MOTIVATION: Taxonomic analysis of environmental microbial communities is now routinely performed thanks to advances in DNA sequencing. Determining the role of these communities in global biogeochemical cycles requires the identification of their metabolic functions, such as hydrogen oxidation, sulfur reduction, and carbon fixation. These functions can be directly inferred from metagenomics data, but in many environmental applications metabarcoding is still the method of choice. The reconstruction of metabolic functions from metabarcoding data and their integration into coarse-grained representations of biogeochemical cycles remains a difficult bioinformatics problem today. RESULTS: We developed a pipeline, called Tabigecy, which exploits taxonomic affiliations to predict metabolic functions constituting biogeochemical cycles. In a first step, Tabigecy uses the tool EsMeCaTa to predict consensus proteomes from input affiliations. To optimize this process, we generated a precomputed database containing information about 2404 taxa from UniProt. The consensus proteomes are searched using bigecyhmm, a newly developed Python package relying on Hidden Markov Models to identify key enzymes involved in metabolic function of biogeochemical cycles. The metabolic functions are then projected on coarse-grained representation of the cycles. We applied Tabigecy to two salt cavern datasets and validated its predictions with microbial activity and hydrochemistry measurements performed on the samples. The results highlight the utility of the approach to investigate the impact of microbial communities on biogeochemical processes. AVAILABILITY AND IMPLEMENTATION: The Tabigecy pipeline is available at https://github.com/ArnaudBelcour/tabigecy. The Python package bigecyhmm and the precomputed EsMeCaTa database are also separately available at https://github.com/ArnaudBelcour/bigecyhmm and https://doi.org/10.5281/zenodo.13354073, respectively.

Synthetic microbial consortia have been increasingly utilized in biotechnology and experimental evidence shows that suitably engineered consortia can outperform individual species in the synthesis of valuable products. Despite significant achievements, though, a quantitative understanding of the conditions that make this possible, and of the trade-offs due to the concurrent growth of multiple species, is still limited. In this work, we contribute to filling this gap by the investigation of a known prototypical synthetic consortium. A first E. coli strain, producing a heterologous protein, is sided by a second E. coli strain engineered to scavenge toxic byproducts, thus favoring the growth of the producer at the expense of diverting part of the resources to the growth of the cleaner. The simplicity of the consortium is ideal to perform an in depth-analysis and draw conclusions of more general interest. We develop a coarse-grained mathematical model that quantitatively accounts for literature data from different key growth phenotypes. Based on this, assuming growth in chemostat, we first investigate the conditions enabling stable coexistence of both strains and the effect of the metabolic load due to heterologous protein production. In these conditions, we establish when and to what extent the consortium outperforms the producer alone in terms of productivity. Finally, we show in chemostat as well as in a fed-batch scenario that gain in productivity comes at the price of a reduced yield, reflecting at the level of the consortium resource allocation trade-offs that are well-known for individual species.

BACKGROUND: Fluorescent reporter genes have become widely used for monitoring gene expression in living cells. When a microbial strain carrying a reporter gene is grown in a microplate reader, the fluorescence and the absorbance (optical density) of the culture can be automatically measured every few minutes in a highly parallelized way. The extraction of useful information from the resulting large amounts of data is not easy to achieve, because the fluorescence and absorbance measurements are only indirectly related to promoter activities and protein concentrations, requiring mathematical models of the expression of reporter genes for their interpretation. Although the principles of the analysis of reporter gene data are well-established today, there is a lack of general-purpose bioinformatics tools based on generic measurement models and sound inference procedures. This has motivated the development of WellInverter, a web application based on well-known methods for regularized linear inversion. RESULTS: We present a new version of WellInverter that considerably improves the performance and usability of the original application. In particular, we have put in place a parallel computing architecture with a load balancer to distribute analysis queries over several back-end servers, we have completely redesigned the graphical user interface to better support the different analysis steps, and we have developed a plug-in system for the parsing of data files produced by microplate readers from different manufacturers. We illustrate the functioning of WellInverter by analyzing data of the expression of a fluorescent reporter gene controlled by a phage promoter in growing Escherichia coli populations. We show that the expression pattern in different growth media, supporting different growth rates, corresponds to the pattern expected for a constitutive gene. CONCLUSIONS: The new version of WellInverter is a robust, easy-to-use and scalable web application, which has been deployed on two publicly accessible web servers and which can also be installed locally. A demo version of the application with two sample datasets is available on-line.

MOTIVATION: Technological advances in metabolomics have made it possible to monitor the concentration of extracellular metabolites over time. From these data, it is possible to compute the rates of uptake and excretion of the metabolites by a growing cell population, providing precious information on the functioning of intracellular metabolism. The computation of the rate of these exchange reactions, however, is difficult to achieve in practice for a number of reasons, notably noisy measurements, correlations between the concentration profiles of the different extracellular metabolites, and discontinuties in the profiles due to sudden changes in metabolic regime. RESULTS: We present a method for precisely estimating time-varying uptake and excretion rates from time-series measurements of extracellular metabolite concentrations, specifically addressing all of the above issues. The estimation problem is formulated in a regularized Bayesian framework and solved by a combination of extended Kalman filtering and smoothing. The method is shown to improve upon methods based on spline smoothing of the data. Moreover, when applied to two actual datasets, the method recovers known features of overflow metabolism in Escherichia coli and Lactococcus lactis , and provides evidence for acetate uptake by L. lactis after glucose exhaustion. The results raise interesting perspectives for further work on rate estimation from measurements of intracellular metabolites. AVAILABILITY AND IMPLEMENTATION: The Matlab code for the estimation method is available for download at https://team.inria.fr/ibis/rate-estimation-software/ , together with the datasets. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Microbial physiology exhibits growth laws that relate the macromolecular composition of the cell to the growth rate. Recent work has shown that these empirical regularities can be derived from coarse-grained models of resource allocation. While these studies focus on steady-state growth, such conditions are rarely found in natural habitats, where microorganisms are continually challenged by environmental fluctuations. The aim of this paper is to extend the study of microbial growth strategies to dynamical environments, using a self-replicator model. We formulate dynamical growth maximization as an optimal control problem that can be solved using Pontryagin's Maximum Principle. We compare this theoretical gold standard with different possible implementations of growth control in bacterial cells. We find that simple control strategies enabling growth-rate maximization at steady state are suboptimal for transitions from one growth regime to another, for example when shifting bacterial cells to a medium supporting a higher growth rate. A near-optimal control strategy in dynamical conditions is shown to require information on several, rather than a single physiological variable. Interestingly, this strategy has structural analogies with the regulation of ribosomal protein synthesis by ppGpp in the enterobacterium Escherichia coli. It involves sensing a mismatch between precursor and ribosome concentrations, as well as the adjustment of ribosome synthesis in a switch-like manner. Our results show how the capability of regulatory systems to integrate information about several physiological variables is critical for optimizing growth in a changing environment.

MOTIVATION: Time-series observations from reporter gene experiments are commonly used for inferring and analyzing dynamical models of regulatory networks. The robust estimation of promoter activities and protein concentrations from primary data is a difficult problem due to measurement noise and the indirect relation between the measurements and quantities of biological interest. RESULTS: We propose a general approach based on regularized linear inversion to solve a range of estimation problems in the analysis of reporter gene data, notably the inference of growth rate, promoter activity, and protein concentration profiles. We evaluate the validity of the approach using in silico simulation studies, and observe that the methods are more robust and less biased than indirect approaches usually encountered in the experimental literature based on smoothing and subsequent processing of the primary data. We apply the methods to the analysis of fluorescent reporter gene data acquired in kinetic experiments with Escherichia coli. The methods are capable of reliably reconstructing time-course profiles of growth rate, promoter activity and protein concentration from weak and noisy signals at low population volumes. Moreover, they capture critical features of those profiles, notably rapid changes in gene expression during growth transitions. AVAILABILITY AND IMPLEMENTATION: The methods described in this article are made available as a Python package (LGPL license) and also accessible through a web interface. For more information, see https://team.inria.fr/ibis/wellinverter.

The inference of regulatory interactions and quantitative models of gene regulation from time-series transcriptomics data has been extensively studied and applied to a range of problems in drug discovery, cancer research, and biotechnology. The application of existing methods is commonly based on implicit assumptions on the biological processes under study. First, the measurements of mRNA abundance obtained in transcriptomics experiments are taken to be representative of protein concentrations. Second, the observed changes in gene expression are assumed to be solely due to transcription factors and other specific regulators, while changes in the activity of the gene expression machinery and other global physiological effects are neglected. While convenient in practice, these assumptions are often not valid and bias the reverse engineering process. Here we systematically investigate, using a combination of models and experiments, the importance of this bias and possible corrections. We measure in real time and in vivo the activity of genes involved in the FliA-FlgM module of the E. coli motility network. From these data, we estimate protein concentrations and global physiological effects by means of kinetic models of gene expression. Our results indicate that correcting for the bias of commonly-made assumptions improves the quality of the models inferred from the data. Moreover, we show by simulation that these improvements are expected to be even stronger for systems in which protein concentrations have longer half-lives and the activity of the gene expression machinery varies more strongly across conditions than in the FliA-FlgM module. The approach proposed in this study is broadly applicable when using time-series transcriptome data to learn about the structure and dynamics of regulatory networks. In the case of the FliA-FlgM module, our results demonstrate the importance of global physiological effects and the active regulation of FliA and FlgM half-lives for the dynamics of FliA-dependent promoters.

MOTIVATION: High-throughput measurement techniques for metabolism and gene expression provide a wealth of information for the identification of metabolic network models. Yet, missing observations scattered over the dataset restrict the number of effectively available datapoints and make classical regression techniques inaccurate or inapplicable. Thorough exploitation of the data by identification techniques that explicitly cope with missing observations is therefore of major importance. RESULTS: We develop a maximum-likelihood approach for the estimation of unknown parameters of metabolic network models that relies on the integration of statistical priors to compensate for the missing data. In the context of the linlog metabolic modeling framework, we implement the identification method by an Expectation-Maximization (EM) algorithm and by a simpler direct numerical optimization method. We evaluate performance of our methods by comparison to existing approaches, and show that our EM method provides the best results over a variety of simulated scenarios. We then apply the EM algorithm to a real problem, the identification of a model for the Escherichia coli central carbon metabolism, based on challenging experimental data from the literature. This leads to promising results and allows us to highlight critical identification issues.

The adaptation of the bacterium Escherichia coli to carbon starvation is controlled by a large network of biochemical reactions involving genes, mRNAs, proteins, and signalling molecules. The dynamics of these networks is difficult to analyze, notably due to a lack of quantitative information on parameter values. To overcome these limitations, model reduction approaches based on quasi-steady-state (QSS) and piecewise-linear (PL) approximations have been proposed, resulting in models that are easier to handle mathematically and computationally. These approximations are not supposed to affect the capability of the model to account for essential dynamical properties of the system, but the validity of this assumption has not been systematically tested. In this paper, we carry out such a study by evaluating a large and complex PL model of the carbon starvation response in E. coli using an ensemble approach. The results show that, in comparison with conventional nonlinear models, the PL approximations generally preserve the dynamics of the carbon starvation response network, although with some deviations concerning notably the quantitative precision of the model predictions. This encourages the application of PL models to the qualitative analysis of bacterial regulatory networks, in situations where the reference time scale is that of protein synthesis and degradation.

MOTIVATION: Investigating the relation between the structure and behavior of complex biological networks often involves posing the question if the hypothesized structure of a regulatory network is consistent with the observed behavior, or if a proposed structure can generate a desired behavior. RESULTS: The above questions can be cast into a parameter search problem for qualitative models of regulatory networks. We develop a method based on symbolic model checking that avoids enumerating all possible parametrizations, and show that this method performs well on real biological problems, using the IRMA synthetic network and benchmark datasets. We test the consistency between IRMA and time-series expression profiles, and search for parameter modifications that would make the external control of the system behavior more robust. AVAILABILITY: GNA and the IRMA model are available at http://ibis.inrialpes.fr/.

MOTIVATION: Fluorescent and luminescent reporter gene systems in combination with automated microplate readers allow real-time monitoring of gene expression on the population level at high precision and sampling density. This generates large amounts of data for the analysis of which computer tools are missing to date. RESULTS: We have developed WellReader, a MATLAB program for the analysis of fluorescent and luminescent reporter gene data. WellReader allows the user to load the output files of microplate readers, remove outliers, correct for background effects and smooth and fit the data. Moreover, it computes biologically relevant quantities from the measured signals, notably promoter activities and protein concentrations, and compares the resulting expression profiles of different genes under different conditions. AVAILABILITY: WellReader is available under a LGPL licence at http://prabi1.inrialpes.fr/trac/wellreader.

Gene regulatory networks consist of direct interactions but also include indirect interactions mediated by metabolites and signaling molecules. We describe how these indirect interactions can be derived from a model of the underlying biochemical reaction network, using weak time-scale assumptions in combination with sensitivity criteria from metabolic control analysis. We apply this approach to a model of the carbon assimilation network in Escherichia coli. Our results show that the derived gene regulatory network is densely connected, contrary to what is usually assumed. Moreover, the network is largely sign-determined, meaning that the signs of the indirect interactions are fixed by the flux directions of biochemical reactions, independently of specific parameter values and rate laws. An inversion of the fluxes following a change in growth conditions may affect the signs of the indirect interactions though. This leads to a feedback structure that is at the same time robust to changes in the kinetic properties of enzymes and that has the flexibility to accommodate radical changes in the environment.

BACKGROUND: The study of biological networks has led to the development of increasingly large and detailed models. Computer tools are essential for the simulation of the dynamical behavior of the networks from the model. However, as the size of the models grows, it becomes infeasible to manually verify the predictions against experimental data or identify interesting features in a large number of simulation traces. Formal verification based on temporal logic and model checking provides promising methods to automate and scale the analysis of the models. However, a framework that tightly integrates modeling and simulation tools with model checkers is currently missing, on both the conceptual and the implementational level. RESULTS: We have developed a generic and modular web service, based on a service-oriented architecture, for integrating the modeling and formal verification of genetic regulatory networks. The architecture has been implemented in the context of the qualitative modeling and simulation tool GNA and the model checkers NUSMV and CADP. GNA has been extended with a verification module for the specification and checking of biological properties. The verification module also allows the display and visual inspection of the verification results. CONCLUSIONS: The practical use of the proposed web service is illustrated by means of a scenario involving the analysis of a qualitative model of the carbon starvation response in E. coli. The service-oriented architecture allows modelers to define the model and proceed with the specification and formal verification of the biological properties by means of a unified graphical user interface. This guarantees a transparent access to formal verification technology for modelers of genetic regulatory networks.

Formal verification based on model checking provides a powerful technology to query qualitative models of dynamical systems. The application of model-checking approaches is hampered, however, by the difficulty for non-expert users to formulate appropriate questions in temporal logic. In order to deal with this problem, we propose the use of patterns, that is, high-level query templates capturing recurring questions which can be automatically translated to temporal logic. We develop a set of patterns for the analysis of qualitative models of genetic regulatory networks, which are sufficiently generic though to be useful in other application domains. The applicability of the patterns has been investigated by the analysis of a model of the network of global regulators controlling the carbon starvation response in Escherichia coli.

Analysis of the attractors of a genetic regulatory network gives a good indication of the possible functional modes of the system. In this paper we are concerned with the problem of finding all steady states of genetic regulatory networks described by piecewise-linear differential equation (PLDE) models. We show that the problem is NP-hard and translate it into a propositional satisfiability (SAT) problem. This allows the use of existing, efficient SAT solvers and has enabled the development of a steady state search module of the computer tool Genetic Network Analyzer (GNA). The practical use of this module is demonstrated by means of the analysis of a number of relatively small bacterial regulatory networks as well as randomly generated networks of several hundreds of genes.

Modelers of molecular interaction networks encounter the paradoxical situation that while large amounts of data are available, these are often insufficient for the formulation and analysis of mathematical models describing the network dynamics. In particular, information on the reaction mechanisms and numerical values of kinetic parameters are usually not available for all but a few well-studied model systems. In this article we review two strategies that have been proposed for dealing with incomplete information in the study of molecular interaction networks: parameter sensitivity analysis and model simplification. These strategies are based on the biologically justified intuition that essential properties of the system dynamics are robust against moderate changes in the value of kinetic parameters or even in the rate laws describing the interactions. Although advanced measurement techniques can be expected to relieve the problem of incomplete information to some extent, the strategies discussed in this article will retain their interest as tools providing an initial characterization of essential properties of the network dynamics.

MOTIVATION: The study of genetic regulatory networks has received a major impetus from the recent development of experimental techniques allowing the measurement of patterns of gene expression in a massively parallel way. This experimental progress calls for the development of appropriate computer tools for the modeling and simulation of gene regulation processes. RESULTS: We present Genetic Network Analyzer (GNA), a computer tool for the modeling and simulation of genetic regulatory networks. The tool is based on a qualitative simulation method that employs coarse-grained models of regulatory networks. The use of GNA is illustrated by a case study of the network of genes and interactions regulating the initiation of sporulation in Bacillus subtilis. AVAILABILITY: GNA and the model of the sporulation network are available at http://www-helix.inrialpes.fr/gna.