Mass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration

Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to mimic this forcing. We provide a general formulation to force an arbitrary large kinetic model in a manner that is still consistent with the existence of a non-equilibrium steady state. We can guarantee the existence of a non-equilibrium steady state assuming only two conditions; that every reaction is mass balanced and that continuous kinetic reaction rate laws never lead to a negative molecule concentration. These conditions can be verified in polynomial time and are flexible enough to permit one to force a system away from equilibrium. In an expository biochemical example we show how a reversible, mass balanced perpetual reaction, with thermodynamically infeasible kinetic parameters, can be used to perpetually force a kinetic model of anaerobic glycolysis in a manner consistent with the existence of a steady state. Easily testable existence conditions are foundational for efforts to reliably compute non-equilibrium steady states in genome-scale biochemical kinetic models.Comment: 11 pages, 2 figures (v2 is now placed in proper context of the excellent 1962 paper by James Wei entitled "Axiomatic treatment of chemical reaction systems". In addition, section 4, on "Utility of steady state existence theorem" has been expanded.

Dynamic optimization of metabolic networks coupled with gene expression

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle

A genome scale model of Geobacillus thermoglucosidasius (C56-YS93) reveals its biotechnological potential on rice straw hydrolysate

Rice straw is a major crop residue which is burnt in many countries, creating signicant air pollution. Thus, alternative routes for disposal of rice straw are needed. Biotechnological treatment of rice straw hydrolysate has potential to convert this agriculture waste into valuable biofuel(s) and platform chemicals. Geobacillus thermoglucosidasius is a thermophile with properties specially suited for use as a biocatalyst in lignocellulosic bioprocesses, such as high optimal temperature and tolerance to high levels of ethanol. However, the capabilities of Geobacillus thermoglucosidasius to utilize sugars in rice straw hydrolysate for making bioethanol and other platform chemicals have not been fully explored. In this work, we have created a genome scale metabolic model (denoted iGT736) of the organism containing 736 gene products, 1159 reactions and 1163 metabolites. The model was validated both by purely theoretical approaches and by comparing the behaviour of the model to previously published experimental results. The model was then used to determine the yields of a variety of platform chemicals from glucose and xylose - two primary sugars in rice straw hydrolysate. A comparison with results from a model of Escherichia coli shows that G. thermoglucosidasius is capable of producing a wider range of products, and that for the products also produced by E. coli , the yields are comparable. We also discuss strategies to utilise arabinose, a minor component of rice straw hydrolysate, and propose additional reactions to lead to the synthesis of xylitol, not currently produced by G. thermoglucosidasius. Our results provide additional motivation for the current exploration of the industrial potential of G. thermoglucosidasius and we make our model publicly available to aid the development of metabolic engineering strategies for this organism

Model-assisted metabolic engineering of Escherichia coli for long chain alkane and alcohol production

Biologically-derived hydrocarbons are considered to have great potential as next-generation biofuels owing to the similarity of their chemical properties to contemporary diesel and jet fuels. However, the low yield of these hydrocarbons in biotechnological production is a major obstacle for commercialization. Several genetic and process engineering approaches have been adopted to increase the yield of hydrocarbon, but a model driven approach has not been implemented so far. Here, we applied a constraint-based metabolic modeling approach in which a variable demand for alkane biosynthesis was imposed, and co-varying reactions were considered as potential targets for further engineering of an E. coli strain already expressing cyanobacterial enzymes towards higher chain alkane production. The reactions that co-varied with the imposed alkane production were found to be mainly associated with the pentose phosphate pathway (PPP) and the lower half of glycolysis. An optimal modeling solution was achieved by imposing increased flux through the reaction catalyzed by glucose-6-phosphate dehydrogenase (zwf) and iteratively removing 7 reactions from the network, leading to an alkane yield of 94.2% of the theoretical maximum conversion determined by in silico analysis at a given biomass rate. To validate the in silico findings, we first performed pathway optimization of the cyanobacterial enzymes in E. coli via different dosages of genes, promoting substrate channelling through protein fusion and inducing substantial equivalent protein expression, which led to a 36-fold increase in alka(e)ne production from 2.8 mg/L to 102 mg/L. Further, engineering of E. coli based on in silico findings, including biomass constraint, led to an increase in the alka(e)ne titer to 425 mg/L (major components being 249 mg/L pentadecane and 160 mg/L heptadecene), a 148.6-fold improvement over the initial strain, respectively; with a yield of 34.2% of the theoretical maximum. The impact of model-assisted engineering was also tested for the production of long chain fatty alcohol, another commercially important molecule sharing the same pathway while differing only at the terminal reaction, and a titer of 1506 mg/L was achieved with a yield of 86.4% of the theoretical maximum. Moreover, the model assisted engineered strains had produced 2.54 g/L and 12.5 g/L of long chain alkane and fatty alcohol, respectively, in the bioreactor under fed-batch cultivation condition. Our study demonstrated successful implementation of a combined in silico modeling approach along with the pathway and process optimization in achieving the highest reported titers of long chain hydrocarbons in E. coli

Genome scale metabolic modelling of Phaeodactylum tricornutum

Diatoms are photoautotrophic unicellular algae and are among the most abundant, adaptable and diverse marine phytoplankton. Their ability to synthesise lipid as a storage compound (20%-50% dry cell weight) makes them a potential sources of biofuel and high-value commodities such as ω fatty acids. However, diatoms have unique features in their biochemistry as compared to higher plants and hence, there is a prior need to understand diatom metabolism to enable physiological and genetic manipulation, and improve their strains. The present work involves construction and analysis of genome scale metabolic models (GSMs) of Phaeodactylum tricornutum, a model diatom, the characterisation of physiological properties and the identification of the potential strategies to optimise the lipid production. GSMs were constructed based on a previously published model and metabolic databases, and were analysed using structural modelling techniques to understand the metabolic responses at different environmental and physiological conditions. The model results suggest change in metabolic responses, mainly associated with the Calvin cycle, reductant transfer, photorespiration, TCA cycle, glyoxylate cycle, lipid metabolism, carbohydrate metabolism and energy dissipation mechanisms under changing environmental and physiological conditions. Carbon xation and triose-phosphate production can take place solely in the chloroplast, despite of differences in the localisation and regulation of the Calvin cycle enzymes as compared to higher plants. Further, model analysis suggests that lipid production in P. tricornutum increases both when exposed to high light and with the availability of glycerol. The potential metabolic routes for lipid production involves phosphoketolase pathway, threonine metabolism, recycling of glycolate and HCO3 fixation. Based on the model analysis, experiments were designed where cultures were exposed to high light, supplemented with HCO3 , under phototrophic and mixotrophic conditions. This resulted to an increase in biomass and lipid productivity. In addition, by revealing the potential metabolic routes involved with lipid production, our work also suggests possible targets for metabolic engineering that could divert carbon towards lipid production

Genome-scale metabolic modelling of Salmonella and Lactobacillus species

Salmonella Typhimurium is a major cause of morbidity and mortality in humans. It is also a commonly used model organism for intracellular Gram negative pathogens, a group of bacteria that is becoming increasingly resistant to available antibiotics. Systemic Salmonella infection involves proliferation in the small intestine followed by infection of epithelial and later macrophage host cells. In order to advance the understanding of the r^ole of metabolism in virulence, a genome-scale metabolic model of S. Typhimurium was constructed, based on genomic and biochemical data obtained from public databases. A method for modelling metabolic interactions between cells was developed and applied to models of S. Typhimurium and the probiotic Lactobacillus plan-tarum, in order to simulate the intestinal stage of infection. The analysis indicated that interactions, involving the transfer of glycolate from L. plantarum to S. Typhimurium, that favour growth of S. Typhimurium, are possible, by unlikely to occur in vivo. Data from Phenotype Microarray (PM), as well as DNA microarray data obtained during infection of cultured macrophage cells, was integrated with the S. Typhimurium model. The PM data was largely in agreement with model results for growth on carbon and nitrogen sources, and indicated moderate agreement for sulphur and phosphorus sources. A model-based method for analysis of nutrient availability during growth inside host cells, based on PM and DNA microarray data, was developed. This environment is poorly characterised and direct experimental methods for obtaining this information are not available. The analysis indicated a nutritionally complex host environment, dominated by glycerol 3-phosphate and certain nucleosides and amino acids. Owing to the complexity of the host environment, a method for identication of a sub-network of the model, required for viability on all growth supporting carbon sources was developed. The impact of sequentially removing combinations of reactions in the sub-network from the genome-scale model was evaluated. This analysis suggested approximately 60 reactions that in various combinations could be of relevance for designing antimicrobial intervention strategies, including antimicrobial agents and live attenuated vaccines

Metabolic Pathway Analysis: from small to genome-scale networks

The need for mathematical modelling of biological processes has grown alongside with the achievements in the experimental field leading to the appearance and development of new fields like systems biology. Systems biology aims at generating new knowledge through modelling and integration of experimental data in order to develop a holistic understanding of organisms. In the first part of my PhD thesis, I compare two different levels of abstraction used for computing metabolic pathways, constraint-based and graph theoretical methods. I show that the current representations of metabolism as a simple graph correspond to wrong mathematical descriptions of metabolic pathways. On the other hand, the use of stoichiometric information and convex analysis as modelling framework like in elementary flux mode analysis, allows to correctly predict metabolic pathways. In the second part of the thesis, I present two of the first methods, based on elementary flux mode analysis, that can compute metabolic pathways in such large metabolic networks: the K-shortest EFMs method and the EFMEvolver method. These methods contribute to an enrichment of the mathematical tools available to model cell biology and more precisely, metabolism. The application of these new methods to biotechnological problems is also explored in this part. In the last part of my thesis, I give an overview of recent achievements in metabolic network reconstruction and constraint-based modelling as well as open issues. Moreover, I discuss possible strategies for integrating experimental data with elementary flux mode analysis. Further improvements in elementary flux mode computation on that direction are put forward

Modeling complex cellular systems: from differential equations to constraint-based models

In the beginning of the 20th century, scientists realized the necessity of purifying enzymes to unravel their mechanistic nature. A century and tremendous progresses in the natural sciences later, molecular and systems biology became fundamental pillars of modern biology. Moreover, natural scientists developed an increasing interest in theoretical models. In the first part of my thesis, I present my contribution to the field of studying the dynamics of biological phenomena. I present fundamental issues arising, when neglecting substrate inhibition in kinetic modeling. Furthermore, I describe a model that considers experimental data to simulate the transition of normal proliferating into cellular senescent cells. Since large-scaled models are more comprehensive, they commonly prohibit a mechanistic modeling approach. In order to analyze such models, nevertheless, constraint-based methods proved to be suitable tools. In the second part of my thesis, I contribute three studies to constraint-based modeling. I describe the established concept of elementary flux modes, which resemble non-decomposable and theoretically feasible pathways of metabolic networks. Subsequently, I present the analysis of the nitrogen metabolism network of Chlamydomonas reinhardtii with respect to circadian regulation, which gives rise to about three million elementary flux modes. In the last study, I present a comprehensive work on metabolic costs of amino acid and protein production in Escherichia coli. These costs were manually calculated as well as based on a flux balance analysis of an E. coli genome-scale metabolic model. Both approaches, either dynamic or constraint-based modeling, proved to be suitable strategies to describe biological processes at different levels. Whereas dynamic modeling allowed for a precise description of the temporal behavior of biological species, constraint-based modeling enabled studies, where the complexity of the investigated phenomena prohibits kinetic modeling

Genome Scale Metabolic Modelling of Arabidopsis thaliana and Chlamydomonas reinhardtii

Recent advances in genome sequencing technology have enabled the elucidation of complete genome sequence for plants and algae. Genome scale metabolic models constructed from genome annotations represent the entire metabolic characteristics of the organism and can be used to integrate other data and study metabolic capabilities of the organisms under different conditions. This framework can help develop new insight about operating characteristic of the organism and propose new hypotheses that can be tested experimentally. In order to advance our understanding of photosynthetic metabolism in plants and algae, GSMs of A. thaliana and C. reinhardtii have been constructed using annotations from their respective BioCyc databases. They satisfy all theoretical considerations and are able to represent known biological behaviors and thus can be used in subsequent investigations. In collaboration with experimental partners, the arabidopsis model was used to study the knock-out phenotype of the Calvin Cycle enzymes. This correctly predicted the viability of single knockouts of 4 Calvin cycle enzymes. Alternate metabolic routes that make such change possible were identified using flux balance analysis. The analysis demonstrated a complementary role of SBPase and FBPase in the Calvin cycle and further proposed a novel role of transaldolase in daytime metabolism under knockout conditions. Both models, were used to investigate likely coordinated changes in metabolic networks to dissipate excess energy under high light conditions. Methods that use correlation coefficient and mixed integer linear programming have been developed for this purpose. Proteomics data obtained under high light conditions was integrated in the model to propose energy dissipating modes that are more likely to occur in vivo. Further, removal of reactions involved in energy dissipation mechanisms showed improve biomass yield

Researchers' Assumptions and Mathematical Models: A Philosophical Study of Metabolic Systems Biology

This thesis examines the philosophical implications of the assumptions made by researchers involved in the development of mathematical models of metabolism. It does this through an analysis of several detailed historical case studies of models between the 1960’s and the present day, thus also contributing to the growing literature on the historiography of biochemical systems biology. The chapters focus on four main topics: the relationship between models and theory, temporal decomposition as a simplifying strategy for building models of complex metabolic systems, interactions between modellers and experimental biochemists, and the role of biochemical data. Four categories of assumptions are shown to play a significant role in these different aspects of model development; ontological assumptions, idealising assumptions, assumptions about data, and researchers’ commitments. Building on this analysis, the thesis brings to light the importance of researcher’s ontological and idealising assumptions about the temporal organisation, alongside the spatial organisation, of metabolic systems. It also offers an account of different forms of interactions between research groups – hostile interactions, closed collaboration, and open collaboration – on the basis of differences in the characteristics of researcher’s commitments. Throughout the case studies, biological data play a powerful role in model development by virtue of the contents of available data sets, as well as researchers’ perceptions of those data, which are in turn influenced by their ontological assumptions. The historical trajectories explored illustrate how the relationships between different facets of model building, and their associated philosophical abstractions, are often best understood as transient features within a highly dynamic research process, whose role depends on the specific stage of modelling in which they are enacted. This thesis provides an expanded perspective on the different types and roles of assumptions in the development of mathematical models of metabolism, which is firmly grounded in a historical analysis of scientific practice.AHR