Thermodynamic analysis of regulation in metabolic networks using constraint-based modeling

Reaction thermodynamics as a constraint on piscine steroidogenesis flux distributions

While a considerable amount is known of the dynamics of piscine steroidogenesis during reproduction, the influence of thermodynamics constraints on its control has not been studied. In this manuscript, Gibbs free energy change of reactions was calculated for piscine steroidogenesis using the in silico eQuilibrator thermodynamics calculator. The analysis identified cytochrome P450 (cyp450) oxidoreductase reactions to have more negative Gibbs free energy changes relative to hydroxysteroid (HSD) and transferase reactions. In addition, a more favorable Gibbs free energy change was predicted for the Δ5 (cyp450 catalyzed) vs. Δ4 (HSD catalyzed) steroidogenesis branch-point, which converts pregnenolone to 17α-hydroxypregnenolone or progesterone respectively. Comparison of in silico predictions with in vivo experimentally measured flux across the Δ5 vs. Δ4 branch-point showed higher flux through the thermodynamically more favorable Δ5 pathway in reproducing or spawning vs. non-spawning fathead minnows (Pimephales promelas). However, the exposure of fish to endocrine stressors such as hypoxia or the synthetic estrogen 17α-ethinylestradiol (EE2), resulted in increased flux through both Δ5 and Δ4 pathways, indicating an adaptive response to increase steroidogenic redundancy. The correspondence of elevated flux through the Δ5 branch-point in spawning fish indicated the use of a thermodynamically favorable pathway to optimize steroid hormone productions during reproduction. We hypothesize that such selective use of a thermodynamically favorable steroidogenesis pathway may conserve reduced equivalents or transcriptional costs for investment to other biosynthetic or catabolic reactions to support reproduction. If generalizable, such an approach can provide novel insights into the structural principles and regulation of steroidogenesis or other metabolic pathways.

Thermodynamically consistent estimation of Gibbs free energy from data: data reconciliation approach

MOTIVATION

Thermodynamic analysis of biological reaction networks requires the availability of accurate and consistent values of Gibbs free energies of reaction and formation. These Gibbs energies can be measured directly via the careful design of experiments or can be computed from the curated Gibbs free energy databases. However, the computed Gibbs free energies of reactions and formations do not satisfy the thermodynamic constraints due to the compounding effect of measurement errors in the experimental data. The propagation of these errors can lead to a false prediction of pathway feasibility and uncertainty in the estimation of thermodynamic parameters.

RESULTS

This work proposes a data reconciliation framework for thermodynamically consistent estimation of Gibbs free energies of reaction, formation and group contributions from experimental data. In this framework, we formulate constrained optimization problems that reduce measurement errors and their effects on the estimation of Gibbs energies such that the thermodynamic constraints are satisfied. When a subset of Gibbs free energies of formations is unavailable, it is shown that the accuracy of their resulting estimates is better than that of existing empirical prediction methods. Moreover, we also show that the estimation of group contributions can be improved using this approach. Further, we provide guidelines based on this approach for performing systematic experiments to estimate unknown Gibbs formation energies.

AVAILABILITY AND IMPLEMENTATION

The MATLAB code for the executing the proposed algorithm is available for free on the GitHub repository: https://github.com/samansalike/DR-thermo.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

In Silico Knockout Screening of Plasmodium falciparum Reactions and Prediction of Novel Essential Reactions by Analysing the Metabolic Network

Malaria is an infectious disease that affects close to half a million individuals every year and Plasmodium falciparum is a major cause of malaria. The treatment of this disease could be done effectively if the essential enzymes of this parasite are specifically targeted. Nevertheless, the development of the parasite in resisting existing drugs now makes discovering new drugs a core responsibility. In this study, a novel computational model that makes the prediction of new and validated antimalarial drug target cheaper, easier, and faster has been developed. We have identified new essential reactions as potential targets for drugs in the metabolic network of the parasite. Among the top seven (7) predicted essential reactions, four (4) have been previously identified in earlier studies with biological evidence and one (1) has been with computational evidence. The results from our study were compared with an extensive list of seventy-seven (77) essential reactions with biological evidence from a previous study. We present a list of thirty-one (31) potential candidates for drug targets in Plasmodium falciparum which includes twenty-four (24) new potential candidates for drug targets.

Quantifying the entropic cost of cellular growth control

Viewing the ways a living cell can organize its metabolism as the phase space of a physical system, regulation can be seen as the ability to reduce the entropy of that space by selecting specific cellular configurations that are, in some sense, optimal. Here we quantify the amount of regulation required to control a cell's growth rate by a maximum-entropy approach to the space of underlying metabolic phenotypes, where a configuration corresponds to a metabolic flux pattern as described by genome-scale models. We link the mean growth rate achieved by a population of cells to the minimal amount of metabolic regulation needed to achieve it through a phase diagram that highlights how growth suppression can be as costly (in regulatory terms) as growth enhancement. Moreover, we provide an interpretation of the inverse temperature β controlling maximum-entropy distributions based on the underlying growth dynamics. Specifically, we show that the asymptotic value of β for a cell population can be expected to depend on (i) the carrying capacity of the environment, (ii) the initial size of the colony, and (iii) the probability distribution from which the inoculum was sampled. Results obtained for E. coli and human cells are found to be remarkably consistent with empirical evidence.

Quantification of Microbial Phenotypes

Metabolite profiling technologies have improved to generate close to quantitative metabolomics data, which can be employed to quantitatively describe the metabolic phenotype of an organism. Here, we review the current technologies available for quantitative metabolomics, present their advantages and drawbacks, and the current challenges to generate fully quantitative metabolomics data. Metabolomics data can be integrated into metabolic networks using thermodynamic principles to constrain the directionality of reactions. Here we explain how to estimate Gibbs energy under physiological conditions, including examples of the estimations, and the different methods for thermodynamics-based network analysis. The fundamentals of the methods and how to perform the analyses are described. Finally, an example applying quantitative metabolomics to a yeast model by 13C fluxomics and thermodynamics-based network analysis is presented. The example shows that (1) these two methods are complementary to each other; and (2) there is a need to take into account Gibbs energy errors. Better estimations of metabolic phenotypes will be obtained when further constraints are included in the analysis.

Quantitative assessment of thermodynamic constraints on the solution space of genome-scale metabolic models

Constraint-based methods provide powerful computational techniques to allow understanding and prediction of cellular behavior. These methods rely on physiochemical constraints to eliminate infeasible behaviors from the space of available behaviors. One such constraint is thermodynamic feasibility, the requirement that intracellular flux distributions obey the laws of thermodynamics. The past decade has seen several constraint-based methods that interpret this constraint in different ways, including those that are limited to small networks, rely on predefined reaction directions, and/or neglect the relationship between reaction free energies and metabolite concentrations. In this work, we utilize one such approach, thermodynamics-based metabolic flux analysis (TMFA), to make genome-scale, quantitative predictions about metabolite concentrations and reaction free energies in the absence of prior knowledge of reaction directions, while accounting for uncertainties in thermodynamic estimates. We applied TMFA to a genome-scale network reconstruction of Escherichia coli and examined the effect of thermodynamic constraints on the flux space. We also assessed the predictive performance of TMFA against gene essentiality and quantitative metabolomics data, under both aerobic and anaerobic, and optimal and suboptimal growth conditions. Based on these results, we propose that TMFA is a useful tool for validating phenotypes and generating hypotheses, and that additional types of data and constraints can improve predictions of metabolite concentrations.

Systematic applications of metabolomics in metabolic engineering

The goals of metabolic engineering are well-served by the biological information provided by metabolomics: information on how the cell is currently using its biochemical resources is perhaps one of the best ways to inform strategies to engineer a cell to produce a target compound. Using the analysis of extracellular or intracellular levels of the target compound (or a few closely related molecules) to drive metabolic engineering is quite common. However, there is surprisingly little systematic use of metabolomics datasets, which simultaneously measure hundreds of metabolites rather than just a few, for that same purpose. Here, we review the most common systematic approaches to integrating metabolite data with metabolic engineering, with emphasis on existing efforts to use whole-metabolome datasets. We then review some of the most common approaches for computational modeling of cell-wide metabolism, including constraint-based models, and discuss current computational approaches that explicitly use metabolomics data. We conclude with discussion of the broader potential of computational approaches that systematically use metabolomics data to drive metabolic engineering.

Variably saturated flow and multicomponent biogeochemical reactive transport modeling of a uranium bioremediation field experiment

Three-dimensional, coupled variably saturated flow and biogeochemical reactive transport modeling of a 2008 in situ uranium bioremediation field experiment is used to better understand the interplay of transport and biogeochemical reactions controlling uranium behavior under pulsed acetate amendment, seasonal water table variation, spatially variable physical (hydraulic conductivity, porosity) and geochemical (reactive surface area) material properties. While the simulation of the 2008 Big Rusty acetate biostimulation field experiment in Rifle, Colorado was generally consistent with behaviors identified in previous field experiments at the Rifle IFRC site, the additional process and property detail provided several new insights. A principal conclusion from this work is that uranium bioreduction is most effective when acetate, in excess of the sulfate-reducing bacteria demand, is available to the metal-reducing bacteria. The inclusion of an initially small population of slow growing sulfate-reducing bacteria identified in proteomic analyses led to an additional source of Fe(II) from the dissolution of Fe(III) minerals promoted by biogenic sulfide. The falling water table during the experiment significantly reduced the saturated thickness of the aquifer and resulted in reactants and products, as well as unmitigated uranium, in the newly unsaturated vadose zone. High permeability sandy gravel structures resulted in locally high flow rates in the vicinity of injection wells that increased acetate dilution. In downgradient locations, these structures created preferential flow paths for acetate delivery that enhanced local zones of TEAP reactivity and subsidiary reactions. Conversely, smaller transport rates associated with the lower permeability lithofacies (e.g., fine) and vadose zone were shown to limit acetate access and reaction. Once accessed by acetate, however, these same zones limited subsequent acetate dilution and provided longer residence times that resulted in higher concentrations of TEAP reaction products when terminal electron donors and acceptors were not limiting. Finally, facies-based porosity and reactive surface area variations were shown to affect aqueous uranium concentration distributions with localized effects of the fine lithofacies having the largest impact on U(VI) surface complexation. The ability to model the comprehensive biogeochemical reaction network, and spatially and temporally variable processes, properties, and conditions controlling uranium behavior during engineered bioremediation in the naturally complex Rifle IFRC subsurface system required a subsurface simulator that could use the large memory and computational performance of a massively parallel computer. In this case, the eSTOMP simulator, operating on 128 processor cores for 12h, was used to simulate the 110-day field experiment and 50 days of post-biostimulation behavior.

A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks

We derive a convex optimization problem on a steady-state nonequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a new variational principle for biochemical networks that can be implemented in a computationally tractable manner. We derive the Lagrange dual of the optimization problem and use strong duality to demonstrate that a biochemical analogue of Tellegen's theorem holds at optimality. Each optimal flux is dependent on a free parameter that we relate to an elementary kinetic parameter when mass action kinetics is assumed.

In situ to in silico and back: elucidating the physiology and ecology of Geobacter spp. using genome-scale modelling

There is a wide diversity of unexplored metabolism encoded in the genomes of microorganisms that have an important environmental role. Genome-scale metabolic modelling enables the individual reactions that are encoded in annotated genomes to be organized into a coherent whole, which can then be used to predict metabolic fluxes that will optimize cell function under a range of conditions. In this Review, we summarize a series of studies in which genome-scale metabolic modelling of Geobacter spp. has resulted in an in-depth understanding of their central metabolism and ecology. A similar iterative modelling and experimental approach could accelerate elucidation of the physiology and ecology of other microorganisms inhabiting a diversity of environments, and could guide optimization of the practical applications of these species.