Computational Models of Metabolism: Stability and Regulation in Metabolic Networks

Challenges and Frontiers in Computational Metabolic Psychiatry

One of the primary challenges in metabolic psychiatry is that the disrupted brain functions that underlie psychiatric conditions arise from a complex set of downstream and feedback processes that span multiple spatiotemporal scales. Importantly, the same circuit can have multiple points of failure, each of which results in a different type of dysregulation, and thus elicits distinct cascades downstream that produce divergent signs and symptoms. Here, we illustrate this challenge by examining how subtle differences in circuit perturbations can lead to divergent clinical outcomes. We also discuss how computational models can perform the spatially heterogeneous integration and bridge in vitro and in vivo paradigms. By leveraging recent methodological advances and tools, computational models can integrate relevant processes across scales (e.g., tricarboxylic acid cycle, ion channel, neural microassembly, whole-brain macrocircuit) and across physiological systems (e.g., neural, endocrine, immune, vascular), providing a framework that can unite these mechanistic processes in a manner that goes beyond the conceptual and descriptive to the quantitative and generative. These hold the potential to sharpen our intuitions toward circuit-based models for personalized diagnostics and treatment.

A quantitative description of light-limited cyanobacterial growth using flux balance analysis

The metabolism of phototrophic cyanobacteria is an integral part of global biogeochemical cycles, and the capability of cyanobacteria to assimilate atmospheric CO2 into organic carbon has manifold potential applications for a sustainable biotechnology. To elucidate the properties of cyanobacterial metabolism and growth, computational reconstructions of genome-scale metabolic networks play an increasingly important role. Here, we present an updated reconstruction of the metabolic network of the cyanobacterium Synechocystis sp. PCC 6803 and its quantitative evaluation using flux balance analysis (FBA). To overcome limitations of conventional FBA, and to allow for the integration of experimental analyses, we develop a novel approach to describe light absorption and light utilization within the framework of FBA. Our approach incorporates photoinhibition and a variable quantum yield into the constraint-based description of light-limited phototrophic growth. We show that the resulting model is capable of predicting quantitative properties of cyanobacterial growth, including photosynthetic oxygen evolution and the ATP/NADPH ratio required for growth and cellular maintenance. Our approach retains the computational and conceptual simplicity of FBA and is readily applicable to other phototrophic microorganisms.

Monitoring and modelling the dynamics of the cellular glycolysis pathway: A review and future perspectives

BACKGROUND

The dynamics of the cellular glycolysis pathway underpin cellular function and dysfunction, and therefore ultimately health, disease, diagnostic and therapeutic strategies. Evolving our understanding of this fundamental process and its dynamics remains critical.

SCOPE OF REVIEW

This paper reviews the medical relevance of glycolytic pathway in depth and explores the current state of the art for monitoring and modelling the dynamics of the process. The future perspectives of label free, vibrational microspectroscopic techniques to overcome the limitations of the current approaches are considered.

MAJOR CONCLUSIONS

Vibrational microspectroscopic techniques can potentially operate in the niche area of limitations of other omics technologies for non-destructive, real-time, in vivo label-free monitoring of glycolysis dynamics at a cellular and subcellular level.

Combining Pharmacokinetics and Vibrational Spectroscopy: MCR-ALS Hard-and-Soft Modelling of Drug Uptake In Vitro Using Tailored Kinetic Constraints

Raman microspectroscopy is a label-free technique which is very suited for the investigation of pharmacokinetics of cellular uptake, mechanisms of interaction, and efficacies of drugs in vitro. However, the complexity of the spectra makes the identification of spectral patterns associated with the drug and subsequent cellular responses difficult. Indeed, multivariate methods that relate spectral features to the inoculation time do not normally take into account the kinetics involved, and important theoretical information which could assist in the elucidation of the relevant spectral signatures is excluded. Here, we propose the integration of kinetic equations in the modelling of drug uptake and subsequent cellular responses using Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) and tailored kinetic constraints, based on a system of ordinary differential equations. Advantages of and challenges to the methodology were evaluated using simulated Raman spectral data sets and real Raman spectra acquired from A549 and Calu-1 human lung cells inoculated with doxorubicin, in vitro. The results suggest a dependency of the outcome on the system of equations used, and the importance of the temporal resolution of the data set to enable the use of complex equations. Nevertheless, the use of tailored kinetic constraints during MCR-ALS allowed a more comprehensive modelling of the system, enabling the elucidation of not only the time-dependent concentration profiles and spectral features of the drug binding and cellular responses, but also an accurate computation of the kinetic constants.

John PC, Crowley MF, Bomble YJ. Prediction of reaction knockouts to maximize succinate production by Actinobacillus succinogenes

Succinate is a precursor of multiple commodity chemicals and bio-based succinate production is an active area of industrial bioengineering research. One of the most important microbial strains for bio-based production of succinate is the capnophilic gram-negative bacterium Actinobacillus succinogenes, which naturally produces succinate by a mixed-acid fermentative pathway. To engineer A. succinogenes to improve succinate yields during mixed acid fermentation, it is important to have a detailed understanding of the metabolic flux distribution in A. succinogenes when grown in suitable media. To this end, we have developed a detailed stoichiometric model of the A. succinogenes central metabolism that includes the biosynthetic pathways for the main components of biomass-namely glycogen, amino acids, DNA, RNA, lipids and UDP-N-Acetyl-α-D-glucosamine. We have validated our model by comparing model predictions generated via flux balance analysis with experimental results on mixed acid fermentation. Moreover, we have used the model to predict single and double reaction knockouts to maximize succinate production while maintaining growth viability. According to our model, succinate production can be maximized by knocking out either of the reactions catalyzed by the PTA (phosphate acetyltransferase) and ACK (acetyl kinase) enzymes, whereas the double knockouts of PEPCK (phosphoenolpyruvate carboxykinase) and PTA or PEPCK and ACK enzymes are the most effective in increasing succinate production.

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.

Parameter estimation in tree graph metabolic networks

We study the glycosylation processes that convert initially toxic substrates to nutritionally valuable metabolites in the flavonoid biosynthesis pathway of tomato (Solanum lycopersicum) seedlings. To estimate the reaction rates we use ordinary differential equations (ODEs) to model the enzyme kinetics. A popular choice is to use a system of linear ODEs with constant kinetic rates or to use Michaelis–Menten kinetics. In reality, the catalytic rates, which are affected among other factors by kinetic constants and enzyme concentrations, are changing in time and with the approaches just mentioned, this phenomenon cannot be described. Another problem is that, in general these kinetic coefficients are not always identifiable. A third problem is that, it is not precisely known which enzymes are catalyzing the observed glycosylation processes. With several hundred potential gene candidates, experimental validation using purified target proteins is expensive and time consuming. We aim at reducing this task via mathematical modeling to allow for the pre-selection of most potential gene candidates. In this article we discuss a fast and relatively simple approach to estimate time varying kinetic rates, with three favorable properties: firstly, it allows for identifiable estimation of time dependent parameters in networks with a tree-like structure. Secondly, it is relatively fast compared to usually applied methods that estimate the model derivatives together with the network parameters. Thirdly, by combining the metabolite concentration data with a corresponding microarray data, it can help in detecting the genes related to the enzymatic processes. By comparing the estimated time dynamics of the catalytic rates with time series gene expression data we may assess potential candidate genes behind enzymatic reactions. As an example, we show how to apply this method to select prominent glycosyltransferase genes in tomato seedlings.

Resource allocation in metabolic networks: kinetic optimization and approximations by FBA

Based on recent theoretical results on optimal flux distributions in kinetic metabolic networks, we explore the congruences and differences between solutions of kinetic optimization problems and results obtained by constraint-based methods. We demonstrate that, for a certain resource allocation problem, kinetic optimization and standard flux balance analysis (FBA) give rise to qualitatively different results. Furthermore, we introduce a variant of FBA, called satFBA, whose predictions are in qualitative agreement with kinetic optimization.

Elucidating temporal resource allocation and diurnal dynamics in phototrophic metabolism using conditional FBA

The computational analysis of phototrophic growth using constraint-based optimization requires to go beyond current time-invariant implementations of flux-balance analysis (FBA). Phototrophic organisms, such as cyanobacteria, rely on harvesting the sun’s energy for the conversion of atmospheric CO2 into organic carbon, hence their metabolism follows a strongly diurnal lifestyle. We describe the growth of cyanobacteria in a periodic environment using a new method called conditional FBA. Our approach enables us to incorporate the temporal organization and conditional dependencies into a constraint-based description of phototrophic metabolism. Specifically, we take into account that cellular processes require resources that are themselves products of metabolism. Phototrophic growth can therefore be formulated as a time-dependent linear optimization problem, such that optimal growth requires a differential allocation of resources during different times of the day. Conditional FBA then allows us to simulate phototrophic growth of an average cell in an environment with varying light intensity, resulting in dynamic time-courses for all involved reaction fluxes, as well as changes in biomass composition over a diurnal cycle. Our results are in good agreement with several known facts about the temporal organization of phototrophic growth and have implications for further analysis of resource allocation problems in phototrophic metabolism.

Integrative analysis of metabolic models - from structure to dynamics

The characterization of biological systems with respect to their behavior and functionality based on versatile biochemical interactions is a major challenge. To understand these complex mechanisms at systems level modeling approaches are investigated. Different modeling formalisms allow metabolic models to be analyzed depending on the question to be solved, the biochemical knowledge and the availability of experimental data. Here, we describe a method for an integrative analysis of the structure and dynamics represented by qualitative and quantitative metabolic models. Using various formalisms, the metabolic model is analyzed from different perspectives. Determined structural and dynamic properties are visualized in the context of the metabolic model. Interaction techniques allow the exploration and visual analysis thereby leading to a broader understanding of the behavior and functionality of the underlying biological system. The System Biology Metabolic Model Framework (SBM (2) - Framework) implements the developed method and, as an example, is applied for the integrative analysis of the crop plant potato.

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

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

Global stability of enzymatic chains of full reversible Michaelis-Menten reactions

We consider a chain of metabolic reactions catalyzed by enzymes, of reversible Michaelis-Menten type with full dynamics, i.e. not reduced with any quasi-steady state approximations. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. The main tool is monotone systems theory. Finally we study the implications of these results for the study of coupled genetic-metabolic systems.

Metabolic network flux analysis for engineering plant systems

Metabolic network flux analysis (NFA) tools have proven themselves to be powerful aids to metabolic engineering of microbes by providing quantitative insights into the flows of material and energy through cellular systems. The development and application of NFA tools to plant systems has advanced in recent years and are yielding significant insights and testable predictions. Plants present substantial opportunities for the practical application of NFA but they also pose serious challenges related to the complexity of plant metabolic networks and to deficiencies in our knowledge of their structure and regulation. By considering the tools available and selected examples, this article attempts to assess where and how NFA is most likely to have a real impact on plant biotechnology.

Modeling metabolic networks for mammalian cell systems: general considerations, modeling strategies, and available tools

Over the past decades, the availability of large amounts of information regarding cellular processes and reaction rates, along with increasing knowledge about the complex mechanisms involved in these processes, has changed the way we approach the understanding of cellular processes. We can no longer rely only on our intuition for interpreting experimental data and evaluating new hypotheses, as the information to analyze is becoming increasingly complex. The paradigm for the analysis of cellular systems has shifted from a focus on individual processes to comprehensive global mathematical descriptions that consider the interactions of metabolic, genomic, and signaling networks. Analysis and simulations are used to test our knowledge by refuting or validating new hypotheses regarding a complex system, which can result in predictive capabilities that lead to better experimental design. Different types of models can be used for this purpose, depending on the type and amount of information available for the specific system. Stoichiometric models are based on the metabolic structure of the system and allow explorations of steady state distributions in the network. Detailed kinetic models provide a description of the dynamics of the system, they involve a large number of reactions with varied kinetic characteristics and require a large number of parameters. Models based on statistical information provide a description of the system without information regarding structure and interactions of the networks involved. The development of detailed models for mammalian cell metabolism has only recently started to grow more strongly, due to the intrinsic complexities of mammalian systems, and the limited availability of experimental information and adequate modeling tools. In this work we review the strategies, tools, current advances, and recent models of mammalian cells, focusing mainly on metabolism, but discussing the methodology applied to other types of networks as well.

Mathematical descriptions of biochemical networks: stability, stochasticity, evolution

In this paper, we review some fundamental aspects, as well as some new developments, in the emerging field of network biology. The focus of attention is placed on mathematical approaches to conceptual modeling of biomolecular networks with special emphasis on dynamic stability, stochasticity and evolution.

Barley grain development toward an integrative view

Seeds are complex structures composed of several maternal and filial tissues which undergo rapid changes during development. In this review, the barley grain is taken as a cereal seed model. Following a brief description of the developing grain, recent progress in grain development modeling is described. 3-D/4-D models based on histological sections or nondestructive NMR measurements can be used to integrate a variety of datasets. Extensive transcriptome data are taken as a frame to augment our understanding of various molecular-physiological processes. Discussed are maternal influences on grain development and the role of different tissues (pericarp, nucellus, nucellar projection, endosperm, endosperm transfer cells). Programmed cell death (PCD) is taken to pinpoint tissue specificities and the importance of remobilization processes for grain development. Transcriptome data have also been used to derive transcriptional networks underlying differentiation and maturation in endosperm and embryo. They suggest that the "maturation hormone" ABA is important also in early grain development. Massive storage product synthesis during maturation is dependent on sufficient energy, which can only be provided by specific metabolic adaptations due to severe oxygen deficiencies within the seed. To integrate the great variety of data from different research areas in complex, predictive computational modeling as part of a systems biology approach is an important challenge of the future. First attempts of modeling barley grain metabolism are summarized.