Flux sampling is a powerful tool to study metabolism under changing environmental conditions

Abstract

The development of high-throughput 'omic techniques has sparked a rising interest in genome-scale metabolic models, with applications ranging from disease diagnostics to crop adaptation. Efficient and accurate methods are required to analyze large metabolic networks. Flux sampling can be used to explore the feasible flux solutions in metabolic networks by generating probability distributions of steady-state reaction fluxes. Unlike other methods, flux sampling can be used without assuming a particular cellular objective. We have undertaken a rigorous comparison of several sampling algorithms and concluded that the coordinate hit-and-run with rounding (CHRR) algorithm is the most efficient based on both run-time and multiple convergence diagnostics. We demonstrate the power of CHRR by using it to study the metabolic changes that underlie photosynthetic acclimation to cold of Arabidopsis thaliana plant leaves. In combination with experimental measurements, we show how the regulated interplay between diurnal starch and organic acid accumulation defines the plant acclimation process. We confirm fumarate accumulation as a requirement for cold acclimation and further predict γ-aminobutyric acid to have a key role in metabolic signaling under cold conditions. These results demonstrate how flux sampling can be used to analyze the feasible flux solutions across changing environmental conditions, whereas eliminating the need to make assumptions which introduce observer bias.

Keywords: Biochemical networks; Plant sciences.

Fig. 1

Summary of the general influx and outflux of the Arnold model, as set up in our analysis. Differences in pathways linking carbon assimilation and diurnal carbon storage were compared across the two temperatures (20 °C and 4 °C) in order to predict metabolic changes required for cold acclimation of A. thaliana

Fig. 2

Run-times for each of the algorithms on their respective platforms (CHRR: MATLAB; ACHR: Python; OPTGP: Python) when sampling flux solution for the Poolman a, Dal’Molin b, and Arnold model c. Trace and autocorrelation (ACF) plots (showing sampling chains and sample dependence, respectively) for chains of length 5000 with thinnings of T = 100, 1000, and 10,000 of the biomass reaction, as obtained when using each of the algorithms on the Arnold model

Fig. 3

Carbon influx and outflux and organic carbon compound accumulation in leaves. Measurements were taken at control conditions (red) and after 7 days of cold treatment (blue), at the beginning of day (BOD) and at the end of day (EOD), using infrared gas analysis and enzyme assays. The s.e.m. of the 3–4 replicates for each measurement is shown as error bars. The above data (excluding carbon outflux) were converted to $\frac{mmol}{gFW\cdot Day}$ and used to constrain the Arnold model as outlined in the method. Significant differences between measurements across the two temperature conditions are indicated by an asterisk

Fig. 4

Flux sampling distributions of key reactions linking photosynthetic input (CO₂) to transient carbon storage for control (red) and cold (blue) conditions. Condition-specific carbon assimilation and fumarate (FUM), malate (MAL), and starch accumulation were constrained according to experimentally measured results. Resulting fluxes of reactions including triose phosphate (TP), fructose 1,6-bisphosphate (F6P), glyceraldehyde 3-phosphate (G3P), pyruvate (PYR), arginosuccinate (AS), arginine (ARG), phosphoenolpyruvate carboxylase (PEP), oxaloacetate (OAA), γ-aminobutyric acid (GABA), acetyl coenzyme A (ACoA), and sucrose (Suc) are shown. We overlaid FBA results for maximum biomass production (under the same model constraints as applied for the sampling) as vertical blue and red bars over the flux sampling distributions. Reactions for which the two distributions are significantly different (p < 0.001; Kruskal–Wallis) are marked with an asterisk in the top right corner