Conditions for duality between fluxes and concentrations in biochemical networks

Cardinality optimization in constraint-based modelling: application to human metabolism

MOTIVATION

Several applications in constraint-based modelling can be mathematically formulated as cardinality optimization problems involving the minimization or maximization of the number of nonzeros in a vector. These problems include testing for stoichiometric consistency, testing for flux consistency, testing for thermodynamic flux consistency, computing sparse solutions to flux balance analysis problems and computing the minimum number of constraints to relax to render an infeasible flux balance analysis problem feasible. Such cardinality optimization problems are computationally complex, with no known polynomial time algorithms capable of returning an exact and globally optimal solution.

RESULTS

By approximating the zero-norm with nonconvex continuous functions, we reformulate a set of cardinality optimization problems in constraint-based modelling into a difference of convex functions. We implemented and numerically tested novel algorithms that approximately solve the reformulated problems using a sequence of convex programs. We applied these algorithms to various biochemical networks and demonstrate that our algorithms match or outperform existing related approaches. In particular, we illustrate the efficiency and practical utility of our algorithms for cardinality optimization problems that arise when extracting a model ready for thermodynamic flux balance analysis given a human metabolic reconstruction.

AVAILABILITY AND IMPLEMENTATION

Open source scripts to reproduce the results are here https://github.com/opencobra/COBRA.papers/2023_cardOpt with general purpose functions integrated within the COnstraint-Based Reconstruction and Analysis toolbox: https://github.com/opencobra/cobratoolbox.

Genome-scale metabolic reconstruction of 7,302 human microorganisms for personalized medicine

The human microbiome influences the efficacy and safety of a wide variety of commonly prescribed drugs. Designing precision medicine approaches that incorporate microbial metabolism would require strain- and molecule-resolved, scalable computational modeling. Here, we extend our previous resource of genome-scale metabolic reconstructions of human gut microorganisms with a greatly expanded version. AGORA2 (assembly of gut organisms through reconstruction and analysis, version 2) accounts for 7,302 strains, includes strain-resolved drug degradation and biotransformation capabilities for 98 drugs, and was extensively curated based on comparative genomics and literature searches. The microbial reconstructions performed very well against three independently assembled experimental datasets with an accuracy of 0.72 to 0.84, surpassing other reconstruction resources and predicted known microbial drug transformations with an accuracy of 0.81. We demonstrate that AGORA2 enables personalized, strain-resolved modeling by predicting the drug conversion potential of the gut microbiomes from 616 patients with colorectal cancer and controls, which greatly varied between individuals and correlated with age, sex, body mass index and disease stages. AGORA2 serves as a knowledge base for the human microbiome and paves the way to personalized, predictive analysis of host-microbiome metabolic interactions.

Metabolomics and Multi-Omics Integration: A Survey of Computational Methods and Resources

As researchers are increasingly able to collect data on a large scale from multiple clinical and omics modalities, multi-omics integration is becoming a critical component of metabolomics research. This introduces a need for increased understanding by the metabolomics researcher of computational and statistical analysis methods relevant to multi-omics studies. In this review, we discuss common types of analyses performed in multi-omics studies and the computational and statistical methods that can be used for each type of analysis. We pinpoint the caveats and considerations for analysis methods, including required parameters, sample size and data distribution requirements, sources of a priori knowledge, and techniques for the evaluation of model accuracy. Finally, for the types of analyses discussed, we provide examples of the applications of corresponding methods to clinical and basic research. We intend that our review may be used as a guide for metabolomics researchers to choose effective techniques for multi-omics analyses relevant to their field of study.

Personalized whole-body models integrate metabolism, physiology, and the gut microbiome

Comprehensive molecular-level models of human metabolism have been generated on a cellular level. However, models of whole-body metabolism have not been established as they require new methodological approaches to integrate molecular and physiological data. We developed a new metabolic network reconstruction approach that used organ-specific information from literature and omics data to generate two sex-specific whole-body metabolic (WBM) reconstructions. These reconstructions capture the metabolism of 26 organs and six blood cell types. Each WBM reconstruction represents whole-body organ-resolved metabolism with over 80,000 biochemical reactions in an anatomically and physiologically consistent manner. We parameterized the WBM reconstructions with physiological, dietary, and metabolomic data. The resulting WBM models could recapitulate known inter-organ metabolic cycles and energy use. We also illustrate that the WBM models can predict known biomarkers of inherited metabolic diseases in different biofluids. Predictions of basal metabolic rates, by WBM models personalized with physiological data, outperformed current phenomenological models. Finally, integrating microbiome data allowed the exploration of host-microbiome co-metabolism. Overall, the WBM reconstructions, and their derived computational models, represent an important step toward virtual physiological humans.

Structural conserved moiety splitting of a stoichiometric matrix

Characterising biochemical reaction network structure in mathematical terms enables the inference of functional biochemical consequences from network structure with existing mathematical techniques and spurs the development of new mathematics that exploits the peculiarities of biochemical network structure. The structure of a biochemical network may be specified by reaction stoichiometry, that is, the relative quantities of each molecule produced and consumed in each reaction of the network. A biochemical network may also be specified at a higher level of resolution in terms of the internal structure of each molecule and how molecular structures are transformed by each reaction in a network. The stoichiometry for a set of reactions can be compiled into a stoichiometric matrix N∈Z^m×n, where each row corresponds to a molecule and each column corresponds to a reaction. We demonstrate that a stoichiometric matrix may be split into the sum of m-rank(N) moiety transition matrices, each of which corresponds to a subnetwork accessible to a structurally identifiable conserved moiety. The existence of this moiety matrix splitting is a property that distinguishes a stoichiometric matrix from an arbitrary rectangular matrix.

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.

Modeling metabolism of the human gut microbiome

The human gut microbiome plays an important part in human health. The complexity of the microbiome makes it difficult to determine the detailed metabolic functions and cross-talk occurs between the individual species. In silico systems biology studies of the microbiome can help to identify metabolite exchanges among gut microbes. Constraint-based reconstruction and analysis methods use biochemically accurate genome-scale metabolic networks of microorganisms to simulate metabolism between species in a given microbiome and help generate novel hypotheses on microbial interactions. Here, we review metabolic modeling studies that have investigated metabolic functions of the gut microbiome.

Non-steady state mass action dynamics without rate constants: dynamics of coupled reactions using chemical potentials

Comprehensive and predictive simulation of coupled reaction networks has long been a goal of biology and other fields. Currently, metabolic network models that utilize enzyme mass action kinetics have predictive power but are limited in scope and application by the fact that the determination of enzyme rate constants is laborious and low throughput. We present a statistical thermodynamic formulation of the law of mass action for coupled reactions at both steady states and non-stationary states. The formulation uses chemical potentials instead of rate constants. When used to model deterministic systems, the method corresponds to a rescaling of the time dependent reactions in such a way that steady states can be reached on the same time scale but with significantly fewer computational steps. The relationships between reaction affinities, free energy changes and generalized detailed balance are central to the discussion. The significance for applications in systems biology are discussed as is the concept and assumption of maximum entropy production rate as a biological principle that links thermodynamics to natural selection.

Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

Constraint-Based Reconstruction and Analysis (COBRA) is currently the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We have developed a quadruple-precision version of our linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.