Structural kinetic modeling of metabolic networks

Bayesian kinetic modeling for tracer-based metabolomic data

BACKGROUND

Stable Isotope Resolved Metabolomics (SIRM) is a new biological approach that uses stable isotope tracers such as uniformly [Formula: see text]-enriched glucose ([Formula: see text]-Glc) to trace metabolic pathways or networks at the atomic level in complex biological systems. Non-steady-state kinetic modeling based on SIRM data uses sets of simultaneous ordinary differential equations (ODEs) to quantitatively characterize the dynamic behavior of metabolic networks. It has been increasingly used to understand the regulation of normal metabolism and dysregulation in the development of diseases. However, fitting a kinetic model is challenging because there are usually multiple sets of parameter values that fit the data equally well, especially for large-scale kinetic models. In addition, there is a lack of statistically rigorous methods to compare kinetic model parameters between different experimental groups.

RESULTS

We propose a new Bayesian statistical framework to enhance parameter estimation and hypothesis testing for non-steady-state kinetic modeling of SIRM data. For estimating kinetic model parameters, we leverage the prior distribution not only to allow incorporation of experts' knowledge but also to provide robust parameter estimation. We also introduce a shrinkage approach for borrowing information across the ensemble of metabolites to stably estimate the variance of an individual isotopomer. In addition, we use a component-wise adaptive Metropolis algorithm with delayed rejection to perform efficient Monte Carlo sampling of the posterior distribution over high-dimensional parameter space. For comparing kinetic model parameters between experimental groups, we propose a new reparameterization method that converts the complex hypothesis testing problem into a more tractable parameter estimation problem. We also propose an inference procedure based on credible interval and credible value. Our method is freely available for academic use at https://github.com/xuzhang0131/MCMCFlux .

CONCLUSIONS

Our new Bayesian framework provides robust estimation of kinetic model parameters and enables rigorous comparison of model parameters between experimental groups. Simulation studies and application to a lung cancer study demonstrate that our framework performs well for non-steady-state kinetic modeling of SIRM data.

Metabolomics and modelling approaches for systems metabolic engineering

Metabolic engineering involves the manipulation of microbes to produce desirable compounds through genetic engineering or synthetic biology approaches. Metabolomics involves the quantitation of intracellular and extracellular metabolites, where mass spectrometry and nuclear magnetic resonance based analytical instrumentation are often used. Here, the experimental designs, sample preparations, metabolite quenching and extraction are essential to the quantitative metabolomics workflow. The resultant metabolomics data can then be used with computational modelling approaches, such as kinetic and constraint-based modelling, to better understand underlying mechanisms and bottlenecks in the synthesis of desired compounds, thereby accelerating research through systems metabolic engineering. Constraint-based models, such as genome scale models, have been used successfully to enhance the yield of desired compounds from engineered microbes, however, unlike kinetic or dynamic models, constraint-based models do not incorporate regulatory effects. Nevertheless, the lack of time-series metabolomic data generation has hindered the usefulness of dynamic models till today. In this review, we show that improvements in automation, dynamic real-time analysis and high throughput workflows can drive the generation of more quality data for dynamic models through time-series metabolomics data generation. Spatial metabolomics also has the potential to be used as a complementary approach to conventional metabolomics, as it provides information on the localization of metabolites. However, more effort must be undertaken to identify metabolites from spatial metabolomics data derived through imaging mass spectrometry, where machine learning approaches could prove useful. On the other hand, single-cell metabolomics has also seen rapid growth, where understanding cell-cell heterogeneity can provide more insights into efficient metabolic engineering of microbes. Moving forward, with potential improvements in automation, dynamic real-time analysis, high throughput workflows, and spatial metabolomics, more data can be produced and studied using machine learning algorithms, in conjunction with dynamic models, to generate qualitative and quantitative predictions to advance metabolic engineering efforts.

Construction of Multiscale Genome-Scale Metabolic Models: Frameworks and Challenges

Genome-scale metabolic models (GEMs) are effective tools for metabolic engineering and have been widely used to guide cell metabolic regulation. However, the single gene–protein-reaction data type in GEMs limits the understanding of biological complexity. As a result, multiscale models that add constraints or integrate omics data based on GEMs have been developed to more accurately predict phenotype from genotype. This review summarized the recent advances in the development of multiscale GEMs, including multiconstraint, multiomic, and whole-cell models, and outlined machine learning applications in GEM construction. This review focused on the frameworks, toolkits, and algorithms for constructing multiscale GEMs. The challenges and perspectives of multiscale GEM development are also discussed.

Structural Thermokinetic Modelling

To translate metabolic networks into dynamic models, the Structural Kinetic Modelling framework (SKM) assumes a given reference state and replaces the reaction elasticities in this state by random numbers. A new variant, called Structural Thermokinetic Modelling (STM), accounts for reversible reactions and thermodynamics. STM relies on a dependence schema in which some basic variables are sampled, fitted to data, or optimised, while all other variables can be easily computed. Correlated elasticities follow from enzyme saturation values and thermodynamic forces, which are physically independent. Probability distributions in the dependence schema define a model ensemble, which allows for probabilistic predictions even if data are scarce. STM highlights the importance of variabilities, dependencies, and covariances of biological variables. By varying network structure, fluxes, thermodynamic forces, regulation, or types of rate laws, the effects of these model features can be assessed. By choosing the basic variables, metabolic networks can be converted into kinetic models with consistent reversible rate laws. Metabolic control coefficients obtained from these models can tell us about metabolic dynamics, including responses and optimal adaptations to perturbations, enzyme synergies and metabolite correlations, as well as metabolic fluctuations arising from chemical noise. To showcase STM, I study metabolic control, metabolic fluctuations, and enzyme synergies, and how they are shaped by thermodynamic forces. Considering thermodynamics can improve predictions of flux control, enzyme synergies, correlated flux and metabolite variations, and the emergence and propagation of metabolic noise.

Generalized Structural Kinetic Modeling: A Survey and Guide

Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional dynamical models of complex systems are rarely mathematically tractable and their numerical exploration suffers both from computational and data limitations. Here we review generalized modeling, an alternative approach for formulating dynamical models to gain insights into dynamics and bifurcations of uncertain systems. We argue that this approach deals elegantly with the uncertainties that exist in real world data and enables analytical insight or highly efficient numerical investigation. We provide a survey of recent successes of generalized modeling and a guide to the application of this modeling approach in future studies such as complex integrative ecological models.

Quantitative metabolic fluxes regulated by trans-omic networks

Cells change their metabolism in response to internal and external conditions by regulating the trans-omic network, which is a global biochemical network with multiple omic layers. Metabolic flux is a direct measure of the activity of a metabolic reaction that provides valuable information for understanding complex trans-omic networks. Over the past decades, techniques to determine metabolic fluxes, including 13C-metabolic flux analysis (13C-MFA), flux balance analysis (FBA), and kinetic modeling, have been developed. Recent studies that acquire quantitative metabolic flux and multi-omic data have greatly advanced the quantitative understanding and prediction of metabolism-centric trans-omic networks. In this review, we present an overview of 13C-MFA, FBA, and kinetic modeling as the main techniques to determine quantitative metabolic fluxes, and discuss their advantages and disadvantages. We also introduce case studies with the aim of understanding complex metabolism-centric trans-omic networks based on the determination of metabolic fluxes.

Metabolic Reprogramming and Reconstruction: Integration of Experimental and Computational Studies to Set the Path Forward in ADPKD

Metabolic reprogramming is a key feature of Autosomal Dominant Polycystic Kidney Disease (ADPKD) characterized by changes in cellular pathways occurring in response to the pathological cell conditions. In ADPKD, a broad range of dysregulated pathways have been found. The studies supporting alterations in cell metabolism have shown that the metabolic preference for abnormal cystic growth is to utilize aerobic glycolysis, increasing glutamine uptake and reducing oxidative phosphorylation, consequently resulting in ADPKD cells shifting their energy to alternative energetic pathways. The mechanism behind the role of the polycystin proteins and how it leads to disease remains unclear, despite the identification of numerous signaling pathways. The integration of computational data analysis that accompanies experimental findings was pivotal in the identification of metabolic reprogramming in ADPKD. Here, we summarize the important results and argue that their exploitation may give further insights into the regulative mechanisms driving metabolic reprogramming in ADPKD. The aim of this review is to provide a comprehensive overview on metabolic focused studies and potential targets for treatment, and to propose that computational approaches could be instrumental in advancing this field of research.

Model Balancing: A Search for In-Vivo Kinetic Constants and Consistent Metabolic States

Enzyme kinetic constants in vivo are largely unknown, which limits the construction of large metabolic models. Given measured metabolic fluxes, metabolite concentrations, and enzyme concentrations, these constants may be inferred by model fitting, but the estimation problems are hard to solve if models are large. Here we show how consistent kinetic constants, metabolite concentrations, and enzyme concentrations can be determined from data if metabolic fluxes are known. The estimation method, called model balancing, can handle models with a wide range of rate laws and accounts for thermodynamic constraints between fluxes, kinetic constants, and metabolite concentrations. It can be used to estimate in-vivo kinetic constants, to complete and adjust available data, and to construct plausible metabolic states with predefined flux distributions. By omitting one term from the log posterior-a term for penalising low enzyme concentrations-we obtain a convex optimality problem with a unique local optimum. As a demonstrative case, we balance a model of E. coli central metabolism with artificial or experimental data and obtain a physically and biologically plausible parameterisation of reaction kinetics in E. coli central metabolism. The example shows what information about kinetic constants can be obtained from omics data and reveals practical limits to estimating in-vivo kinetic constants. While noise-free omics data allow for a reasonable reconstruction of in-vivo kcat and KM values, prediction from noisy omics data are worse. Hence, adjusting kinetic constants and omics data to obtain consistent metabolic models is the main application of model balancing.

Combining Kinetic and Constraint-Based Modelling to Better Understand Metabolism Dynamics

To understand the phenotypic capabilities of organisms, it is useful to characterise cellular metabolism through the analysis of its pathways. Dynamic mathematical modelling of metabolic networks is of high interest as it provides the time evolution of the metabolic components. However, it also has limitations, such as the necessary mechanistic details and kinetic parameters are not always available. On the other hand, large metabolic networks exhibit a complex topological structure which can be studied rather efficiently in their stationary regime by constraint-based methods. These methods produce useful predictions on pathway operations. In this review, we present both modelling techniques and we show how they bring complementary views of metabolism. In particular, we show on a simple example how both approaches can be used in conjunction to shed some light on the dynamics of metabolic networks.

Metabolome and proteome analyses reveal transcriptional misregulation in glycolysis of engineered E. coli

Synthetic metabolic pathways are a burden for engineered bacteria, but the underlying mechanisms often remain elusive. Here we show that the misregulated activity of the transcription factor Cra is responsible for the growth burden of glycerol overproducing E. coli. Glycerol production decreases the concentration of fructose-1,6-bisphoshate (FBP), which then activates Cra resulting in the downregulation of glycolytic enzymes and upregulation of gluconeogenesis enzymes. Because cells grow on glucose, the improper activation of gluconeogenesis and the concomitant inhibition of glycolysis likely impairs growth at higher induction of the glycerol pathway. We solve this misregulation by engineering a Cra-binding site in the promoter controlling the expression of the rate limiting enzyme of the glycerol pathway to maintain FBP levels sufficiently high. We show the broad applicability of this approach by engineering Cra-dependent regulation into a set of constitutive and inducible promoters, and use one of them to overproduce carotenoids in E. coli.

Synthetic pathways represent a metabolic burden on host cells. Here the authors engineer Cra-binding sites to prevent misregulation in glycerol and carotenoid overproducing E. coli strains.

Integrating systemic and molecular levels to infer key drivers sustaining metabolic adaptations

Metabolic adaptations to complex perturbations, like the response to pharmacological treatments in multifactorial diseases such as cancer, can be described through measurements of part of the fluxes and concentrations at the systemic level and individual transporter and enzyme activities at the molecular level. In the framework of Metabolic Control Analysis (MCA), ensembles of linear constraints can be built integrating these measurements at both systemic and molecular levels, which are expressed as relative differences or changes produced in the metabolic adaptation. Here, combining MCA with Linear Programming, an efficient computational strategy is developed to infer additional non-measured changes at the molecular level that are required to satisfy these constraints. An application of this strategy is illustrated by using a set of fluxes, concentrations, and differentially expressed genes that characterize the response to cyclin-dependent kinases 4 and 6 inhibition in colon cancer cells. Decreases and increases in transporter and enzyme individual activities required to reprogram the measured changes in fluxes and concentrations are compared with down-regulated and up-regulated metabolic genes to unveil those that are key molecular drivers of the metabolic response.

Deciphering the essential events in the reprogramming of metabolic networks subjected to complex perturbations, including the response to pharmacological treatments in multifactorial diseases like cancer, is crucial for the design of efficient therapies. Yet, tools to infer the molecular drivers sustaining such metabolic responses remain elusive for large metabolic networks. Here we develop an efficient computational strategy that integrates measured changes at systemic and molecular levels and combines metabolic control analysis with linear programming tools to infer key molecular drivers sustaining the metabolic adaptations to complex perturbations, such as an antitumoral drug therapy. The collective behavior is approximated using linear expressions where the adaptation of systemic concentrations and fluxes to a perturbation is described as a function of the molecular reprogramming of transport and enzyme activities. Starting from measured changes in fluxes and concentrations, we identify changes in the reprogramming of transporter and enzyme activities that are required to orchestrate the metabolic adaptation of colon cancer cells to a cell cycle inhibitor.

Enhancing in silico strain design predictions through next generation metabolic modeling approaches

The reconstruction and analysis of metabolic models has garnered increasing attention due to the multitude of applications in which these have proven to be practical. The growing number of generated metabolic models has been accompanied by an exponentially expanding arsenal of tools used to analyze them. In this work, we discussed the biological relevance of a number of promising modeling frameworks, focusing on the questions and hypotheses each method is equipped to address. To this end, we critically analyzed the steady-state modeling approaches focusing on resource allocation and incorporation of thermodynamic considerations which produce promising results and aid in the generation and experimental validation of numerous predictions. For smaller networks involving more complex regulation, we addressed kinetic modeling techniques which show encouraging results in addressing questions outside the scope of steady-state modeling. Finally, we discussed the potential application of the discussed frameworks within the field of strain design. Adoption of such methodologies is believed to significantly enhance the accuracy of in silico predictions and hence decrease the number of design-build-test cycles required.

Systems biology for crop improvement

In recent years, generation of large-scale data from genome, transcriptome, proteome, metabolome, epigenome, and others, has become routine in several plant species. Most of these datasets in different crop species, however, were studied independently and as a result, full insight could not be gained on the molecular basis of complex traits and biological networks. A systems biology approach involving integration of multiple omics data, modeling, and prediction of the cellular functions is required to understand the flow of biological information that underlies complex traits. In this context, systems biology with multiomics data integration is crucial and allows a holistic understanding of the dynamic system with the different levels of biological organization interacting with external environment for a phenotypic expression. Here, we present recent progress made in the area of various omics studies-integrative and systems biology approaches with a special focus on application to crop improvement. We have also discussed the challenges and opportunities in multiomics data integration, modeling, and understanding of the biology of complex traits underpinning yield and stress tolerance in major cereals and legumes.

Opportunities at the Interface of Network Science and Metabolic Modeling

Metabolism plays a central role in cell physiology because it provides the molecular machinery for growth. At the genome-scale, metabolism is made up of thousands of reactions interacting with one another. Untangling this complexity is key to understand how cells respond to genetic, environmental, or therapeutic perturbations. Here we discuss the roles of two complementary strategies for the analysis of genome-scale metabolic models: Flux Balance Analysis (FBA) and network science. While FBA estimates metabolic flux on the basis of an optimization principle, network approaches reveal emergent properties of the global metabolic connectivity. We highlight how the integration of both approaches promises to deliver insights on the structure and function of metabolic systems with wide-ranging implications in discovery science, precision medicine and industrial biotechnology.

A control theoretic three timescale model for analyzing energy management in mammalian cancer cells

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Developed a three timescale model of integrated biochemical pathway.

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Simulated “Warburg Effect” using support vector regression and genetic algorithm.

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Identified rational drug targets using nonlinear controller.

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Explored energy and cell proliferation management of cancer cells.

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Validated the model by previous in vivo/in vitro/in silico experiments.

Interaction among different pathways, such as metabolic, signaling and gene regulatory networks, of cellular system is responsible to maintain homeostasis in a mammalian cell. Malfunctioning of this cooperation may lead to many complex diseases, such as cancer and type 2 diabetes. Timescale differences among these pathways make their integration a daunting task. Metabolic, signaling and gene regulatory networks have three different timescales, such as, ultrafast, fast and slow respectively.

The article deals with this problem by developing a support vector regression (SVR) based three timescale model with the application of genetic algorithm based nonlinear controller. The proposed model can successfully capture the nonlinear transient dynamics and regulations of such integrated biochemical pathway under consideration. Besides, the model is quite capable of predicting the effects of certain drug targets for many types of complex diseases. Here, energy and cell proliferation management of mammalian cancer cells have been explored and analyzed with the help of the proposed novel approach. Previous investigations including in silico/in vivo/in vitro experiments have validated the results (the regulations of glucose transporter 1 (glut1), hexokinase (HK), and hypoxia-inducible factor-1α (HIF-1α) among others, and the switching of pyruvate kinase (M2 isoform) between dimer and tetramer) generated by this model proving its effectiveness. Subsequently, the model predicts the effects of six selected drug targets, such as, the deactivation of transketolase and glucose-6-phosphate isomerase among others, in the case of mammalian malignant cells in terms of growth, proliferation, fermentation, and energy supply in the form of adenosine triphosphate (ATP).

Seeing the forest for the trees: Retrieving plant secondary biochemical pathways from metabolome networks

Over the last decade, a giant leap forward has been made in resolving the main bottleneck in metabolomics, i.e., the structural characterization of the many unknowns. This has led to the next challenge in this research field: retrieving biochemical pathway information from the various types of networks that can be constructed from metabolome data. Searching putative biochemical pathways, referred to as biotransformation paths, is complicated because several flaws occur during the construction of metabolome networks. Multiple network analysis tools have been developed to deal with these flaws, while in silico retrosynthesis is appearing as an alternative approach. In this review, the different types of metabolome networks, their flaws, and the various tools to trace these biotransformation paths are discussed.

Beyond planetary-scale feedback self-regulation: Gaia as an autopoietic system

The Gaia hypothesis states that the Earth is an instance of life. However, appraisals of it tend to focus on the claim that life is a feedback self-regulator that controls Earth's chemistry and climate dynamics, yet, self-regulation by feedbacks is not a definitive characteristic of living systems. Here, we consider the characterization of biological systems as autopoietic systems (causally organized to self-produce through metabolic efficient closure) and then ask whether the Gaia hypothesis is a tractable question from this standpoint. A proof-of-concept based on Chemical Organization Theory (COT) and the Zero Deficiency Theorem (ZDT) applied on a simple but representative Earth's molecular reaction network supports the thesis of Gaia as an autopoietic system. We identify the formation of self-producing organizations within the reaction network, corresponding to recognizable scenarios of Earth's history. These results provide further opportunities to discuss how the instantiation of autopoiesis at the planetary scale could manifests central features of biological phenomenon, such as autonomy and anticipation, and what this implies for the further development of the Gaia theory, Earth's climate modelling and geoengineering.

Kinetic modeling of microbial growth, enzyme activity, and gene deletions: An integrated model of β-glucosidase function in Cellvibrio japonicus

Understanding the complex growth and metabolic dynamics in microorganisms requires advanced kinetic models containing both metabolic reactions and enzymatic regulation to predict phenotypic behaviors under different conditions and perturbations. Most current kinetic models lack gene expression dynamics and are separately calibrated to distinct media, which consequently makes them unable to account for genetic perturbations or multiple substrates. This challenge limits our ability to gain a comprehensive understanding of microbial processes towards advanced metabolic optimizations that are desired for many biotechnology applications. Here, we present an integrated computational and experimental approach for the development and optimization of mechanistic kinetic models for microbial growth and metabolic and enzymatic dynamics. Our approach integrates growth dynamics, gene expression, protein secretion, and gene-deletion phenotypes. We applied this methodology to build a dynamic model of the growth kinetics in batch culture of the bacterium Cellvibrio japonicus grown using either cellobiose or glucose media. The model parameters were inferred from an experimental data set using an evolutionary computation method. The resulting model was able to explain the growth dynamics of C. japonicus using either cellobiose or glucose media and was also able to accurately predict the metabolite concentrations in the wild-type strain as well as in β-glucosidase gene deletion mutant strains. We validated the model by correctly predicting the non-diauxic growth and metabolite consumptions of the wild-type strain in a mixed medium containing both cellobiose and glucose, made further predictions of mutant strains growth phenotypes when using cellobiose and glucose media, and demonstrated the utility of the model for designing industrially-useful strains. Importantly, the model is able to explain the role of the different β-glucosidases and their behavior under genetic perturbations. This integrated approach can be extended to other metabolic pathways to produce mechanistic models for the comprehensive understanding of enzymatic functions in multiple substrates.

Understanding biochemical design principles with ensembles of canonical non-linear models

Systems biology applies concepts from engineering in order to understand biological networks. If such an understanding was complete, biologists would be able to design ad hoc biochemical components tailored for different purposes, which is the goal of synthetic biology. Needless to say that we are far away from creating biological subsystems as intricate and precise as those found in nature, but mathematical models and high throughput techniques have brought us a long way in this direction. One of the difficulties that still needs to be overcome is finding the right values for model parameters and dealing with uncertainty, which is proving to be an extremely difficult task. In this work, we take advantage of ensemble modeling techniques, where a large number of models with different parameter values are formulated and then tested according to some performance criteria. By finding features shared by successful models, the role of different components and the synergies between them can be better understood. We will address some of the difficulties often faced by ensemble modeling approaches, such as the need to sample a space whose size grows exponentially with the number of parameters, and establishing useful selection criteria. Some methods will be shown to reduce the predictions from many models into a set of understandable “design principles” that can guide us to improve or manufacture a biochemical network. Our proposed framework formulates models within standard formalisms in order to integrate information from different sources and minimize the dimension of the parameter space. Additionally, the mathematical properties of the formalism enable a partition of the parameter space into independent subspaces. Each of these subspaces can be paired with a set of criteria that depend exclusively on it, thus allowing a separate sampling/screening in spaces of lower dimension. By applying tests in a strict order where computationally cheaper tests are applied first to each subspace and applying computationally expensive tests to the remaining subset thereafter, the use of resources is optimized and a larger number of models can be examined. This can be compared to a complex database query where the order of the requests can make a huge difference in the processing time. The method will be illustrated by analyzing a classical model of a metabolic pathway with end-product inhibition. Even for such a simple model, the method provides novel insight.

In silico Metabolic Pathway Analysis Identifying Target Against Leishmaniasis - A Kinetic Modeling Approach

The protozoan Leishmania donovani, from trypanosomatids family is a deadly human pathogen responsible for causing Visceral Leishmaniasis. Unavailability of proper treatment in the developing countries has served as a major threat to the people. The absence of vaccines has made treatment possibilities to rely solely over chemotherapy. Also, reduced drug efficacy due to emerging resistant strains magnifies the threat. Despite years of formulations for an effective drug therapy, complexity of the disease is also unfortunately increasing. Absence of potential drug targets has worsened the scenario. Therefore exploring new therapeutic approach is a priority for the scientific community to combat the disease. One of the most reliable ways to alter the adversities of the infection is finding new biological targets for designing potential drugs. An era of computational biology allows identifying targets, assisting experimental studies. It includes sorting the parasite’s metabolic pathways that pins out proteins essential for its survival. We have directed our study towards a computational methodology for determining targets against L. donovani from the “purine salvage” pathway. This is a mainstay pathway towards the maintenance of purine amounts in the parasitic pool of nutrients proving to be mandatory for its survival. This study represents an integration of metabolic pathway and Protein-Protein Interactions analysis. It consists of incorporating the available experimental data to the theoretical methods with a prospective to develop a kinetic model of Purine salvage pathway. Simulation data revealed the time course mechanism of the enzymes involved in the synthesis of the metabolites. Modeling of the metabolic pathway helped in marking of crucial enzymes. Additionally, the PPI analysis of the pathway assisted in building a static interaction network for the proteins. Topological analysis of the PPI network through centrality measures (MCC and Closeness) detected targets found common with Dynamic Modeling. Therefore our analysis reveals the enzymes ADSL (Adenylosuccinate lyase) and IMPDH (Inosine-5′-monophosphate dehydrogenase) to be important having a central role in the modeled network based on PPI and kinetic modeling techniques. Further the available three dimensional structure of the enzyme “ADSL” aided towards the search for potential inhibitors against the protein. Hence, the study presented the significance of integrating methods to identify key proteins which might be putative targets against the treatment of Visceral Leishmaniasis and their potential inhibitors.

Mathematical Modeling of Plant Metabolism in a Changing Temperature Regime

Changes in environmental temperature regimes significantly affect plant growth, development and reproduction. Within a multigenic process termed acclimation, many plant species of the temperate region are able to adjust their metabolism to low and high temperature. Temperature-induced metabolic reprogramming is a nonlinear process affecting numerous enzyme kinetic reactions and pathways. The analysis of metabolic reprogramming during temperature acclimation is essentially supported by mathematical modeling which enables the study of nonlinear enzyme kinetics in context of metabolic networks and pathway regulation. This chapter introduces mathematical modeling of plant metabolism during a dynamic environmental temperature regime. A focus is laid on kinetic modeling and thermodynamic constraints.

Combined in silico and 19F NMR analysis of 5-fluorouracil metabolism in yeast at low ATP conditions

The cytotoxic effect of 5-fluorouracil (5-FU) on yeast cells is thought to be mainly via a misincorporation of fluoropyrimidines into both RNA and DNA, not only DNA damage via inhibition of thymidylate synthase (TYMS) by fluorodeoxyuridine monophosphate (FdUMP). However, some studies on Saccharomyces cerevisiae show a drastic decrease in ATP concentration under oxidative stress, together with a decrease in concentration of other tri- and diphosphates. This raises a question if hydrolysis of 5-fluoro-2-deoxyuridine diphosphate (FdUDP) under oxidative stress could not lead to the presence of FdUMP and the activation of so-called 'thymine-less death' route. We attempted to answer this question with in silico modeling of 5-FU metabolic pathways, based on new experimental results, where the stages of intracellular metabolism of 5-FU in Saccharomyces cerevisiae were tracked by a combination of 19F and 31P NMR spectroscopic study. We have identified 5-FU, its nucleosides and nucleotides, and subsequent di- and/or triphosphates. Additionally, another wide 19F signal, assigned to fluorinated unstructured short RNA, has been also identified in the spectra. The concentration of individual metabolites was found to vary substantially within hours, however, the initial steady-state was preserved only for an hour, until the ATP concentration dropped by a half, which was monitored independently via 31P NMR spectra. After that, the catabolic process leading from triphosphates through monophosphates and nucleosides back to 5-FU was observed. These results imply careful design and interpretation of studies in 5-FU metabolism in yeast.

Statistical inference in ensemble modeling of cellular metabolism

Kinetic models of metabolism can be constructed to predict cellular regulation and devise metabolic engineering strategies, and various promising computational workflows have been developed in recent years for this. Due to the uncertainty in the kinetic parameter values required to build kinetic models, these workflows rely on ensemble modeling (EM) principles for sampling and building populations of models describing observed physiologies. Sensitivity coefficients from metabolic control analysis (MCA) of kinetic models can provide important insight about cellular control around a given physiological steady state. However, despite considering populations of kinetic models and their model outputs, current approaches do not provide adequate tools for statistical inference. To derive conclusions from model outputs, such as MCA sensitivity coefficients, it is necessary to rank/compare populations of variables with each other. Currently existing workflows consider confidence intervals (CIs) that are derived independently for each comparable variable. Hence, it is important to derive simultaneous CIs for the variables that we wish to rank/compare. Herein, we used an existing large-scale kinetic model of Escherichia Coli metabolism to present how univariate CIs can lead to incorrect conclusions, and we present a new workflow that applies three different multivariate statistical approaches. We use the Bonferroni and the exact normal methods to build symmetric CIs using the normality assumptions. We then suggest how bootstrapping can compute asymmetric CIs whilst relaxing this normality assumption. We conclude that the Bonferroni and the exact normal methods can provide simple and efficient ways for constructing reliable CIs, with the exact normal method favored over the Bonferroni when the compared variables present dependencies. Bootstrapping, despite its significantly higher computational cost, is recommended when comparing non-normal distributions of variables. Additionally, we show how the Bonferroni method can readily be used to estimate required sample numbers to attain a certain CI size.

Engineering microbial chemical factories using metabolic models

Living organisms in analogy with chemical factories use simple molecules such as sugars to produce a variety of compounds which are necessary for sustaining life and some of which are also commercially valuable. The metabolisms of simple (such as bacteria) and higher organisms (such as plants) alike can be exploited to convert low value inputs into high value outputs. Unlike conventional chemical factories, microbial production chassis are not necessarily tuned for a single product overproduction. Despite the same end goal, metabolic and industrial engineers rely on different techniques for achieving productivity goals. Metabolic engineers cannot affect reaction rates by manipulating pressure and temperature, instead they have at their disposal a range of enzymes and transcriptional and translational processes to optimize accordingly. In this review, we first highlight how various analytical approaches used in metabolic engineering and synthetic biology are related to concepts developed in systems and control engineering. Specifically, how algorithmic concepts derived in operations research can help explain the structure and organization of metabolic networks. Finally, we consider the future directions and challenges faced by the field of metabolic network modeling and the possible contributions of concepts drawn from the classical fields of chemical and control engineering. The aim of the review is to offer a current perspective of metabolic engineering and all that it entails without requiring specialized knowledge of bioinformatics or systems biology.

Dynamics of Plant Metabolism during Cold Acclimation

Plants have evolved strategies to tightly regulate metabolism during acclimation to a changing environment. Low temperature significantly constrains distribution, growth and yield of many temperate plant species. Exposing plants to low but non-freezing temperature induces a multigenic processes termed cold acclimation, which eventually results in an increased freezing tolerance. Cold acclimation comprises reprogramming of the transcriptome, proteome and metabolome and affects communication and signaling between subcellular organelles. Carbohydrates play a central role in this metabolic reprogramming. This review summarizes current knowledge about the role of carbohydrate metabolism in plant cold acclimation with a focus on subcellular metabolic reprogramming, its thermodynamic constraints under low temperature and mathematical modelling of metabolism.

Metabolic acclimation-a key to enhancing photosynthesis in changing environments?

Plants adjust their photosynthetic capacity in response to their environment in a way that optimizes their yield and fitness. There is growing evidence that this acclimation is a response to changes in the leaf metabolome, but the extent to which these are linked and how this is optimized remain poorly understood. Using as an example the metabolic perturbations occurring in response to cold, we define the different stages required for acclimation, discuss the evidence for a metabolic temperature sensor, and suggest further work towards designing climate-smart crops. In particular, we discuss how constraint-based and kinetic metabolic modelling approaches can be used to generate targeted hypotheses about relevant pathways, and argue that a stronger integration of experimental and in silico studies will help us to understand the tightly regulated interplay of carbon partitioning and resource allocation required for photosynthetic acclimation to different environmental conditions.

Flux prediction using artificial neural network (ANN) for the upper part of glycolysis

The selection of optimal enzyme concentration in multienzyme cascade reactions for the highest product yield in practice is very expensive and time-consuming process. The modelling of biological pathways is a difficult process because of the complexity of the system. The mathematical modelling of the system using an analytical approach depends on the many parameters of enzymes which rely on tedious and expensive experiments. The artificial neural network (ANN) method has been successively applied in different fields of science to perform complex functions. In this study, ANN models were trained to predict the flux for the upper part of glycolysis as inferred by NADH consumption, using four enzyme concentrations i.e., phosphoglucoisomerase, phosphofructokinase, fructose-bisphosphate-aldolase, triose-phosphate-isomerase. Out of three ANN algorithms, the neuralnet package with two activation functions, “logistic” and “tanh” were implemented. The prediction of the flux was very efficient: RMSE and R² were 0.847, 0.93 and 0.804, 0.94 respectively for logistic and tanh functions using a cross validation procedure. This study showed that a systemic approach such as ANN could be used for accurate prediction of the flux through the metabolic pathway. This could help to save a lot of time and costs, particularly from an industrial perspective. The R-code is available at: https://github.com/DSIMB/ANN-Glycolysis-Flux-Prediction.

Kinetic modeling of the Calvin cycle identifies flux control and stable metabolomes in Synechocystis carbon fixation

Biological fixation of atmospheric CO2 via the Calvin-Benson-Bassham cycle has massive ecological impact and offers potential for industrial exploitation, either by improving carbon fixation in plants and autotrophic bacteria, or by installation into new hosts. A kinetic model of the Calvin-Benson-Bassham cycle embedded in the central carbon metabolism of the cyanobacterium Synechocystis sp. PCC 6803 was developed to investigate its stability and underlying control mechanisms. To reduce the uncertainty associated with a single parameter set, random sampling of the steady-state metabolite concentrations and the enzyme kinetic parameters was employed, resulting in millions of parameterized models which were analyzed for flux control and stability against perturbation. Our results show that the Calvin cycle had an overall high intrinsic stability, but a high concentration of ribulose 1,5-bisphosphate was associated with unstable states. Low substrate saturation and high product saturation of enzymes involved in highly interconnected reactions correlated with increased network stability. Flux control, that is the effect that a change in one reaction rate has on the other reactions in the network, was distributed and mostly exerted by energy supply (ATP), but also by cofactor supply (NADPH). Sedoheptulose 1,7-bisphosphatase/fructose 1,6-bisphosphatase, fructose-bisphosphate aldolase, and transketolase had a weak but positive effect on overall network flux, in agreement with published observations. The identified flux control and relationships between metabolite concentrations and system stability can guide metabolic engineering. The kinetic model structure and parameterizing framework can be expanded for analysis of metabolic systems beyond the Calvin cycle.

Revealing instabilities in a generalized triadic supply network: A bifurcation analysis

Supply networks are exposed to instabilities and thus a high level of risk. To mitigate this risk, it is necessary to understand how instabilities are formed in supply networks. In this paper, we focus on instabilities in inventory dynamics that develop due to the topology of the supply network. To be able to capture these topology-induced instabilities, we use a method called generalized modeling, a minimally specified modeling approach adopted from ecology. This method maps the functional dependencies of production rates on the inventory levels of different parts and products, which are imposed by the network topology, to a set of elasticity parameters. We perform a bifurcation analysis to investigate how these elasticities affect the stability. First, we show that dyads and serial supply chains are immune to topology-induced instabilities. In contrast, in a simple triadic network, where a supplier acts as both a first and a second tier supplier, we can identify instabilities that emerge from saddle-node, Hopf, and global homoclinic bifurcations. These bifurcations lead to different types of dynamical behavior, including exponential convergence to and divergence from a steady state, temporary oscillations around a steady state, and co-existence of different types of dynamics, depending on initial conditions. Finally, we discuss managerial implications of the results.

DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems

Background

Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed.

Results

In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics.

Conclusion

The presented pipeline automates the modelling process for large metabolic networks. From this, users can simulate their pathway of interest and obtain a better understanding of how altering conditions influences cellular dynamics. By testing the effects of different parameterisations we are also able to provide suggestions to help construct more accurate models of complete metabolic systems in the future.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0584-8) contains supplementary material, which is available to authorized users.

Machine Learning Methods for Analysis of Metabolic Data and Metabolic Pathway Modeling

Machine learning uses experimental data to optimize clustering or classification of samples or features, or to develop, augment or verify models that can be used to predict behavior or properties of systems. It is expected that machine learning will help provide actionable knowledge from a variety of big data including metabolomics data, as well as results of metabolism models. A variety of machine learning methods has been applied in bioinformatics and metabolism analyses including self-organizing maps, support vector machines, the kernel machine, Bayesian networks or fuzzy logic. To a lesser extent, machine learning has also been utilized to take advantage of the increasing availability of genomics and metabolomics data for the optimization of metabolic network models and their analysis. In this context, machine learning has aided the development of metabolic networks, the calculation of parameters for stoichiometric and kinetic models, as well as the analysis of major features in the model for the optimal application of bioreactors. Examples of this very interesting, albeit highly complex, application of machine learning for metabolism modeling will be the primary focus of this review presenting several different types of applications for model optimization, parameter determination or system analysis using models, as well as the utilization of several different types of machine learning technologies.

Mathematical Modeling Approaches in Plant Metabolomics

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

Topological and kinetic determinants of the modal matrices of dynamic models of metabolism

Large-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of metabolic networks. Central to linear analysis methods are two key matrices: the Jacobian matrix (J) and the modal matrix (M-1) arising from its eigendecomposition. The modal matrix M-1 contains dynamically independent motions of the kinetic model near a reference state, and it is sparse in practice for metabolic networks. However, connecting the structure of M-1 to the kinetic properties of the underlying reactions is non-trivial. In this study, we analyze the relationship between J, M-1, and the kinetic properties of the underlying network for kinetic models of metabolism. Specifically, we describe the origin of mode sparsity structure based on features of the network stoichiometric matrix S and the reaction kinetic gradient matrix G. First, we show that due to the scaling of kinetic parameters in real networks, diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures with clear biological interpretations. Then, we show that more complicated modes originate from topologically-connected reactions that have similar reaction elasticities in G. These elasticities represent dynamic equilibrium balances within reactions and are key determinants of modal structure. The work presented should prove useful towards obtaining an understanding of the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions.

Formulation, construction and analysis of kinetic models of metabolism: A review of modelling frameworks

Kinetic models are critical to predict the dynamic behaviour of metabolic networks. Mechanistic kinetic models for large networks remain uncommon due to the difficulty of fitting their parameters. Recent modelling frameworks promise new ways to overcome this obstacle while retaining predictive capabilities. In this review, we present an overview of the relevant mathematical frameworks for kinetic formulation, construction and analysis. Starting with kinetic formalisms, we next review statistical methods for parameter inference, as well as recent computational frameworks applied to the construction and analysis of kinetic models. Finally, we discuss opportunities and limitations hindering the development of larger kinetic reconstructions.

Non-steady state mass action dynamics without rate constants: dynamics of coupled reactions using chemical potentials

Comprehensive and predictive simulation of coupled reaction networks has long been a goal of biology and other fields. Currently, metabolic network models that utilize enzyme mass action kinetics have predictive power but are limited in scope and application by the fact that the determination of enzyme rate constants is laborious and low throughput. We present a statistical thermodynamic formulation of the law of mass action for coupled reactions at both steady states and non-stationary states. The formulation uses chemical potentials instead of rate constants. When used to model deterministic systems, the method corresponds to a rescaling of the time dependent reactions in such a way that steady states can be reached on the same time scale but with significantly fewer computational steps. The relationships between reaction affinities, free energy changes and generalized detailed balance are central to the discussion. The significance for applications in systems biology are discussed as is the concept and assumption of maximum entropy production rate as a biological principle that links thermodynamics to natural selection.

Using Structural Kinetic Modeling To Identify Key Determinants of Stability in Reaction Networks

Kinetic modeling is increasingly used to understand the reaction dynamics of metabolic systems. However, one major drawback of kinetic modeling is that appropriate rate parameters required to implement such models are often unavailable. To circumvent this limitation, an approach known as structural kinetic modeling was developed as a way to understand the dynamics of reaction networks without explicitly requiring rate parameters. This study describes a novel approach to use structural kinetic modeling to identify reaction components that contribute most significantly to mediating network stability. We applied this method to analyze the metabolic pathway of glycolysis in yeast. As a result, we identified specific metabolic components that contribute most significantly to defining the stability properties of the glycolysis reaction network and predict the responses of these components to perturbations. These results were validated via comparison to a conventional kinetic model of glycolysis. Thus, applying our approach allows more detailed information about the stability and dynamics of the metabolic network to now be accessible without requiring rate parameters. We anticipate that this method can focus efforts of experimental studies by identifying the susceptibility of reaction components to metabolic engineering. The approach may be applied to a variety of complex reaction networks.

Toward Multiscale Models of Cyanobacterial Growth: A Modular Approach

Oxygenic photosynthesis dominates global primary productivity ever since its evolution more than three billion years ago. While many aspects of phototrophic growth are well understood, it remains a considerable challenge to elucidate the manifold dependencies and interconnections between the diverse cellular processes that together facilitate the synthesis of new cells. Phototrophic growth involves the coordinated action of several layers of cellular functioning, ranging from the photosynthetic light reactions and the electron transport chain, to carbon-concentrating mechanisms and the assimilation of inorganic carbon. It requires the synthesis of new building blocks by cellular metabolism, protection against excessive light, as well as diurnal regulation by a circadian clock and the orchestration of gene expression and cell division. Computational modeling allows us to quantitatively describe these cellular functions and processes relevant for phototrophic growth. As yet, however, computational models are mostly confined to the inner workings of individual cellular processes, rather than describing the manifold interactions between them in the context of a living cell. Using cyanobacteria as model organisms, this contribution seeks to summarize existing computational models that are relevant to describe phototrophic growth and seeks to outline their interactions and dependencies. Our ultimate aim is to understand cellular functioning and growth as the outcome of a coordinated operation of diverse yet interconnected cellular processes.

The Protein Cost of Metabolic Fluxes: Prediction from Enzymatic Rate Laws and Cost Minimization

Bacterial growth depends crucially on metabolic fluxes, which are limited by the cell’s capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as k_cat and K_M constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 4.1 and 2.6, respectively, for the two kinds of data. This result from the cost-optimized metabolic state is significantly better than randomly sampled metabolite profiles, supporting the hypothesis that enzyme cost is important for the fitness of E. coli. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, and could be a valuable computational tool to assist metabolic engineering projects. Furthermore, it establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified.

“Enzyme cost”, the amount of protein needed for a given metabolic flux, is crucial for the metabolic choices cells have to make. However, due to the technical limitations of linear optimization methods, this cost has traditionally been ignored by constraint-based metabolic models such as Flux Balance Analysis. On the other hand, more detailed kinetic models which use ordinary differential equations to simulate fluxes for different choices of enzyme allocation, are computationally demanding and not scalable enough. In this work, we developed a method which utilizes the full kinetic model to predict steady-state enzyme costs, using a scalable and robust algorithm based on convex optimization. We show that the minimization of enzyme cost is a meaningful optimality principle by comparing our predictions to measured enzyme and metabolite levels in exponentially growing E. coli. This method could be used to quantify the enzyme cost of many other pathways and explain why evolution has selected some low-yield metabolic strategies, including aerobic fermentation in yeast and cancer cells. Furthermore, future metabolic engineering projects could benefit from our method by choosing pathways that reduce the total amount of enzyme required for the synthesis of a value-added product.

Quantifying uncertainty in partially specified biological models: how can optimal control theory help us?

Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions-a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.

Steady states and stability in metabolic networks without regulation

Metabolic networks are often extremely complex. Despite intensive efforts many details of these networks, e.g., exact kinetic rates and parameters of metabolic reactions, are not known, making it difficult to derive their properties. Considerable effort has been made to develop theory about properties of steady states in metabolic networks that are valid for any values of parameters. General results on uniqueness of steady states and their stability have been derived with specific assumptions on reaction kinetics, stoichiometry and network topology. For example, deep results have been obtained under the assumptions of mass-action reaction kinetics, continuous flow stirred tank reactors (CFSTR), concordant reaction networks and others. Nevertheless, a general theory about properties of steady states in metabolic networks is still missing. Here we make a step further in the quest for such a theory. Specifically, we study properties of steady states in metabolic networks with monotonic kinetics in relation to their stoichiometry (simple and general) and the number of metabolites participating in every reaction (single or many). Our approach is based on the investigation of properties of the Jacobian matrix. We show that stoichiometry, network topology, and the number of metabolites that participate in every reaction have a large influence on the number of steady states and their stability in metabolic networks. Specifically, metabolic networks with single-substrate-single-product reactions have disconnected steady states, whereas in metabolic networks with multiple-substrates-multiple-product reactions manifolds of steady states arise. Metabolic networks with simple stoichiometry have either a unique globally asymptotically stable steady state or asymptotically stable manifolds of steady states. In metabolic networks with general stoichiometry the steady states are not always stable and we provide conditions for their stability. In order to demonstrate the biological relevance we illustrate the results on the examples of the TCA cycle, the mevalonate pathway and the Calvin cycle.

Construction of feasible and accurate kinetic models of metabolism: A Bayesian approach

Kinetic models are essential to quantitatively understand and predict the behaviour of metabolic networks. Detailed and thermodynamically feasible kinetic models of metabolism are inherently difficult to formulate and fit. They have a large number of heterogeneous parameters, are non-linear and have complex interactions. Many powerful fitting strategies are ruled out by the intractability of the likelihood function. Here, we have developed a computational framework capable of fitting feasible and accurate kinetic models using Approximate Bayesian Computation. This framework readily supports advanced modelling features such as model selection and model-based experimental design. We illustrate this approach on the tightly-regulated mammalian methionine cycle. Sampling from the posterior distribution, the proposed framework generated thermodynamically feasible parameter samples that converged on the true values, and displayed remarkable prediction accuracy in several validation tests. Furthermore, a posteriori analysis of the parameter distributions enabled appraisal of the systems properties of the network (e.g., control structure) and key metabolic regulations. Finally, the framework was used to predict missing allosteric interactions.

Constructing kinetic models of metabolism at genome-scales: A review

Constraint-based modeling of biological networks (metabolism, transcription and signal transduction), although used successfully in many applications, suffer from specific limitations such as the lack of representation of metabolite concentrations and enzymatic regulation, which are necessary for a complete physiologically relevant model. Kinetic models conversely overcome these shortcomings and enable dynamic analysis of biological systems for enhanced in silico hypothesis generation. Nonetheless, kinetic models also have limitations for modeling at genome-scales chiefly due to: (i) model non-linearity; (ii) computational tractability; (iii) parameter identifiability; (iv) estimability; and (v) uncertainty. In order to support further development of kinetic models as viable alternatives to constraint-based models, this review presents a brief description of the existing obstacles towards building genome-scale kinetic models. Specific kinetic modeling frameworks capable of overcoming these obstacles are covered in this review. The tractability and physiological feasibility of these models are discussed with the objective of using available in vivo experimental observations to define the model parameter space. Among the different methods discussed, Monte Carlo kinetic models of metabolism stand out as potentially tractable methods to model genome scale networks while also addressing in vivo parameter uncertainty.

Bacterial metabolism in immediate response to nutritional perturbation with temporal and network view of metabolites

In this study, the initial propagation of metabolic perturbation in Escherichia coli was visualized to understand the dynamic characteristics of the metabolic pathways without the association of transcription alterations. E. coli cells were exposed to the sudden relief of glucose starvation, and time-dependent variances in metabolite balances were traced in the second scale. The acquired time-course data were represented by structural variations of the metabolite-metabolite correlation network. The initial correlation structure was altered immediately by the glucose pulse, followed by further structural variations within a few minutes. It was demonstrated that one metabolite temporally correlated with distinct metabolites with different timings, and such a behavior could imply a regulatory role for the metabolite in the metabolic network. Centrality analysis of the networks and partial correlation analysis indicated that preparation for growth and oxidative stress could be coupled as a structural property of the metabolic pathways.

Probing the Druggability Limits for Enzymes of the NAD Biosynthetic Network in Glioma

The biosynthesis of NAD constitutes an important metabolic module in the cell, since NAD is an essential cofactor involved in several metabolic reactions. NAD concentrations are known to be significantly increased in several cancers, particularly in glioma, consistent with the observation of up-regulation of several enzymes of the network. Modulating NAD biosynthesis in glioma is therefore an attractive therapeutic strategy. Here we report reconstruction of a biochemical network of NAD biosynthesis consisting of 22 proteins, 36 metabolites, and 86 parameters, tuned to mimic the conditions in glioma. Kinetic simulations of the network provide comprehensive insights about the role of individual enzymes. Further, quantitative changes in the same network between different states of health and disease enable identification of drug targets, based on specific alterations in the given disease. Through simulations of enzyme inhibition titrations, we identify NMPRTase as a potential drug target, while eliminating other possible candidates NMNAT, NAPRTase, and NRK. We have also simulated titrations of both binding affinities as well as inhibitor concentrations, which provide insights into the druggability limits of the target, a novel aspect that can provide useful guidelines for designing inhibitors with optimal affinities. Our simulations suggest that an inhibitor affinity of 10 nM used in a concentration range of 0.1 to 10 μM achieves a near maximal inhibition response for NMPRTase and that increasing the affinity any further is not likely to have a significant advantage. Thus, the quantitative appreciation defines a maximal extent of inhibition possible for a chosen enzyme in the context of its network. Knowledge of this type enables an upper affinity threshold to be defined as a goal in lead screening and refinement stages in drug discovery.

Approximating the stabilization of cellular metabolism by compartmentalization

Biochemical regulation in compartmentalized metabolic networks is highly complex and non-intuitive. This is particularly true for cells of higher plants showing one of the most compartmentalized cellular structures across all kingdoms of life. The interpretation and testable hypothesis generation from experimental data on such complex systems is a challenging step in biological research and biotechnological applications. While it is known that subcellular compartments provide defined reaction spaces within a cell allowing for the tight coordination of complex biochemical reaction sequences, its role in the coordination of metabolic signals during metabolic reprogramming due to environmental fluctuations is less clear. In the present study, we numerically analysed the effects of environmental fluctuations in a subcellular metabolic network with regard to the stability of an experimentally observed steady state in the genetic model plant Arabidopsis thaliana. Applying a method for kinetic parameter normalization, several millions of probable enzyme kinetic parameter constellations were simulated and evaluated with regard to the stability information of the metabolic homeostasis. Information about the stability of the metabolic steady state was derived from real parts of eigenvalues of Jacobian matrices. Our results provide evidence for a differential stabilizing contribution of different subcellular compartments. We could identify stabilizing and destabilizing network components which we could classify according to their subcellular localization. The findings prove that a highly dynamic interplay between intracellular compartments is preliminary for an efficient stabilization of a metabolic homeostasis after environmental perturbation. Further, our results provide evidence that feedback-inhibition originating from the cytosol and plastid seem to stabilize the sucrose homeostasis more efficiently than vacuolar control. In summary, our results indicate stabilizing and destabilizing network components in context of their subcellular organization.