Estimation of flux ratios without uptake or release data: Application to serine and methionine metabolism

Abstract

Model-based metabolic flux analysis (MFA) using isotope-labeled substrates has provided great insight into intracellular metabolic activities across a host of organisms. One challenge with applying MFA in mammalian systems, however, is the need for absolute quantification of nutrient uptake, biomass composition, and byproduct release fluxes. Such measurements are often not feasible in complex culture systems or in vivo. One way to address this issue is to estimate flux ratios, the fractional contribution of a flux to a metabolite pool, which are independent of absolute measurements and yet informative for cellular metabolism. Prior work has focused on "local" estimation of a handful of flux ratios for specific metabolites and reactions. Here, we perform systematic, model-based estimation of all flux ratios in a metabolic network using isotope labeling data, in the absence of uptake/release data. In a series of examples, we investigate what flux ratios can be well estimated with reasonably tight confidence intervals, and contrast this with confidence intervals on normalized fluxes. We find that flux ratios can provide useful information on the metabolic state, and is complementary to normalized fluxes: for certain metabolic reactions, only flux ratios can be well estimated, while for others normalized fluxes can be obtained. Simulation studies of a large human metabolic network model suggest that estimation of flux ratios is technically feasible for complex networks, but additional studies on data from actual isotopomer labeling experiments are needed to validate these results. Finally, we experimentally study serine and methionine metabolism in cancer cells using flux ratios. We find that, in these cells, the methionine cycle is truncated with little remethylation from homocysteine, and polyamine synthesis in the absence of methionine salvage leads to loss of 5-methylthioadenosine, suggesting a new mode of overflow metabolism in cancer cells. This work highlights the potential for flux ratio analysis in the absence of absolute quantification, which we anticipate will be important for both in vitro and in vivo studies of cancer metabolism.

Keywords: Cancer metabolism; Metabolic flux analysis; Metabolic network; Methionine; Optimization; Serine; Simulation studies.

Figure 1

Illustration of notation for fluxes v_j, flux ratios ϕ_ij, and summations for a metabolite i. Elements $S_{ik}^{+}$ represent reactions entering into metabolite pool i, and elements of $S_{ik}^{-}$ reactions leaving the pool.

Figure 2

Toy example. (A) Network with flux vector used in simulations indicated. Atoms indicated by circles; top, substrate isotopomer used for simulaton experiments. Isotopomers in remaining metabolites are not shown. (B) Network as in A, augmented with a sink metabolite S, and with fluxes v₁, …, v₇ indicated (release fluxes R = {6, 7}). Asterisks mark a set of free fluxes. (C) Same as B, with flux ratios ϕ_ij indicated at arrowheads. In this example metabolites are indexed by letters for clarity.

Figure 3

Feasible fluxes and flux ratios for the sink-augmented network in Figure 2. (A) Portion of the feasible set of free fluxes, restricted to [0, 1]³ as indicated by dashed lines. With the sink flux v₀ fixed, v₇ is bounded but v₃ is not, due to exchange flux with v₄. (B) Set of feasible flux ratios (gray area) corresponding to the set in A. Cross indicates an infeasible flux state given by ϕ_A3 = 0.1, ϕ_S3 = 0.9.

Figure 4

Objective function f(ϕ) for the example of Figure 2, indicated by gray contours. Black region indicates the 90% confidence set with $f(\varphi )\le {\chi }_1^2(0.9)\approx 2.7$. Thick lines at the axes indicate the corresponding 90% confidence intervals for ϕ_A3 and ϕ_S7.

Figure 5

Simplified view of the TCA cycle model. Numbers indicate the flux vector used to simulate data for testing. Gray arrowheads indicate reversible reactions, while fluxes refer to the direction of black arrows; exchange fluxes were zero. Pyruvate carboxylase was present in the model but zero in the simulated flux state. Citrate lyase was modeled in the cytosolic compartment, here shown separated by double gray lines. Asterisks indicate measured metabolites. Cofactors and some intermediate steps are not shown; see supplementary dataset S1 for full model.

Figure 6

Estimated confidence intervals from human network model. (A) Histogram of width of confidence intervals (CIs) for normalized fluxes. (B) Histogram of width of CIs for flux ratios. Solid line indicates cumulative density function (CDF). (C) Scatter plot of CI widths for normalized fluxes and flux ratios. Examples discussed in text are indicated. GLUN, glutaminase; glu, glutamate; PDH, pyruvate dehydrogenase; accoa, acetyl-CoA; ALT, alanine transaminase; pyr, pyruvate.

Figure 7

Estimates of flux ratios in methionine/serine metabolism identifies a truncated methionine cycle. (A) Simplified view of metabolic network model with estimated parameters. Asterisks indicate metabolites with experimentally measured mass isotopomers. Percentages indicate 90% confidence bounds on flux ratios, other numbers indicate 90% bounds on normalized fluxes. See supplementary dataset S5 for full model. (B) Accumulation of 5-methylthioadenosine (5mta) in spent culture medium. Low values in fresh medium demonstrates that 5mta indeed derives from cells.

Figure A.8

(A) Example network from figure 3 transformed to graph form (fluxes have been renumbered). (B) the adjoint graph of the graph in A, with flux ratios indicated as edge weights.