Mathematical modelling of metabolism

Shedding light on blue-green photosynthesis: A wavelength-dependent mathematical model of photosynthesis in Synechocystis sp. PCC 6803

Cyanobacteria hold great potential to revolutionize conventional industries and farming practices with their light-driven chemical production. To fully exploit their photosynthetic capacity and enhance product yield, it is crucial to investigate their intricate interplay with the environment including the light intensity and spectrum. Mathematical models provide valuable insights for optimizing strategies in this pursuit. In this study, we present an ordinary differential equation-based model for the cyanobacterium Synechocystis sp. PCC 6803 to assess its performance under various light sources, including monochromatic light. Our model can reproduce a variety of physiologically measured quantities, e.g. experimentally reported partitioning of electrons through four main pathways, O2 evolution, and the rate of carbon fixation for ambient and saturated CO2. By capturing the interactions between different components of a photosynthetic system, our model helps in understanding the underlying mechanisms driving system behavior. Our model qualitatively reproduces fluorescence emitted under various light regimes, replicating Pulse-amplitude modulation (PAM) fluorometry experiments with saturating pulses. Using our model, we test four hypothesized mechanisms of cyanobacterial state transitions for ensemble of parameter sets and found no physiological benefit of a model assuming phycobilisome detachment. Moreover, we evaluate metabolic control for biotechnological production under diverse light colors and irradiances. We suggest gene targets for overexpression under different illuminations to increase the yield. By offering a comprehensive computational model of cyanobacterial photosynthesis, our work enhances the basic understanding of light-dependent cyanobacterial behavior and sets the first wavelength-dependent framework to systematically test their producing capacity for biocatalysis.

Applications of Machine Learning (ML) and Mathematical Modeling (MM) in Healthcare with Special Focus on Cancer Prognosis and Anticancer Therapy: Current Status and Challenges

The use of data-driven high-throughput analytical techniques, which has given rise to computational oncology, is undisputed. The widespread use of machine learning (ML) and mathematical modeling (MM)-based techniques is widely acknowledged. These two approaches have fueled the advancement in cancer research and eventually led to the uptake of telemedicine in cancer care. For diagnostic, prognostic, and treatment purposes concerning different types of cancer research, vast databases of varied information with manifold dimensions are required, and indeed, all this information can only be managed by an automated system developed utilizing ML and MM. In addition, MM is being used to probe the relationship between the pharmacokinetics and pharmacodynamics (PK/PD interactions) of anti-cancer substances to improve cancer treatment, and also to refine the quality of existing treatment models by being incorporated at all steps of research and development related to cancer and in routine patient care. This review will serve as a consolidation of the advancement and benefits of ML and MM techniques with a special focus on the area of cancer prognosis and anticancer therapy, leading to the identification of challenges (data quantity, ethical consideration, and data privacy) which are yet to be fully addressed in current studies.

Characterization of the enzyme kinetics of EMP and HMP pathway in Corynebacterium glutamicum: reference for modeling metabolic networks

The model of intracellular metabolic network based on enzyme kinetics parameters plays an important role in understanding the intracellular metabolic process of Corynebacterium glutamicum, and constructing such a model requires a large number of enzymological parameters. In this work, the genes encoding the relevant enzymes of the EMP and HMP metabolic pathways from Corynebacterium glutamicum ATCC 13032 were cloned, and engineered strains for protein expression with E.coli BL21 and P.pastoris X33 as hosts were constructed. The twelve enzymes (GLK, GPI, TPI, GAPDH, PGK, PMGA, ENO, ZWF, RPI, RPE, TKT, and TAL) were successfully expressed and purified by Ni2+ chelate affinity chromatography in their active forms. In addition, the kinetic parameters (V max, K m, and K cat) of these enzymes were measured and calculated at the same pH and temperature. The kinetic parameters of enzymes associated with EMP and the HMP pathway were determined systematically and completely for the first time in C.glutamicum. These kinetic parameters enable the prediction of key enzymes and rate-limiting steps within the metabolic pathway, and support the construction of a metabolic network model for important metabolic pathways in C.glutamicum. Such analyses and models aid in understanding the metabolic behavior of the organism and can guide the efficient production of high-value chemicals using C.glutamicum as a host.

Monitoring and modelling the glutamine metabolic pathway: a review and future perspectives

BACKGROUND

Analysis of the glutamine metabolic pathway has taken a special place in metabolomics research in recent years, given its important role in cell biosynthesis and bioenergetics across several disorders, especially in cancer cell survival. The science of metabolomics addresses the intricate intracellular metabolic network by exploring and understanding how cells function and respond to external or internal perturbations to identify potential therapeutic targets. However, despite recent advances in metabolomics, monitoring the kinetics of a metabolic pathway in a living cell in situ, real-time and holistically remains a significant challenge.

AIM

This review paper explores the range of analytical approaches for monitoring metabolic pathways, as well as physicochemical modeling techniques, with a focus on glutamine metabolism. We discuss the advantages and disadvantages of each method and explore the potential of label-free Raman microspectroscopy, in conjunction with kinetic modeling, to enable real-time and in situ monitoring of the cellular kinetics of the glutamine metabolic pathway.

KEY SCIENTIFIC CONCEPTS

Given its important role in cell metabolism, the ability to monitor and model the glutamine metabolic pathways are highlighted. Novel, label free approaches have the potential to revolutionise metabolic biosensing, laying the foundation for a new paradigm in metabolomics research and addressing the challenges in monitoring metabolic pathways in living cells.

Hybrid computational models of multicellular tumour growth considering glucose metabolism

Cancer cells metabolize glucose through metabolic pathways that differ from those used by healthy and differentiated cells. In particular, tumours have been shown to consume more glucose than their healthy counterparts and to use anaerobic metabolic pathways, even under aerobic conditions. Nevertheless, scientists have still not been able to explain why cancer cells evolved to present an altered metabolism and what evolutionary advantage this might provide them. Experimental and computational models have been increasingly used in recent years to understand some of these biological questions. Multicellular tumour spheroids are effective experimental models as they replicate the initial stages of avascular solid tumour growth. Furthermore, these experiments generate data which can be used to calibrate and validate computational studies that aim to simulate tumour growth. Hybrid models are of particular relevance in this field of research because they model cells as individual agents while also incorporating continuum representations of the substances present in the surrounding microenvironment that may participate in intracellular metabolic networks as concentration or density distributions. Henceforth, in this review, we explore the potential of computational modelling to reveal the role of metabolic reprogramming in tumour growth.

A hybrid kinetic and constraint-based model of leaf metabolism allows predictions of metabolic fluxes in different environments

While flux balance analysis (FBA) provides a framework for predicting steady-state leaf metabolic network fluxes, it does not readily capture the response to environmental variables without being coupled to other modelling formulations. To address this, we coupled an FBA model of 903 reactions of soybean (Glycine max) leaf metabolism with e-photosynthesis, a dynamic model that captures the kinetics of 126 reactions of photosynthesis and associated chloroplast carbon metabolism. Successful coupling was achieved in an iterative formulation in which fluxes from e-photosynthesis were used to constrain the FBA model and then, in turn, fluxes computed from the FBA model used to update parameters in e-photosynthesis. This process was repeated until common fluxes in the two models converged. Coupling did not hamper the ability of the kinetic module to accurately predict the carbon assimilation rate, photosystem II electron flux, and starch accumulation of field-grown soybean at two CO2 concentrations. The coupled model also allowed accurate predictions of additional parameters such as nocturnal respiration, as well as analysis of the effect of light intensity and elevated CO2 on leaf metabolism. Predictions included an unexpected decrease in the rate of export of sucrose from the leaf at high light, due to altered starch-sucrose partitioning, and altered daytime flux modes in the tricarboxylic acid cycle at elevated CO2 . Mitochondrial fluxes were notably different between growing and mature leaves, with greater anaplerotic, tricarboxylic acid cycle and mitochondrial ATP synthase fluxes predicted in the former, primarily to provide carbon skeletons and energy for protein synthesis.

The closure issue related to liquid-cell mass transfer and substrate uptake dynamics in biological systems

An original dynamic model for substrate uptake under transient conditions is established and used to simulate a variety of biological responses to external perturbations. The actual uptake and growth rates, treated as cell properties, are part of the model variables as well as the substrate concentration at the cell-liquid interface. Several regulatory loops inspired by the structure of the glycolytic chain are considered to establish a set of ordinary differential equations. The uptake rate evolves so as to reach an equilibrium between the cell demand and the environmental supply. This model does not contain any of the usual algebraic closure laws relating to the instantaneous uptake, growth rates, and the substrate concentration, nor does it enforce the continuity of mass fluxes at the liquid-cell interface. However, these relationships are found in the steady-state solution. Previously unexplained experimental observations are well reproduced by this model. Also, the model structure is suitable for further coupling with flux-based metabolic models and fluid-flow equations.

Constraint-based metabolic control analysis for rational strain engineering

The advancements in genome editing techniques over the past years have rekindled interest in rational metabolic engineering strategies. While Metabolic Control Analysis (MCA) is a well-established method for quantifying the effects of metabolic engineering interventions on flows in metabolic networks and metabolite concentrations, it does not consider the physiological limitations of the cellular environment and metabolic engineering design constraints. We report here a constraint-based framework, Network Response Analysis (NRA), for rational genetic strain design. NRA is cast as a Mixed-Integer Linear Programming problem that integrates MCA, Thermodynamically-based Flux Analysis (TFA), biologically relevant constraints, as well as genome editing restrictions into a comprehensive platform for identifying metabolic engineering targets. We show that the NRA formulation and its core constraints are equivalent to the ones of Flux Balance Analysis (FBA) and TFA, which allows it to be used for a wide range of optimization criteria and with various physiological constraints. We also show how the parametrization and introduction of biological constraints enhance the NRA formulation compared to the classical MCA approach, and we demonstrate its features and its ability to generate multiple alternative optimal strategies given several user-defined boundaries and objectives. In summary, NRA is a sophisticated alternative to classical MCA for rational metabolic engineering that accommodates the incorporation of physiological data at metabolic flux, metabolite concentration, and enzyme expression levels.

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.

A dynamic model linking cell growth to intracellular metabolism and extracellular by-product accumulation

Mathematical modeling of animal cell growth and metabolism is essential for the understanding and improvement of the production of biopharmaceuticals. Models can explain the dynamic behavior of cell growth and product formation, support the identification of the most relevant parameters for process design, and significantly reduce the number of experiments to be performed for process optimization. Few dynamic models have been established that describe both extracellular and intracellular dynamics of growth and metabolism of animal cells. In this study, a model was developed, which comprises a set of 33 ordinary differential equations to describe batch cultivations of suspension AGE1.HN.AAT cells considered for the production of α1-antitrypsin. This model combines a segregated cell growth model with a structured model of intracellular metabolism. Overall, it considers the viable cell concentration, mean cell diameter, viable cell volume, concentration of extracellular substrates, and intracellular concentrations of key metabolites from the central carbon metabolism. Furthermore, the release of metabolic by-products such as lactate and ammonium was estimated directly from the intracellular reactions. Based on the same set of parameters, this model simulates well the dynamics of four independent batch cultivations. Analysis of the simulated intracellular rates revealed at least two distinct cellular physiological states. The first physiological state was characterized by a high glycolytic rate and high lactate production. Whereas the second state was characterized by efficient adenosine triphosphate production, a low glycolytic rate, and reactions of the TCA cycle running in the reverse direction from α-ketoglutarate to citrate. Finally, we show possible applications of the model for cell line engineering and media optimization with two case studies.

Advanced Modeling of Cellular Proliferation: Toward a Multi-scale Framework Coupling Cell Cycle to Metabolism by Integrating Logical and Constraint-Based Models

Biological functions require a coherent cross talk among multiple layers of regulation within the cell. Computational efforts that aim to understand how these layers are integrated across spatial, temporal, and functional scales represent a challenge in Systems Biology. We have developed a computational, multi-scale framework that couples cell cycle and metabolism networks in the budding yeast cell. Here we describe the methodology at the basis of this framework, which integrates on off-the-shelf logical (Boolean) models of a minimal yeast cell cycle with a constraint-based model of metabolism (i.e., the Yeast 7 metabolic network reconstruction). Models are implemented in Python code using the BooleanNet and COBRApy packages, respectively, and are connected through the Boolean logic. The methodology allows for incorporation of interaction data, and validation through -omics data. Furthermore, evolutionary strategies may be incorporated to explore regulatory structures underlying coherent cross talks among regulatory layers.

Assessing Escherichia coli metabolism models and simulation approaches in phenotype predictions: Validation against experimental data

Over the last years, several genome-scale metabolic models (GEMs) and kinetic models of Escherichia coli were published. Their predictive performance varies according to the evaluation metric considered, the computational simulation methods used, and the type/quality of experimental data available. However, the GEM approach is often not compared with the kinetic modeling framework. Also, the different genome-scale reconstruction versions and simulation methods of mutant phenotypes are usually not validated to predict intracellular fluxes using large experimental datasets. Here, we intended to (i) systematically evaluate the prediction performance of three E. coli GEMs (iJR904, iAF1260, and iJO1366) available in the literature according to predictive growth metrics (intracellular flux distribution); (ii) assess the reliability of a E. coli GEM in the prediction of gene knockout phenotypes when different simulation methods (parsimonious flux balance analysis, Minimization of Metabolic Adjustment, linear version of MoMA, Regulatory on/off minimization, and Minimization of Metabolites Balance) are used; and finally (iii) investigate the flux distribution predictive power of the constrained-based modeling approach (selected stoichiometric GEM) and compare it with the kinetic modeling approach (two published kinetic models) for E. coli central metabolism, in order to assess their accuracy. Results show that the phenotype predictions were not significantly sensitive to the metabolic models, although the GEM iAF1260 was more accurate in the prediction of central carbon fluxes at low dilution rates. Furthermore, we observed that the choice of the appropriate simulation method of mutant phenotypes depends on the biological question to be addressed. In terms of the two modeling approaches, none outperformed the other for all the tested scenarios. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 34:1344-1354, 2018.

Analyzing and Designing Cell Factories with OptFlux

OptFlux was launched in 2010 as the first open-source and user-friendly platform containing all the major methods for performing metabolic engineering tasks in silico. Main features included the possibility of performing microbial strain simulations with widely used methods such as Flux Balance Analysis and strain design using Evolutionary Algorithms. Since then, OptFlux suffered a major re-factoring to improve its efficiency and reliability, while many features were added in the form of novel plug-ins, such as the BioVisualizer and the over/under expression plug-ins. The current chapter described the main mathematical formulations of the major methods implemented within OptFlux, also providing a detailed guide on the usage of those functionalities.

A systematic reconstruction and constraint-based analysis of Leishmania donovani metabolic network: identification of potential antileishmanial drug targets

Visceral leishmaniasis, a lethal parasitic disease, is caused by the protozoan parasite Leishmania donovani. The absence of an effective vaccine, drug toxicity and parasite resistance necessitates the identification of novel drug targets. Reconstruction of genome-scale metabolic models and their simulation has been established as an important tool for systems-level understanding of a microorganism's metabolism. In this work, amalgamating the tools and techniques of computational systems biology with rigorous manual curation, a constraint-based metabolic model for Leishmania donovani BPK282A1 has been developed. New functional annotations for 18 formerly hypothetical or erroneously annotated genes (encountered during iterative refinement of the model) have been proposed. Further, to formulate an accurate biomass objective function, experimental determination of previously uncharacterized biomass constituents was performed. The developed model is a highly compartmentalized metabolic model, comprising 1159 reactions, 1135 metabolites and 604 genes. The model exhibited around 76% accuracy for the prediction of experimental phenotypes of gene knockout studies and drug inhibition assays. Employing in silico gene knockout studies, we identified 28 essential genes with negligible sequence identity to the human proteins. Moreover, by dissecting the functional interdependencies of metabolic pathways, 70 synthetic lethal pairs were identified. Finally, in order to delineate stage-specific metabolism, gene-expression data of the amastigote stage residing in human macrophages were integrated into the model. By comparing the flux distribution, we illustrated the stage-specific differences in metabolism and environmental conditions that are in good agreement with the experimental findings. The developed model can serve as a highly enriched knowledgebase of legacy data and an important tool for generating experimentally verifiable hypotheses.

Mathematical Modeling Approaches in Plant Metabolomics

The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

Identification of metabolic pathways using pathfinding approaches: a systematic review

Metabolic pathways have become increasingly available for various microorganisms. Such pathways have spurred the development of a wide array of computational tools, in particular, mathematical pathfinding approaches. This article can facilitate the understanding of computational analysis of metabolic pathways in genomics. Moreover, stoichiometric and pathfinding approaches in metabolic pathway analysis are discussed. Three major types of studies are elaborated: stoichiometric identification models, pathway-based graph analysis and pathfinding approaches in cellular metabolism. Furthermore, evaluation of the outcomes of the pathways with mathematical benchmarking metrics is provided. This review would lead to better comprehension of metabolism behaviors in living cells, in terms of computed pathfinding approaches.

Quantitative physiology and elemental composition of Kluyveromyces lactis CBS 2359 during growth on glucose at different specific growth rates

The yeast Kluyveromyces lactis has received attention both from academia and industry due to some important features, such as its capacity to grow in lactose-based media, its safe status, its suitability for large-scale cultivation and for heterologous protein synthesis. It has also been considered as a model organism for genomics and metabolic regulation. Despite this, very few studies were carried out hitherto under strictly controlled conditions, such as those found in a chemostat. Here we report a set of quantitative physiological data generated during chemostat cultivations with the K. lactis CBS 2359 strain, obtained under glucose-limiting and fully aerobic conditions. This dataset serves [corrected] as a basis for the comparison of K. lactis with the model yeast Saccharomyces cerevisiae in terms of their elemental compositions, as well as for future metabolic flux analysis and metabolic modelling studies with K. lactis.

Metabolic engineering of Klebsiella pneumoniae based on in silico analysis and its pilot-scale application for 1,3-propanediol and 2,3-butanediol co-production

Klebsiella pneumoniae naturally produces relatively large amounts of 1,3-propanediol (1,3-PD) and 2,3-butanediol (2,3-BD) along with various byproducts using glycerol as a carbon source. The ldhA and mdh genes in K. pneumoniae were deleted based on its in silico gene knockout simulation with the criteria of maximizing 1,3-PD and 2,3-BD production and minimizing byproducts formation and cell growth retardation. In addition, the agitation speed, which is known to strongly affect 1,3-PD and 2,3-BD production in Klebsiella strains, was optimized. The K. pneumoniae ΔldhA Δmdh strain produced 125 g/L of diols (1,3-PD and 2,3-BD) with a productivity of 2.0 g/L/h in the lab-scale (5-L bioreactor) fed-batch fermentation using high-quality guaranteed reagent grade glycerol. To evaluate the industrial capacity of the constructed K. pneumoniae ΔldhA Δmdh strain, a pilot-scale (5000-L bioreactor) fed-batch fermentation was carried out using crude glycerol obtained from the industrial biodiesel plant. The pilot-scale fed-batch fermentation of the K. pneumoniae ΔldhA Δmdh strain produced 114 g/L of diols (70 g/L of 1,3-PD and 44 g/L of 2,3-BD), with a yield of 0.60 g diols per gram glycerol and a productivity of 2.2 g/L/h of diols, which should be suitable for the industrial co-production of 1,3-PD and 2,3-BD.

Mini-review: In vitro Metabolic Engineering for Biomanufacturing of High-value Products

With the breakthroughs in biomolecular engineering and synthetic biology, many valuable biologically active compound and commodity chemicals have been successfully manufactured using cell-based approaches in the past decade. However, because of the high complexity of cell metabolism, the identification and optimization of rate-limiting metabolic pathways for improving the product yield is often difficult, which represents a significant and unavoidable barrier of traditional in vivo metabolic engineering. Recently, some in vitro engineering approaches were proposed as alternative strategies to solve this problem. In brief, by reconstituting a biosynthetic pathway in a cell-free environment with the supplement of cofactors and substrates, the performance of each biosynthetic pathway could be evaluated and optimized systematically. Several value-added products, including chemicals, nutraceuticals, and drug precursors, have been biosynthesized as proof-of-concept demonstrations of in vitro metabolic engineering. This mini-review summarizes the recent progresses on the emerging topic of in vitro metabolic engineering and comments on the potential application of cell-free technology to speed up the “design-build-test” cycles of biomanufacturing.

Synergizing 13C Metabolic Flux Analysis and Metabolic Engineering for Biochemical Production

Metabolic engineering of industrial microorganisms to produce chemicals, fuels, and drugs has attracted increasing interest as it provides an environment-friendly and renewable route that does not depend on depleting petroleum sources. However, the microbial metabolism is so complex that metabolic engineering efforts often have difficulty in achieving a satisfactory yield, titer, or productivity of the target chemical. To overcome this challenge, ¹³C Metabolic Flux Analysis (¹³C-MFA) has been developed to investigate rigorously the cell metabolism and quantify the carbon flux distribution in central metabolic pathways. In the past decade, ¹³C-MFA has been widely used in academic labs and the biotechnology industry to pinpoint the key issues related to microbial-based chemical production and to guide the development of the appropriate metabolic engineering strategies for improving the biochemical production. In this chapter we introduce the basics of ¹³C-MFA and illustrate how ¹³C-MFA has been applied to synergize with metabolic engineering to identify and tackle the rate-limiting steps in biochemical production.

Advances and challenges in logical modeling of cell cycle regulation: perspective for multi-scale, integrative yeast cell models

The eukaryotic cell cycle is robustly designed, with interacting molecules organized within a definite topology that ensures temporal precision of its phase transitions. Its underlying dynamics are regulated by molecular switches, for which remarkable insights have been provided by genetic and molecular biology efforts. In a number of cases, this information has been made predictive, through computational models. These models have allowed for the identification of novel molecular mechanisms, later validated experimentally. Logical modeling represents one of the youngest approaches to address cell cycle regulation. We summarize the advances that this type of modeling has achieved to reproduce and predict cell cycle dynamics. Furthermore, we present the challenge that this type of modeling is now ready to tackle: its integration with intracellular networks, and its formalisms, to understand crosstalks underlying systems level properties, ultimate aim of multi-scale models. Specifically, we discuss and illustrate how such an integration may be realized, by integrating a minimal logical model of the cell cycle with a metabolic network.

The pentose phosphate pathway leads to enhanced succinic acid flux in biofilms of wild-type Actinobacillus succinogenes

Increased pentose phosphate pathway flux, relative to total substrate uptake flux, is shown to enhance succinic acid (SA) yields under continuous, non-growth conditions of Actinobacillus succinogenes biofilms. Separate fermentations of glucose and xylose were conducted in a custom, continuous biofilm reactor at four different dilution rates. Glucose-6-phosphate dehydrogenase assays were performed on cell extracts derived from in situ removal of biofilm at each steady state. The results of the assays were coupled to a kinetic model that revealed an increase in oxidative pentose phosphate pathway (OPPP) flux relative to total substrate flux with increasing SA titre, for both substrates. Furthermore, applying metabolite concentration data to metabolic flux models that include the OPPP revealed similar flux relationships to those observed in the experimental kinetic analysis. A relative increase in OPPP flux produces additional reduction power that enables increased flux through the reductive branch of the TCA cycle, leading to increased SA yields, reduced by-product formation and complete closure of the overall redox balance.

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.

Biomass composition: the "elephant in the room" of metabolic modelling

Genome-scale stoichiometric models, constrained to optimise biomass production are often used to predict mutant phenotypes. However, for Saccharomyces cerevisiae, the representation of biomass in its metabolic model has hardly changed in over a decade, despite major advances in analytical technologies. Here, we use the stoichiometric model of the yeast metabolic network to show that its ability to predict mutant phenotypes is particularly poor for genes encoding enzymes involved in energy generation. We then identify apparently inefficient energy-generating pathways in the model and demonstrate that the network suffers from the high energy burden associated with the generation of biomass. This is tightly connected to the availability of phosphate since this macronutrient links energy generation and structural biomass components. Variations in yeast's biomass composition, within experimentally-determined bounds, demonstrated that flux distributions are very sensitive to such changes and to the identity of the growth-limiting nutrient. The predictive accuracy of the yeast metabolic model is, therefore, compromised by its failure to represent biomass composition in an accurate and context-dependent manner.

Comparative metabolic flux analysis of an Ashbya gossypii wild type strain and a high riboflavin-producing mutant strain

In the present study, we analyzed the central metabolic pathway of an Ashbya gossypii wild type strain and a riboflavin over-producing mutant strain developed in a previous study in order to characterize the riboflavin over-production pathway. (13)C-Metabolic flux analysis ((13)C-MFA) was carried out in both strains, and the resulting data were fit to a steady-state flux isotopomer model using OpenFLUX. Flux to pentose-5-phosphate (P5P) via the pentose phosphate pathway (PPP) was 9% higher in the mutant strain compared to the wild type strain. The flux from purine synthesis to riboflavin in the mutant strain was 1.6%, while that of the wild type strain was only 0.1%, a 16-fold difference. In addition, the flux from the cytoplasmic pyruvate pool to the extracellular metabolites, pyruvate, lactate, and alanine, was 2-fold higher in the mutant strain compared to the wild type strain. This result demonstrates that increased guanosine triphosphate (GTP) flux through the PPP and purine synthesis pathway (PSP) increased riboflavin production in the mutant strain. The present study provides the first insight into metabolic flux through the central carbon pathway in A. gossypii and sets the foundation for development of a quantitative and functional model of the A. gossypii metabolic network.

Study of metabolic network of Cupriavidus necator DSM 545 growing on glycerol by applying elementary flux modes and yield space analysis

A metabolic network consisting of 48 reactions was established to describe intracellular processes during growth and poly-3-hydroxybutyrate (PHB) production for Cupriavidus necator DSM 545. Glycerol acted as the sole carbon source during exponential, steady-state cultivation conditions. Elementary flux modes were obtained by the program Metatool and analyzed by using yield space analysis. Four sets of elementary modes were obtained, depending on whether the pair NAD/NADH or FAD/FADH2 contributes to the reaction of glycerol-3-phosphate dehydrogenase (GLY-3-P DH), and whether 6-phosphogluconate dehydrogenase (6-PG DH) is present or not. Established metabolic network and the related system of equations provide multiple solutions for the simultaneous synthesis of PHB and biomass; this number of solutions can be further increased if NAD/NADH or FAD/FADH2 were assumed to contribute in the reaction of GLY-3-P DH. As a major outcome, it was demonstrated that experimentally determined yields for biomass and PHB with respect to glycerol fit well to the values obtained in silico when the Entner-Doudoroff pathway (ED) dominates over the glycolytic pathway; this is also the case if the Embden-Meyerhof-Parnas pathway dominates over the ED.

k-OptForce: integrating kinetics with flux balance analysis for strain design

Computational strain design protocols aim at the system-wide identification of intervention strategies for the enhanced production of biochemicals in microorganisms. Existing approaches relying solely on stoichiometry and rudimentary constraint-based regulation overlook the effects of metabolite concentrations and substrate-level enzyme regulation while identifying metabolic interventions. In this paper, we introduce k-OptForce, which integrates the available kinetic descriptions of metabolic steps with stoichiometric models to sharpen the prediction of intervention strategies for improving the bio-production of a chemical of interest. It enables identification of a minimal set of interventions comprised of both enzymatic parameter changes (for reactions with available kinetics) and reaction flux changes (for reactions with only stoichiometric information). Application of k-OptForce to the overproduction of L-serine in E. coli and triacetic acid lactone (TAL) in S. cerevisiae revealed that the identified interventions tend to cause less dramatic rearrangements of the flux distribution so as not to violate concentration bounds. In some cases the incorporation of kinetic information leads to the need for additional interventions as kinetic expressions render stoichiometry-only derived interventions infeasible by violating concentration bounds, whereas in other cases the kinetic expressions impart flux changes that favor the overproduction of the target product thereby requiring fewer direct interventions. A sensitivity analysis on metabolite concentrations shows that the required number of interventions can be significantly affected by changing the imposed bounds on metabolite concentrations. Furthermore, k-OptForce was capable of finding non-intuitive interventions aiming at alleviating the substrate-level inhibition of key enzymes in order to enhance the flux towards the product of interest, which cannot be captured by stoichiometry-alone analysis. This study paves the way for the integrated analysis of kinetic and stoichiometric models and enables elucidating system-wide metabolic interventions while capturing regulatory and kinetic effects.

Automatic identification of structured process models based on biological phenomena detected in (fed-)batch experiments

In this paper, we present a set of methods to automatically propose structured process models from an automated analysis of (fed-)batch experiments. Therefore, the measurements are numerically compensated for the influence of feeding and sampling, and the qualitative behavior of the measurements is revealed. As measurements from fermentations are inherently noisy, we introduce a method that divides the compensated curves into several episodes in a probabilistic framework to better handle these shortcomings. The probability of biological phenomena that reveal crucial information about the underlying reaction network is calculated. Since the phenomena detection is measurement-driven, its reliability depends on the measurement situation, e.g., the number of samples taken and experiments considered, measurement noise, etc. We show a possible approach to test the uncertainty of the phenomena detection against these influences. Finally, model structures are proposed automatically based on the detected biological phenomena. An experimental validation of the approach is shown, using real fermentation data from fed-batch cultivations of Streptomyces tendae.

Kinetic modeling, production and characterization of an acidic lipase produced by Enterococcus durans NCIM5427 from fish waste

Enterococcus durans NCIM5427 (ED-27), capable of producing an intracellular acid stable lipase, was isolated from fish processing waste. Its growth and subsequent lipase production was optimized by Box Behneken design (optimized conditions: 5 % v/v fish waste oil (FWO), 0.10 mg/ml fish waste protein hydrolysates (FWPH) at 48 h of fermentation time). Under optimized conditions, ED-27 showed a 3.0 fold increase (207.6 U/ml to 612.53 U/ml) in lipase production, as compared to un-optimized conditions. Cell growth and lipase production was modeled using Logistic and Luedeking-Piret model, respectively; and lipase production by ED-27 was found to be growth-associated. Lipase produced by ED-27 showed stability at low pH ranges from 2 to 5 with its optimal activity at 30 °C , pH 4.6; showed metal ion dependent activity wherein its catalytic activity was activated by barium, sodium, lithium and potassium (10 mM); reduced by calcium and magnesium (10 mM). However, iron and mercury (5 mM) completely inactivated the enzyme. In addition, modifying agents like SDS, DTT, β-ME (1%v/v) increased activity of lipase of ED-27; while, PMSF, DEPC and ascorbic acid resulted in a marked decrease. ED-27 had maximum cell growth of 9.90309 log CFU/ml under optimized conditions as compared to 13 log CFU/ml in MRS. The lipase produced has potential application in poultry and slaughterhouse waste management.

In silico aided metabolic engineering of Klebsiella oxytoca and fermentation optimization for enhanced 2,3-butanediol production

Klebsiella oxytoca naturally produces a large amount of 2,3-butanediol (2,3-BD), a promising bulk chemical with wide industrial applications, along with various byproducts. In this study, the in silico gene knockout simulation of K. oxytoca was carried out for 2,3-BD overproduction by inhibiting the formation of byproducts. The knockouts of ldhA and pflB genes were targeted with the criteria of maximization of 2,3-BD production and minimization of byproducts formation. The constructed K. oxytoca ΔldhA ΔpflB strain showed higher 2,3-BD yields and higher final concentrations than those obtained from the wild-type and ΔldhA strains. However, the simultaneous deletion of both genes caused about a 50 % reduction in 2,3-BD productivity compared with K. oxytoca ΔldhA strain. Based on previous studies and in silico investigation that the agitation speed during 2,3-BD fermentation strongly affected cell growth and 2,3-BD synthesis, the effect of agitation speed on 2,3-BD production was investigated from 150 to 450 rpm in 5-L bioreactors containing 3-L culture media. The highest 2,3-BD productivity (2.7 g/L/h) was obtained at 450 rpm in batch fermentation. Considering the inhibition of acetoin for 2,3-BD production, fed-batch fermentations were performed using K. oxytoca ΔldhA ΔpflB strain to enhance 2,3-BD production. Altering the agitation speed from 450 to 350 rpm at nearly 10 g/L of acetoin during the fed-batch fermentation allowed for the production of 113 g/L 2,3-BD, with a yield of 0.45 g/g, and for the production of 2.1 g/L/h of 2,3-BD.

Genome-scale reconstruction and in silico analysis of Klebsiella oxytoca for 2,3-butanediol production

Background

Klebsiella oxytoca, a Gram-negative, rod-shaped, and facultative anaerobic bacterium, is one of the most promising 2,3-butanediol (2,3-BD) producers. In order to improve the metabolic performance of K. oxytoca as an efficient biofactory, it is necessary to assess its metabolic characteristics with a system-wide scope, and to optimize the metabolic pathways at a systems level. Provision of the complete genome sequence of K. oxytoca enabled the construction of genome-scale metabolic model of K. oxytoca and its in silico analyses.

Results

The genome-scale metabolic model of K. oxytoca was constructed using the annotated genome with biochemical and physiological information. The stoichiometric model, KoxGSC1457, is composed of 1,457 reactions and 1,099 metabolites. The model was further refined by applying biomass composition equations and comparing in silico results with experimental data based on constraints-based flux analyses. Then, the model was applied to in silico analyses to understand the properties of K. oxytoca and also to improve its capabilities for 2,3-BD production according to genetic and environmental perturbations. Firstly, in silico analysis, which tested the effect of augmenting the metabolic flux pool of 2,3-BD precursors, elucidated that increasing the pyruvate pool is primarily important for 2,3-BD synthesis. Secondly, we performed in silico single gene knockout simulation for 2,3-BD overproduction, and investigated the changes of the in silico flux solution space of a ldhA gene knockout mutant in comparison with that of the wild-type strain. Finally, the KoxGSC1457 model was used to optimize the oxygen levels during fermentation for 2,3-BD production.

Conclusions

The genome-scale metabolic model, KoxGSC1457, constructed in this study successfully investigated metabolic characteristics of K. oxytoca at systems level. The KoxGSC1457 model could be employed as an useful tool to analyze its metabolic capabilities, to predict its physiological responses according to environmental and genetic perturbations, and to design metabolic engineering strategies to improve its metabolic performance.

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.

Genome-scale metabolic model of the fission yeast Schizosaccharomyces pombe and the reconciliation of in silico/in vivo mutant growth

Background

Over the last decade, the genome-scale metabolic models have been playing increasingly important roles in elucidating metabolic characteristics of biological systems for a wide range of applications including, but not limited to, system-wide identification of drug targets and production of high value biochemical compounds. However, these genome-scale metabolic models must be able to first predict known in vivo phenotypes before it is applied towards these applications with high confidence. One benchmark for measuring the in silico capability in predicting in vivo phenotypes is the use of single-gene mutant libraries to measure the accuracy of knockout simulations in predicting mutant growth phenotypes.

Results

Here we employed a systematic and iterative process, designated as Reconciling In silico/in vivo mutaNt Growth (RING), to settle discrepancies between in silico prediction and in vivo observations to a newly reconstructed genome-scale metabolic model of the fission yeast, Schizosaccharomyces pombe, SpoMBEL1693. The predictive capabilities of the genome-scale metabolic model in predicting single-gene mutant growth phenotypes were measured against the single-gene mutant library of S. pombe. The use of RING resulted in improving the overall predictive capability of SpoMBEL1693 by 21.5%, from 61.2% to 82.7% (92.5% of the negative predictions matched the observed growth phenotype and 79.7% the positive predictions matched the observed growth phenotype).

Conclusion

This study presents validation and refinement of a newly reconstructed metabolic model of the yeast S. pombe, through improving the metabolic model’s predictive capabilities by reconciling the in silico predicted growth phenotypes of single-gene knockout mutants, with experimental in vivo growth data.

What can causal networks tell us about metabolic pathways?

Graphical models describe the linear correlation structure of data and have been used to establish causal relationships among phenotypes in genetic mapping populations. Data are typically collected at a single point in time. Biological processes on the other hand are often non-linear and display time varying dynamics. The extent to which graphical models can recapitulate the architecture of an underlying biological processes is not well understood. We consider metabolic networks with known stoichiometry to address the fundamental question: “What can causal networks tell us about metabolic pathways?”. Using data from an Arabidopsis BaySha population and simulated data from dynamic models of pathway motifs, we assess our ability to reconstruct metabolic pathways using graphical models. Our results highlight the necessity of non-genetic residual biological variation for reliable inference. Recovery of the ordering within a pathway is possible, but should not be expected. Causal inference is sensitive to subtle patterns in the correlation structure that may be driven by a variety of factors, which may not emphasize the substrate-product relationship. We illustrate the effects of metabolic pathway architecture, epistasis and stochastic variation on correlation structure and graphical model-derived networks. We conclude that graphical models should be interpreted cautiously, especially if the implied causal relationships are to be used in the design of intervention strategies.

High-throughput profiling data are pervasive in modern genetic studies. The large-scale nature of the data can make interpretation challenging. Methods that estimate networks or graphs have become popular tools for proposing causal relationships among traits. However, it is not obvious that these methods are able to capture causal biological mechanisms. Here we address the power and limitations of causal inference methods in biological systems. We examine metabolic data from simulation and from a well-characterized metabolic pathway in plants. We show that variation has to propagate through the pathway for reliable network inference. While it is possible for causal inference methods to recover the ordering of the biological pathway, it should not be expected. Causal relationships create subtle patterns in correlation, which may be dominated by other biological factors that do not reflect the ordering of the underlying pathway. Our results shape expectations about these methods and explain some of the successes and failures of causal graphical models for network inference.

Unraveling the complex regulatory relationships between metabolism and signal transduction in cancer

Cancer cells exhibit an altered metabolic phenotype, known as the Warburg effect, which is characterized by high rates of glucose uptake and glycolysis, even under aerobic conditions. The Warburg effect appears to be an intrinsic component of most cancers and there is evidence linking cancer progression to mutations, translocations, and alternative splicing of genes that directly code for or have downstream effects on key metabolic enzymes. Many of the same signaling pathways are routinely dysregulated in cancer and a number of important oncogenic signaling pathways play important regulatory roles in central carbon metabolism. Unraveling the complex regulatory relationship between cancer metabolism and signaling requires the application of systems biology approaches. Here we discuss computational approaches for modeling protein signal transduction and metabolism as well as how the regulatory relationship between these two important cellular processes can be combined into hybrid models.

Experimental methods and modeling techniques for description of cell population heterogeneity

With the continuous development, in the last decades, of analytical techniques providing complex information at single cell level, the study of cell heterogeneity has been the focus of several research projects within analytical biotechnology. Nonetheless, the complex interplay between environmental changes and cellular responses is yet not fully understood, and the integration of this new knowledge into the strategies for design, operation and control of bioprocesses is far from being an established reality. Indeed, the impact of cell heterogeneity on productivity of large scale cultivations is acknowledged but seldom accounted for. In order to include population heterogeneity mechanisms in the development of novel bioprocess control strategies, a reliable mathematical description of such phenomena has to be developed. With this review, we search to summarize the potential of currently available methods for monitoring cell population heterogeneity as well as model frameworks suitable for describing dynamic heterogeneous cell populations. We will furthermore underline the highly important coordination between experimental and modeling efforts necessary to attain a reliable quantitative description of cell heterogeneity, which is a necessity if such models are to contribute to the development of improved control of bioprocesses.

An algorithm for efficient identification of branched metabolic pathways

This article presents a new graph-based algorithm for identifying branched metabolic pathways in multi-genome scale metabolic data. The term branched is used to refer to metabolic pathways between compounds that consist of multiple pathways that interact biochemically. A branched pathway may produce a target compound through a combination of linear pathways that split compounds into smaller ones, work in parallel with many compounds, and join compounds into larger ones. While branched metabolic pathways predominate in metabolic networks, most previous work has focused on identifying linear metabolic pathways. The ability to automatically identify branched pathways is important in applications that require a deeper understanding of metabolism, such as metabolic engineering and drug target identification. The algorithm presented in this article utilizes explicit atom tracking to identify linear metabolic pathways and then merges them together into branched metabolic pathways. We provide results on several well-characterized metabolic pathways that demonstrate that the new merging approach can efficiently find biologically relevant branched metabolic pathways.

Applications and trends in systems biology in biochemistry

Systems biology has received an ever increasing interest during the last decade. A large amount of third-party funding is spent on this topic, which involves quantitative experimentation integrated with computational modeling. Industrial companies are also starting to use this approach more and more often, especially in pharmaceutical research and biotechnology. This leads to the question of whether such interest is wisely invested and whether there are success stories to be told for basic science and/or technology/biomedicine. In this review, we focus on the application of systems biology approaches that have been employed to shed light on both biochemical functions and previously unknown mechanisms. We point out which computational and experimental methods are employed most frequently and which trends in systems biology research can be observed. Finally, we discuss some problems that we have encountered in publications in the field.

Genome-scale reconstruction and in silico analysis of the Ralstonia eutropha H16 for polyhydroxyalkanoate synthesis, lithoautotrophic growth, and 2-methyl citric acid production

Background

Ralstonia eutropha H16, found in both soil and water, is a Gram-negative lithoautotrophic bacterium that can utillize CO₂ and H₂ as its sources of carbon and energy in the absence of organic substrates. R. eutropha H16 can reach high cell densities either under lithoautotrophic or heterotrophic conditions, which makes it suitable for a number of biotechnological applications. It is the best known and most promising producer of polyhydroxyalkanoates (PHAs) from various carbon substrates and is an environmentally important bacterium that can degrade aromatic compounds. In order to make R. eutropha H16 a more efficient and robust biofactory, system-wide metabolic engineering to improve its metabolic performance is essential. Thus, it is necessary to analyze its metabolic characteristics systematically and optimize the entire metabolic network at systems level.

Results

We present the lithoautotrophic genome-scale metabolic model of R. eutropha H16 based on the annotated genome with biochemical and physiological information. The stoichiometic model, RehMBEL1391, is composed of 1391 reactions including 229 transport reactions and 1171 metabolites. Constraints-based flux analyses were performed to refine and validate the genome-scale metabolic model under environmental and genetic perturbations. First, the lithoautotrophic growth characteristics of R. eutropha H16 were investigated under varying feeding ratios of gas mixture. Second, the genome-scale metabolic model was used to design the strategies for the production of poly[R-(-)-3hydroxybutyrate] (PHB) under different pH values and carbon/nitrogen source uptake ratios. It was also used to analyze the metabolic characteristics of R. eutropha when the phosphofructokinase gene was expressed. Finally, in silico gene knockout simulations were performed to identify targets for metabolic engineering essential for the production of 2-methylcitric acid in R. eutropha H16.

Conclusion

The genome-scale metabolic model, RehMBEL1391, successfully represented metabolic characteristics of R. eutropha H16 at systems level. The reconstructed genome-scale metabolic model can be employed as an useful tool for understanding its metabolic capabilities, predicting its physiological consequences in response to various environmental and genetic changes, and developing strategies for systems metabolic engineering to improve its metabolic performance.