University of Groningen
On a quest for metabolic fluxes: sampling and inference tools using thermodynamics,
metabolome and labelling data
Taborda Saldida Alves, Joana
DOI:
10.33612/diss.157440136
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below.
Document Version
Publisher's PDF, also known as Version of record
Publication date: 2021
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Taborda Saldida Alves, J. (2021). On a quest for metabolic fluxes: sampling and inference tools using thermodynamics, metabolome and labelling data. University of Groningen.
https://doi.org/10.33612/diss.157440136
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summary
As key quantifiers of metabolism, metabolic fluxes are essential for metabolic engineering, medicine and fundamental research. Since they cannot be measured experimentally, mathematical models are used for inference of fluxes in a method called metabolic flux analysis. Diverse types of constraints and techniques are used to tackle the uncertainty in flux estimation that originates from the large number of degrees of freedom of the mathematical problem. Thermodynamics can be used as an extra constraint and sampling allows the exploration of the flux solution space defined by the constraints. However, sampling the flux solution space with thermodynamic constraints is a very challenging problem due to the non-convexity of the space, as discussed in Chapter 1. The current state-of-the-art method to infer fluxes, 13C-metabolic
flux analysis, allies a stoichiometric model to labelling data and exchange fluxes to find the best agreement between model prediction and measurements. However, as demonstrated in Chapter 1, this method suffers from limitations regarding network size and compartmentation. To overcome such limitations, heuristic assumptions are often employed to fix reactions directions and reversibility. The objective of this thesis was to develop new tools for flux inference and uncertainty quantification without use of heuristic assumptions on reaction direction and reversibility.
In Chapter 2, we devised a three-step approach to infer metabolic fluxes. Making use of stoichiometric and thermodynamic constraints, allied with exchange flux and metabolite concentration measurements, we determined the limits of the flux solution space for a specific metabolic mode. To characterise the flux solution space and quantify the uncertainty of fluxes, we developed a new method to sample the high-dimensional, non-convex solution space defined by the employed constraints. This sampling method was achieved by splitting the thermodynamically feasible solution space into convex
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summarypolytopes. Finally, we fitted a stoichiometric model to 13C-labelling data to score the
sampled fluxes and find the most probable values. This last step was also performed including an extra constraint based on the flux force relationship and sampled Gibbs energies of reaction. With this three-step approach, we were able to estimate fluxes while avoiding assumptions on reaction direction and reversibility. Additionally, the new sampling method allowed the characterisation of a flux solution space defined by stoichiometric and thermodynamic constraints, which was not possible before and it can be used for the quantification of flux uncertainty. Applied to two strains of S. cerevisiae, our method unravelled new flux patterns not previously uncovered.
In Chapter 3 we evaluated the strengths and weaknesses of different sampling strate-gies when applied to network models of different complexity. Using the approach of splitting the thermodynamically feasible solution space into convex polytopes, we implemented a Rejection Sampler, a Conditional Sampler, and a Conditional Sampler with parallel tempering, that we applied to two metabolic networks of different size and complexity. The evaluation pipeline consisted of an applicability test, autocor-relation analysis and convergence diagnostics to find the most efficient sampler. For a small network of 82 reactions, we found that the Rejection Sampler was preferable, while for a larger network of 258 reactions the Conditional Sampler was necessary to increase efficiency. With the added complexity of an energy balance constraint, only a Conditional Sampler with parallel tempering was able to sample the flux solution space of either network. We expect that this analysis will increase the confidence in sampling thermodynamically constrained flux solution spaces with the new method.
In conclusion, the new flux inference approach generates flux distributions that are in agreement with stoichiometry, thermodynamics, and data on exchange fluxes, metabolite concentrations and labelling, without use of assumptions on reaction direction or reversibility. Sampling thermodynamically constrained flux solution spaces will be a useful tool in metabolic flux analysis studies, for quantification of flux uncertainty and to explore relationships between different parts of metabolism. We envision that the overall method will be an asset to validate existing hypothesis, uncover new flux patterns and estimate fluxes with more realistic network models or in higher organisms.
