Automated generation of bacterial resource allocation models.

Resource Balance Analysis (RBA) is a computational method based on resource allocation, which performs accurate quantitative predictions of whole-cell states (i.e. growth rate, metabolic fluxes, abundances of molecular machines including enzymes) across growth conditions. We present an integrated workflow of RBA together with the Python package RBApy. RBApy builds bacterial RBA models from annotated genome-scale metabolic models by adding descriptions of cellular processes relevant for growth and maintenance. The package includes functions for model simulation and calibration and for interfacing to Escher maps and Proteomaps for visualization. We demonstrate that RBApy faithfully reproduces results obtained by a hand-curated and experimentally validated RBA model for Bacillus subtilis. We also present a calibrated RBA model of Escherichia coli generated from scratch, which obtained excellent fits to measured flux values and enzyme abundances. RBApy makes whole-cell modelling accessible for a wide range of bacterial wild-type and engineered strains, as illustrated with a CO2-fixing Escherichia coli strain. AVAILABILITY: RBApy is available at /https://github.com/SysBioInra/RBApy, under the licence GNU GPL version 3, and runs on Linux, Mac and Windows distributions.

Carriage of λ Latent Virus Is Costly for Its Bacterial Host due to Frequent Reactivation in Monoxenic Mouse Intestine.

Temperate phages, the bacterial viruses able to enter in a dormant prophage state in bacterial genomes, are present in the majority of bacterial strains for which the genome sequence is available. Although these prophages are generally considered to increase their hosts' fitness by bringing beneficial genes, studies demonstrating such effects in ecologically relevant environments are relatively limited to few bacterial species. Here, we investigated the impact of prophage carriage in the gastrointestinal tract of monoxenic mice. Combined with mathematical modelling, these experimental results provided a quantitative estimation of key parameters governing phage-bacteria interactions within this model ecosystem. We used wild-type and mutant strains of the best known host/phage pair, Escherichia coli and phage λ. Unexpectedly, λ prophage caused a significant fitness cost for its carrier, due to an induction rate 50-fold higher than in vitro, with 1 to 2% of the prophage being induced. However, when prophage carriers were in competition with isogenic phage susceptible bacteria, the prophage indirectly benefited its carrier by killing competitors: infection of susceptible bacteria led to phage lytic development in about 80% of cases. The remaining infected bacteria were lysogenized, resulting overall in the rapid lysogenization of the susceptible lineage. Moreover, our setup enabled to demonstrate that rare events of phage gene capture by homologous recombination occurred in the intestine of monoxenic mice. To our knowledge, this study constitutes the first quantitative characterization of temperate phage-bacteria interactions in a simplified gut environment. The high prophage induction rate detected reveals DNA damage-mediated SOS response in monoxenic mouse intestine. We propose that the mammalian gut, the most densely populated bacterial ecosystem on earth, might foster bacterial evolution through high temperate phage activity.

Optimal resource allocation enables mathematical exploration of microbial metabolic configurations.

Central to the functioning of any living cell, the metabolic network is a complex network of biochemical reactions. It may also be viewed as an elaborate production system, integrating a diversity of internal and external signals in order to efficiently produce the energy and the biochemical precursors to ensure all cellular functions. Even in simple organisms like bacteria, it shows a striking level of coordination, adapting to very different growth media. Constraint-based models constitute an efficient mathematical framework to compute optimal metabolic configurations, at the scale of a whole genome. Combining the constraint-based approach "Resource Balance Analysis" with combinatorial optimization techniques, we propose a general method to explore these configurations, based on the inference of logical rules governing the activation of metabolic fluxes in response to diverse extracellular media. Using the concept of partial Boolean functions, we notably introduce a novel tractable algorithm to infer monotone Boolean functions on a minimal support. Monotonicity seems particularly relevant in this context, since the orderliness exhibited by the metabolic network's dynamical behavior is expected to give rise to relatively simple rules. First results are promising, as the application of the method on Bacillus subtilis central carbon metabolism allows to recover known regulations as well as to investigate lesser known parts of the global regulatory network.

Cell death and life in cancer: mathematical modeling of cell fate decisions.

Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tightly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting with cancer. We present a study of a mathematical model describing cellular choice between survival and two alternative cell death modalities: apoptosis and necrosis. The model is implemented in discrete modeling formalism and allows to predict probabilities of having a particular cellular phenotype in response to engagement of cell death receptors. Using an original parameter sensitivity analysis developed for discrete dynamic systems, we determine variables that appear to be critical in the cellular fate decision and discuss how they are exploited by existing cancer therapies.

Mathematical modelling of cell-fate decision in response to death receptor engagement.

Cytokines such as TNF and FASL can trigger death or survival depending on cell lines and cellular conditions. The mechanistic details of how a cell chooses among these cell fates are still unclear. The understanding of these processes is important since they are altered in many diseases, including cancer and AIDS. Using a discrete modelling formalism, we present a mathematical model of cell fate decision recapitulating and integrating the most consistent facts extracted from the literature. This model provides a generic high-level view of the interplays between NFkappaB pro-survival pathway, RIP1-dependent necrosis, and the apoptosis pathway in response to death receptor-mediated signals. Wild type simulations demonstrate robust segregation of cellular responses to receptor engagement. Model simulations recapitulate documented phenotypes of protein knockdowns and enable the prediction of the effects of novel knockdowns. In silico experiments simulate the outcomes following ligand removal at different stages, and suggest experimental approaches to further validate and specialise the model for particular cell types. We also propose a reduced conceptual model implementing the logic of the decision process. This analysis gives specific predictions regarding cross-talks between the three pathways, as well as the transient role of RIP1 protein in necrosis, and confirms the phenotypes of novel perturbations. Our wild type and mutant simulations provide novel insights to restore apoptosis in defective cells. The model analysis expands our understanding of how cell fate decision is made. Moreover, our current model can be used to assess contradictory or controversial data from the literature. Ultimately, it constitutes a valuable reasoning tool to delineate novel experiments.

Dynamic interspecies interactions and robustness in a four-species model biofilm.

Interspecific interactions within biofilms determine relative species abundance, growth dynamics, community resilience, and success or failure of invasion by an extraneous organism. However, deciphering interspecific interactions and assessing their contribution to biofilm properties and function remain a challenge. Here, we describe the constitution of a model biofilm composed of four bacterial species belonging to four different genera (Rhodocyclus sp., Pseudomonas fluorescens, Kocuria varians, and Bacillus cereus), derived from a biofilm isolated from an industrial milk pasteurization unit. We demonstrate that the growth dynamics and equilibrium composition of this biofilm are highly reproducible. Based on its equilibrium composition, we show that the establishment of this four-species biofilm is highly robust against initial, transient perturbations but less so towards continuous perturbations. By comparing biofilms formed from different numbers and combinations of the constituent species and by fitting a growth model to the experimental data, we reveal a network of dynamic, positive, and negative interactions that determine the final composition of the biofilm. Furthermore, we reveal that the molecular determinant of one negative interaction is the thiocillin I synthesized by the B. cereus strain, and demonstrate its importance for species distribution and its impact on robustness by mutational analysis of the biofilm ecosystem.

Comparing Boolean and piecewise affine differential models for genetic networks.

Multi-level discrete models of genetic networks, or the more general piecewise affine differential models, provide qualitative information on the dynamics of the system, based on a small number of parameters (such as synthesis and degradation rates). Boolean models also provide qualitative information, but are based simply on the structure of interconnections. To explore the relationship between the two formalisms, a piecewise affine differential model and a Boolean model are compared, for the carbon starvation response network in E. coli. The asymptotic dynamics of both models are shown to be quite similar. This study suggests new tools for analysis and reduction of biological networks.

Analysis Tools for Interconnected Boolean Networks With Biological Applications.

Boolean networks with asynchronous updates are a class of logical models particularly well adapted to describe the dynamics of biological networks with uncertain measures. The state space of these models can be described by an asynchronous state transition graph, which represents all the possible exits from every single state, and gives a global image of all the possible trajectories of the system. In addition, the asynchronous state transition graph can be associated with an absorbing Markov chain, further providing a semi-quantitative framework where it becomes possible to compute probabilities for the different trajectories. For large networks, however, such direct analyses become computationally untractable, given the exponential dimension of the graph. Exploiting the general modularity of biological systems, we have introduced the novel concept of asymptotic graph, computed as an interconnection of several asynchronous transition graphs and recovering all asymptotic behaviors of a large interconnected system from the behavior of its smaller modules. From a modeling point of view, the interconnection of networks is very useful to address for instance the interplay between known biological modules and to test different hypotheses on the nature of their mutual regulatory links. This paper develops two new features of this general methodology: a quantitative dimension is added to the asymptotic graph, through the computation of relative probabilities for each final attractor and a companion cross-graph is introduced to complement the method on a theoretical point of view.

Hierarchical analysis of piecewise affine models of gene regulatory networks.

A key point in the analysis of dynamical models of biological systems is to handle systems of relatively high dimensions. In the present paper we propose a method to hierarchically organize a certain type of piecewise affine (PWA) differential systems. This specific class of systems has been extensively studied for the past few years, as it provides a good framework to model gene regulatory networks. The method, shown on several examples, allows a qualitative analysis of the asymptotic behavior of a PWA system, decomposing it into several smaller subsystems. This technique, based on the well-known strongly connected components decomposition, is not new. However, its adaptation to the non-smooth PWA differential equations turns out to be quite relevant because of the strong discrete structure underlying these equations. Its biological relevance is shown on a 7-dimensional PWA system modeling the gene network responsible for the carbon starvation response in Escherichia coli.