Model reduction and a priori kinetic parameter identifiability analysis using metabolome time series for metabolic reaction networks with linlog kinetics

Streamlining the Analysis of Dynamic 13C-Labeling Patterns for the Metabolic Engineering of Corynebacterium glutamicum as l-Histidine Production Host

Today’s possibilities of genome editing easily create plentitudes of strain mutants that need to be experimentally qualified for configuring the next steps of strain engineering. The application of design-build-test-learn cycles requires the identification of distinct metabolic engineering targets as design inputs for subsequent optimization rounds. Here, we present the pool influx kinetics (PIK) approach that identifies promising metabolic engineering targets by pairwise comparison of up- and downstream ¹³C labeling dynamics with respect to a metabolite of interest. Showcasing the complex l-histidine production with engineered Corynebacterium glutamicuml-histidine-on-glucose yields could be improved to 8.6 ± 0.1 mol% by PIK analysis, starting from a base strain. Amplification of purA, purB, purH, and formyl recycling was identified as key targets only analyzing the signal transduction kinetics mirrored in the PIK values.

A scalable method for parameter identification in kinetic models of metabolism using steady-state data

MOTIVATION

In kinetic models of metabolism, the parameter values determine the dynamic behaviour predicted by these models. Estimating parameters from in vivo experimental data require the parameters to be structurally identifiable, and the data to be informative enough to estimate these parameters. Existing methods to determine the structural identifiability of parameters in kinetic models of metabolism can only be applied to models of small metabolic networks due to their computational complexity. Additionally, a priori experimental design, a necessity to obtain informative data for parameter estimation, also does not account for using steady-state data to estimate parameters in kinetic models.

RESULTS

Here, we present a scalable methodology to structurally identify parameters for each flux in a kinetic model of metabolism based on the availability of steady-state data. In doing so, we also address the issue of determining the number and nature of experiments for generating steady-state data to estimate these parameters. By using a small metabolic network as an example, we show that most parameters in fluxes expressed by mechanistic enzyme kinetic rate laws can be identified using steady-state data, and the steady-state data required for their estimation can be obtained from selective experiments involving both substrate and enzyme level perturbations. The methodology can be used in combination with other identifiability and experimental design algorithms that use dynamic data to determine the most informative experiments requiring the least resources to perform.

AVAILABILITY AND IMPLEMENTATION

https://github.com/LMSE/ident.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Black-box kinetic modeling of growth and citric acid production and estimation of ATP maintenance parameters for Candida oleophila ATCC20177

Mathematical modeling represents and predicts biological systems, explains underlying mechanisms, constituting one of the key focus points for fundamental and applied research to improve our understanding and to decrease costs. Organic acids are used in several industries such as monomers for bioplastics, food preservatives and additives, pharmaceuticals, and agriculture. Nonpetrochemical, sustainable production of organic acids is therefore of great interest. An important step in production of organic acids is the determination of growth and acid production dynamics, as the product itself may have direct and indirect inhibitory effects on the host's metabolism. The aim of this study it twofold: (i) to determine the parameters related to energetics of growth and production as growth ( K x ) and nongrowth associated (m_ATP ) maintenance constants and (ii) to set up and analyze an unstructured, black-box kinetic model to describe the dynamics of the growth and production of citric acid by Candida oleophila ATCC20177 using published batch fermentation data. K x and m_ATP were found to be 2.3 ± 1.7 and 5.25 ± 2.75, respectively, for the published P/O ratio of 1.45. The parameter sensitivities and correlations are determined using the Monte Carlo approach, and the final model is tested using chemostat data.

Reducing a model of sugar metabolism in peach to catch different patterns among genotypes

Several studies have been conducted to understand the dynamic of primary metabolisms in fruit by translating them into mathematics models. An ODE kinetic model of sugar metabolism has been developed by Desnoues et al. (2018) to simulate the accumulation of different sugars during peach fruit development. Two major drawbacks of this model are (a) the number of parameters to calibrate and (b) its integration time that can be long due to non-linearity and time-dependent input functions. Together, these issues hamper the use of the model for a large panel of genotypes, for which few data are available. In this paper, we present a model reduction scheme that explicitly addresses the specificity of genetic studies in that: (i) it yields a reduced model that is adapted to the whole expected genetic diversity (ii) it maintains network structure and variable identity, in order to facilitate biological interpretation. The proposed approach is based on the combination and the systematic evaluation of different reduction methods. Thus, we combined multivariate sensitivity analysis, structural simplification and timescale-based approaches to simplify the number and the structure of ordinary differential equations of the model. The original and reduced models were compared based on three criteria, namely the corrected Aikake Information Criterion (AIC_C), the calibration time and the expected error of the reduced model over a progeny of virtual genotypes. The resulting reduced model not only reproduces the predictions of the original one but presents many advantages including a reduced number of parameters to be estimated and shorter calibration time, opening new promising perspectives for genetic studies and virtual breeding. The validity of the reduced model was further evaluated by calibration on 30 additional genotypes of an inter-specific peach progeny for which few data were available.

Bayesian inference of metabolic kinetics from genome-scale multiomics data

Modern biological tools generate a wealth of data on metabolite and protein concentrations that can be used to help inform new strain designs. However, learning from these data to predict how a cell will respond to genetic changes, a key need for engineering, remains challenging. A promising technique for leveraging omics measurements in metabolic modeling involves the construction of kinetic descriptions of the enzymatic reactions that occur within a cell. Parameterizing these models from biological data can be computationally difficult, since methods must also quantify the uncertainty in model parameters resulting from the observed data. While the field of Bayesian inference offers a wide range of methods for efficiently estimating distributions in parameter uncertainty, such techniques are poorly suited to traditional kinetic models due to their complex rate laws and resulting nonlinear dynamics. In this paper, we employ linear-logarithmic kinetics to simplify the calculation of steady-state flux distributions and enable efficient sampling and inference methods. We demonstrate that detailed information on the posterior distribution of parameters can be obtained efficiently at a variety of problem scales, including nearly genome-scale kinetic models trained on multiomics datasets. These results allow modern Bayesian machine learning tools to be leveraged in understanding biological data and in developing new, efficient strain designs.

Metabolic kinetic modeling provides insight into complex biological questions, but hurdles remain

Metabolic models containing kinetic information can answer unique questions about cellular metabolism that are useful to metabolic engineering. Several kinetic modeling frameworks have recently been developed or improved. In addition, techniques for systematic identification of model structure, including regulatory interactions, have been reported. Each framework has advantages and limitations, which can make it difficult to choose the most appropriate framework. Common limitations are data availability and computational time, especially in large-scale modeling efforts. However, recently developed experimental techniques, parameter identification algorithms, as well as model reduction techniques help alleviate these computational bottlenecks. Opportunities for additional improvements may come from the rich literature in catalysis and chemical networks. In all, kinetic models are positioned to make significant impact in cellular engineering.

A Multiscale Agent-Based Model for the Investigation of E. coli K12 Metabolic Response During Biofilm Formation

Bacterial biofilm formation is an organized collective response to biochemical cues that enables bacterial colonies to persist and withstand environmental insults. We developed a multiscale agent-based model that characterizes the intracellular, extracellular, and cellular scale interactions that modulate Escherichia coli MG1655 biofilm formation. Each bacterium's intracellular response and cellular state were represented as an outcome of interactions with the environment and neighboring bacteria. In the intracellular model, environment-driven gene expression and metabolism were captured using statistical regression and Michaelis-Menten kinetics, respectively. In the cellular model, growth, death, and type IV pili- and flagella-dependent movement were based on the bacteria's intracellular state. We implemented the extracellular model as a three-dimensional diffusion model used to describe glucose, oxygen, and autoinducer 2 gradients within the biofilm and bulk fluid. We validated the model by comparing simulation results to empirical quantitative biofilm profiles, gene expression, and metabolic concentrations. Using the model, we characterized and compared the temporal metabolic and gene expression profiles of sessile versus planktonic bacterial populations during biofilm formation and investigated correlations between gene expression and biofilm-associated metabolites and cellular scale phenotypes. Based on our in silico studies, planktonic bacteria had higher metabolite concentrations in the glycolysis and citric acid cycle pathways, with higher gene expression levels in flagella and lipopolysaccharide-associated genes. Conversely, sessile bacteria had higher metabolite concentrations in the autoinducer 2 pathway, with type IV pili, autoinducer 2 export, and cellular respiration genes upregulated in comparison with planktonic bacteria. Having demonstrated results consistent with in vitro static culture biofilm systems, our model enables examination of molecular phenomena within biofilms that are experimentally inaccessible and provides a framework for future exploration of how hypothesized molecular mechanisms impact bulk community behavior.

Fermentation of Saccharomyces cerevisiae - Combining kinetic modeling and optimization techniques points out avenues to effective process design

A combined experimental/theoretical approach is presented, for improving the predictability of Saccharomyces cerevisiae fermentations. In particular, a mathematical model was developed explicitly taking into account the main mechanisms of the fermentation process, allowing for continuous computation of key process variables, including the biomass concentration and the respiratory quotient (RQ). For model calibration and experimental validation, batch and fed-batch fermentations were carried out. Comparison of the model-predicted biomass concentrations and RQ developments with the corresponding experimentally recorded values shows a remarkably good agreement for both batch and fed-batch processes, confirming the adequacy of the model. Furthermore, sensitivity studies were performed, in order to identify model parameters whose variations have significant effects on the model predictions: our model responds with significant sensitivity to the variations of only six parameters. These studies provide a valuable basis for model reduction, as also demonstrated in this paper. Finally, optimization-based parametric studies demonstrate how our model can be utilized for improving the efficiency of Saccharomyces cerevisiae fermentations.

Performance of objective functions and optimisation procedures for parameter estimation in system biology models

Mathematical modelling of signalling pathways aids experimental investigation in system and synthetic biology. Ever increasing data availability prompts the development of large dynamic models with numerous parameters. In this paper, we investigate how the number of unknown parameters affects the convergence of three frequently used optimisation algorithms and four objective functions. We compare objective functions that use data-driven normalisation of the simulations with those that use scaling factors. The data-driven normalisation of the simulation approach implies that simulations are normalised in the same way as the data, making both directly comparable. The scaling factor approach, which is commonly used for parameter estimation in dynamic systems, introduces scaling factors that multiply the simulations to convert them to the scale of the data. Here we show that the scaling factor approach increases, compared to data-driven normalisation of the simulations, the degree of practical non-identifiability, defined as the number of directions in the parameter space, along which parameters are not identifiable. Further, the results indicate that data-driven normalisation of the simulations greatly improve the speed of convergence of all tested algorithms when the overall number of unknown parameters is relatively large (74 parameters in our test problems). Data-driven normalisation of the simulations also markedly improve the performance of the non-gradient-based algorithm tested even when the number of unknown parameters is relatively small (10 parameters in our test problems). As the models and the unknown parameters increase in size, the data-driven normalisation of the simulation approach can be the preferred option, because it does not aggravate non-identifiability and allows for obtaining parameter estimates in a reasonable amount of time.

A systematic comparison of critical choices for faithful parameter-estimation identifies a combination of a hybrid optimisation algorithm (GLSDC) with data-driven normalisation of simulations (DNS) as the generally best option. Experimental data are often provided in relative, arbitrary units. To match simulations to data, two approaches are common: i) using scaling-factors that have to be estimated (SF); or ii) normalising the simulations in the same way as the data (DNS). Using three test-models of increasing complexity, we explored how this choice affects parameter identifiability and estimation performance. We show that in contrast to SF, DNS does not aggravate non-identifiability and a global-hybrid method combined with DNS outperformed local-multi-start methods. The advantage of DNS in terms of estimation speed was particularly pronounced for the most complex test-problem.

Robust identification of metabolic control for microbial l-methionine production following an easy-to-use puristic approach

The identification of promising metabolic engineering targets is a key issue in metabolic control analysis (MCA). Conventional approaches make intensive use of model-based studies, such as exploiting post-pulse metabolic dynamics after proper perturbation of the microbial system. Here, we present an easy-to-use, purely data-driven approach, defining pool efflux capacities (PEC) for identifying reactions that exert the highest flux control in linear pathways. Comparisons with linlog-based MCA and data-driven substrate elasticities (DDSE) showed that similar key control steps were identified using PEC. Using the example of l-methionine production with recombinant Escherichia coli, PEC consistently and robustly identified main flux controls using perturbation data after a non-labeled ¹²C-l-serine stimulus. Furthermore, the application of full-labeled ¹³C-l-serine stimuli yielded additional insights into stimulus propagation to l-methionine. PEC analysis performed on the ¹³C data set revealed the same targets as the ¹²C data set. Notably, the typical drawback of metabolome analysis, namely, the omnipresent leakage of metabolites, was excluded using the ¹³C PEC approach.

Living on the edge: substrate competition explains loss of robustness in mitochondrial fatty-acid oxidation disorders

Background

Defects in genes involved in mitochondrial fatty-acid oxidation (mFAO) reduce the ability of patients to cope with metabolic challenges. mFAO enzymes accept multiple substrates of different chain length, leading to molecular competition among the substrates. Here, we combined computational modeling with quantitative mouse and patient data to investigate whether substrate competition affects pathway robustness in mFAO disorders.

Results

First, we used comprehensive biochemical analyses of wild-type mice and mice deficient for medium-chain acyl-CoA dehydrogenase (MCAD) to parameterize a detailed computational model of mFAO. Model simulations predicted that MCAD deficiency would have no effect on the pathway flux at low concentrations of the mFAO substrate palmitoyl-CoA. However, high concentrations of palmitoyl-CoA would induce a decline in flux and an accumulation of intermediate metabolites. We proved computationally that the predicted overload behavior was due to substrate competition in the pathway. Second, to study the clinical relevance of this mechanism, we used patients’ metabolite profiles and generated a humanized version of the computational model. While molecular competition did not affect the plasma metabolite profiles during MCAD deficiency, it was a key factor in explaining the characteristic acylcarnitine profiles of multiple acyl-CoA dehydrogenase deficient patients. The patient-specific computational models allowed us to predict the severity of the disease phenotype, providing a proof of principle for the systems medicine approach.

Conclusion

We conclude that substrate competition is at the basis of the physiology seen in patients with mFAO disorders, a finding that may explain why these patients run a risk of a life-threatening metabolic catastrophe.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-016-0327-5) contains supplementary material, which is available to authorized users.

Kinetic modeling of cell metabolism for microbial production

Kinetic models of cellular metabolism are important tools for the rational design of metabolic engineering strategies and to explain properties of complex biological systems. The recent developments in high-throughput experimental data are leading to new computational approaches for building kinetic models of metabolism. Herein, we briefly survey the available databases, standards and software tools that can be applied for kinetic models of metabolism. In addition, we give an overview about recently developed ordinary differential equations (ODE)-based kinetic models of metabolism and some of the main applications of such models are illustrated in guiding metabolic engineering design. Finally, we review the kinetic modeling approaches of large-scale networks that are emerging, discussing their main advantages, challenges and limitations.

Simultaneous parameters identifiability and estimation of an E. coli metabolic network model

This work proposes a procedure for simultaneous parameters identifiability and estimation in metabolic networks in order to overcome difficulties associated with lack of experimental data and large number of parameters, a common scenario in the modeling of such systems. As case study, the complex real problem of parameters identifiability of the Escherichia coli K-12 W3110 dynamic model was investigated, composed by 18 differential ordinary equations and 35 kinetic rates, containing 125 parameters. With the procedure, model fit was improved for most of the measured metabolites, achieving 58 parameters estimated, including 5 unknown initial conditions. The results indicate that simultaneous parameters identifiability and estimation approach in metabolic networks is appealing, since model fit to the most of measured metabolites was possible even when important measures of intracellular metabolites and good initial estimates of parameters are not available.

KiMoSys: a web-based repository of experimental data for KInetic MOdels of biological SYStems

BACKGROUND

The kinetic modeling of biological systems is mainly composed of three steps that proceed iteratively: model building, simulation and analysis. In the first step, it is usually required to set initial metabolite concentrations, and to assign kinetic rate laws, along with estimating parameter values using kinetic data through optimization when these are not known. Although the rapid development of high-throughput methods has generated much omics data, experimentalists present only a summary of obtained results for publication, the experimental data files are not usually submitted to any public repository, or simply not available at all. In order to automatize as much as possible the steps of building kinetic models, there is a growing requirement in the systems biology community for easily exchanging data in combination with models, which represents the main motivation of KiMoSys development.

DESCRIPTION

KiMoSys is a user-friendly platform that includes a public data repository of published experimental data, containing concentration data of metabolites and enzymes and flux data. It was designed to ensure data management, storage and sharing for a wider systems biology community. This community repository offers a web-based interface and upload facility to turn available data into publicly accessible, centralized and structured-format data files. Moreover, it compiles and integrates available kinetic models associated with the data.KiMoSys also integrates some tools to facilitate the kinetic model construction process of large-scale metabolic networks, especially when the systems biologists perform computational research.

CONCLUSIONS

KiMoSys is a web-based system that integrates a public data and associated model(s) repository with computational tools, providing the systems biology community with a novel application facilitating data storage and sharing, thus supporting construction of ODE-based kinetic models and collaborative research projects.The web application implemented using Ruby on Rails framework is freely available for web access at http://kimosys.org, along with its full documentation.

On linear models and parameter identifiability in experimental biological systems

A key problem in the biological sciences is to be able to reliably estimate model parameters from experimental data. This is the well-known problem of parameter identifiability. Here, methods are developed for biologists and other modelers to design optimal experiments to ensure parameter identifiability at a structural level. The main results of the paper are to provide a general methodology for extracting parameters of linear models from an experimentally measured scalar function - the transfer function - and a framework for the identifiability analysis of complex model structures using linked models. Linked models are composed by letting the output of one model become the input to another model which is then experimentally measured. The linked model framework is shown to be applicable to designing experiments to identify the measured sub-model and recover the input from the unmeasured sub-model, even in cases that the unmeasured sub-model is not identifiable. Applications for a set of common model features are demonstrated, and the results combined in an example application to a real-world experimental system. These applications emphasize the insight into answering "where to measure" and "which experimental scheme" questions provided by both the parameter extraction methodology and the linked model framework. The aim is to demonstrate the tools' usefulness in guiding experimental design to maximize parameter information obtained, based on the model structure.

A model reduction method for biochemical reaction networks

BACKGROUND

In this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model.

RESULTS

We apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%.

CONCLUSIONS

The method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of interest in a more coarse-grained yet realistic environment.

Kinetic models in industrial biotechnology - Improving cell factory performance

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed.

Reverse engineering and identification in systems biology: strategies, perspectives and challenges

The interplay of mathematical modelling with experiments is one of the central elements in systems biology. The aim of reverse engineering is to infer, analyse and understand, through this interplay, the functional and regulatory mechanisms of biological systems. Reverse engineering is not exclusive of systems biology and has been studied in different areas, such as inverse problem theory, machine learning, nonlinear physics, (bio)chemical kinetics, control theory and optimization, among others. However, it seems that many of these areas have been relatively closed to outsiders. In this contribution, we aim to compare and highlight the different perspectives and contributions from these fields, with emphasis on two key questions: (i) why are reverse engineering problems so hard to solve, and (ii) what methods are available for the particular problems arising from systems biology?

Changes in substrate availability in Escherichia coli lead to rapid metabolite, flux and growth rate responses

The interactions between the intracellular metabolome, fluxome and growth rate of Escherichia coli after sudden glycolytic/gluconeogenic substrate shifts are studied based on pulses of different substrates to an aerobic glucose-limited steady-state (dilution rate=0.1h(-1)). After each added glycolytic (glucose) and gluconeogenic (pyruvate and succinate) substrate pulse, no by-products were secreted and a pseudo steady state in flux and metabolites was achieved in about 30-40s. In the pulse experiments a large oxygen uptake capacity of the cells was observed. The in vivo dynamic responses showed massive reorganization and flexibility (1/100-14-fold change) of extra/intracellular metabolic fluxes, matching with large changes in the concentrations of intracellular metabolites, including reversal of reaction rate for pseudo/near equilibrium reactions. The coupling of metabolome and fluxome could be described by Q-linear kinetics. Remarkably, the three different substrate pulses resulted in a very similar increase in growth rate (0.13-0.3h(-1)). Data analysis showed that there must exist as yet unknown mechanisms which couple the protein synthesis rate to changes in central metabolites.

Systematic applications of metabolomics in metabolic engineering

The goals of metabolic engineering are well-served by the biological information provided by metabolomics: information on how the cell is currently using its biochemical resources is perhaps one of the best ways to inform strategies to engineer a cell to produce a target compound. Using the analysis of extracellular or intracellular levels of the target compound (or a few closely related molecules) to drive metabolic engineering is quite common. However, there is surprisingly little systematic use of metabolomics datasets, which simultaneously measure hundreds of metabolites rather than just a few, for that same purpose. Here, we review the most common systematic approaches to integrating metabolite data with metabolic engineering, with emphasis on existing efforts to use whole-metabolome datasets. We then review some of the most common approaches for computational modeling of cell-wide metabolism, including constraint-based models, and discuss current computational approaches that explicitly use metabolomics data. We conclude with discussion of the broader potential of computational approaches that systematically use metabolomics data to drive metabolic engineering.

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.

Ensemble kinetic modeling of metabolic networks from dynamic metabolic profiles

Kinetic modeling of metabolic pathways has important applications in metabolic engineering, but significant challenges still remain. The difficulties faced vary from finding best-fit parameters in a highly multidimensional search space to incomplete parameter identifiability. To meet some of these challenges, an ensemble modeling method is developed for characterizing a subset of kinetic parameters that give statistically equivalent goodness-of-fit to time series concentration data. The method is based on the incremental identification approach, where the parameter estimation is done in a step-wise manner. Numerical efficacy is achieved by reducing the dimensionality of parameter space and using efficient random parameter exploration algorithms. The shift toward using model ensembles, instead of the traditional "best-fit" models, is necessary to directly account for model uncertainty during the application of such models. The performance of the ensemble modeling approach has been demonstrated in the modeling of a generic branched pathway and the trehalose pathway in Saccharomyces cerevisiae using generalized mass action (GMA) kinetics.

Compartmentation of glycogen metabolism revealed from 13C isotopologue distributions

Background

Stable isotope tracers are used to assess metabolic flux profiles in living cells. The existing methods of measurement average out the isotopic isomer distribution in metabolites throughout the cell, whereas the knowledge of compartmental organization of analyzed pathways is crucial for the evaluation of true fluxes. That is why we accepted a challenge to create a software tool that allows deciphering the compartmentation of metabolites based on the analysis of average isotopic isomer distribution.

Results

The software Isodyn, which simulates the dynamics of isotopic isomer distribution in central metabolic pathways, was supplemented by algorithms facilitating the transition between various analyzed metabolic schemes, and by the tools for model discrimination. It simulated ¹³C isotope distributions in glucose, lactate, glutamate and glycogen, measured by mass spectrometry after incubation of hepatocytes in the presence of only labeled glucose or glucose and lactate together (with label either in glucose or lactate). The simulations assumed either a single intracellular hexose phosphate pool, or also channeling of hexose phosphates resulting in a different isotopic composition of glycogen. Model discrimination test was applied to check the consistency of both models with experimental data. Metabolic flux profiles, evaluated with the accepted model that assumes channeling, revealed the range of changes in metabolic fluxes in liver cells.

Conclusions

The analysis of compartmentation of metabolic networks based on the measured ¹³C distribution was included in Isodyn as a routine procedure. The advantage of this implementation is that, being a part of evaluation of metabolic fluxes, it does not require additional experiments to study metabolic compartmentation. The analysis of experimental data revealed that the distribution of measured ¹³C-labeled glucose metabolites is inconsistent with the idea of perfect mixing of hexose phosphates in cytosol. In contrast, the observed distribution indicates the presence of a separate pool of hexose phosphates that is channeled towards glycogen synthesis.

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.

Escherichia coli responds with a rapid and large change in growth rate upon a shift from glucose-limited to glucose-excess conditions

Glucose pulse experiments at seconds time scale resolution were performed in aerobic glucose-limited Escherichia coli chemostat cultures. The dynamic responses of oxygen-uptake and growth rate at seconds time scale were determined using a new method based on the dynamic liquid-phase mass balance for oxygen and the pseudo-steady-state ATP balance. Significant fold changes in metabolites (10-1/10) and fluxes (4-1/4) were observed during the short (200 s) period of glucose excess. During glucose excess there was no secretion of by-products and the increased glucose uptake rate led within 40s to a 3.7 fold increase in growth rate. Also within 40-60s a new pseudo-steady-state was reached for both metabolite levels and fluxes. Flux changes of reactions were strongly correlated to the concentrations of involved compounds. Surprisingly the 3.7 fold increase in growth rate and hence protein synthesis rate was not matched by a significant increase in amino acid concentrations. This poses interesting questions for the kinetic factors, which drive protein synthesis by ribosomes.

A blueprint of ectoine metabolism from the genome of the industrial producer Halomonas elongata DSM 2581 T

The halophilic γ-proteobacterium Halomonas elongata DSM 2581^T thrives at high salinity by synthesizing and accumulating the compatible solute ectoine. Ectoine levels are highly regulated according to external salt levels but the overall picture of its metabolism and control is not well understood. Apart from its critical role in cell adaptation to halophilic environments, ectoine can be used as a stabilizer for enzymes and as a cell protectant in skin and health care applications and is thus produced annually on a scale of tons in an industrial process using H. elongata as producer strain. This paper presents the complete genome sequence of H. elongata (4 061 296 bp) and includes experiments and analysis identifying and characterizing the entire ectoine metabolism, including a newly discovered pathway for ectoine degradation and its cyclic connection to ectoine synthesis. The degradation of ectoine (doe) proceeds via hydrolysis of ectoine (DoeA) to Nα-acetyl-l-2,4-diaminobutyric acid, followed by deacetylation to diaminobutyric acid (DoeB). In H. elongata, diaminobutyric acid can either flow off to aspartate or re-enter the ectoine synthesis pathway, forming a cycle of ectoine synthesis and degradation. Genome comparison revealed that the ectoine degradation pathway exists predominantly in non-halophilic bacteria unable to synthesize ectoine. Based on the resulting genetic and biochemical data, a metabolic flux model of ectoine metabolism was derived that can be used to understand the way H. elongata survives under varying salt stresses and that provides a basis for a model-driven improvement of industrial ectoine production.

Global parameter estimation methods for stochastic biochemical systems

Background

The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.

Results

Three parameter estimation methods are proposed based on the maximum likelihood and density function distance, including probability and cumulative density functions. Since stochastic models such as chemical master equations are typically solved using a Monte Carlo approach in which only a finite number of Monte Carlo realizations are computationally practical, specific considerations are given to account for the effect of finite sampling in the histogram binning of the state density functions. Applications to three practical case studies showed that while maximum likelihood method can effectively handle low replicate measurements, the density function distance methods, particularly the cumulative density function distance estimation, are more robust in estimating the parameters with consistently higher accuracy, even for systems showing multimodality.

Conclusions

The parameter estimation methodologies described in this work have provided an effective and practical approach in the estimation of kinetic parameters of stochastic systems from either sparse or dense cell population data. Nevertheless, similar to kinetic parameter estimation in other modelling frameworks, not all parameters can be estimated accurately, which is a common problem arising from the lack of complete parameter identifiability from the available data.

The silicon trypanosome

African trypanosomes have emerged as promising unicellular model organisms for the next generation of systems biology. They offer unique advantages, due to their relative simplicity, the availability of all standard genomics techniques and a long history of quantitative research. Reproducible cultivation methods exist for morphologically and physiologically distinct life-cycle stages. The genome has been sequenced, and microarrays, RNA-interference and high-accuracy metabolomics are available. Furthermore, the availability of extensive kinetic data on all glycolytic enzymes has led to the early development of a complete, experiment-based dynamic model of an important biochemical pathway. Here we describe the achievements of trypanosome systems biology so far and outline the necessary steps towards the ambitious aim of creating a 'Silicon Trypanosome', a comprehensive, experiment-based, multi-scale mathematical model of trypanosome physiology. We expect that, in the long run, the quantitative modelling enabled by the Silicon Trypanosome will play a key role in selecting the most suitable targets for developing new anti-parasite drugs.

Catching prompt metabolite dynamics in Escherichia coli with the BioScope at oxygen rich conditions

The design and application of a BioScope, a mini plug-flow reactor for carrying out pulse response experiments, specifically designed for Escherichia coli is presented. Main differences with the previous design are an increased volume-specific membrane surface for oxygen transfer and significantly decreased sampling intervals. The characteristics of the new device (pressure drop, residence time distribution, plug-flow behavior and O2 mass transfer) were determined and evaluated. Subsequently, 2.8 mM glucose perturbation experiments on glucose-limited aerobic E. coli chemostat cultures were carried out directly in the chemostat as well as in the BioScope (for two time frames: 8 and 40 s). It was ensured that fully aerobic conditions were maintained during the perturbation experiments. To avoid metabolite leakage during quenching, metabolite quantification (glycolytic and TCA-cycle intermediates and nucleotides) was carried out with a differential method, whereby the amounts measured in the filtrate were subtracted from the amounts measured in total broth. The dynamic metabolite profiles obtained from the BioScope perturbations were very comparable with the profiles obtained from the chemostat perturbation. This agreement demonstrates that the BioScope is a promising device for studying in vivo kinetics in E. coli that shows much faster response (< 10 s) in comparison with eukaryotes.

Control of ATP homeostasis during the respiro-fermentative transition in yeast

Respiring Saccharomyces cerevisiae cells respond to a sudden increase in glucose concentration by a pronounced drop of their adenine nucleotide content ([ATP]+[ADP]+[AMP]=[AXP]). The unknown fate of 'lost' AXP nucleotides represented a long-standing problem for the understanding of the yeast's physiological response to changing growth conditions. Transient accumulation of the purine salvage pathway intermediate, inosine, accounted for the apparent loss of adenine nucleotides. Conversion of AXPs into inosine was facilitated by AMP deaminase, Amd1, and IMP-specific 5'-nucleotidase, Isn1. Inosine recycling into the AXP pool was facilitated by purine nucleoside phosphorylase, Pnp1, and joint action of the phosphoribosyltransferases, Hpt1 and Xpt1. Analysis of changes in 24 intracellular metabolite pools during the respiro-fermentative growth transition in wild-type, amd1, isn1, and pnp1 strains revealed that only the amd1 mutant exhibited significant deviations from the wild-type behavior. Moreover, mutants that were blocked in inosine production exhibited delayed growth acceleration after glucose addition. It is proposed that interconversion of adenine nucleotides and inosine facilitates rapid and energy-cost efficient adaptation of the AXP pool size to changing environmental conditions.

Impact of thermodynamic principles in systems biology

It is shown that properties of biological systems which are relevant for systems biology motivated mathematical modelling are strongly shaped by general thermodynamic principles such as osmotic limit, Gibbs energy dissipation, near equilibria and thermodynamic driving force. Each of these aspects will be demonstrated both theoretically and experimentally.

High-throughput quantitative metabolomics: workflow for cultivation, quenching, and analysis of yeast in a multiwell format

Metabolomics is a founding pillar of quantitative biology and a valuable tool for studying metabolism and its regulation. Here we present a workflow for metabolomics in microplate format which affords high-throughput and yet quantitative monitoring of primary metabolism in microorganisms and in particular yeast. First, the most critical step of rapid sampling was adapted to a multiplex format by using fritted 96-well plates for cultivation, which ensure fast sample transfer and permit us to use well-established quenching in cold solvents. Second, extensive optimization of large-volume injection on a GC/TOF instrument provided the sensitivity necessary for robust quantification of 30 primary metabolites in 0.6 mg of yeast biomass. The metabolome profiles of baker's yeast cultivated in fritted well plates or in shake flasks were equivalent. Standard deviations of measured metabolites were between 10% and 50% within one plate. As a proof of principle we compared the metabolome of wild-type Saccharomyces cerevisiae and the single-deletion mutant Delta sdh1, which were clearly distinguishable by a 10-fold increase of the intracellular succinate concentration in the mutant. The described workflow allows the production of large amounts of metabolome samples within a day, is compatible with virtually all liquid extraction protocols, and paves the road to quantitative screens.