Refining carbon flux paths using atomic trace data

Global connectivity in genome-scale metabolic networks revealed by comprehensive FBA-based pathway analysis

Background

Graph-based analysis (GBA) of genome-scale metabolic networks has revealed system-level structures such as the bow-tie connectivity that describes the overall mass flow in a network. However, many pathways obtained by GBA are biologically impossible, making it difficult to study how the global structures affect the biological functions of a network. New method that can calculate the biologically relevant pathways is desirable for structural analysis of metabolic networks.

Results

Here, we present a new method to determine the bow-tie connectivity structure by calculating possible pathways between any pairs of metabolites in the metabolic network using a flux balance analysis (FBA) approach to ensure that the obtained pathways are biologically relevant. We tested this method with 15 selected high-quality genome-scale metabolic models from BiGG database. The results confirmed the key roles of central metabolites in network connectivity, locating in the core part of the bow-tie structure, the giant strongly connected component (GSC). However, the sizes of GSCs revealed by GBA are significantly larger than those by FBA approach. A great number of metabolites in the GSC from GBA actually cannot be produced from or converted to other metabolites through a mass balanced pathway and thus should not be in GSC but in other subsets of the bow-tie structure. In contrast, the bow-tie structural classification of metabolites obtained by FBA is more biologically relevant and suitable for the study of the structure-function relationships of genome scale metabolic networks.

Conclusions

The FBA based pathway calculation improve the biologically relevant classification of metabolites in the bow-tie connectivity structure of the metabolic network, taking us one step further toward understanding how such system-level structures impact the biological functions of an organism.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12866-021-02357-1.

NetFlow: A tool for isolating carbon flows in genome-scale metabolic networks

Genome-scale stoichiometric models (GSMs) have been widely utilized to predict and understand cellular metabolism. GSMs and the flux predictions resulting from them have proven indispensable to fields ranging from metabolic engineering to human disease. Nonetheless, it is challenging to parse these flux predictions due to the inherent size and complexity of the GSMs. Several previous approaches have reduced this complexity by identifying key pathways contained within the genome-scale flux predictions. However, a reduction method that overlays carbon atom transitions on stoichiometry and flux predictions is lacking. To fill this gap, we developed NetFlow, an algorithm that leverages genome-scale carbon mapping to extract and quantitatively distinguish biologically relevant metabolic pathways from a given genome-scale flux prediction. NetFlow extends prior approaches by utilizing both full carbon mapping and context-specific flux predictions. Thus, NetFlow is uniquely able to quantitatively distinguish between biologically relevant pathways of carbon flow within the given flux map. NetFlow simulates ¹³C isotope labeling experiments to calculate the extent of carbon exchange, or carbon yield, between every metabolite in the given GSM. Based on the carbon yield, the carbon flow to or from any metabolite or between any pair of metabolites of interest can be isolated and readily visualized. The resulting pathways are much easier to interpret, which enables an in-depth mechanistic understanding of the metabolic phenotype of interest. Here, we first demonstrate NetFlow with a simple network. We then depict the utility of NetFlow on a model of central carbon metabolism in E. coli. Specifically, we isolated the production pathway for succinate synthesis in this model and the metabolic mechanism driving the predicted increase in succinate yield in a double knockout of E. coli. Finally, we describe the application of NetFlow to a GSM of lycopene-producing E. coli, which enabled the rapid identification of the mechanisms behind the measured increases in lycopene production following single, double, and triple knockouts.

Improving the organization and interactivity of metabolic pathfinding with precomputed pathways

Background

The rapid growth of available knowledge on metabolic processes across thousands of species continues to expand the possibilities of producing chemicals by combining pathways found in different species. Several computational search algorithms have been developed for automating the identification of possible heterologous pathways; however, these searches may return thousands of pathway results. Although the large number of results are in part due to the large number of possible compounds and reactions, a subset of core reaction modules is repeatedly observed in pathway results across multiple searches, suggesting that some subpaths between common compounds were more consistently explored than others.To reduce the resources spent on searching the same metabolic space, a new meta-algorithm for metabolic pathfinding, Hub Pathway search with Atom Tracking (HPAT), was developed to take advantage of a precomputed network of subpath modules. To investigate the efficacy of this method, we created a table describing a network of common hub metabolites and how they are biochemically connected and only offloaded searches to and from this hub network onto an interactive webserver capable of visualizing the resulting pathways.

Results

A test set of nineteen known pathways taken from literature and metabolic databases were used to evaluate if HPAT was capable of identifying known pathways. HPAT found the exact pathway for eleven of the nineteen test cases using a diverse set of precomputed subpaths, whereas a comparable pathfinding search algorithm that does not use precomputed subpaths found only seven of the nineteen test cases. The capability of HPAT to find novel pathways was demonstrated by its ability to identify novel 3-hydroxypropanoate (3-HP) synthesis pathways. As for pathway visualization, the new interactive pathway filters enable a reduction of the number of displayed pathways from hundreds down to less than ten pathways in several test cases, illustrating their utility in reducing the amount of presented information while retaining pathways of interest.

Conclusions

This work presents the first step in incorporating a precomputed subpath network into metabolic pathfinding and demonstrates how this leads to a concise, interactive visualization of pathway results. The modular nature of metabolic pathways is exploited to facilitate efficient discovery of alternate pathways.

Exploring the combinatorial space of complete pathways to chemicals

Computational pathway design tools often face the challenges of balancing the stoichiometry of co-metabolites and cofactors, and dealing with reaction rule utilization in a single workflow. To this end, we provide an overview of two complementary stoichiometry-based pathway design tools optStoic and novoStoic developed in our group to tackle these challenges. optStoic is designed to determine the stoichiometry of overall conversion first which optimizes a performance criterion (e.g. high carbon/energy efficiency) and ensures a comprehensive search of co-metabolites and cofactors. The procedure then identifies the minimum number of intervening reactions to connect the source and sink metabolites. We also further the pathway design procedure by expanding the search space to include both known and hypothetical reactions, represented by reaction rules, in a new tool termed novoStoic. Reaction rules are derived based on a mixed-integer linear programming (MILP) compatible reaction operator, which allow us to explore natural promiscuous enzymes, engineer candidate enzymes that are not already promiscuous as well as design de novo enzymes. The identified biochemical reaction rules then guide novoStoic to design routes that expand the currently known biotransformation space using a single MILP modeling procedure. We demonstrate the use of the two computational tools in pathway elucidation by designing novel synthetic routes for isobutanol.

FindPrimaryPairs: An efficient algorithm for predicting element-transferring reactant/product pairs in metabolic networks

The metabolism of individual organisms and biological communities can be viewed as a network of metabolites connected to each other through chemical reactions. In metabolic networks, chemical reactions transform reactants into products, thereby transferring elements between these metabolites. Knowledge of how elements are transferred through reactant/product pairs allows for the identification of primary compound connections through a metabolic network. However, such information is not readily available and is often challenging to obtain for large reaction databases or genome-scale metabolic models. In this study, a new algorithm was developed for automatically predicting the element-transferring reactant/product pairs using the limited information available in the standard representation of metabolic networks. The algorithm demonstrated high efficiency in analyzing large datasets and provided accurate predictions when benchmarked with manually curated data. Applying the algorithm to the visualization of metabolic networks highlighted pathways of primary reactant/product connections and provided an organized view of element-transferring biochemical transformations. The algorithm was implemented as a new function in the open source software package PSAMM in the release v0.30 (https://zhanglab.github.io/psamm/).

Constraining Genome-Scale Models to Represent the Bow Tie Structure of Metabolism for 13C Metabolic Flux Analysis

Determination of internal metabolic fluxes is crucial for fundamental and applied biology because they map how carbon and electrons flow through metabolism to enable cell function. 13C Metabolic Flux Analysis (13C MFA) and Two-Scale 13C Metabolic Flux Analysis (2S-13C MFA) are two techniques used to determine such fluxes. Both operate on the simplifying approximation that metabolic flux from peripheral metabolism into central “core” carbon metabolism is minimal, and can be omitted when modeling isotopic labeling in core metabolism. The validity of this “two-scale” or “bow tie” approximation is supported both by the ability to accurately model experimental isotopic labeling data, and by experimentally verified metabolic engineering predictions using these methods. However, the boundaries of core metabolism that satisfy this approximation can vary across species, and across cell culture conditions. Here, we present a set of algorithms that (1) systematically calculate flux bounds for any specified “core” of a genome-scale model so as to satisfy the bow tie approximation and (2) automatically identify an updated set of core reactions that can satisfy this approximation more efficiently. First, we leverage linear programming to simultaneously identify the lowest fluxes from peripheral metabolism into core metabolism compatible with the observed growth rate and extracellular metabolite exchange fluxes. Second, we use Simulated Annealing to identify an updated set of core reactions that allow for a minimum of fluxes into core metabolism to satisfy these experimental constraints. Together, these methods accelerate and automate the identification of a biologically reasonable set of core reactions for use with 13C MFA or 2S-13C MFA, as well as provide for a substantially lower set of flux bounds for fluxes into the core as compared with previous methods. We provide an open source Python implementation of these algorithms at https://github.com/JBEI/limitfluxtocore.

A review of computational tools for design and reconstruction of metabolic pathways

Metabolic pathways reflect an organism's chemical repertoire and hence their elucidation and design have been a primary goal in metabolic engineering. Various computational methods have been developed to design novel metabolic pathways while taking into account several prerequisites such as pathway stoichiometry, thermodynamics, host compatibility, and enzyme availability. The choice of the method is often determined by the nature of the metabolites of interest and preferred host organism, along with computational complexity and availability of software tools. In this paper, we review different computational approaches used to design metabolic pathways based on the reaction network representation of the database (i.e., graph or stoichiometric matrix) and the search algorithm (i.e., graph search, flux balance analysis, or retrosynthetic search). We also put forth a systematic workflow that can be implemented in projects requiring pathway design and highlight current limitations and obstacles in computational pathway design.

A review of parameters and heuristics for guiding metabolic pathfinding

Recent developments in metabolic engineering have led to the successful biosynthesis of valuable products, such as the precursor of the antimalarial compound, artemisinin, and opioid precursor, thebaine. Synthesizing these traditionally plant-derived compounds in genetically modified yeast cells introduces the possibility of significantly reducing the total time and resources required for their production, and in turn, allows these valuable compounds to become cheaper and more readily available. Most biosynthesis pathways used in metabolic engineering applications have been discovered manually, requiring a tedious search of existing literature and metabolic databases. However, the recent rapid development of available metabolic information has enabled the development of automated approaches for identifying novel pathways. Computer-assisted pathfinding has the potential to save biochemists time in the initial discovery steps of metabolic engineering. In this paper, we review the parameters and heuristics used to guide the search in recent pathfinding algorithms. These parameters and heuristics capture information on the metabolic network structure, compound structures, reaction features, and organism-specificity of pathways. No one metabolic pathfinding algorithm or search parameter stands out as the best to use broadly for solving the pathfinding problem, as each method and parameter has its own strengths and shortcomings. As assisted pathfinding approaches continue to become more sophisticated, the development of better methods for visualizing pathway results and integrating these results into existing metabolic engineering practices is also important for encouraging wider use of these pathfinding methods.

Network design and analysis for multi-enzyme biocatalysis

BACKGROUND

As more and more biological reaction data become available, the full exploration of the enzymatic potential for the synthesis of valuable products opens up exciting new opportunities but is becoming increasingly complex. The manual design of multi-step biosynthesis routes involving enzymes from different organisms is very challenging. To harness the full enzymatic potential, we developed a computational tool for the directed design of biosynthetic production pathways for multi-step catalysis with in vitro enzyme cascades, cell hydrolysates and permeabilized cells.

RESULTS

We present a method which encompasses the reconstruction of a genome-scale pan-organism metabolic network, path-finding and the ranking of the resulting pathway candidates for proposing suitable synthesis pathways. The network is based on reaction and reaction pair data from the Kyoto Encyclopedia of Genes and Genomes (KEGG) and the thermodynamics calculator eQuilibrator. The pan-organism network is especially useful for finding the most suitable pathway to a target metabolite from a thermodynamic or economic standpoint. However, our method can be used with any network reconstruction, e.g. for a specific organism. We implemented a path-finding algorithm based on a mixed-integer linear program (MILP) which takes into account both topology and stoichiometry of the underlying network. Unlike other methods we do not specify a single starting metabolite, but our algorithm searches for pathways starting from arbitrary start metabolites to a target product of interest. Using a set of biochemical ranking criteria including pathway length, thermodynamics and other biological characteristics such as number of heterologous enzymes or cofactor requirement, it is possible to obtain well-designed meaningful pathway alternatives. In addition, a thermodynamic profile, the overall reactant balance and potential side reactions as well as an SBML file for visualization are generated for each pathway alternative.

CONCLUSION

We present an in silico tool for the design of multi-enzyme biosynthetic production pathways starting from a pan-organism network. The method is highly customizable and each module can be adapted to the focus of the project at hand. This method is directly applicable for (i) in vitro enzyme cascades, (ii) cell hydrolysates and (iii) permeabilized cells.

Comparative evaluation of atom mapping algorithms for balanced metabolic reactions: application to Recon 3D

The mechanism of each chemical reaction in a metabolic network can be represented as a set of atom mappings, each of which relates an atom in a substrate metabolite to an atom of the same element in a product metabolite. Genome-scale metabolic network reconstructions typically represent biochemistry at the level of reaction stoichiometry. However, a more detailed representation at the underlying level of atom mappings opens the possibility for a broader range of biological, biomedical and biotechnological applications than with stoichiometry alone. Complete manual acquisition of atom mapping data for a genome-scale metabolic network is a laborious process. However, many algorithms exist to predict atom mappings. How do their predictions compare to each other and to manually curated atom mappings? For more than four thousand metabolic reactions in the latest human metabolic reconstruction, Recon 3D, we compared the atom mappings predicted by six atom mapping algorithms. We also compared these predictions to those obtained by manual curation of atom mappings for over five hundred reactions distributed among all top level Enzyme Commission number classes. Five of the evaluated algorithms had similarly high prediction accuracy of over 91% when compared to manually curated atom mapped reactions. On average, the accuracy of the prediction was highest for reactions catalysed by oxidoreductases and lowest for reactions catalysed by ligases. In addition to prediction accuracy, the algorithms were evaluated on their accessibility, their advanced features, such as the ability to identify equivalent atoms, and their ability to map hydrogen atoms. In addition to prediction accuracy, we found that software accessibility and advanced features were fundamental to the selection of an atom mapping algorithm in practice.

A Method for Finding Metabolic Pathways Using Atomic Group Tracking

A fundamental computational problem in metabolic engineering is to find pathways between compounds. Pathfinding methods using atom tracking have been widely used to find biochemically relevant pathways. However, these methods require the user to define the atoms to be tracked. This may lead to failing to predict the pathways that do not conserve the user-defined atoms. In this work, we propose a pathfinding method called AGPathFinder to find biochemically relevant metabolic pathways between two given compounds. In AGPathFinder, we find alternative pathways by tracking the movement of atomic groups through metabolic networks and use combined information of reaction thermodynamics and compound similarity to guide the search towards more feasible pathways and better performance. The experimental results show that atomic group tracking enables our method to find pathways without the need of defining the atoms to be tracked, avoid hub metabolites, and obtain biochemically meaningful pathways. Our results also demonstrate that atomic group tracking, when incorporated with combined information of reaction thermodynamics and compound similarity, improves the quality of the found pathways. In most cases, the average compound inclusion accuracy and reaction inclusion accuracy for the top resulting pathways of our method are around 0.90 and 0.70, respectively, which are better than those of the existing methods. Additionally, AGPathFinder provides the information of thermodynamic feasibility and compound similarity for the resulting pathways.

MapMaker and PathTracer for tracking carbon in genome-scale metabolic models

Constraint-based reconstruction and analysis (COBRA) modeling results can be difficult to interpret given the large numbers of reactions in genome-scale models. While paths in metabolic networks can be found, existing methods are not easily combined with constraint-based approaches. To address this limitation, two tools (MapMaker and PathTracer) were developed to find paths (including cycles) between metabolites, where each step transfers carbon from reactant to product. MapMaker predicts carbon transfer maps (CTMs) between metabolites using only information on molecular formulae and reaction stoichiometry, effectively determining which reactants and products share carbon atoms. MapMaker correctly assigned CTMs for over 97% of the 2,251 reactions in an Escherichia coli metabolic model (iJO1366). Using CTMs as inputs, PathTracer finds paths between two metabolites. PathTracer was applied to iJO1366 to investigate the importance of using CTMs and COBRA constraints when enumerating paths, to find active and high flux paths in flux balance analysis (FBA) solutions, to identify paths for putrescine utilization, and to elucidate a potential CO2 fixation pathway in E. coli. These results illustrate how MapMaker and PathTracer can be used in combination with constraint-based models to identify feasible, active, and high flux paths between metabolites.

TreeEFM: calculating elementary flux modes using linear optimization in a tree-based algorithm

MOTIVATION

Elementary flux modes (EFMs) analysis constitutes a fundamental tool in systems biology. However, the efficient calculation of EFMs in genome-scale metabolic networks (GSMNs) is still a challenge. We present a novel algorithm that uses a linear programming-based tree search and efficiently enumerates a subset of EFMs in GSMNs.

RESULTS

Our approach is compared with the EFMEvolver approach, demonstrating a significant improvement in computation time. We also validate the usefulness of our new approach by studying the acetate overflow metabolism in the Escherichia coli bacteria. To do so, we computed 1 million EFMs for each energetic amino acid and then analysed the relevance of each energetic amino acid based on gene/protein expression data and the obtained EFMs. We found good agreement between previous experiments and the conclusions reached using EFMs. Finally, we also analysed the performance of our approach when applied to large GSMNs.

AVAILABILITY AND IMPLEMENTATION

The stand-alone software TreeEFM is implemented in C++ and interacts with the open-source linear solver COIN-OR Linear program Solver (CLP).

Direct calculation of elementary flux modes satisfying several biological constraints in genome-scale metabolic networks

MOTIVATION

The concept of Elementary Flux Mode (EFM) has been widely used for the past 20 years. However, its application to genome-scale metabolic networks (GSMNs) is still under development because of methodological limitations. Therefore, novel approaches are demanded to extend the application of EFMs. A novel family of methods based on optimization is emerging that provides us with a subset of EFMs. Because the calculation of the whole set of EFMs goes beyond our capacity, performing a selective search is a proper strategy.

RESULTS

Here, we present a novel mathematical approach calculating EFMs fulfilling additional linear constraints. We validated our approach based on two metabolic networks in which all the EFMs can be obtained. Finally, we analyzed the performance of our methodology in the GSMN of the yeast Saccharomyces cerevisiae by calculating EFMs producing ethanol with a given minimum carbon yield. Overall, this new approach opens new avenues for the calculation of EFMs in GSMNs.

AVAILABILITY AND IMPLEMENTATION

Matlab code is provided in the supplementary online materials

CONTACT

fplanes@ceit.es.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.