Abstract
Metabolic adaptations to complex perturbations, like the response to pharmacological treatments in multifactorial diseases such as cancer, can be described through measurements of part of the fluxes and concentrations at the systemic level and individual transporter and enzyme activities at the molecular level. In the framework of Metabolic Control Analysis (MCA), ensembles of linear constraints can be built integrating these measurements at both systemic and molecular levels, which are expressed as relative differences or changes produced in the metabolic adaptation. Here, combining MCA with Linear Programming, an efficient computational strategy is developed to infer additional non-measured changes at the molecular level that are required to satisfy these constraints. An application of this strategy is illustrated by using a set of fluxes, concentrations, and differentially expressed genes that characterize the response to cyclin-dependent kinases 4 and 6 inhibition in colon cancer cells. Decreases and increases in transporter and enzyme individual activities required to reprogram the measured changes in fluxes and concentrations are compared with down-regulated and up-regulated metabolic genes to unveil those that are key molecular drivers of the metabolic response.
Highlights
Metabolism is a structured network of metabolites connected by transporters and enzyme-catalyzed reactions
On the one hand, when there is a lack of detailed information at the molecular level, the dependencies between systemic reaction fluxes can be explored by stoichiometric models [6]
Several frameworks have been developed in this context of uncertainty, including approximate rate laws, such as-linear or power-law based on linear Taylor’s approximation [11]. These strategies are valid in the proximity of a reference steady-state and usually are associated with Metabolic Control Analysis (MCA) [15,16,17,18,19] or the closely related Biochemical Systems Theory (BST) [20,21]
Summary
Metabolism is a structured network of metabolites connected by transporters and enzyme-catalyzed reactions. A variety of optimization methods have exploited the dependencies among steady-state concentrations, fluxes, and system parameters such as enzyme levels or variations of them They can take advantage of the particular formulation of the rate laws used in time-dependent differential equations, such as (log)-linear in MCA [34,35,36] and S-system and Generalized Mass Action (GMA) in BST [22,23,24,25,37]. In the methodology proposed in this paper, by combining MCA and LP, required decreases and increases previously unknown are extracted from linear constraints involving continuous domains in the form of bounded (closed) intervals measuring the differences in reaction fluxes, metabolite concentrations, and individual activities comparing the initial and final states during the adaptation to a metabolic perturbation. With the cancer-case study, we illustrate the application of the proposed methodology identifying such metabolic drivers by comparing changes in gene expression and changes required in the transporter and enzyme activities identified by the combination of MCA and LP
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