SUMMARY: Shu is a visualization tool that integrates diverse data types into a metabolic map, with a focus on supporting multiple conditions and visualizing distributions. The goal is to provide a unified platform for handling the growing volume of multi-omics data, leveraging the metabolic maps developed by the metabolic modeling community. In addition, shu offers a streamlined python API, based on the Grammar of Graphics, for easy integration with data pipelines. AVAILABILITY AND IMPLEMENTATION: Freely available at https://github.com/biosustain/shu under MIT/Apache 2.0 license. Binaries are available in the release page of the repository and the web application is deployed at https://biosustain.github.io/shu.

BACKGROUND: Uniform random sampling of mass-balanced flux solutions offers an unbiased appraisal of the capabilities of metabolic networks. Unfortunately, it is impossible to avoid thermodynamically infeasible loops in flux samples when using convex samplers on large metabolic models. Current strategies for randomly sampling the non-convex loopless flux space display limited efficiency and lack theoretical guarantees. RESULTS: Here, we present LooplessFluxSampler, an efficient algorithm for exploring the loopless mass-balanced flux solution space of metabolic models, based on an Adaptive Directions Sampling on a Box (ADSB) algorithm. ADSB is rooted in the general Adaptive Direction Sampling (ADS) framework, specifically the Parallel ADS, for which theoretical convergence and irreducibility results are available for sampling from arbitrary distributions. By sampling directions that adapt to the target distribution, ADSB traverses more efficiently the sample space achieving faster mixing than other methods. Importantly, the presented algorithm is guaranteed to target the uniform distribution over convex regions, and it provably converges on the latter distribution over more general (non-convex) regions provided the sample can have full support. CONCLUSIONS: LooplessFluxSampler enables scalable statistical inference of the loopless mass-balanced solution space of large metabolic models. Grounded in a theoretically sound framework, this toolbox provides not only efficient but also reliable results for exploring the properties of the almost surely non-convex loopless flux space. Finally, LooplessFluxSampler includes a Markov Chain diagnostics suite for assessing the quality of the final sample and the performance of the algorithm.

The topology of metabolic networks is recognisably modular with modules weakly connected apart from sharing a pool of currency metabolites. Here, we defined modules as sets of reversible reactions isolated from the rest of metabolism by irreversible reactions except for the exchange of currency metabolites. Our approach identifies topologically independent modules under specific conditions associated with different metabolic functions. As case studies, the E.coli iJO1366 and Human Recon 2.2 genome-scale metabolic models were split in 103 and 321 modules respectively, displaying significant correlation patterns in expression data. Finally, we addressed a fundamental question about the metabolic flexibility conferred by reversible reactions: "Of all Directed Topologies (DTs) defined by fixing directions to all reversible reactions, how many are capable of carrying flux through all reactions?". Enumeration of the DTs for iJO1366 model was performed using an efficient depth-first search algorithm, rejecting infeasible DTs based on mass-imbalanced and loopy flux patterns. We found the direction of 79% of reversible reactions must be defined before all directions in the network can be fixed, granting a high degree of flexibility.

MOTIVATION: We achieve a significant improvement in thermodynamic-based flux analysis (TFA) by introducing multivariate treatment of thermodynamic variables and leveraging component contribution, the state-of-the-art implementation of the group contribution methodology. Overall, the method greatly reduces the uncertainty of thermodynamic variables. RESULTS: We present multiTFA, a Python implementation of our framework. We evaluated our application using the core Escherichia coli model and achieved a median reduction of 6.8 kJ/mol in reaction Gibbs free energy ranges, while three out of 12 reactions in glycolysis changed from reversible to irreversible. AVAILABILITY AND IMPLEMENTATION: Our framework along with documentation is available on https://github.com/biosustain/multitfa. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Random sampling of the solution space has emerged as a popular tool to explore and infer properties of large metabolic networks. However, conventional sampling approaches commonly used do not eliminate thermodynamically unfeasible loops. RESULTS: In order to overcome this limitation, we developed an efficient sampling algorithm called loopless Artificially Centered Hit-and-Run on a Box (ll-ACHRB). This algorithm is inspired by the Hit-and-Run on a Box algorithm for uniform sampling from general regions, but employs the directions of choice approach of Artificially Centered Hit-and-Run. A novel strategy for generating feasible warmup points improved both sampling efficiency and mixing. ll-ACHRB shows overall better performance than current strategies to generate feasible flux samples across several models. Furthermore, we demonstrate that a failure to eliminate unfeasible loops greatly affects sample statistics, in particular the correlation structure. Finally, we discuss recommendations for the interpretation of sampling results and possible algorithmic improvements. AVAILABILITY AND IMPLEMENTATION: Source code for MATLAB and OCTAVE including examples are freely available for download at http://www.aibn.uq.edu.au/cssb-resources under Software. Optimization runs can use Gurobi Optimizer (by default if available) or GLPK (included with the algorithm). CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Computation of steady-state flux solutions in large metabolic models is routinely performed using flux balance analysis based on a simple LP (Linear Programming) formulation. A minimal requirement for thermodynamic feasibility of the flux solution is the absence of internal loops, which are enforced using 'loopless constraints'. The resulting loopless flux problem is a substantially harder MILP (Mixed Integer Linear Programming) problem, which is computationally expensive for large metabolic models. RESULTS: We developed a pre-processing algorithm that significantly reduces the size of the original loopless problem into an easier and equivalent MILP problem. The pre-processing step employs a fast matrix sparsification algorithm-Fast- sparse null-space pursuit (SNP)-inspired by recent results on SNP. By finding a reduced feasible 'loop-law' matrix subject to known directionalities, Fast-SNP considerably improves the computational efficiency in several metabolic models running different loopless optimization problems. Furthermore, analysis of the topology encoded in the reduced loop matrix enabled identification of key directional constraints for the potential permanent elimination of infeasible loops in the underlying model. Overall, Fast-SNP is an effective and simple algorithm for efficient formulation of loop-law constraints, making loopless flux optimization feasible and numerically tractable at large scale. AVAILABILITY AND IMPLEMENTATION: Source code for MATLAB including examples is freely available for download at http://www.aibn.uq.edu.au/cssb-resources under Software. Optimization uses Gurobi, CPLEX or GLPK (the latter is included with the algorithm). CONTACT: [email protected] information: Supplementary data are available at Bioinformatics online.

Kinetic models provide the means to understand and predict the dynamic behaviour of enzymes upon different perturbations. Despite their obvious advantages, classical parameterizations require large amounts of data to fit their parameters. Particularly, enzymes displaying complex reaction and regulatory (allosteric) mechanisms require a great number of parameters and are therefore often represented by approximate formulae, thereby facilitating the fitting but ignoring many real kinetic behaviours. Here, we show that full exploration of the plausible kinetic space for any enzyme can be achieved using sampling strategies provided a thermodynamically feasible parameterization is used. To this end, we developed a General Reaction Assembly and Sampling Platform (GRASP) capable of consistently parameterizing and sampling accurate kinetic models using minimal reference data. The former integrates the generalized MWC model and the elementary reaction formalism. By formulating the appropriate thermodynamic constraints, our framework enables parameterization of any oligomeric enzyme kinetics without sacrificing complexity or using simplifying assumptions. This thermodynamically safe parameterization relies on the definition of a reference state upon which feasible parameter sets can be efficiently sampled. Uniform sampling of the kinetics space enabled dissecting enzyme catalysis and revealing the impact of thermodynamics on reaction kinetics. Our analysis distinguished three reaction elasticity regions for common biochemical reactions: a steep linear region (0> ΔGr >-2 kJ/mol), a transition region (-2> ΔGr >-20 kJ/mol) and a constant elasticity region (ΔGr <-20 kJ/mol). We also applied this framework to model more complex kinetic behaviours such as the monomeric cooperativity of the mammalian glucokinase and the ultrasensitive response of the phosphoenolpyruvate carboxylase of Escherichia coli. In both cases, our approach described appropriately not only the kinetic behaviour of these enzymes, but it also provided insights about the particular features underpinning the observed kinetics. Overall, this framework will enable systematic parameterization and sampling of enzymatic reactions.

Large quantities of information describing the mechanisms of biological pathways continue to be collected in publicly available databases. At the same time, experiments have increased in scale, and biologists increasingly use pathways defined in online databases to interpret the results of experiments and generate hypotheses. Emerging computational techniques that exploit the rich biological information captured in reaction systems require formal standardized descriptions of pathways to extract these reaction networks and avoid the alternative: time-consuming and largely manual literature-based network reconstruction. Here, we systematically evaluate the effects of commonly used knowledge representations on the seemingly simple task of extracting a reaction network describing signal transduction from a pathway database. We show that this process is in fact surprisingly difficult, and the pathway representations adopted by various knowledge bases have dramatic consequences for reaction network extraction, connectivity, capture of pathway crosstalk and in the modelling of cell-cell interactions. Researchers constructing computational models built from automatically extracted reaction networks must therefore consider the issues we outline in this review to maximize the value of existing pathway knowledge.