Jérémie Bourdon

Temporal constraints of a gene regulatory network: Refining a qualitative simulation.

The modelling of gene regulatory networks (GRNs) has classically been addressed through very different approaches. Among others, extensions of Thomass asynchronous Boolean approach have been proposed, to better fit the dynamics of biological systems: genes may reach different discrete expression levels, depending on the states of other genes, called the regulators: thus, activations and inhibitions are triggered conditionally on the proper expression levels of these regulators. In contrast, some fine-grained propositions have focused on the molecular level as modelling the evolution of biological compound concentrations through differential equation systems. Both approaches are limited. The first one leads to an oversimplification of the system, whereas the second is incapable to tackle large GRNs. In this context, hybrid paradigms, that mix discrete and continuous features underlying distinct biological properties, achieve significant advances for investigating biological properties. One of these hybrid formalisms proposes to focus, within a GRN abstraction, on the time delay to pass from a gene expression level to the next. Until now, no research work has been carried out, which attempts to benefit from the modelling of a GRN by differential equations, converting it into a multi-valued logical formalism of Thomas, with the aim of performing biological applications. This paper fills this gap by describing a whole pipelined process which orchestrates the following stages: (i) model conversion from a piece-wise affine differential equation (PADE) modelization scheme into a discrete model with focal points, (ii) characterization of subgraphs through a graph simplification phase which is based on probabilistic criteria, (iii) conversion of the subgraphs into parametric linear hybrid automata, (iv) analysis of dynamical properties (e.g. cyclic behaviours) using hybrid model-checking techniques. The present work is the outcome of a methodological investigation launched to cope with the GRN responsible for the reaction of Escherichia coli bacterium to carbon starvation. As expected, we retrieve a remarkable cycle already exhibited by a previous analysis of the PADE model. Above all, hybrid model-checking enables us to infer temporal properties, whose biological signification is then discussed.

Meneco, a Topology-Based Gap-Filling Tool Applicable to Degraded Genome-Wide Metabolic Networks

Increasing amounts of sequence data are becoming available for a wide range of non-model organisms. Investigating and modelling the metabolic behaviour of those organisms is highly relevant to understand their biology and ecology. As sequences are often incomplete and poorly annotated, draft networks of their metabolism largely suffer from incompleteness. Appropriate gap-filling methods to identify and add missing reactions are therefore required to address this issue. However, current tools rely on phenotypic or taxonomic information, or are very sensitive to the stoichiometric balance of metabolic reactions, especially concerning the co-factors. This type of information is often not available or at least prone to errors for newly-explored organisms. Here we introduce Meneco, a tool dedicated to the topological gap-filling of genome-scale draft metabolic networks. Meneco reformulates gap-filling as a qualitative combinatorial optimization problem, omitting constraints raised by the stoichiometry of a metabolic network considered in other methods, and solves this problem using Answer Set Programming. Run on several artificial test sets gathering 10,800 degraded Escherichia coli networks Meneco was able to efficiently identify essential reactions missing in networks at high degradation rates, outperforming the stoichiometry-based tools in scalability. To demonstrate the utility of Meneco we applied it to two case studies. Its application to recent metabolic networks reconstructed for the brown algal model Ectocarpus siliculosus and an associated bacterium Candidatus Phaeomarinobacter ectocarpi revealed several candidate metabolic pathways for algal-bacterial interactions. Then Meneco was used to reconstruct, from transcriptomic and metabolomic data, the first metabolic network for the microalga Euglena mutabilis. These two case studies show that Meneco is a versatile tool to complete draft genome-scale metabolic networks produced from heterogeneous data, and to suggest relevant reactions that explain the metabolic capacity of a biological system.

Toward Systems Biology in Brown Algae to Explore Acclimation and Adaptation to the Shore Environment

Brown algae belong to a phylogenetic lineage distantly related to land plants and animals. They are almost exclusively found in the intertidal zone, a harsh and frequently changing environment where organisms are submitted to marine and terrestrial constraints. In relation with their unique evolutionary history and their habitat, they feature several peculiarities, including at the level of their primary and secondary metabolism. The establishment of Ectocarpus siliculosus as a model organism for brown algae has represented a framework in which several omics techniques have been developed, in particular, to study the response of these organisms to abiotic stresses. With the recent publication of medium to high throughput profiling data, it is now possible to envision integrating observations at the cellular scale to apply systems biology approaches. As a first step, we propose a protocol focusing on integrating heterogeneous knowledge gained on brown algal metabolism. The resulting abstraction of the system will then help understanding how brown algae cope with changes in abiotic parameters within their unique habitat, and to decipher some of the mechanisms underlying their (1) acclimation and (2) adaptation, respectively consequences of (1) the behavior or (2) the topology of the system resulting from the integrative approach.

Pattern matching statistics on correlated sources

In pattern matching algorithms, two characteristic parameters play an important role: the number of occurrences of a given pattern, and the number of positions where a pattern occurrence ends. Since there may exist many occurrences which end at the same position, these two parameters may differ in a significant way. Here, we consider a general framework where the text is produced by a probabilistic source, which can be built by a dynamical system. Such dynamical sources encompass the classical sources -memoryless sources, and Markov chains-, and may possess a high degree of correlations. We are mainly interested in two situations: the pattern is a general word of a regular expression, and we study the number of occurrence positions - the pattern is a finite set of strings, and we study the number of occurrences. In both cases, we determine the mean and the variance of the parameter, and prove that its distribution is asymptotically Gaussian. In this way, we extend methods and results which have been already obtained for classical sources [for instance in [9] and in [6]] to this general dynamical framework. Our methods use various techniques: formal languages, and generating functions, as in previous works. However, in this correlated model, it is not possible to use a direct transfer into generating functions, and we mainly deal with generating operators which generate... generating functions.

A multi-objective constraint-based approach for modeling genome-scale microbial ecosystems.

Interplay within microbial communities impacts ecosystems on several scales, and elucidation of the consequent effects is a difficult task in ecology. In particular, the integration of genome-scale data within quantitative models of microbial ecosystems remains elusive. This study advocates the use of constraint-based modeling to build predictive models from recent high-resolution -omics datasets. Following recent studies that have demonstrated the accuracy of constraint-based models (CBMs) for simulating single-strain metabolic networks, we sought to study microbial ecosystems as a combination of single-strain metabolic networks that exchange nutrients. This study presents two multi-objective extensions of CBMs for modeling communities: multi-objective flux balance analysis (MO-FBA) and multi-objective flux variability analysis (MO-FVA). Both methods were applied to a hot spring mat model ecosystem. As a result, multiple trade-offs between nutrients and growth rates, as well as thermodynamically favorable relative abundances at community level, were emphasized. We expect this approach to be used for integrating genomic information in microbial ecosystems. Following models will provide insights about behaviors (including diversity) that take place at the ecosystem scale.

A combinatorial approach to products of Pisot substitutions

We define a generic algorithmic framework to prove a pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substitutions. We focus on the families obtained as finite products of the three-letter substitutions associated with the multidimensional continued fraction algorithms of Brun and Jacobi–Perron. Our tools consist in a reformulation of some combinatorial criteria (coincidence conditions), in terms of properties of discrete plane generation using multidimensional (dual) substitutions. We also deduce some topological and dynamical properties of the Rauzy fractals, of the underlying symbolic dynamical systems, as well as some number-theoretical properties of the associated Pisot numbers.

Generating Discrete Planes with Substitutions

Given a finite set S of unimodular Pisot substitutions, we provide a method for characterizing the infinite sequences over S that allow to generate a full discrete plane when, starting from a finite seed, we iterate the multidimensional dual substitutions associated with S. We apply our results to study the substitutions associated with the Brun multidimensional continued fraction algorithm.

Modelization of the regulation of protein synthesis following fertilization in sea urchin shows requirement of two processes: a destabilization of eIF4E:4E-BP complex and a great stimulation of the 4E-BP-degradation mechanism, both rapamycin-sensitive

Fertilization of sea urchin eggs involves an increase in protein synthesis associated with a decrease in the amount of the translation initiation inhibitor 4E-BP. A highly simple reaction model for the regulation of protein synthesis was built and was used to simulate the physiological changes in the total 4E-BP amount observed during time after fertilization. Our study evidenced that two changes occurring at fertilization are necessary to fit with experimental data. The first change was an 8-fold increase in the dissociation parameter (koff1) of the eIF4E:4E-BP complex. The second was an important 32.5-fold activation of the degradation mechanism of the protein 4E-BP. Additionally, the changes in both processes should occur in 5 min time interval post-fertilization. To validate the model, we checked that the kinetic of the predicted 4.2-fold increase of eIF4E:eIF4G complex concentration at fertilization matched the increase of protein synthesis experimentally observed after fertilization (6.6-fold, SD = 2.3, n = 8). The minimal model was also used to simulate changes observed after fertilization in the presence of rapamycin, a FRAP/mTOR inhibitor. The model showed that the eIF4E:4E-BP complex destabilization was impacted and surprisingly, that the mechanism of 4E-BP degradation was also strongly affected, therefore suggesting that both processes are controlled by the protein kinase FRAP/mTOR.

Parallel derivation of isogenic human primed and naive induced pluripotent stem cells

Induced pluripotent stem cells (iPSCs) have considerably impacted human developmental biology and regenerative medicine, notably because they circumvent the use of cells of embryonic origin and offer the potential to generate patient-specific pluripotent stem cells. However, conventional reprogramming protocols produce developmentally advanced, or primed, human iPSCs (hiPSCs), restricting their use to post-implantation human development modeling. Hence, there is a need for hiPSCs resembling preimplantation naive epiblast. Here, we develop a method to generate naive hiPSCs directly from somatic cells, using OKMS overexpression and specific culture conditions, further enabling parallel generation of their isogenic primed counterparts. We benchmark naive hiPSCs against human preimplantation epiblast and reveal remarkable concordance in their transcriptome, dependency on mitochondrial respiration and X-chromosome status. Collectively, our results are essential for the understanding of pluripotency regulation throughout preimplantation development and generate new opportunities for disease modeling and regenerative medicine.Derivation of human induced pluripotent stem cells (hiPSCs) produces primed hiPSCs that can in turn be converted to naive hiPSCs. Here, the authors directly reprogram somatic cells to form both naive and primed isogenic hiPSCs and confirm the similarity of naive hiPSCs to their in vivo counterparts.

Exploring metabolism flexibility in complex organisms through quantitative study of precursor sets for system outputs

BackgroundWhen studying metabolism at the organ level, a major challenge is to understand the matter exchanges between the input and output components of the system. For example, in nutrition, biochemical models have been developed to study the metabolism of the mammary gland in relation to the synthesis of milk components. These models were designed to account for the quantitative constraints observed on inputs and outputs of the system. In these models, a compatible flux distribution is first selected. Alternatively, an infinite family of compatible set of flux rates may have to be studied when the constraints raised by observations are insufficient to identify a single flux distribution. The precursors of output nutrients are traced back with analyses similar to the computation of yield rates. However, the computation of the quantitative contributions of precursors may lack precision, mainly because some precursors are involved in the composition of several nutrients and because some metabolites are cycled in loops.ResultsWe formally modeled the quantitative allocation of input nutrients among the branches of the metabolic network (AIO). It corresponds to yield information which, if standardized across all the outputs of the system, allows a precise quantitative understanding of their precursors. By solving nonlinear optimization problems, we introduced a method to study the variability of AIO coefficients when parsing the space of flux distributions that are compatible with both model stoichiometry and experimental data. Applied to a model of the metabolism of the mammary gland, our method made it possible to distinguish the effects of different nutritional treatments, although it cannot be proved that the mammary gland optimizes a specific linear combination of flux variables, including those based on energy. Altogether, our study indicated that the mammary gland possesses considerable metabolic flexibility.ConclusionOur method enables to study the variability of a metabolic network with respect to efficiency (i.e. yield rates). It allows a quantitative comparison of the respective contributions of precursors to the production of a set of nutrients by a metabolic network, regardless of the choice of the flux distribution within the different branches of the network.