Predicting Nash equilibria for microbial metabolic interactions.

MOTIVATION: Microbial metabolic interactions impact ecosystems, human health and biotechnology profoundly. However, their determination remains elusive, invoking an urgent need for predictive models seamlessly integrating metabolism with evolutionary principles that shape community interactions. RESULTS: Inspired by the evolutionary game theory, we formulated a bi-level optimization framework termed NECom for which any feasible solutions are Nash equilibria of microbial community metabolic models with/without an outer-level (community) objective function. Distinct from discrete matrix games, NECom models the continuous interdependent strategy space of metabolic fluxes. We showed that NECom successfully predicted several classical games in the context of metabolic interactions that were falsely or incompletely predicted by existing methods, including prisoner's dilemma, snowdrift and cooperation. The improved capability originates from the novel formulation to prevent 'forced altruism' hidden in previous static algorithms while allowing for sensing all potential metabolite exchanges to determine evolutionarily favorable interactions between members, a feature missing in dynamic methods. The results provided insights into why mutualism is favorable despite seemingly costly cross-feeding metabolites and demonstrated similarities and differences between games in the continuous metabolic flux space and matrix games. NECom was then applied to a reported algae-yeast co-culture system that shares typical cross-feeding features of lichen, a model system of mutualism. 488 growth conditions corresponding to 3221 experimental data points were simulated. Without training any parameters using the data, NECom is more predictive of species' growth rates given uptake rates compared with flux balance analysis with an overall 63.5% and 81.7% reduction in root-mean-square error for the two species respectively. AVAILABILITY AND IMPLEMENTATION: Simulation code and data are available at https://github.com/Jingyi-Cai/NECom.git. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Bacterial colonization reprograms the neonatal gut metabolome.

Initial microbial colonization and later succession in the gut of human infants are linked to health and disease later in life. The timing of the appearance of the first gut microbiome, and the consequences for the early life metabolome, are just starting to be defined. Here, we evaluated the gut microbiome, proteome and metabolome in 88 African-American newborns using faecal samples collected in the first few days of life. Gut bacteria became detectable using molecular methods by 16 h after birth. Detailed analysis of the three most common species, Escherichia coli, Enterococcus faecalis and Bacteroides vulgatus, did not suggest a genomic signature for neonatal gut colonization. The appearance of bacteria was associated with reduced abundance of approximately 50 human proteins, decreased levels of free amino acids and an increase in products of bacterial fermentation, including acetate and succinate. Using flux balance modelling and in vitro experiments, we provide evidence that fermentation of amino acids provides a mechanism for the initial growth of E. coli, the most common early colonizer, under anaerobic conditions. These results provide a deep characterization of the first microbes in the human gut and show how the biochemical environment is altered by their appearance.

Metabolic Analyses of Nitrogen Fixation in the Soybean Microsymbiont Sinorhizobium fredii Using Constraint-Based Modeling.

Rhizobia are soil bacteria able to establish symbiosis with diverse host plants. Specifically, Sinorhizobium fredii is a soil bacterium that forms nitrogen-fixing root nodules in diverse legumes, including soybean. The strain S. fredii CCBAU45436 is a dominant sublineage of S. fredii that nodulates soybeans in alkaline-saline soils in the Huang-Huai-Hai Plain region of China. Here, we present a manually curated metabolic model of the symbiotic form of Sinorhizobium fredii CCBAU45436. A symbiosis reaction was defined to describe the specific soybean-microsymbiont association. The performance and quality of the reconstruction had a 70% score when assessed using a standardized genome-scale metabolic model test suite. The model was used to evaluate in silico single-gene knockouts to determine the genes controlling the nitrogen fixation process. One hundred forty-one of 541 genes (26%) were found to influence the symbiotic process, wherein 121 genes were predicted as essential and 20 others as having a partial effect. Transcriptomic profiles of CCBAU45436 were used to evaluate the nitrogen fixation capacity in cultivated versus in wild soybean inoculated with the microsymbiont. The model quantified the nitrogen fixation activities of the strain in these two hosts and predicted a higher nitrogen fixation capacity in cultivated soybean. Our results are consistent with published data demonstrating larger amounts of ureides and total nitrogen in cultivated soybean than in wild soybean. This work presents the first metabolic network reconstruction of S. fredii as an example of a useful tool for exploring the potential benefits of microsymbionts to sustainable agriculture and the ecosystem.IMPORTANCE Nitrogen is the most limiting macronutrient for plant growth, and rhizobia are important bacteria for agriculture because they can fix atmospheric nitrogen and make it available to legumes through the establishment of a symbiotic relationship with their host plants. In this work, we studied the nitrogen fixation process in the microsymbiont Sinorhizobium fredii at the genome level. A metabolic model was built using genome annotation and literature to reconstruct the symbiotic form of S. fredii Genes controlling the nitrogen fixation process were identified by simulating gene knockouts. Additionally, the nitrogen-fixing capacities of S. fredii CCBAU45436 in symbiosis with cultivated and wild soybeans were evaluated. The predictions suggested an outperformance of S. fredii with cultivated soybean, consistent with published experimental evidence. The reconstruction presented here will help to understand and improve nitrogen fixation capabilities of S. fredii and will be beneficial for agriculture by reducing the reliance on fertilizer applications.

Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v.3.0.

Constraint-based reconstruction and analysis (COBRA) provides a molecular mechanistic framework for integrative analysis of experimental molecular systems biology data and quantitative prediction of physicochemically and biochemically feasible phenotypic states. The COBRA Toolbox is a comprehensive desktop software suite of interoperable COBRA methods. It has found widespread application in biology, biomedicine, and biotechnology because its functions can be flexibly combined to implement tailored COBRA protocols for any biochemical network. This protocol is an update to the COBRA Toolbox v.1.0 and v.2.0. Version 3.0 includes new methods for quality-controlled reconstruction, modeling, topological analysis, strain and experimental design, and network visualization, as well as network integration of chemoinformatic, metabolomic, transcriptomic, proteomic, and thermochemical data. New multi-lingual code integration also enables an expansion in COBRA application scope via high-precision, high-performance, and nonlinear numerical optimization solvers for multi-scale, multi-cellular, and reaction kinetic modeling, respectively. This protocol provides an overview of all these new features and can be adapted to generate and analyze constraint-based models in a wide variety of scenarios. The COBRA Toolbox v.3.0 provides an unparalleled depth of COBRA methods.

Accelerating flux balance calculations in genome-scale metabolic models by localizing the application of loopless constraints.

Background: Genome-scale metabolic network models and constraint-based modeling techniques have become important tools for analyzing cellular metabolism. Thermodynamically infeasible cycles (TICs) causing unbounded metabolic flux ranges are often encountered. TICs satisfy the mass balance and directionality constraints but violate the second law of thermodynamics. Current practices involve implementing additional constraints to ensure not only optimal but also loopless flux distributions. However, the mixed integer linear programming problems required to solve become computationally intractable for genome-scale metabolic models. Results: We aimed to identify the fewest needed constraints sufficient for optimality under the loopless requirement. We found that loopless constraints are required only for the reactions that share elementary flux modes representing TICs with reactions that are part of the objective function. We put forth the concept of localized loopless constraints (LLCs) to enforce this minimal required set of loopless constraints. By combining with a novel procedure for minimal null-space calculation, the computational time for loopless flux variability analysis (ll-FVA) is reduced by a factor of 10-150 compared to the original loopless constraints and by 4-20 times compared to the current fastest method Fast-SNP with the percent improvement increasing with model size. Importantly, LLCs offer a scalable strategy for loopless flux calculations for multi-compartment/multi-organism models of large sizes, for example, shortening the CPU time for ll-FVA from 35 h to less than 2 h for a model with more than104 reactions. Availability and implementation: Matlab functions are available in the Supplementary Material or at https://github.com/maranasgroup/lll-FVA. Supplementary information: Supplementary data are available at Bioinformatics online.

Standardizing biomass reactions and ensuring complete mass balance in genome-scale metabolic models.

MOTIVATION: In a genome-scale metabolic model, the biomass produced is defined to have a molecular weight (MW) of 1 g mmol-1. This is critical for correctly predicting growth yields, contrasting multiple models and more importantly modeling microbial communities. However, the standard is rarely verified in the current practice and the chemical formulae of biomass components such as proteins, nucleic acids and lipids are often represented by undefined side groups (e.g. X, R). RESULTS: We introduced a systematic procedure for checking the biomass weight and ensuring complete mass balance of a model. We identified significant departures after examining 64 published models. The biomass weights of 34 models differed by 5-50%, while 8 models have discrepancies >50%. In total 20 models were manually curated. By maximizing the original versus corrected biomass reactions, flux balance analysis revealed >10% differences in growth yields for 12 of the curated models. Biomass MW discrepancies are accentuated in microbial community simulations as they can cause significant and systematic errors in the community composition. Microbes with underestimated biomass MWs are overpredicted in the community whereas microbes with overestimated biomass weights are underpredicted. The observed departures in community composition are disproportionately larger than the discrepancies in the biomass weight estimate. We propose the presented procedure as a standard practice for metabolic reconstructions. AVAILABILITY AND IMPLEMENTATION: The MALTAB and Python scripts are available in the Supplementary Material. CONTACT: costas@psu.edu or joshua.chan@connect.polyu.hk. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Farnesoid X Receptor Signaling Shapes the Gut Microbiota and Controls Hepatic Lipid Metabolism.

The gut microbiota modulates obesity and associated metabolic phenotypes in part through intestinal farnesoid X receptor (FXR) signaling. Glycine-ß-muricholic acid (Gly-MCA), an intestinal FXR antagonist, has been reported to prevent or reverse high-fat diet (HFD)-induced and genetic obesity, insulin resistance, and fatty liver; however, the mechanism by which these phenotypes are improved is not fully understood. The current study investigated the influence of FXR activity on the gut microbiota community structure and function and its impact on hepatic lipid metabolism. Predictions about the metabolic contribution of the gut microbiota to the host were made using 16S rRNA-based PICRUSt (phylogenetic investigation of communities by reconstruction of unobserved states), then validated using 1H nuclear magnetic resonance-based metabolomics, and results were summarized by using genome-scale metabolic models. Oral Gly-MCA administration altered the gut microbial community structure, notably reducing the ratio of Firmicutes to Bacteroidetes and its PICRUSt-predicted metabolic function, including reduced production of short-chain fatty acids (substrates for hepatic gluconeogenesis and de novo lipogenesis) in the ceca of HFD-fed mice. Metabolic improvement was intestinal FXR dependent, as revealed by the lack of changes in HFD-fed intestine-specific Fxr-null (FxrΔIE) mice treated with Gly-MCA. Integrative analyses based on genome-scale metabolic models demonstrated an important link between Lactobacillus and Clostridia bile salt hydrolase activity and bacterial fermentation. Hepatic metabolite levels after Gly-MCA treatment correlated with altered levels of gut bacterial species. In conclusion, modulation of the gut microbiota by inhibition of intestinal FXR signaling alters host liver lipid metabolism and improves obesity-related metabolic dysfunction. IMPORTANCE The farnesoid X receptor (FXR) plays an important role in mediating the dialog between the host and gut microbiota, particularly through modulation of enterohepatic circulation of bile acids. Mounting evidence suggests that genetic ablation of Fxr in the gut or gut-restricted chemical antagonism of the FXR promotes beneficial health effects, including the prevention of nonalcoholic fatty liver disease in rodent models. However, questions remain unanswered, including whether modulation of FXR activity plays a role in shaping the gut microbiota community structure and function and what metabolic pathways of the gut microbiota contribute in an FXR-dependent manner to the host phenotype. In this report, new insights are gained into the metabolic contribution of the gut microbiota to the metabolic phenotypes, including establishing a link between FXR antagonism, bacterial bile salt hydrolase activity, and fermentation. Multiple approaches, including unique mouse models as well as metabolomics and genome-scale metabolic models, were employed to confirm these results.

Correlation of pulse wave velocity with left ventricular mass in patients with hypertension once blood pressure has been normalized.

Vascular stiffness has been proposed as a simple method to assess arterial loading conditions of the heart which induce left ventricular hypertrophy (LVH). There is some controversy as to whether the relationship of vascular stiffness to LVH is independent of blood pressure, and which measurement of arterial stiffness, augmentation index (AI) or pulse wave velocity (PWV) is best. Carotid pulse wave contor and pulse wave velocity of patients (n=20) with hypertension whose blood pressure (BP) was under control (<140/90 mmHg) with antihypertensive drug treatment medications, and without valvular heart disease, were measured. Left ventricular mass, calculated from 2D echocardiogram, was adjusted for body size using two different methods: body surface area and height. There was a significant (P<0.05) linear correlation between LV mass index and pulse wave velocity. This was not explained by BP level or lower LV mass in women, as there was no significant difference in PWV according to gender (1140.1+67.8 vs 1110.6+57.7 cm/s). In contrast to PWV, there was no significant correlation between LV mass and AI. In summary, these data suggest that aortic vascular stiffness is an indicator of LV mass even when blood pressure is controlled to less than 140/90 mmHg in hypertensive patients. The data further suggest that PWV is a better proxy or surrogate marker for LV mass than AI and the measurement of PWV may be useful as a rapid and less expensive assessment of the presence of LVH in this patient population.

Parapharyngeal extension of nasopharyngeal carcinoma: still a significant factor in era of modern radiotherapy?

PURPOSE: To retrospectively analyze the prognostic value of parapharyngeal space (PPS) extension after conformal radiotherapy for nasopharyngeal carcinoma. PATIENTS AND METHODS: Between 1998 and 2005, 700 patients were treated with conformal radiotherapy at 2 Gy/fraction daily to a total of 70 Gy. All patients underwent staging with magnetic resonance imaging. The incidence of PPS was determined, and the extent of involvement was further subclassified regarding the presence or absence of carotid space (CS) involvement. The prognostic parameters, including age, gender, stage, chemotherapy, additional boosting, and extent of PPS involvement, were analyzed by univariate and multivariate analyses. RESULTS: The median duration of follow-up was 51 months, and the 5-year overall survival rate for the whole group was 73%. The overall incidence of PPS extension was high (74%), and 29% had additional extension to the CS. Multivariate analysis showed age, gender, chemotherapy, T stage, and N stage to be significant prognostic factors, but not PPS involvement with or without CS extension. In the subgroup of patients with Stage T2 disease (n = 242), the presence of PPS involvement alone or PPS plus CS extension had no statistically significant effect in terms of local control (p = 0.68), distant metastases (p = 0.34), or overall survival (p = 0.24) compared with those without PPS involvement (Stage T2a). CONCLUSIONS: With better tumor delineation by magnetic resonance imaging and improved coverage using modern radiotherapy techniques, PPS extension per se no longer predicts for disease outcome. Hence, subcategorizing Stage T2 disease is no longer important in future International Union Against Cancer/American Joint Committee on Cancer classifications.