The intricate side of systems biology

Modeling Red Blood Cell Metabolism in the Omics Era

Red blood cells (RBCs) are abundant (more than 80% of the total cells in the human body), yet relatively simple, as they lack nuclei and organelles, including mitochondria. Since the earliest days of biochemistry, the accessibility of blood and RBCs made them an ideal matrix for the characterization of metabolism. Because of this, investigations into RBC metabolism are of extreme relevance for research and diagnostic purposes in scientific and clinical endeavors. The relative simplicity of RBCs has made them an eligible model for the development of reconstruction maps of eukaryotic cell metabolism since the early days of systems biology. Computational models hold the potential to deepen knowledge of RBC metabolism, but also and foremost to predict in silico RBC metabolic behaviors in response to environmental stimuli. Here, we review now classic concepts on RBC metabolism, prior work in systems biology of unicellular organisms, and how this work paved the way for the development of reconstruction models of RBC metabolism. Translationally, we discuss how the fields of metabolomics and systems biology have generated evidence to advance our understanding of the RBC storage lesion, a process of decline in storage quality that impacts over a hundred million blood units transfused every year.

Hepatic cholesterol biosynthesis and dioxin-induced dysregulation: A multiscale computational approach

Humans are constantly exposed to lipophilic persistent organic pollutants (POPs) that accumulate in fatty foods. Among the numerous POPs, dioxins, in particular 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), can impact several organ systems. While the hazard is clearly recognized, it is still difficult to develop a comprehensive understanding of the overall health impacts of dioxins. As chemical toxicity testing is steadily adopting new approach methodologies (NAMs), it becomes imperative to develop computational models that can bridge the data gaps between in vitro testing and in vivo outcomes. As an effort to address this challenge, we propose a multiscale computational approach using a "template-and-anchor" (T&A) structure. A template is a high-level umbrella model that permits the integration of information from various, detailed anchor models. In the present study, we use this T&A approach to describe the effect of TCDD on cholesterol dynamics. Specifically, we represent hepatic cholesterol biosynthesis as an anchor model that is perturbed by TCDD, leading to steatosis, along with alterations of plasma cholesterol. In the future, incorporating pertinent information from all anchor models into the template model will allow the characterization of the global effects of dioxin, which can subsequently be translated into overall - and ultimately personalized - human health risk assessment.

Sensitivity analysis methods in the biomedical sciences

Sensitivity analysis is an important part of a mathematical modeller's toolbox for model analysis. In this review paper, we describe the most frequently used sensitivity techniques, discussing their advantages and limitations, before applying each method to a simple model. Also included is a summary of current software packages, as well as a modeller's guide for carrying out sensitivity analyses. Finally, we apply the popular Morris and Sobol methods to two models with biomedical applications, with the intention of providing a deeper understanding behind both the principles of these methods and the presentation of their results.

Systems Biology - A Guide for Understanding and Developing Improved Strains of Lactic Acid Bacteria

Lactic Acid Bacteria (LAB) are extensively employed in the production of various fermented foods, due to their safe status, ability to affect texture and flavor and finally due to the beneficial effect they have on shelf-life. More recently, LAB have also gained interest as production hosts for various useful compounds, particularly compounds with sensitive applications, such as food ingredients and therapeutics. As for all industrial microorganisms, it is important to have a good understanding of the physiology and metabolism of LAB in order to fully exploit their potential, and for this purpose, many systems biology approaches are available. Systems metabolic engineering, an approach that combines optimization of metabolic enzymes/pathways at the systems level, synthetic biology as well as in silico model simulation, has been used to build microbial cell factories for production of biofuels, food ingredients and biochemicals. When developing LAB for use in foods, genetic engineering is in general not an accepted approach. An alternative is to screen mutant libraries for candidates with desirable traits using high-throughput screening technologies or to use adaptive laboratory evolution to select for mutants with special properties. In both cases, by using omics data and data-driven technologies to scrutinize these, it is possible to find the underlying cause for the desired attributes of such mutants. This review aims to describe how systems biology tools can be used for obtaining both engineered as well as non-engineered LAB with novel and desired properties.

Comparative proteomic analysis of four biotechnological strains Lactococcus lactis through label-free quantitative proteomics

Lactococcus lactis is a bacteria with high biotechnological potential, where is frequently used in the amino acid production and production of fermented dairy products, as well as drug delivery systems and mucosal vaccine vector. The knowledge of a functional core proteome is important extremely for both fundamental understanding of cell functions and for synthetic biology applications. In this study, we characterized the L. lacits proteome from proteomic analysis of four biotechnological strains L. lactis: L. lactis subsp. lactis NCDO2118, L. lactis subsp. lactis IL1403, L. lactis subsp. cremoris NZ9000 and L. lactis subsp. cremoris MG1363. Our label-free quantitative proteomic analysis of the whole bacterial lysates from each strains resulted in the characterization of the L. lactis core proteome that was composed by 586 proteins, which might contribute to resistance of this bacterium to different stress conditions as well as involved in the probiotic characteristic of L. lactis. Kegg enrichment analysis shows that ribosome, metabolic pathways, pyruvate metabolism and microbial metabolism in diverse environments were the most enriched. According to our quantitative proteomic analysis, proteins related to translation process were the more abundant in the core proteome, which represent an important step in the synthetic biology. In addition, we identified a subset of conserved proteins that are exclusive of the L. lactis subsp. cremoris or L. lactis subsp. lactis, which some are related to metabolic pathway exclusive. Regarding specific proteome of NCDO2118, we detected 'strain-specific proteins'. Finally, proteogenomics analysis allows the identification of proteins, which were not previously annotated in IL1403 and MG1363. The results obtained in this study allowed to increase our knowledge about the biology of L. lactis, which contributes to the implementation of strategies that make it possible to increase the biotechnological potential of this bacterium.

Regulation of glycolytic flux and overflow metabolism depending on the source of energy generation for energy demand

Overflow metabolism is a common phenomenon observed at higher glycolytic flux in many bacteria, yeast (known as Crabtree effect), and mammalian cells including cancer cells (known as Warburg effect). This phenomenon has recently been characterized as the trade-offs between protein costs and enzyme efficiencies based on coarse-graining approaches. Moreover, it has been recognized that the glycolytic flux increases as the source of energy generation changes from energetically efficient respiration to inefficient respiro-fermentative or fermentative metabolism causing overflow metabolism. It is highly desired to clarify the metabolic regulation mechanisms behind such phenomena. Metabolic fluxes are located on top of the hierarchical regulation systems, and represent the outcome of the integrated response of all levels of cellular regulation systems. In the present article, we discuss about the different levels of regulation systems for the modulation of fluxes depending on the growth rate, growth condition such as oxygen limitation that alters the metabolism towards fermentation, and genetic perturbation affecting the source of energy generation from respiration to respiro-fermentative metabolism in relation to overflow metabolism. The intracellular metabolite of the upper glycolysis such as fructose 1,6-bisphosphate (FBP) plays an important role not only for flux sensing, but also for the regulation of the respiratory activity either directly or indirectly (via transcription factors) at higher growth rate. The glycolytic flux regulation is backed up (enhanced) by unphosphorylated EIIA and HPr of the phosphotransferase system (PTS) components, together with the sugar-phosphate stress regulation, where the transcriptional regulation is further modulated by post-transcriptional regulation via the degradation of mRNA (stability of mRNA) in Escherichia coli. Moreover, the channeling may also play some role in modulating the glycolytic cascade reactions.

The three-legged stool of understanding metabolism: integrating metabolomics with biochemical genetics and computational modeling

Traditional biochemical research has resulted in a good understanding of many aspects of metabolism. However, this reductionist approach is time consuming and requires substantial resources, thus raising the question whether modern metabolomics and genomics should take over and replace the targeted experiments of old. We proffer that such a replacement is neither feasible not desirable and propose instead the tight integration of modern, system-wide omics with traditional experimental bench science and dedicated computational approaches. This integration is an important prerequisite toward the optimal acquisition of knowledge regarding metabolism and physiology in health and disease. The commentary describes advantages and drawbacks of current approaches to assessing metabolism and highlights the challenges to be overcome as we strive to achieve a deeper level of metabolic understanding in the future.

The best models of metabolism

Biochemical systems are among of the oldest application areas of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring a model and for formulating reactions has been constantly growing, and yet, it is still unclear whether or to what degree some models are better than others and how the modeler is to choose among them. In fact, the variety of options has become overwhelming and difficult to maneuver for novices and experts alike. This review outlines the metabolic model design process and discusses the numerous choices for modeling frameworks and mathematical representations. It tries to be inclusive, even though it cannot be complete, and introduces the various modeling options in a manner that is as unbiased as that is feasible. However, the review does end with personal recommendations for the choices of default models. WIREs Syst Biol Med 2017, 9:e1391. doi: 10.1002/wsbm.1391 For further resources related to this article, please visit the WIREs website.

13C based proteinogenic amino acid (PAA) and metabolic flux ratio analysis of Lactococcus lactis reveals changes in pentose phosphate (PP) pathway in response to agitation and temperature related stresses

Lactococcus lactis subsp. cremoris MG1363 is an important starter culture for dairy fermentation. During industrial fermentations, L. lactis is constantly exposed to stresses that affect the growth and performance of the bacterium. Although the response of L. lactis to several stresses has been described, the adaptation mechanisms at the level of in vivo fluxes have seldom been described. To gain insights into cellular metabolism, ¹³C metabolic flux analysis and gas chromatography mass spectrometry (GC-MS) were used to measure the flux ratios of active pathways in the central metabolism of L. lactis when subjected to three conditions varying in temperature (30°C, 37°C) and agitation (with and without agitation at 150 rpm). Collectively, the concentrations of proteinogenic amino acids (PAAs) and free fatty acids (FAAs) were compared, and Pearson correlation analysis (r) was calculated to measure the pairwise relationship between PAAs. Branched chain and aromatic amino acids, threonine, serine, lysine and histidine were correlated strongly, suggesting changes in flux regulation in glycolysis, the pentose phosphate (PP) pathway, malic enzyme and anaplerotic reaction catalysed by pyruvate carboxylase (pycA). Flux ratio analysis revealed that glucose was mainly converted by glycolysis, highlighting the stability of L. lactis’ central carbon metabolism despite different conditions. Higher flux ratios through oxaloacetate (OAA) from pyruvate (PYR) reaction in all conditions suggested the activation of pyruvate carboxylate (pycA) in L. lactis, in response to acid stress during exponential phase. Subsequently, more significant flux ratio differences were seen through the oxidative and non-oxidative pentose phosphate (PP) pathways, malic enzyme, and serine and C1 metabolism, suggesting NADPH requirements in response to environmental stimuli. These reactions could play an important role in optimization strategies for metabolic engineering in L. lactis. Overall, the integration of systematic analysis of amino acids and flux ratio analysis provides a systems-level understanding of how L. lactis regulates central metabolism under various conditions.

New insights into the complex regulation of the glycolytic pathway in Lactococcus lactis. II. Inference of the precisely timed control system regulating glycolysis

The dairy bacterium Lactococcus lactis has to master a complicated task. It must control its essentially linear glycolytic pathway in such a fashion that, when the substrate, glucose, runs out, it retains enough phosphoenolpyruvate and fructose-1,6-bisphosphate to be able to restart glycolysis as soon as new glucose becomes available. Although glycolysis is arguably the best-studied metabolic pathway, its details in L. lactis are still unclear, and it is, in particular, not understood how the bacterium manages the stop-and-start task. The primary purpose of this paper and its companion is a clarification of some of the details of the governing regulatory strategies with which L. lactis manages to retain the necessary metabolites for the restart of glycolysis after periods of starvation. The paper furthermore discusses how the bacterium changes these strategies when it is subjected to aerobic rather than anaerobic conditions.

Inferring the Effects of Honokiol on the Notch Signaling Pathway in SW480 Colon Cancer Cells

In a tumor cell, the development of acquired therapeutic resistance and the ability to survive in extracellular environments that differ from the primary site are the result of molecular adaptations in potentially highly plastic molecular networks. The accurate prediction of intracellular networks in a tumor remains a difficult problem in cancer informatics. In order to make truly rational patient-driven therapeutic decisions, it will be critical to develop methodologies that can accurately infer the molecular circuitry in the cells of a specific tumor. Despite enormous heterogeneity, cellular networks elicit deterministic digital-like responses. We discuss the use and limitations of methodologies that model molecular networks in cancer cells as a digital circuit. We also develop a network model of Notch signaling in colon cancer using a novel reverse engineering logic-based method and published western blot data to elucidate the interactions likely present in the circuits of the SW480 colon cancer cell line. Within this framework, we make predictions related to the role that honokiol may be playing as an anti-cancer drug.

Monte-Carlo modeling of the central carbon metabolism of Lactococcus lactis: insights into metabolic regulation

Metabolic pathways are complex dynamic systems whose response to perturbations and environmental challenges are governed by multiple interdependencies between enzyme properties, reactions rates, and substrate levels. Understanding the dynamics arising from such a network can be greatly enhanced by the construction of a computational model that embodies the properties of the respective system. Such models aim to incorporate mechanistic details of cellular interactions to mimic the temporal behavior of the biochemical reaction system and usually require substantial knowledge of kinetic parameters to allow meaningful conclusions. Several approaches have been suggested to overcome the severe data requirements of kinetic modeling, including the use of approximative kinetics and Monte-Carlo sampling of reaction parameters. In this work, we employ a probabilistic approach to study the response of a complex metabolic system, the central metabolism of the lactic acid bacterium Lactococcus lactis, subject to perturbations and brief periods of starvation. Supplementing existing methodologies, we show that it is possible to acquire a detailed understanding of the control properties of a corresponding metabolic pathway model that is directly based on experimental observations. In particular, we delineate the role of enzymatic regulation to maintain metabolic stability and metabolic recovery after periods of starvation. It is shown that the feedforward activation of the pyruvate kinase by fructose-1,6-bisphosphate qualitatively alters the bifurcation structure of the corresponding pathway model, indicating a crucial role of enzymatic regulation to prevent metabolic collapse for low external concentrations of glucose. We argue that similar probabilistic methodologies will help our understanding of dynamic properties of small-, medium- and large-scale metabolic networks models.

Network reconstruction using nonparametric additive ODE models

Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation.

Coordination of microbial metabolism

Beyond fuelling cellular activities with building blocks and energy, metabolism also integrates environmental conditions into intracellular signals. The underlying regulatory network is complex and multifaceted: it ranges from slow interactions, such as changing gene expression, to rapid ones, such as the modulation of protein activity via post-translational modification or the allosteric binding of small molecules. In this Review, we outline the coordination of common metabolic tasks, including nutrient uptake, central metabolism, the generation of energy, the supply of amino acids and protein synthesis. Increasingly, a set of key metabolites is recognized to control individual regulatory circuits, which carry out specific functions of information input and regulatory output. Such a modular view of microbial metabolism facilitates an intuitive understanding of the molecular mechanisms that underlie cellular decision making.

An extended dynamic model of Lactococcus lactis metabolism for mannitol and 2,3-butanediol production

Biomedical research and biotechnological production are greatly benefiting from the results provided by the development of dynamic models of microbial metabolism. Although several kinetic models of Lactococcus lactis (a Lactic Acid Bacterium (LAB) commonly used in the dairy industry) have been developed so far, most of them are simplified and focus only on specific metabolic pathways. Therefore, the application of mathematical models in the design of an engineering strategy for the production of industrially important products by L. lactis has been very limited. In this work, we extend the existing kinetic model of L. lactis central metabolism to include industrially relevant production pathways such as mannitol and 2,3-butanediol. In this way, we expect to study the dynamics of metabolite production and make predictive simulations in L. lactis. We used a system of ordinary differential equations (ODEs) with approximate Michaelis-Menten-like kinetics for each reaction, where the parameters were estimated from multivariate time-series metabolite concentrations obtained by our team through in vivo Nuclear Magnetic Resonance (NMR). The results show that the model captures observed transient dynamics when validated under a wide range of experimental conditions. Furthermore, we analyzed the model using global perturbations, which corroborate experimental evidence about metabolic responses upon enzymatic changes. These include that mannitol production is very sensitive to lactate dehydrogenase (LDH) in the wild type (W.T.) strain, and to mannitol phosphoenolpyruvate: a phosphotransferase system (PTS(Mtl)) in a LDH mutant strain. LDH reduction has also a positive control on 2,3-butanediol levels. Furthermore, it was found that overproduction of mannitol-1-phosphate dehydrogenase (MPD) in a LDH/PTS(Mtl) deficient strain can increase the mannitol levels. The results show that this model has prediction capability over new experimental conditions and offers promising possibilities to elucidate the effect of alterations in the main metabolism of L. lactis, with application in strain optimization.

Network Connectance Analysis as a Tool to Understand Homeostasis of Plants under Environmental Changes

The homeostasis of plants under environmental constraints may be maintained by alterations in the organization of their physiological networks. The ability to control a network depends on the strength of the connections between network elements, which is called network connectance. Herein, we intend to provide more evidence on the existence of a modulation pattern of photosynthetic networks, in response to adverse environmental conditions. Two species (Glycine max-C3 metabolism, and Brachiaria brizantha-C4 metabolism) were submitted to two environmental constraints (water availability, and high and low temperatures), and from the physiological parameters measured, the global connectance (Cg_total) and the modules connectance (gas exchange-Cg_ge and photochemical-Cg_pho) were analyzed. Both types of environmental constraints impaired the photosynthetic capacity and the growth of the plants, indicating loss of their homeostasis, but in different ways. The results showed that in general the Cg_total of both species increased with temperature increment and water deficit, indicating a higher modulation of photosynthetic networks. However, the Cg variation in both species did not influence the total dry biomass that was reduced by environmental adversities. This outcome is probably associated with a loss of system homeostasis. The connectance network analyses indicated a possible lack of correspondence between the photosynthetic networks modulation patterns and the homeostasis loss. However, this kind of analysis can be a powerful tool to access the degree of stability of a biological system, as well as to allow greater understanding of the dynamics underlying the photosynthetic processes that maintain the identity of the systems under environmental adversities.

Parameter uncertainty in biochemical models described by ordinary differential equations

Improved mechanistic understanding of biochemical networks is one of the driving ambitions of Systems Biology. Computational modeling allows the integration of various sources of experimental data in order to put this conceptual understanding to the test in a quantitative manner. The aim of computational modeling is to obtain both predictive as well as explanatory models for complex phenomena, hereby providing useful approximations of reality with varying levels of detail. As the complexity required to describe different system increases, so does the need for determining how well such predictions can be made. Despite efforts to make tools for uncertainty analysis available to the field, these methods have not yet found widespread use in the field of Systems Biology. Additionally, the suitability of the different methods strongly depends on the problem and system under investigation. This review provides an introduction to some of the techniques available as well as gives an overview of the state-of-the-art methods for parameter uncertainty analysis.

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

Functioning of a metabolic flux sensor in Escherichia coli

Regulation of metabolic operation in response to extracellular cues is crucial for cells' survival. Next to the canonical nutrient sensors, which measure the concentration of nutrients, recently intracellular "metabolic flux" was proposed as a novel impetus for metabolic regulation. According to this concept, cells would have molecular systems ("flux sensors") in place that regulate metabolism as a function of the actually occurring metabolic fluxes. Although this resembles an appealing concept, we have not had any experimental evidence for the existence of flux sensors and also we have not known how these flux sensors would work in detail. Here, we show experimental evidence that supports the hypothesis that Escherichia coli is indeed able to measure its glycolytic flux and uses this signal for metabolic regulation. Combining experiment and theory, we show how this flux-sensing function could emerge from an aggregate of several molecular mechanisms: First, the system of reactions of lower glycolysis and the feedforward activation of fructose-1,6-bisphosphate on pyruvate kinase translate flux information into the concentration of the metabolite fructose-1,6-bisphosphate. The interaction of this "flux-signaling metabolite" with the transcription factor Cra then leads to flux-dependent regulation. By responding to glycolytic flux, rather than to the concentration of individual carbon sources, the cell may minimize sensing and regulatory expenses.

Towards metagenome-scale models for industrial applications--the case of Lactic Acid Bacteria

We review the uses and limitations of modelling approaches that are in use in the field of Lactic Acid Bacteria (LAB). We describe recent developments in model construction and computational methods, starting from application of such models to monocultures. However, since most applications in food biotechnology involve complex nutrient environments and mixed cultures, we extend the scope to discuss developments in modelling such complex systems. With metagenomics and meta-functional genomics data becoming available, the developments in genome-scale community models are discussed. We conclude that exploratory tools are available and useful, but truly predictive mechanistic models will remain a major challenge in the field.

On the identifiability of metabolic network models

A major problem for the identification of metabolic network models is parameter identifiability, that is, the possibility to unambiguously infer the parameter values from the data. Identifiability problems may be due to the structure of the model, in particular implicit dependencies between the parameters, or to limitations in the quantity and quality of the available data. We address the detection and resolution of identifiability problems for a class of pseudo-linear models of metabolism, so-called linlog models. Linlog models have the advantage that parameter estimation reduces to linear or orthogonal regression, which facilitates the analysis of identifiability. We develop precise definitions of structural and practical identifiability, and clarify the fundamental relations between these concepts. In addition, we use singular value decomposition to detect identifiability problems and reduce the model to an identifiable approximation by a principal component analysis approach. The criterion is adapted to real data, which are frequently scarce, incomplete, and noisy. The test of the criterion on a model with simulated data shows that it is capable of correctly identifying the principal components of the data vector. The application to a state-of-the-art dataset on central carbon metabolism in Escherichia coli yields the surprising result that only 4 out of 31 reactions, and 37 out of 100 parameters, are identifiable. This underlines the practical importance of identifiability analysis and model reduction in the modeling of large-scale metabolic networks. Although our approach has been developed in the context of linlog models, it carries over to other pseudo-linear models, such as generalized mass-action (power-law) models. Moreover, it provides useful hints for the identifiability analysis of more general classes of nonlinear models of metabolism.

Nutritional metabolomics: progress in addressing complexity in diet and health

Nutritional metabolomics is rapidly maturing to use small-molecule chemical profiling to support integration of diet and nutrition in complex biosystems research. These developments are critical to facilitate transition of nutritional sciences from population-based to individual-based criteria for nutritional research, assessment, and management. This review addresses progress in making these approaches manageable for nutrition research. Important concept developments concerning the exposome, predictive health, and complex pathobiology serve to emphasize the central role of diet and nutrition in integrated biosystems models of health and disease. Improved analytic tools and databases for targeted and nontargeted metabolic profiling, along with bioinformatics, pathway mapping, and computational modeling, are now used for nutrition research on diet, metabolism, microbiome, and health associations. These new developments enable metabolome-wide association studies (MWAS) and provide a foundation for nutritional metabolomics, along with genomics, epigenomics, and health phenotyping, to support the integrated models required for personalized diet and nutrition forecasting.

Understanding regulation of metabolism through feasibility analysis

Understanding cellular regulation of metabolism is a major challenge in systems biology. Thus far, the main assumption was that enzyme levels are key regulators in metabolic networks. However, regulation analysis recently showed that metabolism is rarely controlled via enzyme levels only, but through non-obvious combinations of hierarchical (gene and enzyme levels) and metabolic regulation (mass action and allosteric interaction). Quantitative analyses relating changes in metabolic fluxes to changes in transcript or protein levels have revealed a remarkable lack of understanding of the regulation of these networks. We study metabolic regulation via feasibility analysis (FA). Inspired by the constraint-based approach of Flux Balance Analysis, FA incorporates a model describing kinetic interactions between molecules. We enlarge the portfolio of objectives for the cell by defining three main physiologically relevant objectives for the cell: function, robustness and temporal responsiveness. We postulate that the cell assumes one or a combination of these objectives and search for enzyme levels necessary to achieve this. We call the subspace of feasible enzyme levels the feasible enzyme space. Once this space is constructed, we can study how different objectives may (if possible) be combined, or evaluate the conditions at which the cells are faced with a trade-off among those. We apply FA to the experimental scenario of long-term carbon limited chemostat cultivation of yeast cells, studying how metabolism evolves optimally. Cells employ a mixed strategy composed of increasing enzyme levels for glucose uptake and hexokinase and decreasing levels of the remaining enzymes. This trade-off renders the cells specialized in this low-carbon flux state to compete for the available glucose and get rid of over-overcapacity. Overall, we show that FA is a powerful tool for systems biologists to study regulation of metabolism, interpret experimental data and evaluate hypotheses.

Optimization of time-course experiments for kinetic model discrimination

Systems biology relies heavily on the construction of quantitative models of biochemical networks. These models must have predictive power to help unveiling the underlying molecular mechanisms of cellular physiology, but it is also paramount that they are consistent with the data resulting from key experiments. Often, it is possible to find several models that describe the data equally well, but provide significantly different quantitative predictions regarding particular variables of the network. In those cases, one is faced with a problem of model discrimination, the procedure of rejecting inappropriate models from a set of candidates in order to elect one as the best model to use for prediction.

In this work, a method is proposed to optimize the design of enzyme kinetic assays with the goal of selecting a model among a set of candidates. We focus on models with systems of ordinary differential equations as the underlying mathematical description. The method provides a design where an extension of the Kullback-Leibler distance, computed over the time courses predicted by the models, is maximized. Given the asymmetric nature this measure, a generalized differential evolution algorithm for multi-objective optimization problems was used.

The kinetics of yeast glyoxalase I (EC 4.4.1.5) was chosen as a difficult test case to evaluate the method. Although a single-substrate kinetic model is usually considered, a two-substrate mechanism has also been proposed for this enzyme. We designed an experiment capable of discriminating between the two models by optimizing the initial substrate concentrations of glyoxalase I, in the presence of the subsequent pathway enzyme, glyoxalase II (EC 3.1.2.6). This discriminatory experiment was conducted in the laboratory and the results indicate a two-substrate mechanism for the kinetics of yeast glyoxalase I.

Standardized assay medium to measure Lactococcus lactis enzyme activities while mimicking intracellular conditions

Knowledge of how the activity of enzymes is affected under in vivo conditions is essential for analyzing their regulation and constructing models that yield an integrated understanding of cell behavior. Current kinetic parameters for Lactococcus lactis are scattered through different studies and performed under different assay conditions. Furthermore, assay conditions often diverge from conditions prevailing in the intracellular environment. To establish uniform assay conditions that resemble intracellular conditions, we analyzed the intracellular composition of anaerobic glucose-limited chemostat cultures of L. lactis subsp. cremoris MG 1363. Based on this, we designed a new assay medium for enzyme activity measurements of growing cells of L. lactis, mimicking as closely as practically possible its intracellular environment. Procedures were optimized to be carried out in 96-well plates, and the reproducibility and dynamic range were checked for all enzyme activity measurements. The effects of freezing and the carryover of ammonium sulfate from the addition of coupling enzymes were also established. Activities of all 10 glycolytic and 4 fermentative enzymes were measured. Remarkably, most in vivo-like activities were lower than previously published data. Yet, the ratios of V(max) over measured in vivo fluxes were above 1. With this work, we have developed and extensively validated standard protocols for enzyme activity measurements for L. lactis.

Systems biology of lactic acid bacteria: a critical review

Understanding the properties of a system as emerging from the interaction of well described parts is the most important goal of Systems Biology. Although in the practice of Lactic Acid Bacteria (LAB) physiology we most often think of the parts as the proteins and metabolites, a wider interpretation of what a part is can be useful. For example, different strains or species can be the parts of a community, or we could study only the chemical reactions as the parts of metabolism (and forgetting about the enzymes that catalyze them), as is done in flux balance analysis. As long as we have some understanding of the properties of these parts, we can investigate whether their interaction leads to novel or unanticipated behaviour of the system that they constitute.

There has been a tendency in the Systems Biology community to think that the collection and integration of data should continue ad infinitum, or that we will otherwise not be able to understand the systems that we study in their details. However, it may sometimes be useful to take a step back and consider whether the knowledge that we already have may not explain the system behaviour that we find so intriguing. Reasoning about systems can be difficult, and may require the application of mathematical techniques. The reward is sometimes the realization of unexpected conclusions, or in the worst case, that we still do not know enough details of the parts, or of the interactions between them.

We will discuss a number of cases, with a focus on LAB-related work, where a typical systems approach has brought new knowledge or perspective, often counterintuitive, and clashing with conclusions from simpler approaches. Also novel types of testable hypotheses may be generated by the systems approach, which we will illustrate. Finally we will give an outlook on the fields of research where the systems approach may point the way for the near future.

Analysis of operating principles with S-system models

Operating principles address general questions regarding the response dynamics of biological systems as we observe or hypothesize them, in comparison to a priori equally valid alternatives. In analogy to design principles, the question arises: Why are some operating strategies encountered more frequently than others and in what sense might they be superior? It is at this point impossible to study operation principles in complete generality, but the work here discusses the important situation where a biological system must shift operation from its normal steady state to a new steady state. This situation is quite common and includes many stress responses. We present two distinct methods for determining different solutions to this task of achieving a new target steady state. Both methods utilize the property of S-system models within Biochemical Systems Theory (BST) that steady states can be explicitly represented as systems of linear algebraic equations. The first method uses matrix inversion, a pseudo-inverse, or regression to characterize the entire admissible solution space. Operations on the basis of the solution space permit modest alterations of the transients toward the target steady state. The second method uses standard or mixed integer linear programming to determine admissible solutions that satisfy criteria of functional effectiveness, which are specified beforehand. As an illustration, we use both methods to characterize alternative response patterns of yeast subjected to heat stress, and compare them with observations from the literature.

Subcellular metabolic organization in the context of dynamic energy budget and biochemical systems theories

The dynamic modelling of metabolic networks aims to describe the temporal evolution of metabolite concentrations in cells. This area has attracted increasing attention in recent years owing to the availability of high-throughput data and the general development of systems biology as a promising approach to study living organisms. Biochemical Systems Theory (BST) provides an accurate formalism to describe biological dynamic phenomena. However, knowledge about the molecular organization level, used in these models, is not enough to explain phenomena such as the driving forces of these metabolic networks. Dynamic Energy Budget (DEB) theory captures the quantitative aspects of the organization of metabolism at the organism level in a way that is non-species-specific. This imposes constraints on the sub-organismal organization that are not present in the bottom-up approach of systems biology. We use in vivo data of lactic acid bacteria under various conditions to compare some aspects of BST and DEB approaches. Due to the large number of parameters to be estimated in the BST model, we applied powerful parameter identification techniques. Both models fitted equally well, but the BST model employs more parameters. The DEB model uses similarities of processes under growth and no-growth conditions and under aerobic and anaerobic conditions, which reduce the number of parameters. This paper discusses some future directions for the integration of knowledge from these two rich and promising areas, working top-down and bottom-up simultaneously. This middle-out approach is expected to bring new ideas and insights to both areas in terms of describing how living organisms operate.

Computational systems chemical biology

There is a critical need for improving the level of chemistry awareness in systems biology. The data and information related to modulation of genes and proteins by small molecules continue to accumulate at the same time as simulation tools in systems biology and whole body physiologically based pharmacokinetics (PBPK) continue to evolve. We called this emerging area at the interface between chemical biology and systems biology systems chemical biology (SCB) (Nat Chem Biol 3: 447-450, 2007).The overarching goal of computational SCB is to develop tools for integrated chemical-biological data acquisition, filtering and processing, by taking into account relevant information related to interactions between proteins and small molecules, possible metabolic transformations of small molecules, as well as associated information related to genes, networks, small molecules, and, where applicable, mutants and variants of those proteins. There is yet an unmet need to develop an integrated in silico pharmacology/systems biology continuum that embeds drug-target-clinical outcome (DTCO) triplets, a capability that is vital to the future of chemical biology, pharmacology, and systems biology. Through the development of the SCB approach, scientists will be able to start addressing, in an integrated simulation environment, questions that make the best use of our ever-growing chemical and biological data repositories at the system-wide level. This chapter reviews some of the major research concepts and describes key components that constitute the emerging area of computational systems chemical biology.

Alkalizing reactions streamline cellular metabolism in acidogenic microorganisms

An understanding of the integrated relationships among the principal cellular functions that govern the bioenergetic reactions of an organism is necessary to determine how cells remain viable and optimise their fitness in the environment. Urease is a complex enzyme that catalyzes the hydrolysis of urea to ammonia and carbonic acid. While the induction of urease activity by several microorganisms has been predominantly considered a stress-response that is initiated to generate a nitrogen source in response to a low environmental pH, here we demonstrate a new role of urease in the optimisation of cellular bioenergetics. We show that urea hydrolysis increases the catabolic efficiency of Streptococcus thermophilus, a lactic acid bacterium that is widely used in the industrial manufacture of dairy products. By modulating the intracellular pH and thereby increasing the activity of β-galactosidase, glycolytic enzymes and lactate dehydrogenase, urease increases the overall change in enthalpy generated by the bioenergetic reactions. A cooperative altruistic behaviour of urease-positive microorganisms on the urease-negative microorganisms within the same environment was also observed. The physiological role of a single enzymatic activity demonstrates a novel and unexpected view of the non-transcriptional regulatory mechanisms that govern the bioenergetics of a bacterial cell, highlighting a new role for cytosol-alkalizing biochemical pathways in acidogenic microorganisms.

Estimation of metabolic pathway systems from different data sources

Parameter estimation is the main bottleneck of metabolic pathway modelling. It may be addressed from the bottom up, using information on metabolites, enzymes and modulators, or from the top down, using metabolic time series data, which have become more prevalent in recent years. The authors propose here that it is useful to combine the two strategies and to complement time-series analysis with kinetic information. In particular, the authors investigate how the recent method of dynamic flux estimation (DFE) may be supplemented with other types of estimation. Using the glycolytic pathway in Lactococcus lactis as an illustration example, the authors demonstrate some strategies of such supplementation.

Identification of neutral biochemical network models from time series data

BACKGROUND

The major difficulty in modeling biological systems from multivariate time series is the identification of parameter sets that endow a model with dynamical behaviors sufficiently similar to the experimental data. Directly related to this parameter estimation issue is the task of identifying the structure and regulation of ill-characterized systems. Both tasks are simplified if the mathematical model is canonical, i.e., if it is constructed according to strict guidelines.

RESULTS

In this report, we propose a method for the identification of admissible parameter sets of canonical S-systems from biological time series. The method is based on a Monte Carlo process that is combined with an improved version of our previous parameter optimization algorithm. The method maps the parameter space into the network space, which characterizes the connectivity among components, by creating an ensemble of decoupled S-system models that imitate the dynamical behavior of the time series with sufficient accuracy. The concept of sloppiness is revisited in the context of these S-system models with an exploration not only of different parameter sets that produce similar dynamical behaviors but also different network topologies that yield dynamical similarity.

CONCLUSION

The proposed parameter estimation methodology was applied to actual time series data from the glycolytic pathway of the bacterium Lactococcus lactis and led to ensembles of models with different network topologies. In parallel, the parameter optimization algorithm was applied to the same dynamical data upon imposing a pre-specified network topology derived from prior biological knowledge, and the results from both strategies were compared. The results suggest that the proposed method may serve as a powerful exploration tool for testing hypotheses and the design of new experiments.

Identification of neutral biochemical network models from time series data

Background

The major difficulty in modeling biological systems from multivariate time series is the identification of parameter sets that endow a model with dynamical behaviors sufficiently similar to the experimental data. Directly related to this parameter estimation issue is the task of identifying the structure and regulation of ill-characterized systems. Both tasks are simplified if the mathematical model is canonical, i.e., if it is constructed according to strict guidelines.

Results

In this report, we propose a method for the identification of admissible parameter sets of canonical S-systems from biological time series. The method is based on a Monte Carlo process that is combined with an improved version of our previous parameter optimization algorithm. The method maps the parameter space into the network space, which characterizes the connectivity among components, by creating an ensemble of decoupled S-system models that imitate the dynamical behavior of the time series with sufficient accuracy. The concept of sloppiness is revisited in the context of these S-system models with an exploration not only of different parameter sets that produce similar dynamical behaviors but also different network topologies that yield dynamical similarity.

Conclusion

The proposed parameter estimation methodology was applied to actual time series data from the glycolytic pathway of the bacterium Lactococcus lactis and led to ensembles of models with different network topologies. In parallel, the parameter optimization algorithm was applied to the same dynamical data upon imposing a pre-specified network topology derived from prior biological knowledge, and the results from both strategies were compared. The results suggest that the proposed method may serve as a powerful exploration tool for testing hypotheses and the design of new experiments.

Network dynamics

Probably one of the most characteristic features of a living system is its continual propensity to change as it juggles the demands of survival with the need to replicate. Internally these adjustments are manifest as changes in metabolite, protein, and gene activities. Such changes have become increasingly obvious to experimentalists, with the advent of high-throughput technologies. In this chapter we highlight some of the quantitative approaches used to rationalize the study of cellular dynamics. The chapter focuses attention on the analysis of quantitative models based on differential equations using biochemical control theory. Basic pathway motifs are discussed, including straight chain, branched, and cyclic systems. In addition, some of the properties conferred by positive and negative feedback loops are discussed, particularly in relation to bistability and oscillatory dynamics.

Dynamics of Positional Enrichment: Theoretical Development and Application to Carbon Labeling in Zymomonas mobilis

Positional enrichment analysis has become an important technique for assessing detailed flux distributions and the fates of specific atoms in metabolic pathway systems. The typical approach to positional enrichment analysis is performed by supplying specifically labeled substrate to a cell system, letting the system reach steady state, and measuring where label had arrived and accumulated. The data are then evaluated mathematically with the help of a linear stoichiometric flux distribution model. While this procedure has proven to yield new and valuable insights, it does not address the transient dynamics between providing label and its ultimate steady-state distribution, which is often of great interest to the experimentalist (pulse labeling experiments). We show here that an extension of a recent mathematical method for dynamic labeling analysis is able to shed light on these transitions, thereby revealing insights not obtained with traditional positional enrichment analyses. The method traces the dynamics of one or more carbons through fully regulated metabolic pathways, which, in principle, may be arbitrarily complex. After a brief review of the earlier method and description of the theoretical extension, we illustrate the method with an analysis of the pentose phosphate pathway in Zymomonas mobilis, which has been used for traditional positional enrichment analyses in the past. We show how different labeling schemes result in distinctly different transients, which nevertheless eventually lead to a steady-state labeling profile that coincides exactly with the corresponding profile from traditional analysis. Thus, over the domain of commonality, the proposed method leads to results equivalent to those from state-of-the-art existing methods. However, these steady-state results constitute only a small portion of the insights obtainable with the proposed method. Our method can also be used as an "inverse" technique for elucidating the topology and regulation of pathway systems, if appropriate time series data are available. While such dynamic data are still rather rare, they are now being generated with increasing frequency and we believe it is desirable, and indeed necessary, to accompany this trend with an adequate, rigorous method of analysis.

Parameter optimization in S-system models

BACKGROUND

The inverse problem of identifying the topology of biological networks from their time series responses is a cornerstone challenge in systems biology. We tackle this challenge here through the parameterization of S-system models. It was previously shown that parameter identification can be performed as an optimization based on the decoupling of the differential S-system equations, which results in a set of algebraic equations.

RESULTS

A novel parameterization solution is proposed for the identification of S-system models from time series when no information about the network topology is known. The method is based on eigenvector optimization of a matrix formed from multiple regression equations of the linearized decoupled S-system. Furthermore, the algorithm is extended to the optimization of network topologies with constraints on metabolites and fluxes. These constraints rejoin the system in cases where it had been fragmented by decoupling. We demonstrate with synthetic time series why the algorithm can be expected to converge in most cases.

CONCLUSION

A procedure was developed that facilitates automated reverse engineering tasks for biological networks using S-systems. The proposed method of eigenvector optimization constitutes an advancement over S-system parameter identification from time series using a recent method called Alternating Regression. The proposed method overcomes convergence issues encountered in alternate regression by identifying nonlinear constraints that restrict the search space to computationally feasible solutions. Because the parameter identification is still performed for each metabolite separately, the modularity and linear time characteristics of the alternating regression method are preserved. Simulation studies illustrate how the proposed algorithm identifies the correct network topology out of a collection of models which all fit the dynamical time series essentially equally well.

Lactate favours the dissociation of skeletal muscle 6-phosphofructo-1-kinase tetramers down-regulating the enzyme and muscle glycolysis

For a long period lactate was considered as a dead-end product of glycolysis in many cells and its accumulation correlated with acidosis and cellular and tissue damage. At present, the role of lactate in several physiological processes has been investigated based on its properties as an energy source, a signalling molecule and as essential for tissue repair. It is noteworthy that lactate accumulation alters glycolytic flux independently from medium acidification, thereby this compound can regulate glucose metabolism within cells. PFK (6-phosphofructo-1-kinase) is the key regulatory glycolytic enzyme which is regulated by diverse molecules and signals. PFK activity is directly correlated with cellular glucose consumption. The present study shows the property of lactate to down-regulate PFK activity in a specific manner which is not dependent on acidification of the medium. Lactate reduces the affinity of the enzyme for its substrates, ATP and fructose 6-phosphate, as well as reducing the affinity for ATP at its allosteric inhibitory site at the enzyme. Moreover, we demonstrated that lactate inhibits PFK favouring the dissociation of enzyme active tetramers into less active dimers. This effect can be prevented by tetramer-stabilizing conditions such as the presence of fructose 2,6-bisphosphate, the binding of PFK to f-actin and phosphorylation of the enzyme by protein kinase A. In conclusion, our results support evidence that lactate regulates the glycolytic flux through modulating PFK due to its effects on the enzyme quaternary structure.

Universally sloppy parameter sensitivities in systems biology models

Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring in vivo biochemical parameters is difficult, and collectively fitting them to other experimental data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a "sloppy" spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our growth-factor-signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters.

Systems chemical biology

The increasing availability of data related to genes, proteins and their modulation by small molecules has provided a vast amount of biological information leading to the emergence of systems biology and the broad use of simulation tools for data analysis. However, there is a critical need to develop cheminformatics tools that can integrate chemical knowledge with these biological databases and simulation approaches, with the goal of creating systems chemical biology.