Machine learning for the advancement of genome-scale metabolic modeling

Constraint-based modeling (CBM) has evolved as the core systems biology tool to map the interrelations between genotype, phenotype, and external environment. The recent advancement of high-throughput experimental approaches and multi-omics strategies has generated a plethora of new and precise information from wide-ranging biological domains. On the other hand, the continuously growing field of machine learning (ML) and its specialized branch of deep learning (DL) provide essential computational architectures for decoding complex and heterogeneous biological data. In recent years, both multi-omics and ML have assisted in the escalation of CBM. Condition-specific omics data, such as transcriptomics and proteomics, helped contextualize the model prediction while analyzing a particular phenotypic signature. At the same time, the advanced ML tools have eased the model reconstruction and analysis to increase the accuracy and prediction power. However, the development of these multi-disciplinary methodological frameworks mainly occurs independently, which limits the concatenation of biological knowledge from different domains. Hence, we have reviewed the potential of integrating multi-disciplinary tools and strategies from various fields, such as synthetic biology, CBM, omics, and ML, to explore the biochemical phenomenon beyond the conventional biological dogma. How the integrative knowledge of these intersected domains has improved bioengineering and biomedical applications has also been highlighted. We categorically explained the conventional genome-scale metabolic model (GEM) reconstruction tools and their improvement strategies through ML paradigms. Further, the crucial role of ML and DL in omics data restructuring for GEM development has also been briefly discussed. Finally, the case-study-based assessment of the state-of-the-art method for improving biomedical and metabolic engineering strategies has been elaborated. Therefore, this review demonstrates how integrating experimental and in silico strategies can help map the ever-expanding knowledge of biological systems driven by condition-specific cellular information. This multiview approach will elevate the application of ML-based CBM in the biomedical and bioengineering fields for the betterment of society and the environment.

Biobased short chain fatty acid production - Exploring microbial community dynamics and metabolic networks through kinetic and microbial modeling approaches

In recent years, there has been growing interest in harnessing anaerobic digestion technology for resource recovery from waste streams. This approach has evolved beyond its traditional role in energy generation to encompass the production of valuable carboxylic acids, especially volatile fatty acids (VFAs) like acetic acid, propionic acid, and butyric acid. VFAs hold great potential for various industries and biobased applications due to their versatile properties. Despite increasing global demand, over 90% of VFAs are currently produced synthetically from petrochemicals. Realizing the potential of large-scale biobased VFA production from waste streams offers significant eco-friendly opportunities but comes with several key challenges. These include low VFA production yields, unstable acid compositions, complex and expensive purification methods, and post-processing needs. Among these, production yield and acid composition stand out as the most critical obstacles impacting economic viability and competitiveness. This paper seeks to offer a comprehensive view of combining complementary modeling approaches, including kinetic and microbial modeling, to understand the workings of microbial communities and metabolic pathways in VFA production, enhance production efficiency, and regulate acid profiles through the integration of omics and bioreactor data.

Microbial interactions from a new perspective: reinforcement learning reveals new insights into microbiome evolution

MOTIVATION

Microbes are essential part of all ecosystems, influencing material flow and shaping their surroundings. Metabolic modeling has been a useful tool and provided tremendous insights into microbial community metabolism. However, current methods based on flux balance analysis (FBA) usually fail to predict metabolic and regulatory strategies that lead to long-term survival and stability especially in heterogenous communities.

RESULTS

Here, we introduce a novel reinforcement learning algorithm, Self-Playing Microbes in Dynamic FBA, which treats microbial metabolism as a decision-making process, allowing individual microbial agents to evolve by learning and adapting metabolic strategies for enhanced long-term fitness. This algorithm predicts what microbial flux regulation policies will stabilize in the dynamic ecosystem of interest in the presence of other microbes with minimal reliance on predefined strategies. Throughout this article, we present several scenarios wherein our algorithm outperforms existing methods in reproducing outcomes, and we explore the biological significance of these predictions.

AVAILABILITY AND IMPLEMENTATION

The source code for this article is available at: https://github.com/chan-csu/SPAM-DFBA.

A neural-mechanistic hybrid approach improving the predictive power of genome-scale metabolic models

Constraint-based metabolic models have been used for decades to predict the phenotype of microorganisms in different environments. However, quantitative predictions are limited unless labor-intensive measurements of media uptake fluxes are performed. We show how hybrid neural-mechanistic models can serve as an architecture for machine learning providing a way to improve phenotype predictions. We illustrate our hybrid models with growth rate predictions of Escherichia coli and Pseudomonas putida grown in different media and with phenotype predictions of gene knocked-out Escherichia coli mutants. Our neural-mechanistic models systematically outperform constraint-based models and require training set sizes orders of magnitude smaller than classical machine learning methods. Our hybrid approach opens a doorway to enhancing constraint-based modeling: instead of constraining mechanistic models with additional experimental measurements, our hybrid models grasp the power of machine learning while fulfilling mechanistic constrains, thus saving time and resources in typical systems biology or biological engineering projects.

A Genome-Scale Metabolic Model of Marine Heterotroph Vibrio splendidus Strain 1A01

While Vibrio splendidus is best known as an opportunistic pathogen in oysters, Vibrio splendidus strain 1A01 was first identified as an early colonizer of synthetic chitin particles incubated in seawater. To gain a better understanding of its metabolism, a genome-scale metabolic model (GSMM) of V. splendidus 1A01 was reconstructed. GSMMs enable us to simulate all metabolic reactions in a bacterial cell using flux balance analysis. A draft model was built using an automated pipeline from BioCyc. Manual curation was then performed based on experimental data, in part by gap-filling metabolic pathways and tailoring the model's biomass reaction to V. splendidus 1A01. The challenges of building a metabolic model for a marine microorganism like V. splendidus 1A01 are described. IMPORTANCE A genome-scale metabolic model of V. splendidus 1A01 was reconstructed in this work. We offer solutions to the technical problems associated with model reconstruction for a marine bacterial strain like V. splendidus 1A01, which arise largely from the high salt concentration found in both seawater and culture media that simulate seawater.

Towards inferring absolute concentrations from relative abundance in time-course GC-MS metabolomics data

Metabolomics, the large-scale study of metabolites, has significant appeal as a source of information for metabolic modeling and other scientific applications. One common approach for measuring metabolomics data is gas chromatography-mass spectrometry (GC-MS). However, GC-MS metabolomics data are typically reported as relative abundances, precluding their use with approaches and tools where absolute concentrations are necessary. While chemical standards can be used to help provide quantification, their use is time-consuming, expensive, or even impossible due to their limited availability. The ability to infer absolute concentrations from GC-MS metabolomics data without chemical standards would have significant value. We hypothesized that when analyzing time-course metabolomics datasets, the mass balances of metabolism and other biological information could provide sufficient information towards inference of absolute concentrations. To demonstrate this, we developed and characterized MetaboPAC, a computational framework that uses two approaches-one based on kinetic equations and another using biological heuristics-to predict the most likely response factors that allow translation between relative abundances and absolute concentrations. When used to analyze noiseless synthetic data generated from multiple types of kinetic rate laws, MetaboPAC performs significantly better than negative control approaches when 20% of kinetic terms are known a priori. Under conditions of lower sampling frequency and high noise, MetaboPAC is still able to provide significant inference of concentrations in 3 of 4 models studied. This provides a starting point for leveraging biological knowledge to extract concentration information from time-course intracellular GC-MS metabolomics datasets, particularly for systems that are well-studied and have partially known kinetic structures.

Metabolic Engineering: Methodologies and Applications

Metabolic engineering aims to improve the production of economically valuable molecules through the genetic manipulation of microbial metabolism. While the discipline is a little over 30 years old, advancements in metabolic engineering have given way to industrial-level molecule production benefitting multiple industries such as chemical, agriculture, food, pharmaceutical, and energy industries. This review describes the design, build, test, and learn steps necessary for leading a successful metabolic engineering campaign. Moreover, we highlight major applications of metabolic engineering, including synthesizing chemicals and fuels, broadening substrate utilization, and improving host robustness with a focus on specific case studies. Finally, we conclude with a discussion on perspectives and future challenges related to metabolic engineering.

A Practical Guide to Integrating Multimodal Machine Learning and Metabolic Modeling

Complex, distributed, and dynamic sets of clinical biomedical data are collectively referred to as multimodal clinical data. In order to accommodate the volume and heterogeneity of such diverse data types and aid in their interpretation when they are combined with a multi-scale predictive model, machine learning is a useful tool that can be wielded to deconstruct biological complexity and extract relevant outputs. Additionally, genome-scale metabolic models (GSMMs) are one of the main frameworks striving to bridge the gap between genotype and phenotype by incorporating prior biological knowledge into mechanistic models. Consequently, the utilization of GSMMs as a foundation for the integration of multi-omic data originating from different domains is a valuable pursuit towards refining predictions. In this chapter, we show how cancer multi-omic data can be analyzed via multimodal machine learning and metabolic modeling. Firstly, we focus on the merits of adopting an integrative systems biology led approach to biomedical data mining. Following this, we propose how constraint-based metabolic models can provide a stable yet adaptable foundation for the integration of multimodal data with machine learning. Finally, we provide a step-by-step tutorial for the combination of machine learning and GSMMs, which includes: (i) tissue-specific constraint-based modeling; (ii) survival analysis using time-to-event prediction for cancer; and (iii) classification and regression approaches for multimodal machine learning. The code associated with the tutorial can be found at https://github.com/Angione-Lab/Tutorials_Combining_ML_and_GSMM .

How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review

Metabolic flux analysis is often (not to say almost always) faced with system underdeterminacy. Indeed, the linear algebraic system formed by the steady-state mass balance equations around the intracellular metabolites and the equality constraints related to the measurements of extracellular fluxes do not define a unique solution for the distribution of intracellular fluxes, but instead a set of solutions belonging to a convex polytope. Various methods have been proposed to tackle this underdeterminacy, including flux pathway analysis, flux balance analysis, flux variability analysis and sampling. These approaches are reviewed in this article and a toy example supports the discussion with illustrative numerical results.

A new strategy for dynamic metabolic flux estimation by integrating transient metabolome data into genome-scale metabolic models

Metabolic flux analysis (MFA) is a powerful tool for studying microbial cell physiology. Isotope-based MFA is the accepted standard for studying metabolic fluxes under steady-state conditions. However, its application under dynamic extracellular conditions is limited due to lack of proper techniques, such as rapid sampling and quenching, high cost and laborious execution. Here, we propose a new strategy to tackle this through incorporating dynamic metabolite abundance data into genome-scale metabolic models (GEM). First, a dummy extracellular pool concept is proposed for each dynamically changing metabolite, which represents a "sink" or "source", with corresponding dummy reactions coded into the GEM model. The dynamic model (expressed as differential equations) is then transformed into a quasi-steady-state model (expressed as linear equations), which can be easily solved by constraining the GEM model with the dynamic metabolite quantification data. For this, common linear-programming optimization algorithms were utilized to estimate the dynamic fluxes. Dynamic high-accuracy metabolite abundance data were obtained through the Isotope Dilution Mass Spectrometry (IDMS) method and high-speed sampling-quenching, and it was demonstrated that the newly proposed strategy could be successfully applied to obtain intracellular dynamic fluxes of Aspergillus niger under regimes of single and periodic extracellular glucose pulses. The applicability of the new method was also tested on dynamic fluxes estimation in a glucose pulse-response study of Saccharomyces cerevisiae. The proposed method provides a powerful tool to investigate cell physiology under dynamic conditions, especially relevant for bioprocess scale-up to industrial-scale bioreactors.

Recent advances in constraint and machine learning-based metabolic modeling by leveraging stoichiometric balances, thermodynamic feasibility and kinetic law formalisms

Understanding the governing principles behind organisms' metabolism and growth underpins their effective deployment as bioproduction chassis. A central objective of metabolic modeling is predicting how metabolism and growth are affected by both external environmental factors and internal genotypic perturbations. The fundamental concepts of reaction stoichiometry, thermodynamics, and mass action kinetics have emerged as the foundational principles of many modeling frameworks designed to describe how and why organisms allocate resources towards both growth and bioproduction. This review focuses on the latest algorithmic advancements that have integrated these foundational principles into increasingly sophisticated quantitative frameworks.

Metabolic Modelling as a Framework for Metabolomics Data Integration and Analysis

Metabolic networks are regulated to ensure the dynamic adaptation of biochemical reaction fluxes to maintain cell homeostasis and optimal metabolic fitness in response to endogenous and exogenous perturbations. To this end, metabolism is tightly controlled by dynamic and intricate regulatory mechanisms involving allostery, enzyme abundance and post-translational modifications. The study of the molecular entities involved in these complex mechanisms has been boosted by the advent of high-throughput technologies. The so-called omics enable the quantification of the different molecular entities at different system layers, connecting the genotype with the phenotype. Therefore, the study of the overall behavior of a metabolic network and the omics data integration and analysis must be approached from a holistic perspective. Due to the close relationship between metabolism and cellular phenotype, metabolic modelling has emerged as a valuable tool to decipher the underlying mechanisms governing cell phenotype. Constraint-based modelling and kinetic modelling are among the most widely used methods to study cell metabolism at different scales, ranging from cells to tissues and organisms. These approaches enable integrating metabolomic data, among others, to enhance model predictive capabilities. In this review, we describe the current state of the art in metabolic modelling and discuss future perspectives and current challenges in the field.

Escherichia coli metabolism under short-term repetitive substrate dynamics: adaptation and trade-offs

Background

Microbial metabolism is highly dependent on the environmental conditions. Especially, the substrate concentration, as well as oxygen availability, determine the metabolic rates. In large-scale bioreactors, microorganisms encounter dynamic conditions in substrate and oxygen availability (mixing limitations), which influence their metabolism and subsequently their physiology. Earlier, single substrate pulse experiments were not able to explain the observed physiological changes generated under large-scale industrial fermentation conditions.

Results

In this study we applied a repetitive feast–famine regime in an aerobic Escherichia coli culture in a time-scale of seconds. The regime was applied for several generations, allowing cells to adapt to the (repetitive) dynamic environment. The observed response was highly reproducible over the cycles, indicating that cells were indeed fully adapted to the regime. We observed an increase of the specific substrate and oxygen consumption (average) rates during the feast–famine regime, compared to a steady-state (chemostat) reference environment. The increased rates at same (average) growth rate led to a reduced biomass yield (30% lower). Interestingly, this drop was not followed by increased by-product formation, pointing to the existence of energy-spilling reactions. During the feast–famine cycle, the cells rapidly increased their uptake rate. Within 10 s after the beginning of the feeding, the substrate uptake rate was higher (4.68 μmol/g_CDW/s) than reported during batch growth (3.3 μmol/g_CDW/s). The high uptake led to an accumulation of several intracellular metabolites, during the feast phase, accounting for up to 34% of the carbon supplied. Although the metabolite concentrations changed rapidly, the cellular energy charge remained unaffected, suggesting well-controlled balance between ATP producing and ATP consuming reactions.

Conclusions

The adaptation of the physiology and metabolism of E. coli under substrate dynamics, representative for large-scale fermenters, revealed the existence of several cellular mechanisms coping with stress. Changes in the substrate uptake system, storage potential and energy-spilling processes resulted to be of great importance. These metabolic strategies consist a meaningful step to further tackle reduced microbial performance, observed under large-scale cultivations.

Absolute Quantification of the Central Carbon Metabolome in Eight Commonly Applied Prokaryotic and Eukaryotic Model Systems

Absolute quantification of intracellular metabolite pools is a prerequisite for modeling and in-depth biological interpretation of metabolomics data. It is the final step of an elaborate metabolomics workflow, with challenges associated with all steps—from sampling to quantifying the physicochemically diverse metabolite pool. Chromatographic separation combined with mass spectrometric (MS) detection is the superior platform for high coverage, selective, and sensitive detection of metabolites. Herein, we apply our quantitative MS-metabolomics workflow to measure and present the central carbon metabolome of a panel of commonly applied biological model systems. The workflow includes three chromatographic methods combined with isotope dilution tandem mass spectrometry to allow for absolute quantification of 68 metabolites of glycolysis, the pentose phosphate pathway, the tricarboxylic acid cycle, and the amino acid and (deoxy) nucleoside pools. The biological model systems; Bacillus subtilis, Saccharomyces cerevisiae, two microalgal species, and four human cell lines were all cultured in commonly applied culture media and sampled in exponential growth phase. Both literature and databases are scarce with comprehensive metabolite datasets, and existing entries range over several orders of magnitude. The workflow and metabolite panel presented herein can be employed to expand the list of reference metabolomes, as encouraged by the metabolomics community, in a continued effort to develop and refine high-quality quantitative metabolomics workflows.

Seeing the wood for the trees: a forest of methods for optimization and omic-network integration in metabolic modelling

Metabolic modelling has entered a mature phase with dozens of methods and software implementations available to the practitioner and the theoretician. It is not easy for a modeller to be able to see the wood (or the forest) for the trees. Driven by this analogy, we here present a 'forest' of principal methods used for constraint-based modelling in systems biology. This provides a tree-based view of methods available to prospective modellers, also available in interactive version at http://modellingmetabolism.net, where it will be kept updated with new methods after the publication of the present manuscript. Our updated classification of existing methods and tools highlights the most promising in the different branches, with the aim to develop a vision of how existing methods could hybridize and become more complex. We then provide the first hands-on tutorial for multi-objective optimization of metabolic models in R. We finally discuss the implementation of multi-view machine learning approaches in poly-omic integration. Throughout this work, we demonstrate the optimization of trade-offs between multiple metabolic objectives, with a focus on omic data integration through machine learning. We anticipate that the combination of a survey, a perspective on multi-view machine learning and a step-by-step R tutorial should be of interest for both the beginner and the advanced user.

Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v.3.0

Constraint-based reconstruction and analysis (COBRA) provides a molecular mechanistic framework for integrative analysis of experimental molecular systems biology data and quantitative prediction of physicochemically and biochemically feasible phenotypic states. The COBRA Toolbox is a comprehensive desktop software suite of interoperable COBRA methods. It has found widespread application in biology, biomedicine, and biotechnology because its functions can be flexibly combined to implement tailored COBRA protocols for any biochemical network. This protocol is an update to the COBRA Toolbox v.1.0 and v.2.0. Version 3.0 includes new methods for quality-controlled reconstruction, modeling, topological analysis, strain and experimental design, and network visualization, as well as network integration of chemoinformatic, metabolomic, transcriptomic, proteomic, and thermochemical data. New multi-lingual code integration also enables an expansion in COBRA application scope via high-precision, high-performance, and nonlinear numerical optimization solvers for multi-scale, multi-cellular, and reaction kinetic modeling, respectively. This protocol provides an overview of all these new features and can be adapted to generate and analyze constraint-based models in a wide variety of scenarios. The COBRA Toolbox v.3.0 provides an unparalleled depth of COBRA methods.

Dynamic elementary mode modelling of non-steady state flux data

BACKGROUND

A novel framework is proposed to analyse metabolic fluxes in non-steady state conditions, based on the new concept of dynamic elementary mode (dynEM): an elementary mode activated partially depending on the time point of the experiment.

RESULTS

Two methods are introduced here: dynamic elementary mode analysis (dynEMA) and dynamic elementary mode regression discriminant analysis (dynEMR-DA). The former is an extension of the recently proposed principal elementary mode analysis (PEMA) method from steady state to non-steady state scenarios. The latter is a discriminant model that permits to identify which dynEMs behave strongly different depending on the experimental conditions. Two case studies of Saccharomyces cerevisiae, with fluxes derived from simulated and real concentration data sets, are presented to highlight the benefits of this dynamic modelling.

CONCLUSIONS

This methodology permits to analyse metabolic fluxes at early stages with the aim of i) creating reduced dynamic models of flux data, ii) combining many experiments in a single biologically meaningful model, and iii) identifying the metabolic pathways that drive the organism from one state to another when changing the environmental conditions.

Metabolite secretion in microorganisms: the theory of metabolic overflow put to the test

INTRODUCTION

Microbial cells secrete many metabolites during growth, including important intermediates of the central carbon metabolism. This has not been taken into account by researchers when modeling microbial metabolism for metabolic engineering and systems biology studies.

MATERIALS AND METHODS

The uptake of metabolites by microorganisms is well studied, but our knowledge of how and why they secrete different intracellular compounds is poor. The secretion of metabolites by microbial cells has traditionally been regarded as a consequence of intracellular metabolic overflow.

CONCLUSIONS

Here, we provide evidence based on time-series metabolomics data that microbial cells eliminate some metabolites in response to environmental cues, independent of metabolic overflow. Moreover, we review the different mechanisms of metabolite secretion and explore how this knowledge can benefit metabolic modeling and engineering.

Elucidating dynamic metabolic physiology through network integration of quantitative time-course metabolomics

The increasing availability of metabolomics data necessitates novel methods for deeper data analysis and interpretation. We present a flux balance analysis method that allows for the computation of dynamic intracellular metabolic changes at the cellular scale through integration of time-course absolute quantitative metabolomics. This approach, termed "unsteady-state flux balance analysis" (uFBA), is applied to four cellular systems: three dynamic and one steady-state as a negative control. uFBA and FBA predictions are contrasted, and uFBA is found to be more accurate in predicting dynamic metabolic flux states for red blood cells, platelets, and Saccharomyces cerevisiae. Notably, only uFBA predicts that stored red blood cells metabolize TCA intermediates to regenerate important cofactors, such as ATP, NADH, and NADPH. These pathway usage predictions were subsequently validated through ¹³C isotopic labeling and metabolic flux analysis in stored red blood cells. Utilizing time-course metabolomics data, uFBA provides an accurate method to predict metabolic physiology at the cellular scale for dynamic systems.

Dynamic flux balance modeling to increase the production of high-value compounds in green microalgae

BACKGROUND

Photosynthetic organisms can be used for renewable and sustainable production of fuels and high-value compounds from natural resources. Costs for design and operation of large-scale algae cultivation systems can be reduced if data from laboratory scale cultivations are combined with detailed mathematical models to evaluate and optimize the process.

RESULTS

In this work we present a flexible modeling formulation for accumulation of high-value storage molecules in microalgae that provides quantitative predictions under various light and nutrient conditions. The modeling approach is based on dynamic flux balance analysis (DFBA) and includes regulatory models to predict the accumulation of pigment molecules. The accuracy of the model predictions is validated through independent experimental data followed by a subsequent model-based fed-batch optimization. In our experimentally validated fed-batch optimization study we increase biomass and [Formula: see text]-carotene density by factors of about 2.5 and 2.1, respectively.

CONCLUSIONS

The analysis shows that a model-based approach can be used to develop and significantly improve biotechnological processes for biofuels and pigments.

Dynamic metabolic models in context: biomass backtracking

Mathematical modeling has proven to be a powerful tool to understand and predict functional and regulatory properties of metabolic processes. High accuracy dynamic modeling of individual pathways is thereby opposed by simplified but genome scale constraint based approaches. A method that links these two powerful techniques would greatly enhance predictive power but is so far lacking. We present biomass backtracking, a workflow that integrates the cellular context in existing dynamic metabolic models via stoichiometrically exact drain reactions based on a genome scale metabolic model. With comprehensive examples, for different species and environmental contexts, we show the importance and scope of applications and highlight the improvement compared to common boundary formulations in existing metabolic models. Our method allows for the contextualization of dynamic metabolic models based on all available information. We anticipate this to greatly increase their accuracy and predictive power for basic research and also for drug development and industrial applications.

Genome scale models of yeast: towards standardized evaluation and consistent omic integration

Genome scale models (GEMs) have enabled remarkable advances in systems biology, acting as functional databases of metabolism, and as scaffolds for the contextualization of high-throughput data. In the case of Saccharomyces cerevisiae (budding yeast), several GEMs have been published and are currently used for metabolic engineering and elucidating biological interactions. Here we review the history of yeast's GEMs, focusing on recent developments. We study how these models are typically evaluated, using both descriptive and predictive metrics. Additionally, we analyze the different ways in which all levels of omics data (from gene expression to flux) have been integrated in yeast GEMs. Relevant conclusions and current challenges for both GEM evaluation and omic integration are highlighted.

A Strategy for Functional Interpretation of Metabolomic Time Series Data in Context of Metabolic Network Information

The functional connection of experimental metabolic time series data with biochemical network information is an important, yet complex, issue in systems biology. Frequently, experimental analysis of diurnal, circadian, or developmental dynamics of metabolism results in a comprehensive and multidimensional data matrix comprising information about metabolite concentrations, protein levels, and/or enzyme activities. While, irrespective of the type of organism, the experimental high-throughput analysis of the transcriptome, proteome, and metabolome has become a common part of many systems biological studies, functional data integration in a biochemical and physiological context is still challenging. Here, an approach is presented which addresses the functional connection of experimental time series data with biochemical network information which can be inferred, for example, from a metabolic network reconstruction. Based on a time-continuous and variance-weighted regression analysis of experimental data, metabolic functions, i.e., first-order derivatives of metabolite concentrations, were related to time-dependent changes in other biochemically relevant metabolic functions, i.e., second-order derivatives of metabolite concentrations. This finally revealed time points of perturbed dependencies in metabolic functions indicating a modified biochemical interaction. The approach was validated using previously published experimental data on a diurnal time course of metabolite levels, enzyme activities, and metabolic flux simulations. To support and ease the presented approach of functional time series analysis, a graphical user interface including a test data set and a manual is provided which can be run within the numerical software environment Matlab®.

Kinetic modeling of cell metabolism for microbial production

Kinetic models of cellular metabolism are important tools for the rational design of metabolic engineering strategies and to explain properties of complex biological systems. The recent developments in high-throughput experimental data are leading to new computational approaches for building kinetic models of metabolism. Herein, we briefly survey the available databases, standards and software tools that can be applied for kinetic models of metabolism. In addition, we give an overview about recently developed ordinary differential equations (ODE)-based kinetic models of metabolism and some of the main applications of such models are illustrated in guiding metabolic engineering design. Finally, we review the kinetic modeling approaches of large-scale networks that are emerging, discussing their main advantages, challenges and limitations.

Genome-scale modelling of microbial metabolism with temporal and spatial resolution

Most natural microbial systems have evolved to function in environments with temporal and spatial variations. A major limitation to understanding such complex systems is the lack of mathematical modelling frameworks that connect the genomes of individual species and temporal and spatial variations in the environment to system behaviour. The goal of this review is to introduce the emerging field of spatiotemporal metabolic modelling based on genome-scale reconstructions of microbial metabolism. The extension of flux balance analysis (FBA) to account for both temporal and spatial variations in the environment is termed spatiotemporal FBA (SFBA). Following a brief overview of FBA and its established dynamic extension, the SFBA problem is introduced and recent progress is described. Three case studies are reviewed to illustrate the current state-of-the-art and possible future research directions are outlined. The author posits that SFBA is the next frontier for microbial metabolic modelling and a rapid increase in methods development and system applications is anticipated.

Using Petri nets for experimental design in a multi-organ elimination pathway

Genistein is a soy metabolite with estrogenic activity that may result in (un)favorable effects on human health. Elucidation of the mechanisms through which food additives such as genistein exert their beneficiary effects is a major challenge for the food industry. A better understanding of the genistein elimination pathway could shed light on such mechanisms. We developed a Petri net model that represents this multi-organ elimination pathway and which assists in the design of future experiments. Using this model we show that metabolic profiles solely measured in venous blood are not sufficient to uniquely parameterize the model. Based on simulations we suggest two solutions that provide better results: parameterize the model using gut epithelium profiles or add additional biological constrains in the model.