Resource allocation modeling for autonomous prediction of plant cell phenotypes.

Predicting the plant cell response in complex environmental conditions is a challenge in plant biology. Here we developed a resource allocation model of cellular and molecular scale for the leaf photosynthetic cell of Arabidopsis thaliana, based on the Resource Balance Analysis (RBA) constraint-based modeling framework. The RBA model contains the metabolic network and the major macromolecular processes involved in the plant cell growth and survival and localized in cellular compartments. We simulated the model for varying environmental conditions of temperature, irradiance, partial pressure of CO2 and O2, and compared RBA predictions to known resource distributions and quantitative phenotypic traits such as the relative growth rate, the C:N ratio, and finally to the empirical characteristics of CO2 fixation given by the well-established Farquhar model. In comparison to other standard constraint-based modeling methods like Flux Balance Analysis, the RBA model makes accurate quantitative predictions without the need for empirical constraints. Altogether, we show that RBA significantly improves the autonomous prediction of plant cell phenotypes in complex environmental conditions, and provides mechanistic links between the genotype and the phenotype of the plant cell.

Stochastic models of regulation of transcription in biological cells.

In this paper we study an important global regulation mechanism of transcription of biological cells using specific macro-molecules, 6S RNAs. The functional property of 6S RNAs is of blocking the transcription of RNAs when the environment of the cell is not favorable. We investigate the efficiency of this mechanism with a scaling analysis of a stochastic model. The evolution equations of our model are driven by the law of mass action and the total number of polymerases is used as a scaling parameter. Two regimes are analyzed: exponential phase when the environment of the cell is favorable to its growth, and the stationary phase when resources are scarce. In both regimes, by defining properly occupation measures of the model, we prove an averaging principle for the associated multi-dimensional Markov process on a convenient timescale, as well as convergence results for "fast" variables of the system. An analytical expression of the asymptotic fraction of sequestrated polymerases in stationary phase is in particular obtained. The consequences of these results are discussed.

BiPSim: a flexible and generic stochastic simulator for polymerization processes.

Detailed whole-cell modeling requires an integration of heterogeneous cell processes having different modeling formalisms, for which whole-cell simulation could remain tractable. Here, we introduce BiPSim, an open-source stochastic simulator of template-based polymerization processes, such as replication, transcription and translation. BiPSim combines an efficient abstract representation of reactions and a constant-time implementation of the Gillespie's Stochastic Simulation Algorithm (SSA) with respect to reactions, which makes it highly efficient to simulate large-scale polymerization processes stochastically. Moreover, multi-level descriptions of polymerization processes can be handled simultaneously, allowing the user to tune a trade-off between simulation speed and model granularity. We evaluated the performance of BiPSim by simulating genome-wide gene expression in bacteria for multiple levels of granularity. Finally, since no cell-type specific information is hard-coded in the simulator, models can easily be adapted to other organismal species. We expect that BiPSim should open new perspectives for the genome-wide simulation of stochastic phenomena in biology.

Statistical modelling of bacterial promoter sequences for regulatory motif discovery with the help of transcriptome data: application to Listeria monocytogenes.

Automatic de novo identification of the main regulons of a bacterium from genome and transcriptome data remains a challenge. To address this task, we propose a statistical model that can use information on exact positions of the transcription start sites and condition-dependent expression profiles. The central idea of this model is to improve the probabilistic representation of the promoter DNA sequences by incorporating covariates summarizing expression profiles (e.g. coordinates in projection spaces or hierarchical clustering trees). A dedicated trans-dimensional Markov chain Monte Carlo algorithm adjusts the width and palindromic properties of the corresponding position-weight matrices, the number of parameters to describe exact position relative to the transcription start site, and chooses the expression covariates relevant for each motif. All parameters are estimated simultaneously, for many motifs and many expression covariates. The method is applied to a dataset of transcription start sites and expression profiles available for Listeria monocytogenes. The results validate the approach and provide a new global view of the transcription regulatory network of this important pathogen. Remarkably, a previously unreported motif is found in promoter regions of ribosomal protein genes, suggesting a role in the regulation of growth.

BiPOm: a rule-based ontology to represent and infer molecule knowledge from a biological process-centered viewpoint.

BACKGROUND: Managing and organizing biological knowledge remains a major challenge, due to the complexity of living systems. Recently, systemic representations have been promising in tackling such a challenge at the whole-cell scale. In such representations, the cell is considered as a system composed of interlocked subsystems. The need is now to define a relevant formalization of the systemic description of cellular processes. RESULTS: We introduce BiPOm (Biological interlocked Process Ontology for metabolism) an ontology to represent metabolic processes as interlocked subsystems using a limited number of classes and properties. We explicitly formalized the relations between the enzyme, its activity, the substrates and the products of the reaction, as well as the active state of all involved molecules. We further showed that the information of molecules such as molecular types or molecular properties can be deduced by automatic reasoning using logical rules. The information necessary to populate BiPOm can be extracted from existing databases or existing bio-ontologies. CONCLUSION: BiPOm provides a formal rule-based knowledge representation to relate all cellular components together by considering the cellular system as a whole. It relies on a paradigm shift where the anchorage of knowledge is rerouted from the molecule to the biological process. AVAILABILITY: BiPOm can be downloaded at https://github.com/SysBioInra/SysOnto.

Models of protein production along the cell cycle: An investigation of possible sources of noise.

In this article, we quantitatively study, through stochastic models, the effects of several intracellular phenomena, such as cell volume growth, cell division, gene replication as well as fluctuations of available RNA polymerases and ribosomes. These phenomena are indeed rarely considered in classic models of protein production and no relative quantitative comparison among them has been performed. The parameters for a large and representative class of proteins are determined using experimental measures. The main important and surprising conclusion of our study is to show that despite the significant fluctuations of free RNA polymerases and free ribosomes, they bring little variability to protein production contrary to what has been previously proposed in the literature. After verifying the robustness of this quite counter-intuitive result, we discuss its possible origin from a theoretical view, and interpret it as the result of a mean-field effect.

Thermodynamic Approaches in Flux Analysis.

Networks of reactions inside the cell are constrained by the laws of mass and energy balance. Constrained-based modelling (CBM) is the most used method to describe the mass balance of metabolic network. The main key concepts in CBM are stoichiometric analysis such as elementary flux mode analysis or flux balance analysis. Some of these methods have focused on adding thermodynamics constraints to eliminate non-physical fluxes or inconsistencies in the metabolic system. Here, we review the main different approaches and how they tackle the different class of problems.

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.

The bacterial interlocked process ONtology (BiPON): a systemic multi-scale unified representation of biological processes in prokaryotes.

BACKGROUND: High-throughput technologies produce huge amounts of heterogeneous biological data at all cellular levels. Structuring these data together with biological knowledge is a critical issue in biology and requires integrative tools and methods such as bio-ontologies to extract and share valuable information. In parallel, the development of recent whole-cell models using a systemic cell description opened alternatives for data integration. Integrating a systemic cell description within a bio-ontology would help to progress in whole-cell data integration and modeling synergistically. RESULTS: We present BiPON, an ontology integrating a multi-scale systemic representation of bacterial cellular processes. BiPON consists in of two sub-ontologies, bioBiPON and modelBiPON. bioBiPON organizes the systemic description of biological information while modelBiPON describes the mathematical models (including parameters) associated with biological processes. bioBiPON and modelBiPON are related using bridge rules on classes during automatic reasoning. Biological processes are thus automatically related to mathematical models. 37% of BiPON classes stem from different well-established bio-ontologies, while the others have been manually defined and curated. Currently, BiPON integrates the main processes involved in bacterial gene expression processes. CONCLUSIONS: BiPON is a proof of concept of the way to combine formally systems biology and bio-ontology. The knowledge formalization is highly flexible and generic. Most of the known cellular processes, new participants or new mathematical models could be inserted in BiPON. Altogether, BiPON opens up promising perspectives for knowledge integration and sharing and can be used by biologists, systems and computational biologists, and the emerging community of whole-cell modeling.

Resource allocation in living organisms.

Quantitative prediction of resource allocation for living systems has been an intensive area of research in the field of biology. Resource allocation was initially investigated in higher organisms by using empirical mathematical models based on mass distribution. A challenge is now to go a step further by reconciling the cellular scale to the individual scale. In the present paper, we review the foundations of modelling of resource allocation, particularly at the cellular scale: from small macro-molecular models to genome-scale cellular models. We enlighten how the combination of omic measurements and computational advances together with systems biology has contributed to dramatic progresses in the current understanding and prediction of cellular resource allocation. Accurate genome-wide predictive methods of resource allocation based on the resource balance analysis (RBA) framework have been developed and ensure a good trade-off between the complexity/tractability and the prediction capability of the model. The RBA framework shows promise for a wide range of applications in metabolic engineering and synthetic biology, and for pursuing investigations of the design principles of cellular and multi-cellular organisms.

Contrasting mechanisms of growth in two model rod-shaped bacteria.

How cells control their shape and size is a long-standing question in cell biology. Many rod-shaped bacteria elongate their sidewalls by the action of cell wall synthesizing machineries that are associated to actin-like MreB cortical patches. However, little is known about how elongation is regulated to enable varied growth rates and sizes. Here we use total internal reflection fluorescence microscopy and single-particle tracking to visualize MreB isoforms, as a proxy for cell wall synthesis, in Bacillus subtilis and Escherichia coli cells growing in different media and during nutrient upshift. We find that these two model organisms appear to use orthogonal strategies to adapt to growth regime variations: B. subtilis regulates MreB patch speed, while E. coli may mainly regulate the production capacity of MreB-associated cell wall machineries. We present numerical models that link MreB-mediated sidewall synthesis and cell elongation, and argue that the distinct regulatory mechanism employed might reflect the different cell wall integrity constraints in Gram-positive and Gram-negative bacteria.

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.

A stochastic analysis of autoregulation of gene expression.

This paper analyzes, in the context of a prokaryotic cell, the stochastic variability of the number of proteins when there is a control of gene expression by an autoregulation scheme. The goal of this work is to estimate the efficiency of the regulation to limit the fluctuations of the number of copies of a given protein. The autoregulation considered in this paper relies mainly on a negative feedback: the proteins are repressors of their own gene expression. The efficiency of a production process without feedback control is compared to a production process with an autoregulation of the gene expression assuming that both of them produce the same average number of proteins. The main characteristic used for the comparison is the standard deviation of the number of proteins at equilibrium. With a Markovian representation and a simple model of repression, we prove that, under a scaling regime, the repression mechanism follows a Hill repression scheme with an hyperbolic control. An explicit asymptotic expression of the variance of the number of proteins under this regulation mechanism is obtained. Simulations are used to study other aspects of autoregulation such as the rate of convergence to equilibrium of the production process and the case where the control of the production process of proteins is achieved via the inhibition of mRNAs.

Translation elicits a growth rate-dependent, genome-wide, differential protein production in Bacillus subtilis.

Complex regulatory programs control cell adaptation to environmental changes by setting condition-specific proteomes. In balanced growth, bacterial protein abundances depend on the dilution rate, transcript abundances and transcript-specific translation efficiencies. We revisited the current theory claiming the invariance of bacterial translation efficiency. By integrating genome-wide transcriptome datasets and datasets from a library of synthetic gfp-reporter fusions, we demonstrated that translation efficiencies in Bacillus subtilis decreased up to fourfold from slow to fast growth. The translation initiation regions elicited a growth rate-dependent, differential production of proteins without regulators, hence revealing a unique, hard-coded, growth rate-dependent mode of regulation. We combined model-based data analyses of transcript and protein abundances genome-wide and revealed that this global regulation is extensively used in B. subtilis We eventually developed a knowledge-based, three-step translation initiation model, experimentally challenged the model predictions and proposed that a growth rate-dependent drop in free ribosome abundance accounted for the differential protein production.

Reconstruction of the Regulatory Network for Bacillus subtilis and Reconciliation with Gene Expression Data.

We introduce a manually constructed and curated regulatory network model that describes the current state of knowledge of transcriptional regulation of Bacillus subtilis. The model corresponds to an updated and enlarged version of the regulatory model of central metabolism originally proposed in 2008. We extended the original network to the whole genome by integration of information from DBTBS, a compendium of regulatory data that includes promoters, transcription factors (TFs), binding sites, motifs, and regulated operons. Additionally, we consolidated our network with all the information on regulation included in the SporeWeb and Subtiwiki community-curated resources on B. subtilis. Finally, we reconciled our network with data from RegPrecise, which recently released their own less comprehensive reconstruction of the regulatory network for B. subtilis. Our model describes 275 regulators and their target genes, representing 30 different mechanisms of regulation such as TFs, RNA switches, Riboswitches, and small regulatory RNAs. Overall, regulatory information is included in the model for ∼2500 of the ∼4200 genes in B. subtilis 168. In an effort to further expand our knowledge of B. subtilis regulation, we reconciled our model with expression data. For this process, we reconstructed the Atomic Regulons (ARs) for B. subtilis, which are the sets of genes that share the same "ON" and "OFF" gene expression profiles across multiple samples of experimental data. We show how ARs for B. subtilis are able to capture many sets of genes corresponding to regulated operons in our manually curated network. Additionally, we demonstrate how ARs can be used to help expand or validate the knowledge of the regulatory networks by looking at highly correlated genes in the ARs for which regulatory information is lacking. During this process, we were also able to infer novel stimuli for hypothetical genes by exploring the genome expression metadata relating to experimental conditions, gaining insights into novel biology.

Quantitative prediction of genome-wide resource allocation in bacteria.

Predicting resource allocation between cell processes is the primary step towards decoding the evolutionary constraints governing bacterial growth under various conditions. Quantitative prediction at genome-scale remains a computational challenge as current methods are limited by the tractability of the problem or by simplifying hypotheses. Here, we show that the constraint-based modeling method Resource Balance Analysis (RBA), calibrated using genome-wide absolute protein quantification data, accurately predicts resource allocation in the model bacterium Bacillus subtilis for a wide range of growth conditions. The regulation of most cellular processes is consistent with the objective of growth rate maximization except for a few suboptimal processes which likely integrate more complex objectives such as coping with stressful conditions and survival. As a proof of principle by using simulations, we illustrated how calibrated RBA could aid rational design of strains for maximizing protein production, offering new opportunities to investigate design principles in prokaryotes and to exploit them for biotechnological applications.

Highly precise quantification of protein molecules per cell during stress and starvation responses in Bacillus subtilis.

Systems biology based on high quality absolute quantification data, which are mandatory for the simulation of biological processes, successively becomes important for life sciences. We provide protein concentrations on the level of molecules per cell for more than 700 cytosolic proteins of the Gram-positive model bacterium Bacillus subtilis during adaptation to changing growth conditions. As glucose starvation and heat stress are typical challenges in B. subtilis' natural environment and induce both, specific and general stress and starvation proteins, these conditions were selected as models for starvation and stress responses. Analyzing samples from numerous time points along the bacterial growth curve yielded reliable and physiologically relevant data suitable for modeling of cellular regulation under altered growth conditions. The analysis of the adaptational processes based on protein molecules per cell revealed stress-specific modulation of general adaptive responses in terms of protein amount and proteome composition. Furthermore, analysis of protein repartition during glucose starvation showed that biomass seems to be redistributed from proteins involved in amino acid biosynthesis to enzymes of the central carbon metabolism. In contrast, during heat stress most resources of the cell, namely those from amino acid synthetic pathways, are used to increase the amount of chaperones and proteases. Analysis of dynamical aspects of protein synthesis during heat stress adaptation revealed, that these proteins make up almost 30% of the protein mass accumulated during early phases of this stress.

Comprehensive absolute quantification of the cytosolic proteome of Bacillus subtilis by data independent, parallel fragmentation in liquid chromatography/mass spectrometry (LC/MS(E)).

In the growing field of systems biology, the knowledge of protein concentrations is highly required to truly understand metabolic and adaptational networks within the cells. Therefore we established a workflow relying on long chromatographic separation and mass spectrometric analysis by data independent, parallel fragmentation of all precursor ions at the same time (LC/MS(E)). By prevention of discrimination of co-eluting low and high abundant peptides a high average sequence coverage of 40% could be achieved, resulting in identification of almost half of the predicted cytosolic proteome of the Gram-positive model organism Bacillus subtilis (>1,050 proteins). Absolute quantification was achieved by correlation of average MS signal intensities of the three most intense peptides of a protein to the signal intensity of a spiked standard protein digest. Comparative analysis with heavily labeled peptides (AQUA approach) showed the use of only one standard digest is sufficient for global quantification. The quantification results covered almost four orders of magnitude, ranging roughly from 10 to 150,000 copies per cell. To prove this method for its biological relevance selected physiological aspects of B. subtilis cells grown under conditions requiring either amino acid synthesis or alternatively amino acid degradation were analyzed. This allowed both in particular the validation of the adjustment of protein levels by known regulatory events and in general a perspective of new insights into bacterial physiology. Within new findings the analysis of "protein costs" of cellular processes is extremely important. Such a comprehensive and detailed characterization of cellular protein concentrations based on data independent, parallel fragmentation in liquid chromatography/mass spectrometry (LC/MS(E)) data has been performed for the first time and should pave the way for future comprehensive quantitative characterization of microorganisms as physiological entities.

(Im)Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis.

BACKGROUND: Metabolic control analysis (MCA) and supply-demand theory have led to appreciable understanding of the systems properties of metabolic networks that are subject exclusively to metabolic regulation. Supply-demand theory has not yet considered gene-expression regulation explicitly whilst a variant of MCA, i.e. Hierarchical Control Analysis (HCA), has done so. Existing analyses based on control engineering approaches have not been very explicit about whether metabolic or gene-expression regulation would be involved, but designed different ways in which regulation could be organized, with the potential of causing adaptation to be perfect. RESULTS: This study integrates control engineering and classical MCA augmented with supply-demand theory and HCA. Because gene-expression regulation involves time integration, it is identified as a natural instantiation of the 'integral control' (or near integral control) known in control engineering. This study then focuses on robustness against and adaptation to perturbations of process activities in the network, which could result from environmental perturbations, mutations or slow noise. It is shown however that this type of 'integral control' should rarely be expected to lead to the 'perfect adaptation': although the gene-expression regulation increases the robustness of important metabolite concentrations, it rarely makes them infinitely robust. For perfect adaptation to occur, the protein degradation reactions should be zero order in the concentration of the protein, which may be rare biologically for cells growing steadily. CONCLUSIONS: A proposed new framework integrating the methodologies of control engineering and metabolic and hierarchical control analysis, improves the understanding of biological systems that are regulated both metabolically and by gene expression. In particular, the new approach enables one to address the issue whether the intracellular biochemical networks that have been and are being identified by genomics and systems biology, correspond to the 'perfect' regulatory structures designed by control engineering vis-à-vis optimal functions such as robustness. To the extent that they are not, the analyses suggest how they may become so and this in turn should facilitate synthetic biology and metabolic engineering.

A comparative transcriptomic, fluxomic and metabolomic analysis of the response of Saccharomyces cerevisiae to increases in NADPH oxidation.

BACKGROUND: Redox homeostasis is essential to sustain metabolism and growth. We recently reported that yeast cells meet a gradual increase in imposed NADPH demand by progressively increasing flux through the pentose phosphate (PP) and acetate pathways and by exchanging NADH for NADPH in the cytosol, via a transhydrogenase-like cycle. Here, we studied the mechanisms underlying this metabolic response, through a combination of gene expression profiling and analyses of extracellular and intracellular metabolites and 13 C-flux analysis. RESULTS: NADPH oxidation was increased by reducing acetoin to 2,3-butanediol in a strain overexpressing an engineered NADPH-dependent butanediol dehydrogenase cultured in the presence of acetoin. An increase in NADPH demand to 22 times the anabolic requirement for NADPH was accompanied by the intracellular accumulation of PP pathway metabolites consistent with an increase in flux through this pathway. Increases in NADPH demand were accompanied by the successive induction of several genes of the PP pathway. NADPH-consuming pathways, such as amino-acid biosynthesis, were upregulated as an indirect effect of the decrease in NADPH availability. Metabolomic analysis showed that the most extreme modification of NADPH demand resulted in an energetic problem. Our results also highlight the influence of redox status on aroma production. CONCLUSIONS: Combined 13 C-flux, intracellular metabolite levels and microarrays analyses revealed that NADPH homeostasis, in response to a progressive increase in NADPH demand, was achieved by the regulation, at several levels, of the PP pathway. This pathway is principally under metabolic control, but regulation of the transcription of PP pathway genes can exert a stronger effect, by redirecting larger amounts of carbon to this pathway to satisfy the demand for NADPH. No coordinated response of genes involved in NADPH metabolism was observed, suggesting that yeast has no system for sensing NADPH/NADP+ ratio. Instead, the induction of NADPH-consuming amino-acid pathways in conditions of NADPH limitation may indirectly trigger the transcription of a set of PP pathway genes.