Optimal protein production by a synthetic microbial consortium: coexistence, distribution of labor, and syntrophy

The bacterium E. coli is widely used to produce recombinant proteins such as growth hormone and insulin. One inconvenience with E. coli cultures is the secretion of acetate through overflow metabolism. Acetate inhibits cell growth and represents a carbon diversion, which results in several negative effects on protein production. One way to overcome this problem is the use of a synthetic consortium of two different E. coli strains, one producing recombinant proteins and one reducing the acetate concentration. In this paper, we study a mathematical model of such a synthetic community in a chemostat where both strains are allowed to produce recombinant proteins. We give necessary and sufficient conditions for the existence of a coexistence equilibrium and show that it is unique. Based on this equilibrium, we define a multi-objective optimization problem for the maximization of two important bioprocess performance metrics, process yield and productivity. Solving numerically this problem, we find the best available trade-offs between the metrics. Under optimal operation of the mixed community, both strains must produce the protein of interest, and not only one (distribution instead of division of labor). Moreover, in this regime acetate secretion by one strain is necessary for the survival of the other (syntrophy). The results thus illustrate how complex multi-level dynamics shape the optimal production of recombinant proteins by synthetic microbial consortia.

Maturation models of fluorescent proteins are necessary for unbiased estimates of promoter activity

Fluorescent proteins (FPs) are a powerful tool to quantitatively monitor gene expression. The dynamics of a promoter and its regulation can be inferred from fluorescence data. The interpretation of fluorescent data, however, is strongly dependent on the maturation of FPs since different proteins mature in distinct ways. We propose a novel approach for analyzing fluorescent reporter data by incorporating maturation dynamics in the reconstruction of promoter activities. Our approach consists of developing and calibrating mechanistic maturation models for distinct FPs. These models are then used alongside a Bayesian approach to estimate promoter activities from fluorescence data. We demonstrate by means of targeted experiments in Escherichia coli that our approach provides robust estimates and that accounting for maturation is, in many cases, essential for the interpretation of gene expression data.

Inheritance and variability of kinetic gene expression parameters in microbial cells: modeling and inference from lineage tree data

Motivation

Modern experimental technologies enable monitoring of gene expression dynamics in individual cells and quantification of its variability in isogenic microbial populations. Among the sources of this variability is the randomness that affects inheritance of gene expression factors at cell division. Known parental relationships among individually observed cells provide invaluable information for the characterization of this extrinsic source of gene expression noise. Despite this fact, most existing methods to infer stochastic gene expression models from single-cell data dedicate little attention to the reconstruction of mother–daughter inheritance dynamics.

Results

Starting from a transcription and translation model of gene expression, we propose a stochastic model for the evolution of gene expression dynamics in a population of dividing cells. Based on this model, we develop a method for the direct quantification of inheritance and variability of kinetic gene expression parameters from single-cell gene expression and lineage data. We demonstrate that our approach provides unbiased estimates of mother–daughter inheritance parameters, whereas indirect approaches using lineage information only in the post-processing of individual-cell parameters underestimate inheritance. Finally, we show on yeast osmotic shock response data that daughter cell parameters are largely determined by the mother, thus confirming the relevance of our method for the correct assessment of the onset of gene expression variability and the study of the transmission of regulatory factors.

Availability and implementation

Software code is available at https://github.com/almarguet/IdentificationWithARME. Lineage tree data is available upon request.

Supplementary information

Supplementary material is available at Bioinformatics online.

Enhanced production of heterologous proteins by a synthetic microbial community: Conditions and trade-offs

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.

In nature, microorganisms occur in communities comprising a variety of mutually interacting species. Established through evolution, these interactions allow for the survival and growth of microorganisms in their natural environment, and give rise to complex dynamics that could not be exhibited by any of the species in isolation. The richness of microbial community dynamics has been leveraged to outperform individual species in biotechnological production processes and other processes of high societal value. Yet, in view of their complexity, natural communities are difficult to study and control. In order to overcome these issues, a rapidly growing research field concerns the rational design and engineering of synthetic microbial consortia. Despite the great potential of synthetic microbial consortia, and significant efforts devoted to their mathematical modelling and analysis, a detailed understanding of how enhanced production can be achieved, and at what cost, is still unavailable. In this work, based on a quantitative model of a prototypical synthetic microbial consortium, we determine precise conditions under which a consortium outperforms individual species in the production of a recombinant protein. Moreover, we identify the inherent trade-offs between productivity and efficiency of substrate utilization.

Estimation of time-varying growth, uptake and excretion rates from dynamic metabolomics data

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.

Supplementary information

Supplementary data are available at Bioinformatics online.

Mathematical modelling of microbes: metabolism, gene expression and growth

The growth of microorganisms involves the conversion of nutrients in the environment into biomass, mostly proteins and other macromolecules. This conversion is accomplished by networks of biochemical reactions cutting across cellular functions, such as metabolism, gene expression, transport and signalling. Mathematical modelling is a powerful tool for gaining an understanding of the functioning of this large and complex system and the role played by individual constituents and mechanisms. This requires models of microbial growth that provide an integrated view of the reaction networks and bridge the scale from individual reactions to the growth of a population. In this review, we derive a general framework for the kinetic modelling of microbial growth from basic hypotheses about the underlying reaction systems. Moreover, we show that several families of approximate models presented in the literature, notably flux balance models and coarse-grained whole-cell models, can be derived with the help of additional simplifying hypotheses. This perspective clearly brings out how apparently quite different modelling approaches are related on a deeper level, and suggests directions for further research.

Inference of protein kinetics by stochastic modeling and simulation of fluorescence recovery after photobleaching experiments

MOTIVATION

Fluorescence recovery after photobleaching (FRAP) is a functional live cell imaging technique that permits the exploration of protein dynamics in living cells. To extract kinetic parameters from FRAP data, a number of analytical models have been developed. Simplifications are inherent in these models, which may lead to inexhaustive or inaccurate exploitation of the experimental data. An appealing alternative is offered by the simulation of biological processes in realistic environments at a particle level. However, inference of kinetic parameters using simulation-based models is still limited.

RESULTS

We introduce and demonstrate a new method for the inference of kinetic parameter values from FRAP data. A small number of in silico FRAP experiments is used to construct a mapping from FRAP recovery curves to the parameters of the underlying protein kinetics. Parameter estimates from experimental data can then be computed by applying the mapping to the observed recovery curves. A bootstrap process is used to investigate identifiability of the physical parameters and determine confidence regions for their estimates. Our method circumvents the computational burden of seeking the best-fitting parameters via iterative simulation. After validation on synthetic data, the method is applied to the analysis of the nuclear proteins Cdt1, PCNA and GFPnls. Parameter estimation results from several experimental samples are in accordance with previous findings, but also allow us to discuss identifiability issues as well as cell-to-cell variability of the protein kinetics.

IMPLEMENTATION

All methods were implemented in MATLAB R2011b. Monte Carlo simulations were run on the HPC cluster Brutus of ETH Zurich.

CONTACT

lygeros@control.ee.ethz.ch or lygerou@med.upatras.gr

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

On the identifiability of metabolic network models

A major problem for the identification of metabolic network models is parameter identifiability, that is, the possibility to unambiguously infer the parameter values from the data. Identifiability problems may be due to the structure of the model, in particular implicit dependencies between the parameters, or to limitations in the quantity and quality of the available data. We address the detection and resolution of identifiability problems for a class of pseudo-linear models of metabolism, so-called linlog models. Linlog models have the advantage that parameter estimation reduces to linear or orthogonal regression, which facilitates the analysis of identifiability. We develop precise definitions of structural and practical identifiability, and clarify the fundamental relations between these concepts. In addition, we use singular value decomposition to detect identifiability problems and reduce the model to an identifiable approximation by a principal component analysis approach. The criterion is adapted to real data, which are frequently scarce, incomplete, and noisy. The test of the criterion on a model with simulated data shows that it is capable of correctly identifying the principal components of the data vector. The application to a state-of-the-art dataset on central carbon metabolism in Escherichia coli yields the surprising result that only 4 out of 31 reactions, and 37 out of 100 parameters, are identifiable. This underlines the practical importance of identifiability analysis and model reduction in the modeling of large-scale metabolic networks. Although our approach has been developed in the context of linlog models, it carries over to other pseudo-linear models, such as generalized mass-action (power-law) models. Moreover, it provides useful hints for the identifiability analysis of more general classes of nonlinear models of metabolism.

Identification of metabolic network models from incomplete high-throughput datasets

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.

Contact:sara.berthoumieux@inria.fr; eugenio.cinquemani@inria.fr

Supplementary information:Supplementary data are available at Bioinformatics online.

Identification of genetic network dynamics with unate structure

MOTIVATION

Modern experimental techniques for time course measurement of gene expression enable the identification of dynamical models of genetic regulatory networks. In general, identification involves fitting appropriate network structures and parameters to the data. For a given set of genes, exploring all possible network structures is clearly prohibitive. Modelling and identification methods for the a priori selection of network structures compatible with biological knowledge and experimental data are necessary to make the identification problem tractable.

RESULTS

We propose a differential equation modelling framework where the regulatory interactions among genes are expressed in terms of unate functions, a class of gene activation rules commonly encountered in Boolean network modelling. We establish analytical properties of the models in the class and exploit them to devise a two-step procedure for gene network reconstruction from product concentration and synthesis rate time series. The first step isolates a family of model structures compatible with the data from a set of most relevant biological hypotheses. The second step explores this family and returns a pool of best fitting models along with estimates of their parameters. The method is tested on a simulated network and compared with state-of-the-art network inference methods on the benchmark synthetic network IRMA.