Integrating cybernetic modeling with pathway analysis provides a dynamic, systems-level description of metabolic control

The Molecular Basis of Differentiation Wave Activity in Embryogenesis

As development varies greatly across the tree of life, it may seem difficult to suggest a model that proposes a single mechanism for understanding collective cell behaviors and the coordination of tissue formation. Here we propose a mechanism called differentiation waves, which unify many disparate results involving developmental systems from across the tree of life. We demonstrate how a relatively simple model of differentiation proceeds not from function-related molecular mechanisms, but from so-called differentiation waves. A phenotypic model of differentiation waves is introduced, and its relation to molecular mechanisms is proposed. These waves contribute to a differentiation tree, which is an alternate way of viewing cell lineage and local action of the molecular factors. We construct a model of differentiation wave-related molecular mechanisms (genome, epigenome, and proteome) based on bioinformatic data from the nematode Caenorhabditis elegans. To validate this approach across different modes of development, we evaluate protein expression across different types of development by comparing Caenorhabditis elegans with several model organisms: fruit flies (Drosophila melanogaster), yeast (Saccharomyces cerevisiae), and mouse (Mus musculus). Inspired by gene regulatory networks, two Models of Interactive Contributions (fully-connected MICs and ordered MICs) are used to suggest potential genomic contributions to differentiation wave-related proteins. This, in turn, provides a framework for understanding differentiation and development.

Genome-Scale Reconstruction of Microbial Dynamic Phenotype: Successes and Challenges

This review is a part of the SI 'Genome-Scale Modeling of Microorganisms in the Real World'. The goal of GEM is the accurate prediction of the phenotype from its respective genotype under specified environmental conditions. This review focuses on the dynamic phenotype; prediction of the real-life behaviors of microorganisms, such as cell proliferation, dormancy, and mortality; balanced and unbalanced growth; steady-state and transient processes; primary and secondary metabolism; stress responses; etc. Constraint-based metabolic reconstructions were successfully started two decades ago as FBA, followed by more advanced models, but this review starts from the earlier nongenomic predecessors to show that some GEMs inherited the outdated biokinetic frameworks compromising their performances. The most essential deficiencies are: (i) an inadequate account of environmental conditions, such as various degrees of nutrients limitation and other factors shaping phenotypes; (ii) a failure to simulate the adaptive changes of MMCC (MacroMolecular Cell Composition) in response to the fluctuating environment; (iii) the misinterpretation of the SGR (Specific Growth Rate) as either a fixed constant parameter of the model or independent factor affecting the conditional expression of macromolecules; (iv) neglecting stress resistance as an important objective function; and (v) inefficient experimental verification of GEM against simple growth (constant MMCC and SGR) data. Finally, we propose several ways to improve GEMs, such as replacing the outdated Monod equation with the SCM (Synthetic Chemostat Model) that establishes the quantitative relationships between primary and secondary metabolism, growth rate and stress resistance, process kinetics, and cell composition.

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.

Modeling coordinated enzymatic control of saccharification and fermentation by Clostridium thermocellum during consolidated bioprocessing of cellulose

Consolidated bioprocessing (CBP) of cellulose is a cost-effective route to produce valuable biochemicals by integrating saccharification, fermentation and cellulase synthesis in a single step. However, the lack of understanding of governing factors of interdependent saccharification and fermentation in CBP eludes reliable process optimization. Here, we propose a new framework that synergistically couples population balances (to simulate cellulose depolymerization) and cybernetic models (to model enzymatic regulation of fermentation) to enable improved understanding of CBP. The resulting framework, named the unified cybernetic-population balance model (UC-PBM), enables simulation of CBP driven by coordinated control of enzyme synthesis through closed-loop interactions. UC-PBM considers two key aspects in controlling CBP: (1) heterogeneity in cellulose properties and (2) cellular regulation of competing cell growth and cellulase secretion. In a case study on Clostridium thermocellum, UC-PBM not only provides a decent fit with various exometabolomic data, but also reveals that: (i) growth-decoupled cellulase-secreting pathways are only activated during famine conditions to promote the production of growth substrates, and (ii) starting cellulose concentration has a strong influence on the overall flux distribution. Equipped with mechanisms of cellulose degradation and fermentative regulations, UC-PBM is practical to explore phenotypic functions for primary evaluation of microorganisms' potential for metabolic engineering and optimal design of bioprocess.

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed.

Cooperative metabolic resource allocation in spatially-structured systems

Natural selection has shaped the evolution of cells and multi-cellular organisms such that social cooperation can often be preferred over an individualistic approach to metabolic regulation. This paper extends a framework for dynamic metabolic resource allocation based on the maximum entropy principle to spatiotemporal models of metabolism with cooperation. Much like the maximum entropy principle encapsulates 'bet-hedging' behaviour displayed by organisms dealing with future uncertainty in a fluctuating environment, its cooperative extension describes how individuals adapt their metabolic resource allocation strategy to further accommodate limited knowledge about the welfare of others within a community. The resulting theory explains why local regulation of metabolic cross-feeding can fulfil a community-wide metabolic objective if individuals take into consideration an ensemble measure of total population performance as the only form of global information. The latter is likely supplied by quorum sensing in microbial systems or signalling molecules such as hormones in multi-cellular eukaryotic organisms.

Dynamic metabolic resource allocation based on the maximum entropy principle

Organisms have evolved a variety of mechanisms to cope with the unpredictability of environmental conditions, and yet mainstream models of metabolic regulation are typically based on strict optimality principles that do not account for uncertainty. This paper introduces a dynamic metabolic modelling framework that is a synthesis of recent ideas on resource allocation and the powerful optimal control formulation of Ramkrishna and colleagues. In particular, their work is extended based on the hypothesis that cellular resources are allocated among elementary flux modes according to the principle of maximum entropy. These concepts both generalise and unify prior approaches to dynamic metabolic modelling by establishing a smooth interpolation between dynamic flux balance analysis and dynamic metabolic models without regulation. The resulting theory is successful in describing 'bet-hedging' strategies employed by cell populations dealing with uncertainty in a fluctuating environment, including heterogenous resource investment, accumulation of reserves in growth-limiting conditions, and the observed behaviour of yeast growing in batch and continuous cultures. The maximum entropy principle is also shown to yield an optimal control law consistent with partitioning resources between elementary flux mode families, which has important practical implications for model reduction, selection, and simulation.

A Cybernetic Approach to Modeling Lipid Metabolism in Mammalian Cells

The goal-oriented control policies of cybernetic models have been used to predict metabolic phenomena such as the behavior of gene knockout strains, complex substrate uptake patterns, and dynamic metabolic flux distributions. Cybernetic theory builds on the principle that metabolic regulation is driven towards attaining goals that correspond to an organism’s survival or displaying a specific phenotype in response to a stimulus. Here, we have modeled the prostaglandin (PG) metabolism in mouse bone marrow derived macrophage (BMDM) cells stimulated by Kdo2-Lipid A (KLA) and adenosine triphosphate (ATP), using cybernetic control variables. Prostaglandins are a well characterized set of inflammatory lipids derived from arachidonic acid. The transcriptomic and lipidomic data for prostaglandin biosynthesis and conversion were obtained from the LIPID MAPS database. The model parameters were estimated using a two-step hybrid optimization approach. A genetic algorithm was used to determine the population of near optimal parameter values, and a generalized constrained non-linear optimization employing a gradient search method was used to further refine the parameters. We validated our model by predicting an independent data set, the prostaglandin response of KLA primed ATP stimulated BMDM cells. We show that the cybernetic model captures the complex regulation of PG metabolism and provides a reliable description of PG formation.

Regulation-Structured Dynamic Metabolic Model Provides a Potential Mechanism for Delayed Enzyme Response in Denitrification Process

In a recent study of denitrification dynamics in hyporheic zone sediments, we observed a significant time lag (up to several days) in enzymatic response to the changes in substrate concentration. To explore an underlying mechanism and understand the interactive dynamics between enzymes and nutrients, we developed a trait-based model that associates a community's traits with functional enzymes, instead of typically used species guilds (or functional guilds). This enzyme-based formulation allows to collectively describe biogeochemical functions of microbial communities without directly parameterizing the dynamics of species guilds, therefore being scalable to complex communities. As a key component of modeling, we accounted for microbial regulation occurring through transcriptional and translational processes, the dynamics of which was parameterized based on the temporal profiles of enzyme concentrations measured using a new signature peptide-based method. The simulation results using the resulting model showed several days of a time lag in enzymatic responses as observed in experiments. Further, the model showed that the delayed enzymatic reactions could be primarily controlled by transcriptional responses and that the dynamics of transcripts and enzymes are closely correlated. The developed model can serve as a useful tool for predicting biogeochemical processes in natural environments, either independently or through integration with hydrologic flow simulators.

Cardiolipin promotes electron transport between ubiquinone and complex I to rescue PINK1 deficiency

Parkinson’s disease–causing mutations in PINK1 yield mitochondrial defects including inefficient electron transport between complex I and ubiquinone. Vos et al. show that genetic and pharmacological inhibition of fatty acid synthase bypass these complex I defects in fly, mouse, and human Parkinson’s disease models.

PINK1 is mutated in Parkinson’s disease (PD), and mutations cause mitochondrial defects that include inefficient electron transport between complex I and ubiquinone. Neurodegeneration is also connected to changes in lipid homeostasis, but how these are related to PINK1-induced mitochondrial dysfunction is unknown. Based on an unbiased genetic screen, we found that partial genetic and pharmacological inhibition of fatty acid synthase (FASN) suppresses toxicity induced by PINK1 deficiency in flies, mouse cells, patient-derived fibroblasts, and induced pluripotent stem cell–derived dopaminergic neurons. Lower FASN activity in PINK1 mutants decreases palmitate levels and increases the levels of cardiolipin (CL), a mitochondrial inner membrane–specific lipid. Direct supplementation of CL to isolated mitochondria not only rescues the PINK1-induced complex I defects but also rescues the inefficient electron transfer between complex I and ubiquinone in specific mutants. Our data indicate that genetic or pharmacologic inhibition of FASN to increase CL levels bypasses the enzymatic defects at complex I in a PD model.

Optimal control analysis of the dynamic growth behavior of microorganisms

Understanding the growth behavior of microorganisms using modeling and optimization techniques is an active area of research in the fields of biochemical engineering and systems biology. In this paper, we propose a general modeling framework, based on Monod model, to model the growth of microorganisms. Utilizing the general framework, we formulate an optimal control problem with the objective of maximizing a long-term cellular goal and solve it analytically under various constraints for the growth of microorganisms in a two substrate batch environment. We investigate the relation between long term and short term cellular goals and show that the objective of maximizing cellular concentration at a fixed final time is equivalent to maximization of instantaneous growth rate. We then establish the mathematical connection between the generalized framework and optimal and cybernetic modeling frameworks and derive generalized governing dynamic equations for optimal and cybernetic models. We finally illustrate the influence of various constraints in the cybernetic modeling framework on the optimal growth behavior of microorganisms by solving several dynamic optimization problems using genetic algorithms.

Revitalizing personalized medicine: respecting biomolecular complexities beyond gene expression

Despite recent advancements in "omic" technologies, personalized medicine has not realized its fullest potential due to isolated and incomplete application of gene expression tools. In many instances, pharmacogenomics is being interchangeably used for personalized medicine, when actually it is one of the many facets of personalized medicine. Herein, we highlight key issues that are hampering the advancement of personalized medicine and highlight emerging predictive tools that can serve as a decision support mechanism for physicians to personalize treatments.

Metabolic flux analysis of Escherichia coli knockouts: lessons from the Keio collection and future outlook

Cellular metabolic and regulatory systems are of fundamental interest to biologists and engineers. Incomplete understanding of these complex systems remains an obstacle to progress in biotechnology and metabolic engineering. An established method for obtaining new information on network structure, regulation and dynamics is to study the cellular system following a perturbation such as a genetic knockout. The Keio collection of all viable Escherichia coli single-gene knockouts is facilitating a systematic investigation of the regulation and metabolism of E. coli. Of all omics measurements available, the metabolic flux profile (the fluxome) provides the most direct and relevant representation of the cellular phenotype. Recent advances in (13)C-metabolic flux analysis are now permitting highly precise and accurate flux measurements for investigating cellular systems and guiding metabolic engineering efforts.

Kinetic modelling of GlmU reactions - prioritization of reaction for therapeutic application

Mycobacterium tuberculosis(Mtu), a successful pathogen, has developed resistance against the existing anti-tubercular drugs necessitating discovery of drugs with novel action. Enzymes involved in peptidoglycan biosynthesis are attractive targets for antibacterial drug discovery. The bifunctional enzyme mycobacterial GlmU (Glucosamine 1-phosphate N-acetyltransferase/ N-acetylglucosamine-1-phosphate uridyltransferase) has been a target enzyme for drug discovery. Its C- and N- terminal domains catalyze acetyltransferase (rxn-1) and uridyltransferase (rxn-2) activities respectively and the final product is involved in peptidoglycan synthesis. However, the bifunctional nature of GlmU poses difficulty in deciding which function to be intervened for therapeutic advantage. Genetic analysis showed this as an essential gene but it is still unclear whether any one or both of the activities are critical for cell survival. Often enzymatic activity with suitable high-throughput assay is chosen for random screening, which may not be the appropriate biological function inhibited for maximal effect. Prediction of rate-limiting function by dynamic network analysis of reactions could be an option to identify the appropriate function. With a view to provide insights into biochemical assays with appropriate activity for inhibitor screening, kinetic modelling studies on GlmU were undertaken. Kinetic model of Mtu GlmU-catalyzed reactions was built based on the available kinetic data on Mtu and deduction from Escherichia coli data. Several model variants were constructed including coupled/decoupled, varying metabolite concentrations and presence/absence of product inhibitions. This study demonstrates that in coupled model at low metabolite concentrations, inhibition of either of the GlmU reactions cause significant decrement in the overall GlmU rate. However at higher metabolite concentrations, rxn-2 showed higher decrement. Moreover, with available intracellular concentration of the metabolites and in vivo variant of model, uncompetitive inhibition of rxn-2 caused highest decrement. Thus, at physiologically relevant metabolite concentrations, targeting uridyltranferase activity of Mtu GlmU would be a better choice for therapeutic intervention.

Prediction of dynamic behavior of mutant strains from limited wild-type data

Metabolic engineering is the field of introducing genetic changes in organisms so as to modify their function towards synthesizing new products of high impact to society. However, engineered cells frequently have impaired growth rates thus seriously limiting the rate at which such products are made. The problem is attributable to inadequate understanding of how a metabolic network functions in a dynamic sense. Predictions of mutant strain behavior in the past have been based on steady state theories such as flux balance analysis (FBA), minimization of metabolic adjustment (MOMA), and regulatory on/off minimization (ROOM). Such predictions are restricted to product yields and cannot address productivity, which is of focal interest to applications. We demonstrate that our framework ( [Song and Ramkrishna, 2010] and [Song and Ramkrishna, 2011]), based on a “cybernetic” view of metabolic systems, makes predictions of the dynamic behavior of mutant strains of Escherichia coli from a limited amount of data obtained from the wild-type. Dynamic frameworks must necessarily address the issue of metabolic regulation, which the cybernetic approach does by postulating that metabolism is an optimal dynamic response of the organism to the environment in driving reactions towards ensuring survival. The predictions made in this paper are without parallel in the literature and lay the foundation for rational metabolic engineering.

Elementary mode analysis: a useful metabolic pathway analysis tool for reprograming microbial metabolic pathways

Elementary mode analysis is a useful metabolic pathway analysis tool to characterize cellular metabolism. It can identify all feasible metabolic pathways known as elementary modes that are inherent to a metabolic network. Each elementary mode contains a minimal and unique set of enzymatic reactions that can support cellular functions at steady state. Knowledge of all these pathway options enables systematic characterization of cellular phenotypes, analysis of metabolic network properties (e.g. structure, regulation, robustness, and fragility), phenotypic behavior discovery, and rational strain design for metabolic engineering application. This chapter focuses on the application of elementary mode analysis to reprogram microbial metabolic pathways for rational strain design and the metabolic pathway evolution of designed strains.

Genome-scale metabolic models: reconstruction and analysis

Metabolism can be defined as the complete set of chemical reactions that occur in living organisms in order to maintain life. Enzymes are the main players in this process as they are responsible for catalyzing the chemical reactions. The enzyme-reaction relationships can be used for the reconstruction of a network of reactions, which leads to a metabolic model of metabolism. A genome-scale metabolic network of chemical reactions that take place inside a living organism is primarily reconstructed from the information that is present in its genome and the literature and involves steps such as functional annotation of the genome, identification of the associated reactions and determination of their stoichiometry, assignment of localization, determination of the biomass composition, estimation of energy requirements, and definition of model constraints. This information can be integrated into a stoichiometric model of metabolism that can be used for detailed analysis of the metabolic potential of the organism using constraint-based modeling approaches and hence is valuable in understanding its metabolic capabilities.

Modeling formalisms in Systems Biology

Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future.

A survey on methods for modeling and analyzing integrated biological networks

Understanding how cellular systems build up integrated responses to their dynamically changing environment is one of the open questions in Systems Biology. Despite their intertwinement, signaling networks, gene regulation and metabolism have been frequently modeled independently in the context of well-defined subsystems. For this purpose, several mathematical formalisms have been developed according to the features of each particular network under study. Nonetheless, a deeper understanding of cellular behavior requires the integration of these various systems into a model capable of capturing how they operate as an ensemble. With the recent advances in the "omics" technologies, more data is becoming available and, thus, recent efforts have been driven toward this integrated modeling approach. We herein review and discuss methodological frameworks currently available for modeling and analyzing integrated biological networks, in particular metabolic, gene regulatory and signaling networks. These include network-based methods and Chemical Organization Theory, Flux-Balance Analysis and its extensions, logical discrete modeling, Petri Nets, traditional kinetic modeling, Hybrid Systems and stochastic models. Comparisons are also established regarding data requirements, scalability with network size and computational burden. The methods are illustrated with successful case studies in large-scale genome models and in particular subsystems of various organisms.

Genome-scale metabolic networks

During the last decade, models have been developed to characterize cellular metabolism at the level of an entire metabolic network. The main concept that underlies whole-network metabolic modeling is the identification and mathematical definition of constraints. Here, we review large-scale metabolic network modeling, in particular, stoichiometric- and constraint-based approaches. Although many such models have been reconstructed, few networks have been extensively validated and tested experimentally, and we focus on these. We describe how metabolic networks can be represented using stoichiometric matrices and well-defined constraints on metabolic fluxes. We then discuss relatively successful approaches, including flux balance analysis (FBA), pathway analysis, and common extensions or modifications to these approaches. Finally, we describe techniques for integrating these approaches with models of other biological processes.

Characterizing the metabolism of Dehalococcoides with a constraint-based model

Dehalococcoides strains respire a wide variety of chloro-organic compounds and are important for the bioremediation of toxic, persistent, carcinogenic, and ubiquitous ground water pollutants. In order to better understand metabolism and optimize their application, we have developed a pan-genome-scale metabolic network and constraint-based metabolic model of Dehalococcoides. The pan-genome was constructed from publicly available complete genome sequences of Dehalococcoides sp. strain CBDB1, strain 195, strain BAV1, and strain VS. We found that Dehalococcoides pan-genome consisted of 1118 core genes (shared by all), 457 dispensable genes (shared by some), and 486 unique genes (found in only one genome). The model included 549 metabolic genes that encoded 356 proteins catalyzing 497 gene-associated model reactions. Of these 497 reactions, 477 were associated with core metabolic genes, 18 with dispensable genes, and 2 with unique genes. This study, in addition to analyzing the metabolism of an environmentally important phylogenetic group on a pan-genome scale, provides valuable insights into Dehalococcoides metabolic limitations, low growth yields, and energy conservation. The model also provides a framework to anchor and compare disparate experimental data, as well as to give insights on the physiological impact of "incomplete" pathways, such as the TCA-cycle, CO(2) fixation, and cobalamin biosynthesis pathways. The model, referred to as iAI549, highlights the specialized and highly conserved nature of Dehalococcoides metabolism, and suggests that evolution of Dehalococcoides species is driven by the electron acceptor availability.

Prediction of metabolic function from limited data: Lumped hybrid cybernetic modeling (L-HCM)

Motivated by the need for a quick quantitative assessment of metabolic function without extensive data, we present an adaptation of the cybernetic framework, denoted as the lumped hybrid cybernetic model (L-HCM), which combines the attributes of the classical lumped cybernetic model (LCM) and the recently developed HCM. The basic tenet of L-HCM and HCM is the same, that is, they both view the uptake flux as being split among diverse pathways in an optimal way as a result of cellular regulation such that some chosen metabolic objective is realized. The L-HCM, however, portrays this flux distribution to occur in a hierarchical way, that is, first among lumped pathways, and next among individual elementary modes (EM) in each lumped pathway. Both splits are described by the cybernetic control laws using operational and structural return-on-investments, respectively. That is, the distribution of uptake flux at the first split is dynamically regulated according to environmental conditions, while the subsequent split is based purely on the stoichiometry of EMs. The resulting model is conveniently represented in terms of lumped pathways which are fully identified with respect to yield coefficients of all products unlike classical LCMs based on instinctive lumping. These characteristics enable the model to account for the complete set of EMs for arbitrarily large metabolic networks despite containing only a small number of parameters which can be identified using minimal data. However, the inherent conflict of questing for quantification of larger networks with smaller number of parameters cannot be resolved without a mechanism for parameter tuning of an empirical nature. In this work, this is accomplished by manipulating the relative importance of EMs by tuning the cybernetic control of mode-averaged enzyme activity with an empirical parameter. In a case study involving aerobic batch growth of Saccharomyces cerevisiae, L-HCM is compared with LCM. The former provides a much more satisfactory prediction than the latter when parameters are identified from a few primary metabolites. On the other hand, the classical model is more accurate than L-HCM when sufficient datasets are involved in parameter identification. In applying the two models to a chemostat scenario, L-HCM shows a reasonable prediction on metabolic shift from respiration to fermentation due to the Crabtree effect, which LCM predicts unsatisfactorily. While L-HCM appears amenable to expeditious estimates of metabolic function with minimal data, the more detailed dynamic models [such as HCM or those of Young et al. (Young et al., Biotechnol Bioeng, 2008; 100: 542-559)] are best suited for accurate treatment of metabolism when the potential of modern omic technology is fully realized. However, in view of the monumental effort surrounding the development of detailed models from extensive omic measurements, the preliminary insight into the behavior of a genotype and metabolic engineering directives that can come from L-HCM is indeed valuable.

A systems biology framework for modeling metabolic enzyme inhibition of Mycobacterium tuberculosis

BACKGROUND

Because metabolism is fundamental in sustaining microbial life, drugs that target pathogen-specific metabolic enzymes and pathways can be very effective. In particular, the metabolic challenges faced by intracellular pathogens, such as Mycobacterium tuberculosis, residing in the infected host provide novel opportunities for therapeutic intervention.

RESULTS

We developed a mathematical framework to simulate the effects on the growth of a pathogen when enzymes in its metabolic pathways are inhibited. Combining detailed models of enzyme kinetics, a complete metabolic network description as modeled by flux balance analysis, and a dynamic cell population growth model, we quantitatively modeled and predicted the dose-response of the 3-nitropropionate inhibitor on the growth of M. tuberculosis in a medium whose carbon source was restricted to fatty acids, and that of the 5'-O-(N-salicylsulfamoyl) adenosine inhibitor in a medium with low-iron concentration.

CONCLUSION

The predicted results quantitatively reproduced the experimentally measured dose-response curves, ranging over three orders of magnitude in inhibitor concentration. Thus, by allowing for detailed specifications of the underlying enzymatic kinetics, metabolic reactions/constraints, and growth media, our model captured the essential chemical and biological factors that determine the effects of drug inhibition on in vitro growth of M. tuberculosis cells.

Systematic development of hybrid cybernetic models: application to recombinant yeast co-consuming glucose and xylose

The hybrid cybernetic modeling approach of Kim et al. (Kim et al. [2008] Biotechnol. Prog., in press) views the substrate uptake flux in microorganisms as being distributed in a regulated way among different elementary modes (EMs) of a metabolic network, which intracellular fluxes related to the uptake rates by the pseudo-steady-state approximation on intracellular metabolites. While the conceptual development has been demonstrated by Kim et al. (Kim et al. [2008] Biotechnol. Prog., in press) using a rather simple example (i.e., Escherichia coli metabolizing a single substrate), its extension to a larger scale network involving multiple substrates results in serious overparameterization (which implies an excessive number of parameters relative to the measurements available to determine them). Through the case study of recombinant Saccharomyces yeast co-consuming glucose and xylose, we present a systematic way of formulating a minimal order hybrid cybernetic model (HCM) for a general metabolic network. The overparameterization problem mostly arising from a large number of EMs is avoided using a model reduction technique developed by Song and Ramkrishna (Song and Ramkrishna [2009a] Biotechnol. Bioeng. 102(2):554-568) where an original set of EMs is condensed to a much smaller subset. Detailed discussions follow on the issue of determining the minimal set of active modes needed for the description of the simultaneous consumption of multiple substrates. The developed HCM is compared with other metabolic models: macroscopic bioreaction models (Provost et al. [2006] Bioprocess Biosyt. Eng. 29(5-6):349-366), and dynamic flux balance analysis. It is shown that the HCM outperforms the other two as validated using various sets of fermentation data. The difference among the models is more dramatic in a situation such as the sequential utilization of glucose and xylose, which is observed under realistic fermentation conditions.

A hybrid model of anaerobic E. coli GJT001: combination of elementary flux modes and cybernetic variables

Flux balance analysis (FBA) in combination with the decomposition of metabolic networks into elementary modes has provided a route to modeling cellular metabolism. It is dependent, however, on the availability of external fluxes such as substrate uptake or growth rate before estimates can become available of intracellular fluxes. The framework classically does not allow modeling of metabolic regulation or the formulation of dynamic models except through dynamic measurement of external fluxes. The cybernetic modeling approach of Ramkrishna and coworkers provides a dynamic framework for modeling metabolic systems because of its focus on describing regulatory processes based on cybernetic arguments and hence has the capacity to describe both external and internal fluxes. In this article, we explore the alternative of developing hybrid models combining cybernetic models for the external fluxes with the flux balance approach for estimation of the internal fluxes. The approach has the merit of the simplicity of the early cybernetic models and hence computationally facile while also providing detailed information on intracellular fluxes. The hybrid model of this article is based on elementary mode decomposition of the metabolic network. The uptake rates for the various elementary modes are combined using global cybernetic variables based on maximizing substrate uptake rates. Estimation of intracellular metabolism is based on its stoichiometric coupling with the external fluxes under the assumption of (pseudo-) steady state conditions. The set of parameters of the hybrid model was estimated with the aid of nonlinear optimization routine, by fitting simulations with dynamic experimental data on concentrations of biomass, substrate, and fermentation products. The hybrid model estimations were tested with FBA (based on measured substrate uptake rate) for two different metabolic networks (one is a reduced network which fixes ATP contribution to the biomass and maintenance requirement of ATP, and the other network is a more complex network which has a separate reaction for maintenance.) for the same experiment involving anaerobic growth of E. coli GJT001. The hybrid model estimated glucose consumption and all fermentation byproducts to better than 10%. The FBA makes similar estimations of fermentation products, however, with the exception of succinate. The simulation results show that the global cybernetic variables alone can regulate the metabolic reactions obtaining a very satisfactory fit to the measured fermentation byproducts. In view of the hybrid model's ability to predict biomass growth and fermentation byproducts of anaerobic E. coli GJT001, this reduced order model offers a computationally efficient alternative to more detailed models of metabolism and hence useful for the simulation of bioreactors.