MOTIVATION: Microbes are essential part of all ecosystems, influencing material flow and shaping their surroundings. Metabolic modeling has been a useful tool and provided tremendous insights into microbial community metabolism. However, current methods based on flux balance analysis (FBA) usually fail to predict metabolic and regulatory strategies that lead to long-term survival and stability especially in heterogenous communities. RESULTS: Here, we introduce a novel reinforcement learning algorithm, Self-Playing Microbes in Dynamic FBA, which treats microbial metabolism as a decision-making process, allowing individual microbial agents to evolve by learning and adapting metabolic strategies for enhanced long-term fitness. This algorithm predicts what microbial flux regulation policies will stabilize in the dynamic ecosystem of interest in the presence of other microbes with minimal reliance on predefined strategies. Throughout this article, we present several scenarios wherein our algorithm outperforms existing methods in reproducing outcomes, and we explore the biological significance of these predictions. AVAILABILITY AND IMPLEMENTATION: The source code for this article is available at: https://github.com/chan-csu/SPAM-DFBA.

Microbial genome annotation is the process of identifying structural and functional elements in DNA sequences and subsequently attaching biological information to those elements. DRAM is a tool developed to annotate bacterial, archaeal, and viral genomes derived from pure cultures or metagenomes. DRAM goes beyond traditional annotation tools by distilling multiple gene annotations to genome level summaries of functional potential. Despite these benefits, a downside of DRAM is the requirement of large computational resources, which limits its accessibility. Further, it did not integrate with downstream metabolic modeling tools that require genome annotation. To alleviate these constraints, DRAM and the viral counterpart, DRAM-v, are now available and integrated with the freely accessible KBase cyberinfrastructure. With kb_DRAM users can generate DRAM annotations and functional summaries from microbial or viral genomes in a point-and-click interface, as well as generate genome-scale metabolic models from DRAM annotations. AVAILABILITY AND IMPLEMENTATION: For kb_DRAM users, the kb_DRAM apps on KBase can be found in the catalog at https://narrative.kbase.us/#catalog/modules/kb_DRAM. For kb_DRAM users, a tutorial workflow with all documentation is available at https://narrative.kbase.us/narrative/129480. For kb_DRAM developers, software is available at https://github.com/shafferm/kb_DRAM.

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.

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.

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: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Genome-scale metabolic modeling has become widespread for analyzing microbial metabolism. Extending this established paradigm to more complex microbial communities is emerging as a promising way to unravel the interactions and biochemical repertoire of these omnipresent systems. While several modeling techniques have been developed for microbial communities, little emphasis has been placed on the need to impose a time-averaged constant growth rate across all members for a community to ensure co-existence and stability. In the absence of this constraint, the faster growing organism will ultimately displace all other microbes in the community. This is particularly important for predicting steady-state microbiota composition as it imposes significant restrictions on the allowable community membership, composition and phenotypes. In this study, we introduce the SteadyCom optimization framework for predicting metabolic flux distributions consistent with the steady-state requirement. SteadyCom can be rapidly converged by iteratively solving linear programming (LP) problem and the number of iterations is independent of the number of organisms. A significant advantage of SteadyCom is compatibility with flux variability analysis. SteadyCom is first demonstrated for a community of four E. coli double auxotrophic mutants and is then applied to a gut microbiota model consisting of nine species, with representatives from the phyla Bacteroidetes, Firmicutes, Actinobacteria and Proteobacteria. In contrast to the direct use of FBA, SteadyCom is able to predict the change in species abundance in response to changes in diets with minimal additional imposed constraints on the model. By randomizing the uptake rates of microbes, an abundance profile with a good agreement to experimental gut microbiota is inferred. SteadyCom provides an important step towards the cross-cutting task of predicting the composition of a microbial community in a given environment.

MOTIVATION: Elementary flux mode (EFM) is a useful tool in constraint-based modeling of metabolic networks. The property that every flux distribution can be decomposed as a weighted sum of EFMs allows certain applications of EFMs to studying flux distributions. The existence of biologically infeasible EFMs and the non-uniqueness of the decomposition, however, undermine the applicability of such methods. Efforts have been made to find biologically feasible EFMs by incorporating information from transcriptional regulation and thermodynamics. Yet, no attempt has been made to distinguish biologically feasible EFMs by considering their graphical properties. A previous study on the transcriptional regulation of metabolic genes found that distinct branches at a branch point metabolite usually belong to distinct metabolic pathways. This suggests an intuitive property of biologically feasible EFMs, i.e. minimal branching. RESULTS: We developed the concept of minimal branching EFM and derived the minimal branching decomposition (MBD) to decompose flux distributions. Testing in the core Escherichia coli metabolic network indicated that MBD can distinguish branches at branch points and greatly reduced the solution space in which the decomposition is often unique. An experimental flux distribution from a previous study on mouse cardiomyocyte was decomposed using MBD. Comparison with decomposition by a minimum number of EFMs showed that MBD found EFMs more consistent with established biological knowledge, which facilitates interpretation. Comparison of the methods applied to a complex flux distribution in Lactococcus lactis similarly showed the advantages of MBD. The minimal branching EFM concept underlying MBD should be useful in other applications. CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Elementary flux mode (EFM) is a fundamental concept as well as a useful tool in metabolic pathway analysis. One important role of EFMs is that every flux distribution can be decomposed into a set of EFMs and a number of methods to study flux distributions originated from it. Yet finding such decompositions requires the complete set of EFMs, which is intractable in genome-scale metabolic networks due to combinatorial explosion. RESULTS: In this article, we proposed an algorithm to decompose flux distributions into EFMs in genome-scale networks. It is an iterative scheme of a mixed integer linear program. Unlike previous optimization models to find pathways, any feasible solutions can become EFMs in our algorithm. This advantage enables the algorithm to approximate the EFM of largest contribution to an objective reaction in a flux distribution. Our algorithm is able to find EFMs of flux distributions with complex structures, closer to the realistic case in which a cell is subject to various constraints. A case of Escherichia coli growth in the Lysogeny broth (LB) medium containing various carbon sources was studied. Essential metabolites and their syntheses were located. Information on the contribution of each carbon source not obvious from the apparent flux distribution was also revealed. Our work further confirms the utility of finding EFMs by optimization models in genome-scale metabolic networks. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.