Constraint-based Modeling Research Articles

Metabolic flux configuration determination using information entropy.

Constraint-based models use steady-state mass balances to define a solution space of flux configurations, which can be narrowed down by measuring as many fluxes as possible. Due to loops and redundant pathways, this process typically yields multiple alternative solutions. To address this ambiguity, flux sampling can estimate the probability distribution of each flux, or a flux configuration can be singled out by further minimizing the sum of fluxes according to the assumption that cellular metabolism favors states where enzyme-related costs are economized. However, flux sampling is susceptible to artifacts introduced by thermodynamically infeasible cycles and is it not clear if the economy of fluxes assumption (EFA) is universally valid. Here, we formulated a constraint-based approach, MaxEnt, based on the principle of maximum entropy, which in this context states that if more than one flux configuration is consistent with a set of experimentally measured fluxes, then the one with the minimum amount of unwarranted assumptions corresponds to the best estimation of the non-observed fluxes. We compared MaxEnt predictions to Escherichia coli and Saccharomyces cerevisiae publicly available flux data. We found that the mean square error (MSE) between experimental and predicted fluxes by MaxEnt and EFA-based methods are three orders of magnitude lower than the median of 1,350,000 MSE values obtained using flux sampling. However, only MaxEnt and flux sampling correctly predicted flux through E. coli’s glyoxylate cycle, whereas EFA-based methods, in general, predict no flux cycles. We also tested MaxEnt predictions at increasing levels of overflow metabolism. We found that MaxEnt accuracy is not affected by overflow metabolism levels, whereas the EFA-based methods show a decreasing performance. These results suggest that MaxEnt is less sensitive than flux sampling to artifacts introduced by thermodynamically infeasible cycles and that its predictions are less susceptible to overfitting than EFA-based methods.

Flux Coupling and the Objective Functions' Length in EFMs.

Structural analysis of constraint-based metabolic network models attempts to find the network’s properties by searching for subsets of suitable modes or Elementary Flux Modes (EFMs). One useful approach is based on Linear Program (LP) techniques, which introduce an objective function to convert the stoichiometric and thermodynamic constraints into a linear program (LP), using additional constraints to generate different nontrivial modes. This work introduces FLFS-FC (Fixed Length Function Sampling with Flux Coupling), a new approach to increase the efficiency of generation of large sets of different EFMs for the network. FLFS-FC is based on the importance of the length of the objective functions used in the associated LP problem and the imposition of additional negative constraints. Our proposal overrides some of the known drawbacks associated with the EFM extraction, such as the appearance of unfeasible problems or multiple repeated solutions arising from different LP problems.

Scalable computation of intracellular metabolite concentrations

Quantitative characterization of intracellular metabolite concentrations is central to predictive models of cellular functions. Current constraint-based models of metabolism and macromolecular expression provide genotype-phenotype predictions without accounting for intracellular concentrations using simplifying assumptions and optimality principles. However, optimality principles do not generally apply under stress conditions, rendering these predictions unreliable. Incorporation of intracellular concentrations into constraint-based or kinetic models of cellular functions introduces nonlinearities that are computationally challenging to handle, limiting their applicability to small-scale biological networks. Here, we introduce tractable computational techniques to characterize intracellular metabolite concentrations within a constraint-based modeling framework. This model provides a feasible concentration set, which can generally be nonconvex and disconnected. We examine three approaches based on polynomial optimization, random sampling, and global optimization. We leverage the sparsity and algebraic structure of the underlying biophysical models to enhance the computational efficiency of these techniques. We then compare their performance in two case studies, showing that the global-optimization formulation exhibits more desirable scaling properties than the random-sampling and polynomial-optimization formulation, and, thus, is a promising candidate for handling large-scale metabolic networks.

Genome-Scale Metabolic Modeling for Unraveling Molecular Mechanisms of High Threat Pathogens.

Pathogens give rise to a wide range of diseases threatening global health and hence drawing public health agencies' attention to establish preventative and curative solutions. Genome-scale metabolic modeling is ever increasingly used tool for biomedical applications including the elucidation of antibiotic resistance, virulence, single pathogen mechanisms and pathogen-host interaction systems. With this approach, the sophisticated cellular system of metabolic reactions inside the pathogens as well as between pathogen and host cells are represented in conjunction with their corresponding genes and enzymes. Along with essential metabolic reactions, alternate pathways and fluxes are predicted by performing computational flux analyses for the growth of pathogens in a very short time. The genes or enzymes responsible for the essential metabolic reactions in pathogen growth are regarded as potential drug targets, as a priori guide to researchers in the pharmaceutical field. Pathogens alter the key metabolic processes in infected host, ultimately the objective of these integrative constraint-based context-specific metabolic models is to provide novel insights toward understanding the metabolic basis of the acute and chronic processes of infection, revealing cellular mechanisms of pathogenesis, identifying strain-specific biomarkers and developing new therapeutic approaches including the combination drugs. The reaction rates predicted during different time points of pathogen development enable us to predict active pathways and those that only occur during certain stages of infection, and thus point out the putative drug targets. Among others, fatty acid and lipid syntheses reactions are recent targets of new antimicrobial drugs. Genome-scale metabolic models provide an improved understanding of how intracellular pathogens utilize the existing microenvironment of the host. Here, we reviewed the current knowledge of genome-scale metabolic modeling in pathogen cells as well as pathogen host interaction systems and the promising applications in the extension of curative strategies against pathogens for global preventative healthcare.

Simulating chain elongation with constraint-based metabolic modelling

Contribution to the International Chain Elongation Conference 2020 | ICEC 2020. An abstract can be found in the right column.

Model-driven design allows growth of Mycoplasma pneumoniae on serum-free media

Mycoplasma pneumoniae is a slow-growing, human pathogen that causes atypical pneumonia. Because it lacks a cell wall, many antibiotics are ineffective. Due to its reduced genome and dearth of many biosynthetic pathways, this fastidious bacterium depends on rich, undefined medium for growth, which makes large-scale cultivation challenging and expensive. To understand factors limiting growth, we developed a genome-scale, constraint-based model of M. pneumoniae called iEG158_mpn to describe the metabolic potential of this bacterium. We have put special emphasis on cell membrane formation to identify key lipid components to maximize bacterial growth. We have used this knowledge to predict essential components validated with in vitro serum-free media able to sustain growth. Our findings also show that glycolysis and lipid metabolism are much less efficient under hypoxia; these findings suggest that factors other than metabolism and membrane formation alone affect the growth of M. pneumoniae. Altogether, our modelling approach allowed us to optimize medium composition, enabled growth in defined media and streamlined operational requirements, thereby providing the basis for stable, reproducible and less expensive production.

A constraint-based modeling of negative polarity items in result clause constructions in Romanian

SummaryThe paper discusses the occurrence of emphatic negative polarity items (NPIs) in high degree result clause constructions. We will identify four distributional patterns for Romanian emphatic NPIs. These will range from NPIs that only occur occasionally in result constructions to NPIs that are bound to such constructions and even do not show any truth-conditionally relevant semantic contribution. We reformulate a scalar, pragmatic theory of NPIs in a constraint-based, representational framework,Lexical Resource Semantics. We propose a scalar extension of a standard semantics of result clauses in order to capture the high degree, i.e. intensification readings. The constraint-based, representational perspective of this paper allows for an elegant modeling of the data: (i) We can capture the four distributional patterns as a lexical property of the discussed NPIs. (ii) The semantics and pragmatics of Romanian result clause constructions is accounted for by lexical properties of the result clause complementizers. (iii) A scalar analysis of emphatic NPIs can be applied in embedded clauses and even when the NPI itself does not contribute to the at-issue content of the overall utterance.

Systematically gap-filling the genome-scale metabolic model of CHO cells.

Chinese hamster ovary (CHO) cells are the leading cell factories for producing recombinant proteins in the biopharmaceutical industry. In this regard, constraint-based metabolic models are useful platforms to perform computational analysis of cell metabolism. These models need to be regularly updated in order to include the latest biochemical data of the cells, and to increase their predictive power. Here, we provide an update to iCHO1766, the metabolic model of CHO cells. We expanded the existing model of Chinese hamster metabolism with the help of four gap-filling approaches, leading to the addition of 773 new reactions and 335 new genes. We incorporated these into an updated genome-scale metabolic network model of CHO cells, named iCHO2101. In this updated model, the number of reactions and pathways capable of carrying flux is substantially increased. The present CHO model is an important step towards more complete metabolic models of CHO cells.

Intelligent Feedback on Hypothesis Testing

Hypothesis testing involves a complex stepwise procedure that is challenging for many students in introductory university statistics courses. In this paper we assess how feedback from an Intelligent Tutoring System can address the logic of hypothesis testing and whether such feedback contributes to first-year social sciences students’ proficiency in carrying out hypothesis tests. Feedback design combined elements of the model-tracing and constraint-based modeling paradigms, to address both the individual steps as well as the relations between steps. To evaluate the feedback, students in an experimental group (N = 163) received the designed intelligent feedback in six hypothesis-testing construction tasks, while students in a control group (N = 151) only received stepwise verification feedback in these tasks. Results showed that students receiving intelligent feedback spent more time on the tasks, solved more tasks and made fewer errors than students receiving only verification feedback. These positive results did not transfer to follow-up tasks, which might be a consequence of the isolated nature of these tasks. We conclude that the designed feedback may support students in learning to solve hypothesis-testing construction tasks independently and that it facilitates the creation of more hypothesis-testing construction tasks.

Assessment of transcriptomic constraint-based methods for central carbon flux inference.

Determining intracellular metabolic flux through isotope labeling techniques such as 13C metabolic flux analysis (13C-MFA) incurs significant cost and effort. Previous studies have shown transcriptomic data coupled with constraint-based metabolic modeling can determine intracellular fluxes that correlate highly with 13C-MFA measured fluxes and can achieve higher accuracy than constraint-based metabolic modeling alone. These studies, however, used validation data limited to E. coli and S. cerevisiae grown on glucose, with significantly similar flux distribution for central metabolism. It is unclear whether those results apply to more diverse metabolisms, and therefore further, extensive validation is needed. In this paper, we formed a dataset of transcriptomic data coupled with corresponding 13C-MFA flux data for 21 experimental conditions in different unicellular organisms grown on varying carbon substrates and conditions. Three computational flux-balance analysis (FBA) methods were comparatively assessed. The results show when uptake rates of carbon sources and key metabolites are known, transcriptomic data provides no significant advantage over constraint-based metabolic modeling (average correlation coefficients, transcriptomic E-Flux2 0.725 and SPOT 0.650 vs non-transcriptomic pFBA 0.768). When uptake rates are unknown, however, predictions obtained utilizing transcriptomic data are generally good and significantly better than those obtained using constraint-based metabolic modeling alone (E-Flux2 0.385 and SPOT 0.583 vs pFBA 0.237). Thus, transcriptomic data coupled with constraint-based metabolic modeling is a promising method to obtain intracellular flux estimates in microorganisms, particularly in cases where uptake rates of key metabolites cannot be easily determined, such as for growth in complex media or in vivo conditions.

Constraint-based and Fuzzy Logic Student Modeling for Arabic Grammar

Computer-Assisted Language Learning (CALL) are computer-based tutoring systems that deal with linguistic skills. Adding intelligence in such systems is mainly based on using Natural Language Processing (NLP) tools to diagnose student errors, especially in language grammar. However, most such systems do not consider the modeling of student competence in linguistic skills, especially for the Arabic language. In this paper, we will deal with basic grammar concepts of the Arabic language taught for the fourth grade of the elementary school in Egypt. This is through Arabic Grammar Trainer (AGTrainer) which is an Intelligent CALL. The implemented system (AGTrainer) trains the students through different questions that deal with the different concepts and have different difficulty levels. Constraint-based student modeling (CBSM) technique is used as a short-term student model. CBSM is used to define in small grain level the different grammar skills through the defined skill structures. The main contribution of this paper is the hierarchal representation of the system's basic grammar skills as domain knowledge. That representation is used as a mechanism for efficiently checking constraints to model the student knowledge and diagnose the student errors and identify their cause. In addition, satisfying constraints and the number of trails the student takes for answering each question and fuzzy logic decision system are used to determine the student learning level for each lesson as a long-term model. The results of the evaluation showed the system's effectiveness in learning in addition to the satisfaction of students and teachers with its features and abilities.

Defining the nutritional input for genome-scale metabolic models: A roadmap.

The reconstruction and application of genome-scale metabolic network models is a central topic in the field of systems biology with numerous applications in biotechnology, ecology, and medicine. However, there is no agreed upon standard for the definition of the nutritional environment for these models. The objective of this article is to provide a guideline and a clear paradigm on how to translate nutritional information into an in-silico representation of the chemical environment. Step-by-step procedures explain how to characterise and categorise the nutritional input and to successfully apply it to constraint-based metabolic models. In parallel, we illustrate the proposed procedure with a case study of the growth of Escherichia coli in a complex nutritional medium and show that an accurate representation of the medium is crucial for physiological predictions. The proposed framework will assist researchers to expand their existing metabolic models of their microbial systems of interest with detailed representations of the nutritional environment, which allows more accurate and reproducible predictions of microbial metabolic processes.

Constraint bubbles and affine regions

We propose to enhance the capability of standard free-surface flow simulators with efficient support for immersed bubbles through two new models: constraint-based bubbles and affine fluid regions. Unlike its predecessors, our constraint-based model entirely dispenses with the need for advection or projection inside zero-density bubbles, with extremely modest additional computational overhead that is proportional to the surface area of all bubbles. This surface-only approach is easy to implement, realistically captures many familiar bubble behaviors, and even allows two or more distinct liquid bodies to correctly interact across completely unsimulated air. We augment this model with a per-bubble volume-tracking and correction framework to minimize the cumulative effects of gradual volume drift. To support bubbles with non-zero densities, we propose a novel reduced model for an irregular fluid region with a single pointwise incompressible affine vector field. This model requires only 11 interior velocity degrees of freedom per affine fluid region in 3D, and correctly reproduces buoyant, stationary, and sinking behaviors of a secondary fluid phase with non-zero density immersed in water. Since the pressure projection step in both the above schemes is a slightly modified Poisson-style system, we propose novel Multigrid-based preconditioners for Conjugate Gradients for fast numerical solutions of our new discretizations. Furthermore, we observe that by enforcing an incompressible affine vector field over a coalesced set of grid cells, our reduced model is effectively an irregular coarse super-cell. This offers a convenient and flexible adaptive coarsening strategy that integrates readily with the standard staggered grid approach for fluid simulation, yet supports coarsened regions that are arbitrary voxelized shapes, and provides an analytically divergence-free interior. We demonstrate its effectiveness with a new adaptive liquid simulator whose interior regions are coarsened into a mix of tiles with regular and irregular shapes.

In silico co-factor balance estimation using constraint-based modelling informs metabolic engineering in Escherichia coli.

In the growing field of metabolic engineering, where cells are treated as 'factories' that synthesize industrial compounds, it is essential to consider the ability of the cells' native metabolism to accommodate the demands of synthetic pathways, as these pathways will alter the homeostasis of cellular energy and electron metabolism. From the breakdown of substrate, microorganisms activate and reduce key co-factors such as ATP and NAD(P)H, which subsequently need to be hydrolysed and oxidized, respectively, in order to restore cellular balance. A balanced supply and consumption of such co-factors, here termed co-factor balance, will influence biotechnological performance. To aid the strain selection and design process, we used stoichiometric modelling (FBA, pFBA, FVA and MOMA) and the Escherichia coli (E.coli) core stoichiometric model to investigate the network-wide effect of butanol and butanol precursor production pathways differing in energy and electron demand on product yield. An FBA-based co-factor balance assessment (CBA) algorithm was developed to track and categorise how ATP and NAD(P)H pools are affected in the presence of a new pathway. CBA was compared to the balance calculations proposed by Dugar et al. (Nature Biotechnol. 29 (12), 1074-1078). Predicted solutions were compromised by excessively underdetermined systems, displaying greater flexibility in the range of reaction fluxes than experimentally measured by 13C-metabolic flux analysis (MFA) and the appearance of unrealistic futile co-factor cycles. With the assumption that futile cycles are tightly regulated in reality, the FBA models were manually constrained in a step-wise manner. Solutions with minimal futile cycling diverted surplus energy and electrons towards biomass formation. As an alternative, the use of loopless FBA or constraining the models with measured flux ranges were tried but did not prevent futile co-factor cycles. The results highlight the need to account for co-factor imbalance and confirm that better-balanced pathways with minimal diversion of surplus towards biomass formation present the highest theoretical yield. The analysis also suggests that ATP and NAD(P)H balancing cannot be assessed in isolation from each other, or even from the balance of additional co-factors such as AMP and ADP. We conclude that, through revealing the source of co-factor imbalance CBA can facilitate pathway and host selection when designing new biocatalysts for implementation by metabolic engineering.

Metabolic Modelling as a Framework for Metabolomics Data Integration and Analysis.

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

Characterization of maximal enzyme catalytic rates in central metabolism of Arabidopsis thaliana.

Availability of plant-specific enzyme kinetic data is scarce, limiting the predictive power of metabolic models and precluding identification of genetic factors of enzyme properties. Enzyme kinetic data are measured in vitro, often under non-physiological conditions, and conclusions elicited from modeling warrant caution. Here we estimate maximal in vivo catalytic rates for 168 plant enzymes, including photosystems I and II, cytochrome-b6f complex, ATP-citrate synthase, sucrose-phosphate synthase as well as enzymes from amino acid synthesis with previously undocumented enzyme kinetic data in BRENDA. The estimations are obtained by integrating condition-specific quantitative proteomics data, maximal rates of selected enzymes, growth measurements from Arabidopsis thaliana rosette with and fluxes through canonical pathways in a constraint-based model of leaf metabolism. In comparison to findings in Escherichia coli, we demonstrate weaker concordance between the plant-specific in vitro and in vivo enzyme catalytic rates due to a low degree of enzyme saturation. This is supported by the finding that concentrations of nicotinamide adenine dinucleotide (phosphate), adenosine triphosphate and uridine triphosphate, calculated based on our maximal in vivo catalytic rates, and available quantitative metabolomics data are below reported values and, therefore, indicate undersaturation of respective enzymes. Our findings show that genome-wide profiling of enzyme kinetic properties is feasible in plants, paving the way for understanding resource allocation.

Model-assisted identification of metabolic engineering strategies for Jatropha curcas lipid pathways.

Efficient approaches to increase plant lipid production are necessary to meet current industrial demands for this important resource. While Jatropha curcas cell culture can be used for in vitro lipid production, scaling up the system for industrial applications requires an understanding of how growth conditions affect lipid metabolism and yield. Here we present a bottom-up metabolic reconstruction of J.curcas supported with labeling experiments and biomass characterization under three growth conditions. We show that the metabolic model can accurately predict growth and distribution of fluxes in cell cultures and use these findings to pinpoint energy expenditures that affect lipid biosynthesis and metabolism. In addition, by using constraint-based modeling approaches we identify network reactions whose joint manipulation optimizes lipid production. The proposed model and computational analyses provide a stepping stone for future rational optimization of other agronomically relevant traits in J.curcas.

Towards an ecological-dynamics design framework for embodied-interaction conceptual learning: the case of dynamic mathematics environments

Designers of educational modules for conceptual learning often rely on procedural frameworks to chart out interaction mechanics through which users will develop target understandings. To date, however, there has been no systematic comparative evaluation of such frameworks in terms of their consequences for learning. This lack of empirical evaluation, we submit, is due to the intellectual challenge of pinning down in what fundamental sense these various frameworks differ and, therefore, along which parameters to conduct controlled comparative experimentation. Toward an empirical evaluation of educational-technology design frameworks, this conceptual paper considers the case of dynamic mathematics environments (DME), interactive modules for learning curricular content through manipulating virtual objects. We consider user activities in two paradigmatic DME genres that utilize similar HCI yet different mechanics. To compare these mechanics, we draw from complex dynamic systems theory a constraint-based model of embodied interaction. Task analyses suggest that whereas in one DME genre (GeoGebra) the interaction constraints are a priori inherent in the environment, in another DME genre (Mathematics Imagery Trainer) the constraints are ad hoc emergent in the task. We conjecture differential learning effects of these distinct constraint regimes, concluding that ad hoc emergent task constraints may better facilitate the naturalistic development of cognitive structures grounding targeted conceptual learning. We outline a future empirical research design to compare the pedagogical entailments of these two design frameworks.

A system architecture for parallel analysis of flux-balanced metabolic pathways

Elementary flux mode (EFM) analysis is a well-studied method in constraint-based modeling of metabolic networks. In EFM analysis, a network is decomposed into minimal functional pathways based on the assumption of balanced metabolic fluxes. In this paper, a system architecture is proposed that approximately models the functionality of metabolic networks. The AND/OR graph model is used to represent the metabolic network and each processing element in the system emulates the functionality of a metabolite. The system is implemented on a graphics processing unit (GPU) as the hardware platform using CUDA environment. The proposed architecture takes advantage of the inherent parallelism in the network structure in terms of both pathway and metabolite traversal. The function of each element is defined such that it can find flux-balanced pathways. Pathways in both small and large metabolic networks are applied to the proposed architecture and the results are discussed.

A Systems-Based Approach for Cyanide Overproduction by Bacillus megaterium for Gold Bioleaching Enhancement.

With the constant accumulation of electronic waste, extracting precious metals contained therein is becoming a major challenge for sustainable development. Bacillus megaterium is currently one of the microbes used for the production of cyanide, which is the main leaching agent for gold recovery. The present study aimed to propose a strategy for metabolic engineering of B. megaterium to overproduce cyanide, and thus ameliorate the bioleaching process. For this, we employed constraint-based modeling, running in silico simulations on iJA1121, the genome-scale metabolic model of B. megaterium DSM319. Flux balance analysis (FBA) was initially used to identify amino acids to be added to the culture medium. Considering cyanide as the desired product, we used growth-coupled methods, constrained minimal cut sets (cMCSs) and OptKnock to identify gene inactivation targets. To identify gene overexpression targets, flux scanning based on enforced objective flux (FSEOF) was performed. Further analysis was carried out on the identified targets to determine compounds with beneficial regulatory effects. We have proposed a chemical-defined medium for accelerating cyanide production on the basis of microplate assays to evaluate the components with the greatest improving effects. Accordingly, the cultivation of B. megaterium DSM319 in a chemically-defined medium with 5.56 mM glucose as the carbon source, and supplemented with 413 μM cysteine, led to the production of considerably increased amounts of cyanide. Bioleaching experiments were successfully performed in this medium to recover gold and copper from telecommunication printed circuit boards. The results of inductively coupled plasma (ICP) analysis confirmed that gold recovery peaked out at around 55% after 4 days, whereas copper recovery continued to increase for several more days, peaking out at around 85%. To further validate the bioleaching results, FESEM, XRD, FTIR, and EDAX mapping analyses were performed. We concluded that the proposed strategy represents a viable route for improving the performance of the bioleaching processes.