Metabolic regulation and mathematical models

Nonlinear dynamics in phosphoinositide metabolism

Phosphoinositides broadly impact membrane dynamics, signal transduction and cellular physiology. The orchestration of signaling complexity by this seemingly simple metabolic pathway remains an open question. It is increasingly evident that comprehending the complexity of the phosphoinositides metabolic network requires a systems view based on nonlinear dynamics, where the products of metabolism can either positively or negatively modulate enzymatic function. These feedback and feedforward loops may be paradoxical, leading to counterintuitive effects. In this review, we introduce the framework of nonlinear dynamics, emphasizing distinct dynamical regimes such as the excitable state, oscillations, and mixed-mode oscillations-all of which have been experimentally observed in phosphoinositide metabolisms. We delve into how these dynamical behaviors arise from one or multiple network motifs, including positive and negative feedback loops, coherent and incoherent feedforward loops. We explore the current understanding of the molecular circuits responsible for these behaviors. While mapping these circuits presents both conceptual and experimental challenges, redefining cellular behavior based on dynamical state, lipid fluxes, time delay, and network topology is likely essential for a comprehensive understanding of this fundamental metabolic network.

Erythrocyte metabolism

Our aim is to present an updated overview of the erythrocyte metabolism highlighting its richness and complexity. We have manually collected and connected the available biochemical pathways and integrated them into a functional metabolic map. The focus of this map is on the main biochemical pathways consisting of glycolysis, the pentose phosphate pathway, redox metabolism, oxygen metabolism, purine/nucleoside metabolism, and membrane transport. Other recently emerging pathways are also curated, like the methionine salvage pathway, the glyoxalase system, carnitine metabolism, and the lands cycle, as well as remnants of the carboxylic acid metabolism. An additional goal of this review is to present the dynamics of erythrocyte metabolism, providing key numbers used to perform basic quantitative analyses. By synthesizing experimental and computational data, we conclude that glycolysis, pentose phosphate pathway, and redox metabolism are the foundations of erythrocyte metabolism. Additionally, the erythrocyte can sense oxygen levels and oxidative stress adjusting its mechanics, metabolism, and function. In conclusion, fine-tuning of erythrocyte metabolism controls one of the most important biological processes, that is, oxygen loading, transport, and delivery.

On paradoxes between optimal growth, metabolic control analysis, and flux balance analysis

In Microbiology it is often assumed that growth rate is maximal. This may be taken to suggest that the dependence of the growth rate on every enzyme activity is at the top of an inverse-parabolic function, i.e. that all flux control coefficients should equal zero. This might seem to imply that the sum of these flux control coefficients equals zero. According to the summation law of Metabolic Control Analysis (MCA) the sum of flux control coefficients should equal 1 however. And in Flux Balance Analysis (FBA) catabolism is often limited by a hard bound, causing catabolism to fully control the fluxes, again in apparent contrast with a flux control coefficient of zero. Here we resolve these paradoxes (apparent contradictions) in an analysis that uses the 'Edinburgh pathway', the 'Amsterdam pathway', as well as a generic metabolic network providing the building blocks or Gibbs energy for microbial growth. We review and show that (i) optimization depends on so-called enzyme control coefficients rather than the 'catalytic control coefficients' of MCA's summation law, (ii) when optimization occurs at fixed total protein, the former differ from the latter to the extent that they may all become equal to zero in the optimum state, (iii) in more realistic scenarios of optimization where catalytically inert biomass is compensating or maintenance metabolism is taken into consideration, the optimum enzyme concentrations should not be expected to equal those that maximize the specific growth rate, (iv) optimization may be in terms of yield rather than specific growth rate, which resolves the paradox because the sum of catalytic control coefficients on yield equals 0, (v) FBA effectively maximizes growth yield, and for yield the summation law states 0 rather than 1, thereby removing the paradox, (vi) furthermore, FBA then comes more often to a 'hard optimum' defined by a maximum catabolic flux and a catabolic-enzyme control coefficient of 1. The trade-off between maintenance metabolism and growth is highlighted as worthy of further analysis.

Reinhart Heinrich: In memoriam of an exceptional scholar

In the Mathematical Biology community, Reinhart Heinrich (1946-2006) is well-known as one of the founders of Metabolic Control Analysis. Moreover, he made significant contributions to the modelling of erythrocyte metabolism and signal transduction cascades, optimality principles in metabolism, theoretical membrane biophysics and other topics. Here, the historical context of his scientific work is outlined and numerous personal memories of the scholarship of, and cooperation with, Reinhart Heinrich are narrated. Attention is drawn again to the pros and cons of normalized and non-normalized control coefficients. The role of the Golden Ratio in a dynamic optimization problem in genetic regulation of metabolism is discussed. Overall, this article is aimed at keeping alive the memory of a unique university teacher, researcher and friend.

Oscillations for active sensing in olfaction: bioinspiration from insect antennal movements

Crustacean and insect antennal scanning movements have been postulated to increase odorant capture but the exact mechanisms as well as measures of efficiency are wanting. The aim of this work is to test the hypothesis that an increase in oscillation frequency of a simplified insect antenna model translates to an increase of odorant capture, and to quantify by how much and through which mechanism. We approximate the antennal movements of bumblebees, quantified in a previous study, by a vertical oscillatory movement of a cylinder in a homogeneous horizontal flow with odorants. We test our multiphysics flow and mass transfer numerical model with dedicated experiments using particle image velocimetry. A new entire translating experimental measurement setup containing an oil tank enables us to work at appropriate Strouhal and Reynolds numbers. Increasing antennal oscillating frequency does increase the odorant capture rate, up to 200%, proving this behavior being active sensing. This result holds however only up to a critical frequency. A decrease of efficiency characterizes higher frequencies, due to molecules depletion within oversampled regions, themselves defined by overlaying boundary layers. Despite decades of work on thermal and mass transfer studies on oscillating cylinders, no analogy with published cases was found. This is due to the unique flow regimes studied here, resulting from the combination of organ small size and low frequencies of oscillations. A theory for such flow regimes is thus to be developed, with applications to fundamental research on animal perception up to bioinspired olfaction.

Stable Isotopes for Tracing Cardiac Metabolism in Diseases

Although metabolic remodeling during cardiovascular diseases has been well-recognized for decades, the recent development of analytical platforms and mathematical tools has driven the emergence of assessing cardiac metabolism using tracers. Metabolism is a critical component of cellular functions and adaptation to stress. The pathogenesis of cardiovascular disease involves metabolic adaptation to maintain cardiac contractile function even in advanced disease stages. Stable-isotope tracer measurements are a powerful tool for measuring flux distributions at the whole organism level and assessing metabolic changes at a systems level in vivo. The goal of this review is to summarize techniques and concepts for in vivo or ex vivo stable isotope labeling in cardiovascular research, to highlight mathematical concepts and their limitations, to describe analytical methods at the tissue and single-cell level, and to discuss opportunities to leverage metabolic models to address important mechanistic questions relevant to all patients with cardiovascular disease.

Programmatic modeling for biological systems

Computational modeling has become an established technique to encode mathematical representations of cellular processes and gain mechanistic insights that drive testable predictions. These models are often constructed using graphical user interfaces or domain-specific languages, with community standards used for interchange. Models undergo steady state or dynamic analysis, which can include simulation and calibration within a single application, or transfer across various tools. Here, we describe a novel programmatic modeling paradigm, whereby modeling is augmented with software engineering best practices. We focus on Python - a popular programming language with a large scientific package ecosystem. Models can be encoded as programs, adding benefits such as modularity, testing, and automated documentation generators, while still being extensible and exportable to standardized formats for use with external tools if desired. Programmatic modeling is a key technology to enable collaborative model development and enhance dissemination, transparency, and reproducibility.

A brief note on the properties of linear pathways

Linear metabolic pathways are the simplest network architecture we find in metabolism and are a good starting point to gain insight into the operating principles of metabolic control. Linear pathways possess some well-known properties, such as a bias of flux control towards the first few steps of the pathway as well as the lack of flux control at reactions close to equilibrium. In both cases, a rationale for these behaviors is given in terms of how elasticities transmit changes through a pathway. A discussion is given on the fundamental role that two reaction step sections play in a linear pathway when transmitting changes. For a pathway with irreversible steps, the deconstruction is straight forward and includes a product of local response coefficients that cascade along the pathway. When reversibility is included, the picture became more complex but a relationship in terms of the local response coefficients if derived that includes the reverse response coefficients and highlights the interplay between the forward and backward transmission of changes during a perturbation.

Agent-based model of multicellular tumor spheroid evolution including cell metabolism

Computational models aiming at the spatio-temporal description of cancer evolution are a suitable framework for testing biological hypotheses from experimental data, and generating new ones. Building on our recent work (J. Theor. Biol. 389, 146 (2016)) we develop a 3D agent-based model, capable of tracking hundreds of thousands of interacting cells, over time scales ranging from seconds to years. Cell dynamics is driven by a Monte Carlo solver, incorporating partial differential equations to describe chemical pathways and the activation/repression of "genes", leading to the up- or down-regulation of specific cell markers. Each cell-agent of different kind (stem, cancer, stromal etc.) runs through its cycle, undergoes division, can exit to a dormant, senescent, necrotic state, or apoptosis, according to the inputs from its systemic network. The basic network at this stage describes glucose/oxygen/ATP cycling, and can be readily extended to cancer-cell specific markers. Eventual accumulation of chemical/radiation damage to each cell's DNA is described by a Markov chain of internal states, and by a damage-repair network, whose evolution is linked to the cell systemic network. Aimed at a direct comparison with experiments of tumorsphere growth from stem cells, the present model will allow to quantitatively study the role of transcription factors involved in the reprogramming and variable radio-resistance of simulated cancer-stem cells, evolving in a realistic computer simulation of a growing multicellular tumorsphere.

Analyzing the Function of Catalase and the Ascorbate-Glutathione Pathway in H2O2 Processing: Insights from an Experimentally Constrained Kinetic Model

SIGNIFICANCE

Plant stress involves redox signaling linked to reactive oxygen species such as hydrogen peroxide (H₂O₂), which can be generated at high rates in photosynthetic cells. The systems that process H₂O₂ include catalase (CAT) and the ascorbate-glutathione pathway, but interactions between them remain unclear. Modeling can aid interpretation and pinpoint areas for investigation. Recent Advances: Based on emerging data and concepts, we introduce a new experimentally constrained kinetic model to analyze interactions between H₂O₂, CAT, ascorbate, glutathione, and NADPH. The sensitivity points required for accurate simulation of experimental observations are analyzed, and the implications for H₂O₂-linked redox signaling are discussed.

CRITICAL ISSUES

We discuss several implications of the modeled results, in particular the following. (i) CAT and ascorbate peroxidase can share the load in H₂O₂ processing even in optimal conditions. (ii) Intracellular H₂O₂ concentrations more than the low μM range may rarely occur. (iii) Ascorbate redox turnover is largely independent of glutathione until ascorbate peroxidation exceeds a certain value. (iv) NADPH availability may determine glutathione redox status through its influence on monodehydroascorbate reduction. (v) The sensitivity of glutathione status to oxidative stress emphasizes its potential suitability as a sensor of increased H₂O₂.

FUTURE DIRECTIONS

Important future questions include the roles of other antioxidative systems in interacting with CAT and the ascorbate-glutathione pathway as well as the nature and significance of processes that achieve redox exchange between different subcellular compartments. Progress in these areas is likely to be favored by integrating kinetic modeling analyses into experimentally based programs, allowing each approach to inform the other.

Insights into Dynamic Network States Using Metabolomic Data

Metabolomic data is the youngest of the high-throughput data types; however, it is potentially one of the most informative, as it provides a direct, quantitative biochemical phenotype. There are a number of ways in which metabolomic data can be analyzed in systems biology; however, the thermodynamic and kinetic relevance of these data cannot be overstated. Genome-scale metabolic network reconstructions provide a natural context to incorporate metabolomic data in order to provide insight into the condition-specific kinetic characteristics of metabolic networks. Herein we discuss how metabolomic data can be incorporated into constraint-based models in a flexible framework that enables scaling from small pathways to cell-scale models, while being able to accommodate coarse-grained to more detailed, allosteric interactions, all using the well-known principle of mass action.

Modeling Cell-to-Cell Communication Networks Using Response-Time Distributions

Cell-to-cell communication networks have critical roles in coordinating diverse organismal processes, such as tissue development or immune cell response. However, compared with intracellular signal transduction networks, the function and engineering principles of cell-to-cell communication networks are far less understood. Major complications include: cells are themselves regulated by complex intracellular signaling networks; individual cells are heterogeneous; and output of any one cell can recursively become an additional input signal to other cells. Here, we make use of a framework that treats intracellular signal transduction networks as "black boxes" with characterized input-to-output response relationships. We study simple cell-to-cell communication circuit motifs and find conditions that generate bimodal responses in time, as well as mechanisms for independently controlling synchronization and delay of cell-population responses. We apply our modeling approach to explain otherwise puzzling data on cytokine secretion onset times in T cells. Our approach can be used to predict communication network structure using experimentally accessible input-to-output measurements and without detailed knowledge of intermediate steps.

Principles for circadian orchestration of metabolic pathways

Circadian rhythms govern multiple aspects of animal metabolism. Transcriptome-, proteome- and metabolome-wide measurements have revealed widespread circadian rhythms in metabolism governed by a cellular genetic oscillator, the circadian core clock. However, it remains unclear if and under which conditions transcriptional rhythms cause rhythms in particular metabolites and metabolic fluxes. Here, we analyzed the circadian orchestration of metabolic pathways by direct measurement of enzyme activities, analysis of transcriptome data, and developing a theoretical method called circadian response analysis. Contrary to a common assumption, we found that pronounced rhythms in metabolic pathways are often favored by separation rather than alignment in the times of peak activity of key enzymes. This property holds true for a set of metabolic pathway motifs (e.g., linear chains and branching points) and also under the conditions of fast kinetics typical for metabolic reactions. By circadian response analysis of pathway motifs, we determined exact timing separation constraints on rhythmic enzyme activities that allow for substantial rhythms in pathway flux and metabolite concentrations. Direct measurements of circadian enzyme activities in mouse skeletal muscle confirmed that such timing separation occurs in vivo.

On the role of topology in regulating transcriptional cascades

Topology of interactions in a transcriptional cascade determines the behavior of its signal-response profile and the activation states of genes.

Life at the boundary: photosynthesis at the soil-fluid interface. A synthesis focusing on mosses

Mosses are among the earliest branching embryophytes and probably originated not later than the early Ordovician when atmospheric CO2 was higher and O2 was lower than today. The C3 biochemistry and physiology of their photosynthesis suggests, by analogy with tracheophytes, that growth of extant bryophytes in high CO2 approximating Ordovician values would increase the growth rate. This occurs for many mosses, including Physcomitrella patens in suspension culture, although recently published transcriptomic data on this species at high CO2 and present-day CO2 show down-regulation of the transcription of several genes related to photosynthesis. It would be useful if transcriptomic (and proteomic) data comparing growth conditions are linked to measurements of growth and physiology on the same, or parallel, cultures. Mosses (like later-originating embryophytes) have been subject to changes in bulk atmospheric CO2 and O2 throughout their existence, with evidence, albeit limited, for positive selection of moss Rubisco. Extant mosses are subject to a large range of CO2 and O2 concentrations in their immediate environments, especially aquatic mosses, and mosses are particularly influenced by CO2 generated by, and O2 consumed by, soil chemoorganotrophy from organic C produced by tracheophytes (if present) and bryophytes.

Genome-scale estimate of the metabolic turnover of E. coli from the energy balance analysis

In this article the notion of metabolic turnover is revisited in the light of recent results of out-of-equilibrium thermodynamics. By means of Monte Carlo methods we perform an exact sampling of the enzymatic fluxes in a genome scale metabolic network of E. coli in stationary growth conditions from which we infer the metabolites turnover times. However the latter are inferred from net fluxes, and we argue that this approximation is not valid for enzymes working nearby thermodynamic equilibrium. We recalculate turnover times from total fluxes by performing an energy balance analysis of the network and recurring to the fluctuation theorem. We find in many cases values one of order of magnitude lower, implying a faster picture of intermediate metabolism.

Targeting glycolysis in the malaria parasite Plasmodium falciparum

Glycolysis is the main pathway for ATP production in the malaria parasite Plasmodium falciparum and essential for its survival. Following a sensitivity analysis of a detailed kinetic model for glycolysis in the parasite, the glucose transport reaction was identified as the step whose activity needed to be inhibited to the least extent to result in a 50% reduction in glycolytic flux. In a subsequent inhibitor titration with cytochalasin B, we confirmed the model analysis experimentally and measured a flux control coefficient of 0.3 for the glucose transporter. In addition to the glucose transporter, the glucokinase and phosphofructokinase had high flux control coefficients, while for the ATPase a small negative flux control coefficient was predicted. In a broader comparative analysis of glycolytic models, we identified a weakness in the P. falciparum pathway design with respect to stability towards perturbations in the ATP demand.

DATABASE

The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.bio.vu.nl/database/vanniekerk1. The SEEK-study including the experimental data set is available at DOI 10.15490/seek.1.

INVESTIGATION

56 (http://dx.doi.org/10.15490/seek.1.

INVESTIGATION

56).

Modeling and Simulation Tools: From Systems Biology to Systems Medicine

Modeling is an integral component of modern biology. In this chapter we look into the role of the model, as it pertains to Systems Medicine, and the software that is required to instantiate and run it. We do this by comparing the development, implementation, and characteristics of tools that have been developed to work with two divergent methodologies: Systems Biology and Pharmacometrics. From the Systems Biology perspective we consider the concept of "Software as a Medical Device" and what this may imply for the migration of research-oriented, simulation software into the domain of human health.In our second perspective, we see how in practice hundreds of computational tools already accompany drug discovery and development at every stage of the process. Standardized exchange formats are required to streamline the model exchange between tools, which would minimize translation errors and reduce the required time. With the emergence, almost 15 years ago, of the SBML standard, a large part of the domain of interest is already covered and models can be shared and passed from software to software without recoding them. Until recently the last stage of the process, the pharmacometric analysis used in clinical studies carried out on subject populations, lacked such an exchange medium. We describe a new emerging exchange format in Pharmacometrics which covers the non-linear mixed effects models, the standard statistical model type used in this area. By interfacing these two formats the entire domain can be covered by complementary standards and subsequently the according tools.

Metabolomics in transfusion medicine

Biochemical investigations on the regulatory mechanisms of red blood cell (RBC) and platelet (PLT) metabolism have fostered a century of advances in the field of transfusion medicine. Owing to these advances, storage of RBCs and PLT concentrates has become a lifesaving practice in clinical and military settings. There, however, remains room for improvement, especially with regard to the introduction of novel storage and/or rejuvenation solutions, alternative cell processing strategies (e.g., pathogen inactivation technologies), and quality testing (e.g., evaluation of novel containers with alternative plasticizers). Recent advancements in mass spectrometry-based metabolomics and systems biology, the bioinformatics integration of omics data, promise to speed up the design and testing of innovative storage strategies developed to improve the quality, safety, and effectiveness of blood products. Here we review the currently available metabolomics technologies and briefly describe the routine workflow for transfusion medicine-relevant studies. The goal is to provide transfusion medicine experts with adequate tools to navigate through the otherwise overwhelming amount of metabolomics data burgeoning in the field during the past few years. Descriptive metabolomics data have represented the first step omics researchers have taken into the field of transfusion medicine. However, to up the ante, clinical and omics experts will need to merge their expertise to investigate correlative and mechanistic relationships among metabolic variables and transfusion-relevant variables, such as 24-hour in vivo recovery for transfused RBCs. Integration with systems biology models will potentially allow for in silico prediction of metabolic phenotypes, thus streamlining the design and testing of alternative storage strategies and/or solutions.

Discrimination of time-dependent inflow properties with a cooperative dynamical system

Many physical, chemical, and biological systems exhibit a cooperative or sigmoidal response with respect to the input. In biochemistry, such behavior is called an allosteric effect. Here, we demonstrate that a system with such properties can be used to discriminate the amplitude or frequency of an external periodic perturbation. Numerical simulations performed for a model sigmoidal kinetics illustrate that there exists a narrow range of frequencies and amplitudes within which the system evolves toward significantly different states. Therefore, observation of system evolution should provide information about the characteristics of the perturbation. The discrimination properties for periodic perturbation are generic. They can be observed in various dynamical systems and for different types of periodic perturbation.

Oxidative protein folding: from thiol-disulfide exchange reactions to the redox poise of the endoplasmic reticulum

This review examines oxidative protein folding within the mammalian endoplasmic reticulum (ER) from an enzymological perspective. In protein disulfide isomerase-first (PDI-first) pathways of oxidative protein folding, PDI is the immediate oxidant of reduced client proteins and then addresses disulfide mispairings in a second isomerization phase. In PDI-second pathways the initial oxidation is PDI-independent. Evidence for the rapid reduction of PDI by reduced glutathione is presented in the context of PDI-first pathways. Strategies and challenges are discussed for determination of the concentrations of reduced and oxidized glutathione and of the ratios of PDI(red):PDI(ox). The preponderance of evidence suggests that the mammalian ER is more reducing than first envisaged. The average redox state of major PDI-family members is largely to almost totally reduced. These observations are consistent with model studies showing that oxidative protein folding proceeds most efficiently at a reducing redox poise consistent with a stoichiometric insertion of disulfides into client proteins. After a discussion of the use of natively encoded fluorescent probes to report the glutathione redox poise of the ER, this review concludes with an elaboration of a complementary strategy to discontinuously survey the redox state of as many redox-active disulfides as can be identified by ratiometric LC-MS-MS methods. Consortia of oxidoreductases that are in redox equilibrium can then be identified and compared to the glutathione redox poise of the ER to gain a more detailed understanding of the factors that influence oxidative protein folding within the secretory compartment.

An in-silico study of the regulation of CHO cells glycolysis

In this work, a kinetic-metabolic model previously developed for CHO cells is used to study glycolysis regulation. The model is assessed for its biological relevance by analyzing its ability to simulate metabolic events induced following a hypoxic perturbation. Feedback and feedforward regulatory mechanisms known to occur to either inhibit or activate fluxes of glycolysis, are implemented in various combined scenarios and their effects on the metabolic response were analyzed. This study aims at characterizing the role of intermediates of glycolysis and of the cell energetic state, described as the AMP-to-ATP ratio, as inhibitors and activators of glycolysis pathway. In addition to the glycolysis pathway, we here describe the transient metabolic response of pathways that are connected to glycolysis, such as the pentose phosphate pathway, TCA cycle, cell bioenergetics system, glutamine and amino acids metabolisms. Taken individually, each regulatory mechanism leads to an oscillatory behavior in response to a hypoxic perturbation, while their combination clearly damps oscillations. However, only the addition of the cell energetic state to the regulatory mechanisms results in a non-oscillating response leading to metabolic flux rate rearrangement corresponding to the anaerobic metabolism expected to prevail under hypoxic conditions. We thus demonstrate in this work, from model simulations, that the robustness of a cell energetic metabolism can be described from a combination of feedback and feedforward inhibition and activation regulatory mechanisms of glycolysis fluxes, involving intermediates of glycolysis and the cell energetic state itself.

Models in biology: 'accurate descriptions of our pathetic thinking'

In this essay I will sketch some ideas for how to think about models in biology. I will begin by trying to dispel the myth that quantitative modeling is somehow foreign to biology. I will then point out the distinction between forward and reverse modeling and focus thereafter on the former. Instead of going into mathematical technicalities about different varieties of models, I will focus on their logical structure, in terms of assumptions and conclusions. A model is a logical machine for deducing the latter from the former. If the model is correct, then, if you believe its assumptions, you must, as a matter of logic, also believe its conclusions. This leads to consideration of the assumptions underlying models. If these are based on fundamental physical laws, then it may be reasonable to treat the model as 'predictive', in the sense that it is not subject to falsification and we can rely on its conclusions. However, at the molecular level, models are more often derived from phenomenology and guesswork. In this case, the model is a test of its assumptions and must be falsifiable. I will discuss three models from this perspective, each of which yields biological insights, and this will lead to some guidelines for prospective model builders.

Analyzing clonal variation of monoclonal antibody-producing CHO cell lines using an in silico metabolomic platform

Monoclonal antibody producing Chinese hamster ovary (CHO) cells have been shown to undergo metabolic changes when engineered to produce high titers of recombinant proteins. In this work, we have studied the distinct metabolism of CHO cell clones harboring an efficient inducible expression system, based on the cumate gene switch, and displaying different expression levels, high and low productivities, compared to that of the parental cells from which they were derived. A kinetic model for CHO cell metabolism was further developed to include metabolic regulation. Model calibration was performed using intracellular and extracellular metabolite profiles obtained from shake flask batch cultures. Model simulations of intracellular fluxes and ratios known as biomarkers revealed significant changes correlated with clonal variation but not to the recombinant protein expression level. Metabolic flux distribution mostly differs in the reactions involving pyruvate metabolism, with an increased net flux of pyruvate into the tricarboxylic acid (TCA) cycle in the high-producer clone, either being induced or non-induced with cumate. More specifically, CHO cell metabolism in this clone was characterized by an efficient utilization of glucose and a high pyruvate dehydrogenase flux. Moreover, the high-producer clone shows a high rate of anaplerosis from pyruvate to oxaloacetate, through pyruvate carboxylase and from glutamate to α-ketoglutarate, through glutamate dehydrogenase, and a reduced rate of cataplerosis from malate to pyruvate, through malic enzyme. Indeed, the increase of flux through pyruvate carboxylase was not driven by an increased anabolic demand. It is in fact linked to an increase of the TCA cycle global flux, which allows better regulation of higher redox and more efficient metabolic states. To the best of our knowledge, this is the first time a dynamic in silico platform is proposed to analyze and compare the metabolomic behavior of different CHO clones.

New types of experimental data shape the use of enzyme kinetics for dynamic network modeling

Since the publication of Leonor Michaelis and Maude Menten's paper on the reaction kinetics of the enzyme invertase in 1913, molecular biology has evolved tremendously. New measurement techniques allow in vivo characterization of the whole genome, proteome or transcriptome of cells, whereas the classical enzyme essay only allows determination of the two Michaelis-Menten parameters V and K(m). Nevertheless, Michaelis-Menten kinetics are still commonly used, not only in the in vitro context of enzyme characterization but also as a rate law for enzymatic reactions in larger biochemical reaction networks. In this review, we give an overview of the historical development of kinetic rate laws originating from Michaelis-Menten kinetics over the past 100 years. Furthermore, we briefly summarize the experimental techniques used for the characterization of enzymes, and discuss web resources that systematically store kinetic parameters and related information. Finally, describe the novel opportunities that arise from using these data in dynamic mathematical modeling. In this framework, traditional in vitro approaches may be combined with modern genome-scale measurements to foster thorough understanding of the underlying complex mechanisms.

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric, thermodynamic and physiological constraints

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works considered only mass action kinetics for reactions in metabolic networks. Herein, we applied the optimization and risk analysis of complex living entities (ORACLE) framework and constructed a large-scale mechanistic kinetic model of optimally grown Escherichia coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of metabolic fluxes and metabolite concentrations. Our results further suggest that enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of cellular metabolism.

Red blood cell metabolism under prolonged anaerobic storage

Oxygen dependent modulation of red blood cell metabolism is a long investigated issue. However, the recent introduction of novel mass spectrometry-based approaches lends itself to implement our understanding of the effects of red blood cell prolonged exposure to anaerobiosis. Indeed, most of the studies conducted so far have addressed the short term issue, while the limited body of literature covering a 42 days storage period only takes into account a handful of metabolic parameters (ATP, DPG, glucose, glyceraldehyde 3-phosphate, and lactate). We hereby performed a mass spectrometry-based untargeted metabolomics analysis in order to highlight metabolic species in erythrocyte concentrates stored anaerobically in SAGM additive solutions for up to 42 days, by testing cells on a weekly basis. We could confirm previous evidence about long term anaerobiosis promoting glycolytic metabolism in RBCs and prolonging the conservation of high energy phosphate reservoirs and purine homeostasis. In parallel, we evidenced that, in contrast to aerobic storage, anaerobiosis impairs erythrocyte capacity to cope with oxidative stress by blocking metabolic diversion towards the pentose phosphate pathway, which negatively affects glutathione homeostasis. Therefore, although oxidative stress was less sustained than in aerobically stored counterparts, oxidative stress markers still accumulate over anaerobic storage progression.

In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae: II. Mathematical model

A mathematical model of glycolysis in Saccharomyces cerevisiae is presented. The model is based on rate equations for the individual reactions and aims to predict changes in the levels of intra- and extracellular metabolites after a glucose pulse, as described in part I of this study. Kinetic analysis focuses on a time scale of seconds, thereby neglecting biosynthesis of new enzymes. The model structure and experimental observations are related to the aerobic growth of the yeast. The model is based on material balance equations of the key metabolites in the extracellular environment, the cytoplasm and the mitochondria, and includes mechanistically based, experimentally matched rate equations for the individual enzymes. The model includes removal of metabolites from glycolysis and TCC for biosynthesis, and also compartmentation and translocation of adenine nucleotides. The model was verified by in vivo diagnosis of intracellular enzymes, which includes the decomposition of the network of reactions to reduce the number of parameters to be estimated simultaneously. Additionally, sensitivity analysis guarantees that only those parameters are estimated that contribute to systems trajectory with reasonable sensitivity. The model predictions and experimental observations agree reasonably well for most of the metabolites, except for pyruvate and adenine nucleotides. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 592-608, 1997.

Parametric sensitivity of stoichiometric flux balance models applied to wild-type Escherichia coli metabolism

Stoichiometrically based flux balance models provide a method to quantify the metabolic pathway fluxes within a living cell. Predictions of flux balance models are expected to have applications in pathway engineering as well as in bioprocess design and control. These models utilize optimality principles applied to metabolic pathway stoichiometry along with the metabolic requirements for growth to determine the flux distribution in a metabolic network. A flux balance model has been developed for Escherichia coli W3110 using five experimentally determined strain-specific parameters. In this report, we determine the sensitivity of the predictions of the flux balance model to these five strain-specific parameters. Model predictions are shown to be sensitive to the two parameters describing metabolic capacity, while they are relatively insensitive to the three parameters that describe the metabolic requirements for growth. Thus, when stoichiometrically based models are formulated for additional strains one needs to measure the metabolic capacity (maximum rates of nutrient and oxygen utilization) accurately. Determination of metabolic capacity from batch experiments is relatively easy to perform. On the other hand, the harder to determine maintenance parameters need not be as accurately determined. (c) 1995 John Wiley & Sons, Inc.

Kinetic analysis of cephalosporin biosynthesis in Streptomyces clavuligerus

A kinetic model describing the cephalosporin biosynthesis in Streptomyces clavuligerus was developed. Using previously reported kinetic data of biosynthetic enzymes, we examined the kinetics of cephalosporin production. The predicted time profile of the specific production rate during a batch culture parallels that of experimental observation. Sensitivity analysis reveals that delta-(L-alpha-aminoadipyl)-L-cysteinyl-D-valine (ACV) synthetase is the rate-limiting enzyme. The effect of amplifying ACV synthetase on the specific production rate was analyzed theoretically. Increasing ACV synthetase enhances the production rate initially until ACV synthetase enhances the production rate initially until deacetocycephalosporin C hydroxylase becomes rate-limiting. Such kinetic analysis can provide a rational basis for modifying the biosynthetic machinery of cephalosporin through gene cloning.

Acute and chronic effects of bupivacaine on muscle energetics during contraction in vivo: a modular metabolic control analysis

Bupivacaine is a widely used anaesthetic injected locally in clinical practice for short-term neurotransmission blockade. However, persistent side effects on mitochondrial integrity have been demonstrated in muscle parts surrounding the injection site. We use the precise language of metabolic control analysis in the present study to describe in vivo consequences of bupivacaine injection on muscle energetics during contraction. We define a model system of muscle energy metabolism in rats with a sciatic nerve catheter that consists of two modules of reactions, ATP/PCr (phosphocreatine) supply and ATP/PCr demand, linked by the common intermediate PCr detected in vivo by 31P-MRS (magnetic resonance spectroscopy). Measured system variables were [PCr] (intermediate) and contraction (flux). We first applied regulation analysis to quantify acute effects of bupivacaine. After bupivacaine injection, contraction decreased by 15.7% and, concomitantly, [PCr] increased by 11.2%. The regulation analysis quantified that demand was in fact directly inhibited by bupivacaine (−21.3%), causing an increase in PCr. This increase in PCr indirectly reduced mitochondrial activity (−22.4%). Globally, the decrease in contractions was almost fully explained by inhibition of demand (−17.0%) without significant effect through energy supply. Finally we applied elasticity analysis to quantify chronic effects of bupivacaine iterative injections. The absence of a difference in elasticities obtained in treated rats when compared with healthy control rats clearly shows the absence of dysfunction in energetic control of muscle contraction energetics. The present study constitutes the first and direct evidence that bupivacaine myotoxicity is compromised by other factors during contraction in vivo, and illustrates the interest of modular approaches to appreciate simple rules governing bioenergetic systems when affected by drugs.

Reaction kinetics of catalyzed competitive heteropolymer cleavage

A theoretical formulation for complete heteropolymer degradation is developed in terms of Michaelis-Menten reaction kinetics under the quasi-steady-state approximation. This allows the concentration of the entire intermediate decomposition cascade to be accounted for as well as each species of emerging final product. The formulation is implemented computationally and results in stable reaction kinetics across a range of orders of magnitude for K(M) and k(cat). The model is compared with experiment, specifically in vitro HIV-1 protease-catalyzed retroviral Gag-polyprotein processing. Using an experimentally determined cleavage-polypeptide parameter set, good qualitative agreement is reached with Gag degradation kinetics, given the difference in experimental conditions. A parameter search within 1 order of magnitude of variation of the experimental set results in the determination of an optimal parameter set in complete agreement with experiment which allows the time evolution of each individual as well as intermediate species in Gag to be accurately followed. Future investigations that determine the required enzymatic parameters to populate such a scheme will allow for the model to be refined in order to track the time for viral maturation and infectivity.

Inhibitors of succinate: quinone reductase/Complex II regulate production of mitochondrial reactive oxygen species and protect normal cells from ischemic damage but induce specific cancer cell death

Succinate:quinone reductase (SQR) of Complex II occupies a unique central point in the mitochondrial respiratory system as a major source of electrons driving reactive oxygen species (ROS) production. It is an ideal pharmaceutical target for modulating ROS levels in normal cells to prevent oxidative stress-induced damage or alternatively,increase ROS in cancer cells, inducing cell death.The value of drugs like diazoxide to prevent ROS production,protecting normal cells, whereas vitamin E analogues promote ROS in cancer cells to kill them is highlighted. As pharmaceuticals these agents may prevent degenerative disease and their modes of action are presently being fully explored. The evidence that SDH/Complex II is tightly coupled to the NADH/NAD+ ratio in all cells,impacted by the available supplies of Krebs cycle intermediates as essential NAD-linked substrates, and the NAD+-dependent regulation of SDH/Complex II are reviewed, as are links to the NAD+-dependent dehydrogenases, Complex I and the E3 dihiydrolipoamide dehydrogenase to produce ROS. This review collates and discusses diverse sources of information relating to ROS production in different biological systems, focussing on evidence for SQR as the main source of ROS production in mitochondria, particularly its relevance to protection from oxidative stress and to the mitochondrial-targeted anti cancer drugs (mitocans) as novel cancer therapies [corrected].

Automated refinement and inference of analytical models for metabolic networks

The reverse engineering of metabolic networks from experimental data is traditionally a labor-intensive task requiring a priori systems knowledge. Using a proven model as a test system, we demonstrate an automated method to simplify this process by modifying an existing or related model--suggesting nonlinear terms and structural modifications--or even constructing a new model that agrees with the system's time series observations. In certain cases, this method can identify the full dynamical model from scratch without prior knowledge or structural assumptions. The algorithm selects between multiple candidate models by designing experiments to make their predictions disagree. We performed computational experiments to analyze a nonlinear seven-dimensional model of yeast glycolytic oscillations. This approach corrected mistakes reliably in both approximated and overspecified models. The method performed well to high levels of noise for most states, could identify the correct model de novo, and make better predictions than ordinary parametric regression and neural network models. We identified an invariant quantity in the model, which accurately derived kinetics and the numerical sensitivity coefficients of the system. Finally, we compared the system to dynamic flux estimation and discussed the scaling and application of this methodology to automated experiment design and control in biological systems in real time.

A kinetic model of TBP auto-regulation exhibits bistability

Background

TATA Binding Protein (TBP) is required for transcription initiation by all three eukaryotic RNA polymerases. It participates in transcriptional initiation at the majority of eukaryotic gene promoters, either by direct association to the TATA box upstream of the transcription start site or by indirectly localizing to the promoter through other proteins. TBP exists in solution in a dimeric form but binds to DNA as a monomer. Here, we present the first mathematical model for auto-catalytic TBP expression and use it to study the role of dimerization in maintaining the steady state TBP level.

Results

We show that the autogenous regulation of TBP results in a system that is capable of exhibiting three steady states: an unstable low TBP state, one stable state corresponding to a physiological TBP concentration, and another stable steady state corresponding to unviable cells where no TBP is expressed. Our model predicts that a basal level of TBP is required to establish the transcription of the TBP gene, and hence for cell viability. It also predicts that, for the condition corresponding to a typical mammalian cell, the high-TBP state and cell viability is sensitive to variation in DNA binding strength. We use the model to explore the effect of the dimer in buffering the response to changes in TBP levels, and show that for some physiological conditions the dimer is not important in buffering against perturbations.

Conclusions

Results on the necessity of a minimum basal TBP level support the in vivo observations that TBP is maternally inherited, providing the small amount of TBP required to establish its ubiquitous expression. The model shows that the system is sensitive to variations in parameters indicating that it is vulnerable to mutations in TBP. A reduction in TBP-DNA binding constant can lead the system to a regime where the unviable state is the only steady state. Contrary to the current hypotheses, we show that under some physiological conditions the dimer is not very important in restoring the system to steady state. This model demonstrates the use of mathematical modelling to investigate system behaviour and generate hypotheses governing the dynamics of such nonlinear biological systems.

Reviewers

This article was reviewed by Tomasz Lipniacki, James Faeder and Anna Marciniak-Czochra.

An indirect optimization method for biochemical systems: description of method and application to the maximization of the rate of ethanol, glycerol, and carbohydrate production in Saccharomyces cerevisiae

Three metabolic models for the production of ethanol, glycerol, and carbohydrates in yeast are optimized with respect to different production rates. While originally nonlinear, all three optimization problems are reduced in such a way that methods of linear programming can be used. The optimizations lead to profiles of enzyme activities that are compatible with the physiology of the cells, which guarantees their viability and fitness, and yield higher rates of the desired final end products than the original systems. In order to increase ethanol rate production at least three times, six enzymes must be modulated. By contrast, when the production of glycerol or carbohydrates is optimized, modulation of just one enzyme (in the case of glycerol) or two enzymes (in the case of carbohydrates) is necessary to yield significant increases in product flux rate. Comparisons of our results with those obtained from other methods show great similarities and demonstrate that both are valid methods. The choice of one or the other method depends on the question of interest. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 758-772, 1997.

Sensitivity summation theorems for stochastic biochemical reaction systems

We investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic sensitivities for mean and covariance values of reactant concentrations and reaction fluxes and show that there exist MCA-like summation theorems among these sensitivities. The summation theorems for flux variances is shown to depend on the size of the measurement time window () within which reaction events are counted for measuring a single flux. It is found that the degree of the -dependency can become significant for processes involving multi-time-scale dynamics and is estimated by introducing a new measure of time-scale separation. This -dependency is shown to be closely related to the power-law scaling observed in flux fluctuations in various complex networks.

Flux-concentration duality in dynamic nonequilibrium biological networks

The structure of dynamic states in biological networks is of fundamental importance in understanding their function. Considering the elementary reaction structure of reconstructed metabolic networks, we show how appreciation of a gradient matrix, G =dv/dx (where v is the vector of fluxes and x is the vector of concentrations), enables the formulation of dual Jacobian matrices. One is for concentrations, J(x) =S x G, and the other is for fluxes, J(v) =G x S. The fundamental properties of these two Jacobians and the underlying duality that relates them are delineated. We describe a generalized approach to decomposing reaction networks in terms of the thermodynamic and kinetic components in the context of the network structure. The thermodynamic and kinetic influences can be viewed in terms of direction-driver relationships in the network.

3D structure of phosphofructokinase from Pichia pastoris: Localization of the novel gamma-subunits

The largest and one of the most complex ATP-dependent allosteric phosphofructokinase (Pfk) has been found in the methylotrophic yeast, Pichia pastoris. The enzyme is a hetero-oligomer ( approximately 1MDa) composed of three distinct subunits (alpha, beta and gamma) with molecular masses of 109, 104 and 41kDa, respectively. While the alpha- and beta-subunits show sequence similarities to other phosphofructokinase subunits, the gamma-subunit does not show high homology to any known protein in the databases. We have determined the first quaternary structure of P. pastoris phosphofructokinase by 3D electron microscopy. Random conical techniques and tomography have been instrumental to ascertain the quality of the sample preparations for structural studies and to obtain a reliable 3D structure. The final reconstruction of P. pastoris Pfk resembles its yeast counterparts with four additional densities, assigned to four gamma-subunits, bridging the N-terminal domains of the four pairs of alpha- and beta-subunits. Our data has evidenced novel interactions between the gamma- and the alpha-subunits comparable in intensity to the interactions, shown by cross-linking and limited proteolytic degradation experiments, between the gamma- and beta-subunits. The structural data provides clear insights into the allosteric fine-tuned regulation of the enzyme by ATP and AMP observed in this yeast species.

Forty years of helminth biochemistry

This review describes some of the developments in helminth biochemistry that have taken place over the last 40 years. Since the early 1970s the main anabolic and catabolic pathways in parasitic helminths have been worked out. The mode of action of the majority of anthelmintics is now known, but in many cases the mechanisms of resistance remain elusive. Developments in helminth biochemistry have depended heavily on developments in other areas. High throughput methods such as proteomics, transcriptomics and genome sequencing are now generating vast amounts of new data. The challenge for the future is to interpret and understand the biological relevance of this new information.