Constraint-Based Reconstruction and Analyses of Metabolic Models: Open-Source Python Tools and Applications to Cancer

Abstract

The influence of metabolism on signaling, epigenetic markers, and transcription is highly complex yet important for understanding cancer physiology. Despite the development of high-resolution multi-omics technologies, it is difficult to infer metabolic activity from these indirect measurements. Fortunately, genome-scale metabolic models and constraint-based modeling provide a systems biology framework to investigate the metabolic states and define the genotype-phenotype associations by integrations of multi-omics data. Constraint-Based Reconstruction and Analysis (COBRA) methods are used to build and simulate metabolic networks using mathematical representations of biochemical reactions, gene-protein reaction associations, and physiological and biochemical constraints. These methods have led to advancements in metabolic reconstruction, network analysis, perturbation studies as well as prediction of metabolic state. Most computational tools for performing these analyses are written for MATLAB, a proprietary software. In order to increase accessibility and handle more complex datasets and models, community efforts have started to develop similar open-source tools in Python. To date there is a comprehensive set of tools in Python to perform various flux analyses and visualizations; however, there are still missing algorithms in some key areas. This review summarizes the availability of Python software for several components of COBRA methods and their applications in cancer metabolism. These tools are evolving rapidly and should offer a readily accessible, versatile way to model the intricacies of cancer metabolism for identifying cancer-specific metabolic features that constitute potential drug targets.

Keywords: cancer; constraint-based modeling; genome-scale metabolic models; metabolism; omics; python; single-cell analysis; systems biology.

Figure 1

Constraint-based metabolic modeling. (A) A genome-scale metabolic model is a compartmentalized network of mass-balanced reactions that convert products to reactants, and boundary pseudo-reactions that import or export metabolites. Biological objectives, such as biomass production, require activity through a subset of internal reactions. (B) The metabolic model is converted into a stoichiometric matrix (S) of size m × n, with rows representing m metabolites and columns n reactions. Reaction flux through all internal reaction (v_i ) and exchange reactions (e_i ) is represented by vector v of length n. Objective function Z = c ^T v is formulated as a linear combination of desired fluxes, weighted by vector c. (C) At steady state, the rate of production and consumption of a metabolite must be zero, which is described by the system of equations Sv = 0. There are many solutions to this system of equations, but the solution space can be constrained by imposing flux bounds (v _lb ≤ v ≤ v _ub ) and optimization such as maximization of objective function.

Figure 2

Overview of Python software for major components of COBRA methods. Constraint-based metabolic modeling first requires loading a metabolic model into software that handles the various parts of the modeling framework (grey), such as metabolites, reactions, genes, stoichiometric matrix, and flux solutions. New metabolic models can be reconstructed from genome sequences and database, quality-checked by model testing software, made consistent using gap-filling tools, and visualized using web-based packages. Using the metabolic model, FBA (yellow) finds an optimal flux distribution that follows stoichiometry under steady state and can further be extended to dynamic systems. Since there are alternative optima (blue) to FBA, FVA and geometric FBA can be used to characterize the solution space. We can perturb (red) the system to predict the effect of knockouts and use such predictions to design an optimal system (‘strain’). To improve FBA predictions, we can add biophysical (green) constraints based on thermodynamics, proteins, and macromolecular expression. Metabolic modeling can be further enhanced by integration of multi-omics (purple) data, such as extracting reduced models based on omics data and adding regulatory constraints. Using omics data, metabolic modeling can become high-dimensional (brown), through single cell modeling and community modeling. Multiple metabolic models can be reduced into ensemble objects. In contrast to FBA, unbiased (pink) approaches do not require an objective function. These include methods for sampling flux distributions and pathway analyses. Names of software packages are in bold.

Figure 3

Overview of metabolic interactions within the tumor microenvironment. The TME is composed of cancer cells, immune cells, and stromal cells embedded in extracellular matrix (ECM). Limited nutrients and oxygen lead to metabolic competition between cancer and various lymphocytes, especially hampering anti-tumor activity of effector T cells (T_EFF). Cancer cells adapts via upregulating nutrient transport and altering cancer-associated fibroblasts (CAF) to replenish metabolites. T cell immunity is further suppressed by cancer cells’ release of lactate produced by glycolysis and by recruitment of immune-suppressive cells due to Indoleamine 2,3-dioxygenase (IDO) activity. T_MEM, memory T cell; NK, natural killer cell; Treg, regulatory T cell; TAM, tumor-associated macrophage.

Figure 4

Applications of COBRA methods to cancer research. Workflow diagram of using various COBRA methods (colored) in combination to achieve different objectives (grey).