An improved multi-parametric programming algorithm for flux balance analysis of metabolic networks

Flux balance analysis has proven an effective tool for analyzing metabolic networks. In flux balance analysis, reaction rates and optimal pathways are ascertained by solving a linear program, in which the growth rate is maximized subject to mass-balance constraints. A variety of cell functions in response to environmental stimuli can be quantified using flux balance analysis by parameterizing the linear program with respect to extracellular conditions. However, for most large, genome-scale metabolic networks of practical interest, the resulting parametric problem has multiple and highly degenerate optimal solutions, which are computationally challenging to handle. An improved multi-parametric programming algorithm based on active-set methods is introduced in this paper to overcome these computational difficulties. Degeneracy and multiplicity are handled, respectively, by introducing generalized inverses and auxiliary objective functions into the formulation of the optimality conditions. These improvements are especially effective for metabolic networks because their stoichiometry matrices are generally sparse; thus, fast and efficient algorithms from sparse linear algebra can be leveraged to compute generalized inverses and null-space bases. We illustrate the application of our algorithm to flux balance analysis of metabolic networks by studying a reduced metabolic model of Corynebacterium glutamicum and a genome-scale model of Escherichia coli. We then demonstrate how the critical regions resulting from these studies can be associated with optimal metabolic modes and discuss the physical relevance of optimal pathways arising from various auxiliary objective functions. Achieving more than five-fold improvement in computational speed over existing multi-parametric programming tools, the proposed algorithm proves promising in handling genome-scale metabolic models.Comment: Accepted in J. Optim. Theory Appl. First draft was submitted on August 4th, 201

Updates in metabolomics tools and resources: 2014-2015

Data processing and interpretation represent the most challenging and time-consuming steps in high-throughput metabolomic experiments, regardless of the analytical platforms (MS or NMR spectroscopy based) used for data acquisition. Improved machinery in metabolomics generates increasingly complex datasets that create the need for more and better processing and analysis software and in silico approaches to understand the resulting data. However, a comprehensive source of information describing the utility of the most recently developed and released metabolomics resources—in the form of tools, software, and databases—is currently lacking. Thus, here we provide an overview of freely-available, and open-source, tools, algorithms, and frameworks to make both upcoming and established metabolomics researchers aware of the recent developments in an attempt to advance and facilitate data processing workflows in their metabolomics research. The major topics include tools and researches for data processing, data annotation, and data visualization in MS and NMR-based metabolomics. Most in this review described tools are dedicated to untargeted metabolomics workflows; however, some more specialist tools are described as well. All tools and resources described including their analytical and computational platform dependencies are summarized in an overview Table

Modeling the metabolic dynamics at the genome-scale by optimized yield analysis

The hybrid cybernetic model (HCM) approach is a dynamic modeling framework that integrates enzyme synthesis and activity regulation. It has been widely applied in bioreaction engineering, particularly in the simulation of microbial growth in different mixtures of carbon sources. In a HCM, the metabolic network is decomposed into elementary flux modes (EFMs), whereby the network can be reduced into a few pathways by yield analysis. However, applying the HCM approach on conventional genome-scale metabolic models (GEMs) is still a challenge due to the high computational demands. Here, we present a HCM strategy that introduced an optimized yield analysis algorithm (opt-yield-FBA) to simulate metabolic dynamics at the genome-scale without the need for EFMs calculation. The opt-yield-FBA is a flux-balance analysis (FBA) based method that can calculate optimal yield solutions and yield space for GEM. With the opt-yield-FBA algorithm, the HCM strategy can be applied to get the yield spaces and avoid the computational burden of EFMs, and it can therefore be applied for developing dynamic models for genome-scale metabolic networks. Here, we illustrate the strategy by applying the concept to simulate the dynamics of microbial communities

Control and optimization methods in biomedical systems: from cells to humans

Optimization and control theory are well developed techniques to quantize, model, understand and optimize real world systems and they have been widely used in engineering, economics, and science. In this thesis, we focus on applications in biomedical systems ranging from cells to microbial communities, and to something as complex as the human body. The first problem we consider is that of medication dosage control for drugs delivered intravenously to the patient. We focus specifically on a blood thinner (called bivalirudin) used in the post cardiac surgery Intensive Care Unit (ICU). We develop two approaches (a model-free and a model-based one) that predict the effect of bivalirudin. After obtaining the model and its best fit parameters by solving a non-linear optimization problem, we develop automatic dosage controllers that adaptively regulate its effect to desired levels. Our algorithms are validated using actual data from a large hospital in the Boston area. In the second problem, we introduce a cellular objective function inference mechanism in metabolic networks. We develop an inverse optimization method, called InvFBA (Inverse Flux Balance Analysis), to infer the objective functions of growing cells by using their reaction fluxes. InvFBA can be seen as an inverse version of FBA (Flux Balance Analysis) which predicts the distribution of the cell's reaction fluxes by using a hypothetical objective function. The objective functions can be linear, quadratic and non-parametric. The efficiency of the InvFBA approach matches the structure of the FBA and ensures scalability to large networks and optimality of the solution. After testing our algorithm on simulated E. coli data and time-dependent S. oneidensis fluxes inferred from gene expression data, we apply our inverse approach to flux measurements in long-term evolved E. coli strains, revealing objective functions that provide insight into metabolic adaptation trajectories. In the final problem in this thesis, we formulate a novel resource allocation problem in microbial ecosystems. We consider a given number of microbial species living symbiotically in a community and a list of all metabolic reactions present in the community, expressed in terms of the metabolite proportions involved in each reaction. We are interested in allocating reactions to organisms so that each organism maintains a minimal level of growth and the community optimizes certain objectives, such as maximizing growth and/or the uptake of specific compounds from the common environment. We leverage tools from Flux Balance Analysis (FBA) and formulate the problem as a mixed integer linear programming problem. We test our method in a toy model involving two organisms that can only survive through cross-feeding, demonstrating that the method can recover this interaction. We also test the method in a community of two simplified bacteria described in terms of their core, simplified metabolic network. We demonstrate that the method can obtain syntrophic cross-feeding species that would be very difficult to design manually

Modeling and optimization of extracellular polysaccharides production by Enterobacter A47

Polysaccharides are gaining increasing attention as potential environmental friendly and sustainable building blocks in many fields of the (bio)chemical industry. The microbial production of polysaccharides is envisioned as a promising path, since higher biomass growth rates are possible and therefore higher productivities may be achieved compared to vegetable or animal polysaccharides sources. This Ph.D. thesis focuses on the modeling and optimization of a particular microbial polysaccharide, namely the production of extracellular polysaccharides (EPS) by the bacterial strain Enterobacter A47. Enterobacter A47 was found to be a metabolically versatile organism in terms of its adaptability to complex media, notably capable of achieving high growth rates in media containing glycerol byproduct from the biodiesel industry. However, the industrial implementation of this production process is still hampered due to a largely unoptimized process. Kinetic rates from the bioreactor operation are heavily dependent on operational parameters such as temperature, pH, stirring and aeration rate. The increase of culture broth viscosity is a common feature of this culture and has a major impact on the overall performance. This fact complicates the mathematical modeling of the process, limiting the possibility to understand, control and optimize productivity. In order to tackle this difficulty, data-driven mathematical methodologies such as Artificial Neural Networks can be employed to incorporate additional process data to complement the known mathematical description of the fermentation kinetics. In this Ph.D. thesis, we have adopted such an hybrid modeling framework that enabled the incorporation of temperature, pH and viscosity effects on the fermentation kinetics in order to improve the dynamical modeling and optimization of the process. A model-based optimization method was implemented that enabled to design bioreactor optimal control strategies in the sense of EPS productivity maximization. It is also critical to understand EPS synthesis at the level of the bacterial metabolism, since the production of EPS is a tightly regulated process. Methods of pathway analysis provide a means to unravel the fundamental pathways and their controls in bioprocesses. In the present Ph.D. thesis, a novel methodology called Principal Elementary Mode Analysis (PEMA) was developed and implemented that enabled to identify which cellular fluxes are activated under different conditions of temperature and pH. It is shown that differences in these two parameters affect the chemical composition of EPS, hence they are critical for the regulation of the product synthesis. In future studies, the knowledge provided by PEMA could foster the development of metabolically meaningful control strategies that target the EPS sugar content and oder product quality parameters

Scalable computation of intracellular metabolite concentrations

Current mathematical frameworks for predicting the flux state and macromolecular composition of the cell do not rely on thermodynamic constraints to determine the spontaneous direction of reactions. These predictions may be biologically infeasible as a result. Imposing thermodynamic constraints requires accurate estimations of intracellular metabolite concentrations. These concentrations are constrained within physiologically possible ranges to enable an organism to grow in extreme conditions and adapt to its environment. Here, we introduce tractable computational techniques to characterize intracellular metabolite concentrations within a constraint-based modeling framework. This model provides a feasible concentration set, which can generally be nonconvex and disconnected. We examine three approaches based on polynomial optimization, random sampling, and global optimization. We leverage the sparsity and algebraic structure of the underlying biophysical models to enhance the computational efficiency of these techniques. We then compare their performance in two case studies, showing that the global-optimization formulation exhibits more desirable scaling properties than the random-sampling and polynomial-optimization formulation, and, thus, is a promising candidate for handling large-scale metabolic networks

Predictive macroscopic modeling of Chinese hamster ovary cells in fed-batch processes

This thesis focuses on developing a systematic modeling method that can capture the essential features for prediction of cell metabolism, growth and monoclonal antibody (mAb) production in Chinese Hamster Ovary (CHO) cells. In a first step all specific consumption rates are calculated based on time courses of extracellular metabolites, viable cell density and mAb. Then the metabolic phases within which the metabolic pseudo-steady state approximation is verified are identified. In a third step, all metabolic rates are expressed as a function of the specific growth rate within each metabolic phase. We have applied this method to a set of small bioreactor data and have shown that the model obtained can predict specific conversion rates both small and also at large scale. In the second part of this thesis, a kinetic model of the cell growth has been developed. Together with previously described methodology, this kinetic model results in a predictive metabolic model for each experimental cell growth data are not required. The kinetic model is based on Monod kinetics with a few modifications such as a varying the maximum specific growth rate as a function of the integral viable cell density. The full kinetic model can be used off line to design optimal feeding profiles. The results of this thesis demonstrate that rich knowledge can be derived from macroscopic data that can then be used to predict new production conditions in an industrial environment at small and large scale.Der Schwerpunkt dieser Dissertation liegt auf der systematischen Entwicklung Modellen für die Vorhersage des zellulären Stoffwechsels, des Wachstums und der Produktion von monoklonalen Antikörpern (mAb) in Kulturen von Chinesischen Hamster-Ovarzellen (CHO). Zunächst wurden mit segmentierter linearer Regression metabolischer Phasen identifiziert. Diese Identifizierung beruht auf der Annahme eines pseudo-stationären Zustands und somit, dass in einer Phase alle Raten linear miteinander korreliert waren. Die spezifischen Raten wurden aus den Zeitverläufen der Konzentrationen der Metabolite und des mAb sowie der Lebendzellzahl bestimmt. Durch die Korrelation konnten alle Raten über die Wachstumsrate im 2 L und im 2000 L Maßstab berechnet werden. Danach wurde ein kinetisches Modell des Wachstums der Zellen etabliert, was die Vorhersage aller Raten auch in fed-batch Kulturen erlaubt. Die Kinetik basiert auf der Monod-Kinetik modifiziert mit einer variablen maximalen spezifischen Wachstumsrate. Das kinetische Modell erlaubt eine rechnerische Optimierung der Substratzuführung für eine maximale Produktion. Damit wurde gezeigt, dass aus makroskopischen Daten, d.h. ohne intrazelluläre Messungen, wesentliche Informationen erhalten werden können, mit denen neue Experimente in einem industriellen Umfeld vorhergesagt werden können. Diese innovative und systematische Vorgangsweise eröffnet neue Perspektiven für die Reduzierung von Kosten und für eine Beschleunigung der Prozessentwicklung

The metaRbolomics Toolbox in Bioconductor and beyond

Metabolomics aims to measure and characterise the complex composition of metabolites in a biological system. Metabolomics studies involve sophisticated analytical techniques such as mass spectrometry and nuclear magnetic resonance spectroscopy, and generate large amounts of high-dimensional and complex experimental data. Open source processing and analysis tools are of major interest in light of innovative, open and reproducible science. The scientific community has developed a wide range of open source software, providing freely available advanced processing and analysis approaches. The programming and statistics environment R has emerged as one of the most popular environments to process and analyse Metabolomics datasets. A major benefit of such an environment is the possibility of connecting different tools into more complex workflows. Combining reusable data processing R scripts with the experimental data thus allows for open, reproducible research. This review provides an extensive overview of existing packages in R for different steps in a typical computational metabolomics workflow, including data processing, biostatistics, metabolite annotation and identification, and biochemical network and pathway analysis. Multifunctional workflows, possible user interfaces and integration into workflow management systems are also reviewed. In total, this review summarises more than two hundred metabolomics specific packages primarily available on CRAN, Bioconductor and GitHub

Computational strategies for a system-level understanding of metabolism

Cell metabolism is the biochemical machinery that provides energy and building blocks to sustain life. Understanding its fine regulation is of pivotal relevance in several fields, from metabolic engineering applications to the treatment of metabolic disorders and cancer. Sophisticated computational approaches are needed to unravel the complexity of metabolism. To this aim, a plethora of methods have been developed, yet it is generally hard to identify which computational strategy is most suited for the investigation of a specific aspect of metabolism. This review provides an up-to-date description of the computational methods available for the analysis of metabolic pathways, discussing their main advantages and drawbacks. In particular, attention is devoted to the identification of the appropriate scale and level of accuracy in the reconstruction of metabolic networks, and to the inference of model structure and parameters, especially when dealing with a shortage of experimental measurements. The choice of the proper computational methods to derive in silico data is then addressed, including topological analyses, constraint-based modeling and simulation of the system dynamics. A description of some computational approaches to gain new biological knowledge or to formulate hypotheses is finally provided