Improved metabolite profile smoothing for flux estimation

Towards inferring absolute concentrations from relative abundance in time-course GC-MS metabolomics data

Metabolomics, the large-scale study of metabolites, has significant appeal as a source of information for metabolic modeling and other scientific applications. One common approach for measuring metabolomics data is gas chromatography-mass spectrometry (GC-MS). However, GC-MS metabolomics data are typically reported as relative abundances, precluding their use with approaches and tools where absolute concentrations are necessary. While chemical standards can be used to help provide quantification, their use is time-consuming, expensive, or even impossible due to their limited availability. The ability to infer absolute concentrations from GC-MS metabolomics data without chemical standards would have significant value. We hypothesized that when analyzing time-course metabolomics datasets, the mass balances of metabolism and other biological information could provide sufficient information towards inference of absolute concentrations. To demonstrate this, we developed and characterized MetaboPAC, a computational framework that uses two approaches-one based on kinetic equations and another using biological heuristics-to predict the most likely response factors that allow translation between relative abundances and absolute concentrations. When used to analyze noiseless synthetic data generated from multiple types of kinetic rate laws, MetaboPAC performs significantly better than negative control approaches when 20% of kinetic terms are known a priori. Under conditions of lower sampling frequency and high noise, MetaboPAC is still able to provide significant inference of concentrations in 3 of 4 models studied. This provides a starting point for leveraging biological knowledge to extract concentration information from time-course intracellular GC-MS metabolomics datasets, particularly for systems that are well-studied and have partially known kinetic structures.

Diverse classes of constraints enable broader applicability of a linear programming-based dynamic metabolic modeling framework

Current metabolic modeling tools suffer from a variety of limitations, from scalability to simplifying assumptions, that preclude their use in many applications. We recently created a modeling framework, Linear Kinetics-Dynamic Flux Balance Analysis (LK-DFBA), that addresses a key gap: capturing metabolite dynamics and regulation while retaining a potentially scalable linear programming structure. Key to this framework's success are the linear kinetics and regulatory constraints imposed on the system. However, while the linearity of these constraints reduces computational complexity, it may not accurately capture the behavior of many biochemical systems. Here, we developed three new classes of LK-DFBA constraints to better model interactions between metabolites and the reactions they regulate. We tested these new approaches on several synthetic and biological systems, and also performed the first-ever comparison of LK-DFBA predictions to experimental data. We found that no single constraint approach was optimal across all systems examined, and systems with the same topological structure but different parameters were often best modeled by different types of constraints. However, we did find that when genetic perturbations were implemented in the systems, the optimal constraint approach typically remained the same as for the wild-type regardless of the model topology or parameterization, indicating that just a single wild-type dataset could allow identification of the ideal constraint to enable model predictivity for a given system. These results suggest that the availability of multiple constraint approaches will allow LK-DFBA to model a wider range of metabolic systems.

SCOUR: a stepwise machine learning framework for predicting metabolite-dependent regulatory interactions

BACKGROUND

The topology of metabolic networks is both well-studied and remarkably well-conserved across many species. The regulation of these networks, however, is much more poorly characterized, though it is known to be divergent across organisms-two characteristics that make it difficult to model metabolic networks accurately. While many computational methods have been built to unravel transcriptional regulation, there have been few approaches developed for systems-scale analysis and study of metabolic regulation. Here, we present a stepwise machine learning framework that applies established algorithms to identify regulatory interactions in metabolic systems based on metabolic data: stepwise classification of unknown regulation, or SCOUR.

RESULTS

We evaluated our framework on both noiseless and noisy data, using several models of varying sizes and topologies to show that our approach is generalizable. We found that, when testing on data under the most realistic conditions (low sampling frequency and high noise), SCOUR could identify reaction fluxes controlled only by the concentration of a single metabolite (its primary substrate) with high accuracy. The positive predictive value (PPV) for identifying reactions controlled by the concentration of two metabolites ranged from 32 to 88% for noiseless data, 9.2 to 49% for either low sampling frequency/low noise or high sampling frequency/high noise data, and 6.6-27% for low sampling frequency/high noise data, with results typically sufficiently high for lab validation to be a practical endeavor. While the PPVs for reactions controlled by three metabolites were lower, they were still in most cases significantly better than random classification.

CONCLUSIONS

SCOUR uses a novel approach to synthetically generate the training data needed to identify regulators of reaction fluxes in a given metabolic system, enabling metabolomics and fluxomics data to be leveraged for regulatory structure inference. By identifying and triaging the most likely candidate regulatory interactions, SCOUR can drastically reduce the amount of time needed to identify and experimentally validate metabolic regulatory interactions. As high-throughput experimental methods for testing these interactions are further developed, SCOUR will provide critical impact in the development of predictive metabolic models in new organisms and pathways.

LK-DFBA: a linear programming-based modeling strategy for capturing dynamics and metabolite-dependent regulation in metabolism

BACKGROUND

The systems-scale analysis of cellular metabolites, "metabolomics," provides data ideal for applications in metabolic engineering. However, many of the computational tools for strain design are built around Flux Balance Analysis (FBA), which makes assumptions that preclude direct integration of metabolomics data into the underlying models. Finding a way to retain the advantages of FBA's linear structure while relaxing some of its assumptions could allow us to account for metabolite levels and metabolite-dependent regulation in strain design tools built from FBA, improving the accuracy of predictions made by these tools. We designed, implemented, and characterized a modeling strategy based on Dynamic FBA (DFBA), called Linear Kinetics-Dynamic Flux Balance Analysis (LK-DFBA), to satisfy these specifications. Our strategy adds constraints describing the dynamics and regulation of metabolism that are strictly linear. We evaluated LK-DFBA against alternative modeling frameworks using simulated noisy data from a small in silico model and a larger model of central carbon metabolism in E. coli, and compared each framework's ability to recapitulate the original system.

RESULTS

In the smaller model, we found that we could use regression from a dynamic flux estimation (DFE) with an optional non-linear parameter optimization to reproduce metabolite concentration dynamic trends more effectively than an ordinary differential equation model with generalized mass action rate laws when tested under realistic data sampling frequency and noise levels. We observed detrimental effects across all tested modeling approaches when metabolite time course data were missing, but found these effects to be smaller for LK-DFBA in most cases. With the E. coli model, we produced qualitatively reasonable results with similar properties to the smaller model and explored two different parameterization structures that yield trade-offs in computation time and accuracy.

CONCLUSIONS

LK-DFBA allows for calculation of metabolite concentrations and considers metabolite-dependent regulation while still retaining many computational advantages of FBA. This provides the proof-of-principle for a new metabolic modeling framework with the potential to create genome-scale dynamic models and the potential to be applied in strain engineering tools that currently use FBA.