved in the pattern formation process, complete molecular explanations of positional information/value are still far from reality.

We review studies on tissue transplantation experiments for various species: one piece of the donor tissue is excised and transplanted into a slit in the host tissue, then observe the behavior of this grafted tissue. Although we have known the results of some transplantation experiments, there are many more possible experiments with unknown results. We develop a penalty function-based method that uses the known experimental results to infer the unknown experimental results. Similar experiments without similar results get penalized and correspond to smaller probability. This method can provide the most probable results of a group of experiments or the probability of a specific result for each experiment. This method is also generalized to other situations. Besides, we solve a problem: how to design experiments so that such a method can be applied most efficiently.

In most taxa of plant and animal kingdoms the initial steps of embryogenesis and the final morphology of an organism are strongly determined. However, these two phenomena do not correlate from phylogenetic point of view, namely, different unrelated taxa can have the same type of early embryogenesis, while there can be different types of cleavage inside one taxon. Here we discuss an approach enabling giving an insight into the understanding of this phenomenon. First, we propose a strategy for constructing developmental graphs (trees) that provide mathematical formalization of a process of embryogenesis. Second, we suggested an algorithm of trees comparison, developed specifically for this type of labeled graphs, which allows calculating a distance between two developmental trees, and thus clustering them into groups. Next we performed the analysis of correspondence between the obtained clusters and the inception of morphological characters in given clustered groups of organisms, which allows describing several particular cases of interrelation between developmental trends and formation of morphological structures. Here we present some illustrations of the suggested methodology on the analysis of plant angiosperm species belonging to different taxa of various ranks.

We build a theoretical model of morphogenesis. This model describes cell fate in the developing organism using the notion of epigenetic code of each cell. Namely, given the epigenetic spectra of a cell and its neighboring cells, we can determine the corresponding cell event it will perform. This means that the properties of a group of cells (comprising an embryo or its part) at any time point are also known, and thus, the evolution of an embryo can be described. By this strategy, it is possible to establish the tissue, organ, or embryo shapes at any time, starting from a zygote. As an essential part of the model, the formalization of the notion of cell potency is introduced, and the related properties are discussed.

The process of morphogenesis is an evolution of shape of an organism together with the differentiation of its parts. This process encompasses numerous biological processes ranging from embryogenesis to regeneration following crisis such as amputation or transplantation. A fundamental theoretical question is where exactly do these instructions for (re-)construction reside and how are they implemented? We have recently proposed a set of concepts, aiming to respond to these questions and to provide an appropriate mathematical formalization of the geometry of morphogenesis [1]. First, we consider a possibility that the evolution of shape is determined by epigenetic information, responsible for realization of different types of cell events. Second, we suggest a set of rules for converting this epigenetic information into instructive signals for cell event for each cell, as well as for transforming it after each cell event. Next we give notions of cell state, determined by its epigenetic array, and cell event, which is a change of cell state, and formalize development as a graph (tree) of cell states connected by 5 types of cell events, corresponding to the processes of cell division, cell growth, cell death, cell movement and cell differentiation. Here we present a Morphogenesis software capable to simulate an evolution of a 3D embryo starting from zygote, following a set of rules, based on our theoretical assumptions, and thus to provide a proof-of-concept of the hypothesis of epigenetic code regulation. The software creates a developing embryo and a corresponding graph of cell events according to the zygotic epigenetic spectrum and chosen parameters of the developmental rules. Variation of rules influencing the resulting shape of an embryo may help elucidating the principal laws underlying pattern formation., SCOPUS: ar.j, info:eu-repo/semantics/published

Cancer Stem Cells (CSC), a subset of cancer cells resembling normal stem cells with self-renewal and asymmetric division capabilities, are present at various but low proportions in many tumors and are thought to be responsible for tumor relapses following conventional cancer therapies. In vitro, most intriguingly, when isolated, CSCs return to their original proportion level as shown by various investigators. This phenomenon still remains to be explained.We suggest a mathematical model of cancer cell population dynamics, based on the main parameters of cell population dynamics, including the proliferation rates, the rates of cell death and the frequency of symmetric and asymmetric cell divisions both in CSCs and in non-CSCs. This model should help elucidating some important factors underlying the dynamics of the two populations, first of all, the phenomena of cancer stem cell population stabilization.Author SummaryCancer Stem Cells (CSC) present a subset of cancer cells which is thought to be responsible for tumor growth. That is why CSC are also named “tumor initiation cells”. Additionally, it was shown that CSC are resistant to chemo- and radio-therapies which suggests that these cells can be responsible for tumor relapses after these treatments. Experimental data in cancer cell lines have shown the intriguing phenomena of CSC population stability, which means that isolated CSC population rapidly stabilizes at its characteristic level (the relative proportion of CSC in a whole cancer population). We suggest a mathematical model of cancer cell population dynamics, based on experimentally measured dynamics of CSC population stabilization and including main parameters of cell population growth.We have computationally predicted probability of different scenarios of cancer cell behavior for each experimental case with measurable growth parameters. Moreover, we provide an analytical tool for elucidating important biochemical factors responsible for a particular dynamics of CSC population.The results may have important implications in therapeutic, because the destroying of a set of factors underlying CSC stability may help to avoid tumor relapses.

A model of morphogenesis is proposed based on seven explicit postulates. The mathematical import and biological significance of the postulates are explored and discussed.

Functional genomics employs several experimental techniques to investigate gene functions. These techniques such as loss-of-function screening and transcriptome profiling performed in a high-throughput manner give as result a list of genes involved in the biological process of interest. There exist several computational methods for analysis and interpretation of the list. The most widespread methods aim at investigation of biological processes significantly represented in the list or at extracting significantly represented subnetworks. Here we present a new exploratory network analysis method that employs the shortest path approach and centrality measure to uncover members of active molecular pathways leading to the studied phenotype based on the results of functional genomics screening data. We present the method and we demonstrate what data can be retrieved by its application to the terminal muscle differentiation miRNA loss-of-function screening and transcriptomic profiling data and to the ‘druggable’ loss-of-function RNAi screening data of the DNA repair process.

A network is one of the most convenient way to represent interactions between biological entities in systems biology. A network of molecular interactions is a graph in which the vertices are biological component and the edges correspond to the interactions between them. Many notions and approaches for network analysis came to systems biology from the theory of graphs – a field of mathematics that study graphs. We focused on the study of the shortest path approach in this work. We investigated whether this approach yields valid molecular paths. To perform this, the shortest paths in the human interactome (derived from HPRD and HIPPIE databases) were found between all relevant combinations of proteins taken from eight well-studied highly conserved signaling pathways from the KEGG database (NF-kappa B, MAPK, Jak-STAT, mTOR, ErbB, Wnt, TGF-beta and the signaling part of the apoptotic process). Canonical paths were systematically compared with the shortest counterparts and centrality of vertices and paths in subnetworks induced by the shortest paths were analyzed. We found that the sets of the shortest paths contain the canonical counterparts only for very short canonical paths (length 2-3 interactions). We also found that high centrality vertices tend to belong to canonical counterparts, to less extent this can also be said about high centrality paths.

International audience; CNOT6L is a deadenylase subunit belonging to the CCR4-NOT complex, a major deadenylase complex in eukaryotes involved at multiple levels in regulation of gene expression. While CNOT6L is expressed in skeletal muscle cells, its specific functions in this tissue are still largely unknown. Our previous work highlighted the functional of CNOT6L in skeletal muscle cell differentiation. To further explore how CNOT6L regulates myogenesis, we used here gene expression analysis to identify CNOT6L mRNA targets in human myoblasts. Among these novel targets, IL-8 (interleukin 8) mRNA was the most upregulated in CNOT6L knock-down (KD) cells. Biochemical approaches and poly (A) tail length assays showed that IL-8 mRNA is a direct target of CNOT6L, and further investigations by loss- and gain-of-function assays pointed out that IL-8 is an important effector of myogenesis. Therefore, we have characterized CNOT6L-IL-8 as a new signaling axis that regulates myogenesis.

In this work we developed a new exploratory network analysis method, that works on an integrated network (the network consists of protein-protein, transcriptional, miRNA-mRNA, metabolic interactions) and aims at uncovering potential members of molecular pathways important for a given phenotype using hit list dataset from “omics” experiments. The method extracts subnetwork built from the shortest paths of 4 different types (with only protein-protein interactions, with at least one transcription interaction, with at least one miRNA-mRNA interaction, with at least one metabolic interaction) between hit genes and so called “final implementers” – biological components that are involved in molecular events responsible for final phenotypical realization (if known) or between hit genes (if “final implementers” are not known). The method calculates centrality score for each node and each path in the subnetwork as a number of the shortest paths found in the previous step that pass through the node and the path. Then, the statistical significance of each centrality score is assessed by comparing it with centrality scores in subnetworks built from the shortest paths for randomly sampled hit lists. It is hypothesized that the nodes and the paths with statistically significant centrality score can be considered as putative members of molecular pathways leading to the studied phenotype. In case experimental scores and p-values are available for a large number of nodes in the network, the method can also calculate paths’ experiment-based scores (as an average of the experimental scores of the nodes in the path) and experiment-based p-values (by aggregating p-values of the nodes in the path using Fisher’s combined probability test and permutation approach). The method is illustrated by analyzing the results of miRNA loss-of-function screening and transcriptomic profiling of terminal muscle differentiation and of ‘druggable’ loss-of-function screening of the DNA repair process. The Java source code is available on GitHub page https://github.com/daggoo/masterPATH; Dans ce travail nous avons élaboré une nouvelle méthode de l'analyse de réseau à définir des membres possibles des voies moléculaires qui sont important pour ce phénotype en utilisant la « hit-liste » des expériences « omics » qui travaille dans le réseau intégré (le réseau comprend des interactions protéine-protéine, de transcription, l’acide ribonucléique micro-l’acide ribonucléique messager et celles métaboliques). La méthode tire des sous-réseaux qui sont construit des voies de quatre types les plus courtes (qui ne se composent des interactions protéine-protéine, ayant au minimum une interaction de transcription, ayant au minimum une interaction l’acide ribonucléique micro-l’acide ribonucléique messager, ayant au minimum une interaction métabolique) entre des hit –gènes et des soi-disant « exécuteurs terminaux » - les composants biologiques qui participent à la réalisation du phénotype finale (s’ils sont connus) ou entre les hit-gènes (si « des exécuteurs terminaux » sont inconnus). La méthode calcule la valeur de la centralité de chaque point culminant et de chaque voie dans le sous-réseau comme la quantité des voies les plus courtes trouvées sur la route précédente et passant à travers le point culminant et la voie. L'importance statistique des valeurs de la centralité est estimée en comparaison avec des valeurs de la centralité dans les sous-réseaux construit des voies les plus courtes pour les hit-listes choisi occasionnellement. Il est supposé que les points culminant et les voies avec les valeurs de la centralité statistiquement signifiantes peuvent être examinés comme les membres possibles des voies moléculaires menant à ce phénotype. S’il y a des valeurs expérimentales et la P-valeur pour un grand nombre des points culminant dans le réseau, la méthode fait possible de calculer les valeurs expérimentales pour les voies (comme le moyen des valeurs expérimentales des points culminant sur la route) et les P-valeurs expérimentales (en utilisant la méthode de Fischer et des transpositions multiples).A l'aide de la méthode masterPATH on a analysé les données de la perte de fonction criblage de l’acide ribonucléique micro et l'analyse de transcription de la différenciation terminal musculaire et les données de la perte de fonction criblage du procès de la réparation de l'ADN. On peut trouver le code initial de la méthode si l’on suit le lien https://github.com/daggoo/masterPATH

In this work we developed a new exploratory network analysis method, that works on an integrated network (the network consists of protein-protein, transcriptional, miRNA-mRNA, metabolic interactions) and aims at uncovering potential members of molecular pathways important for a given phenotype using hit list dataset from “omics” experiments. The method extracts subnetwork built from the shortest paths of 4 different types (with only protein-protein interactions, with at least one transcription interaction, with at least one miRNA-mRNA interaction, with at least one metabolic interaction) between hit genes and so called “final implementers” – biological components that are involved in molecular events responsible for final phenotypical realization (if known) or between hit genes (if “final implementers” are not known). The method calculates centrality score for each node and each path in the subnetwork as a number of the shortest paths found in the previous step that pass through the node and the path. Then, the statistical significance of each centrality score is assessed by comparing it with centrality scores in subnetworks built from the shortest paths for randomly sampled hit lists. It is hypothesized that the nodes and the paths with statistically significant centrality score can be considered as putative members of molecular pathways leading to the studied phenotype. In case experimental scores and p-values are available for a large number of nodes in the network, the method can also calculate paths’ experiment-based scores (as an average of the experimental scores of the nodes in the path) and experiment-based p-values (by aggregating p-values of the nodes in the path using Fisher’s combined probability test and permutation approach). The method is illustrated by analyzing the results of miRNA loss-of-function screening and transcriptomic profiling of terminal muscle differentiation and of ‘druggable’ loss-of-function screening of the DNA repair process. The Java source code is available on GitHub page https://github.com/daggoo/masterPATH; Dans ce travail nous avons élaboré une nouvelle méthode de l'analyse de réseau à définir des membres possibles des voies moléculaires qui sont important pour ce phénotype en utilisant la « hit-liste » des expériences « omics » qui travaille dans le réseau intégré (le réseau comprend des interactions protéine-protéine, de transcription, l’acide ribonucléique micro-l’acide ribonucléique messager et celles métaboliques). La méthode tire des sous-réseaux qui sont construit des voies de quatre types les plus courtes (qui ne se composent des interactions protéine-protéine, ayant au minimum une interaction de transcription, ayant au minimum une interaction l’acide ribonucléique micro-l’acide ribonucléique messager, ayant au minimum une interaction métabolique) entre des hit –gènes et des soi-disant « exécuteurs terminaux » - les composants biologiques qui participent à la réalisation du phénotype finale (s’ils sont connus) ou entre les hit-gènes (si « des exécuteurs terminaux » sont inconnus). La méthode calcule la valeur de la centralité de chaque point culminant et de chaque voie dans le sous-réseau comme la quantité des voies les plus courtes trouvées sur la route précédente et passant à travers le point culminant et la voie. L'importance statistique des valeurs de la centralité est estimée en comparaison avec des valeurs de la centralité dans les sous-réseaux construit des voies les plus courtes pour les hit-listes choisi occasionnellement. Il est supposé que les points culminant et les voies avec les valeurs de la centralité statistiquement signifiantes peuvent être examinés comme les membres possibles des voies moléculaires menant à ce phénotype. S’il y a des valeurs expérimentales et la P-valeur pour un grand nombre des points culminant dans le réseau, la méthode fait possible de calculer les valeurs expérimentales pour les voies (comme le moyen des valeurs expérimentales des points culminant sur la route) et les P-valeurs expérimentales (en utilisant la méthode de Fischer et des transpositions multiples).A l'aide de la méthode masterPATH on a analysé les données de la perte de fonction criblage de l’acide ribonucléique micro et l'analyse de transcription de la différenciation terminal musculaire et les données de la perte de fonction criblage du procès de la réparation de l'ADN. On peut trouver le code initial de la méthode si l’on suit le lien https://github.com/daggoo/masterPATH