# Bidirectionality and Compartmentation of Metabolic Fluxes Are Revealed in the Dynamics of Isotopomer Networks

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{13}C

_{1,2}acetate and unlabeled glucose.

#### 1.1. Motivation for exploiting the dynamic transient

^{13}C NMR to track metabolite dynamics. Although little is known about protein turnover rates in vivo prokaryotes are expected to display less protein turnover than eukaryotes [14]. Isotopic dynamics in prokaryotes avoids the most obvious types of compartmentalization, so most examples of MFA in this review are taken from eukaryotic systems.

## 2. Dynamic MFA in eukaryotic systems

#### 2.1. Flux analysis with non-steady metabolism

#### 2.2. Utilizing metabolic oscillations

## 3. Building predictive kinetic models

#### 3.1. Measurement of in vivo kinetics

^{31}P NMR to study the energy metabolism in hearts is a good example of how compartmentalization and bi-directionality of reaction steps complicates the analysis of a small network of reactions.

_{1}value [39].

^{18}O atoms as a function of the enrichment of

^{18}O in the water [43]. The size of metabolic pools can be calculated from the distribution of these molecular species at isotopic equilibrium, and using the time course of

^{18}O incorporation into the high-energy phosphoryls one can determine the rate of hydrolysis of the energy metabolites [43].

^{18}O transient is induced, followed by freeze clamping in liquid nitrogen and a long preparatory procedure prior to analysis in the mass spectrometer.

^{18}O in the energy metabolites of toad skeletal muscle, Dawis et al. [43] assumed that the fluxes through the enzymatic complexes were uni-directional and only one

^{18}O could be incorporated per molecular turnover. They judiciously discussed the issues bi-directional reaction steps within enzymatic complexes and wrote that “In practice, it will be difficult to verify a multiple-reversal model for the intact cell. Consequently, it will not be easy to choose between a multiple reversal model and a compartmentalization model.” Dawis et al. [43] also stressed that the influence of bi-directional reaction steps “should be examined but will be difficult to prove.”

^{18}O transfer studies is probably not enough to distinguish between possible reaction networks with various combinations of compartmentalization and bi-directional fluxes. Because of these limitations the above assumption of uni-directional fluxes was applied in a series of papers that explored the kinetics and compartmentalization of energy metabolism in rat skeletal muscle [44, 45, 46, 47, 48]. However, the assumption of uni-directional fluxes is not a necessary limitation of the method and should be evaluated in future studies.

^{31}P NMR can be enhanced by the use of either a

^{17}O or

^{18}O induced isotope shift in the

^{31}P NMR spectra. Pucar et al. [49] introduced the

^{18}O assisted

^{31}P NMR method to study energetics in mouse heart. The method was employed in a series of papers exploring compartmentalized energetics [50, 51, 52] [53, Pages 178–181], with each study using the above mass spectroscopy method to determine longer time

^{18}O transfer kinetics, all with the same assumption of uni-directional fluxes. The development of improved methods utilizing NMR saturation and inversion will extend the range of applicability of this powerful technique [54, 55] while reducing the labor required.

## 4. Simulation of isotopic transients

#### 4.1. Composition of the metabolic network

#### 4.2. Solving for the isotopic transient state

^{13}C and end at isotopic equilibrium at an enriched

^{13}C state with steady isotopomer population distribution. Thus, the steady state isotopomer distribution for each metabolite is found from the last points of the simulation when the system has reached isotopic steady state.

^{12}C and 1’s representing

^{13}C.

^{13}C

_{1,2}acetate. Two simulations were made with two different sets of metabolic pool sizes (A and B). The pool sizes of all metabolites in both sets were selected at random over three orders of magnitude. All net flux and exchange flux parameters were the same in both simulations. Since only metabolic pool sizes were changed between simulations, the steady state isotopomer distribution are identical for both simulations, as expected. The isotopic transients of the most highly enriched isotopomers of mitochondrial citrate from both simulations are given in Figure 2. Comparing the transient curves for the same isotopomers between pool size set A and B, it is clear that they exhibit the same general transient shape with the main difference being the time scale of the transient. Figure 2 does not show every isotopomer, however all carbons become enriched in

^{13}C when acetate is used as the tracer illustrating the usefulness of this inexpensive tracer for studying the TCA cycle.

^{13}C

_{1,2,3}pyruvate, and (3) a step change in both fully labeled acetate and fully labeled pyruvate together. All other parameters, including metabolic pool sizes, net fluxes, and exchange fluxes were the same in all three simulations. The citrate isotopomers from these three simulations are given in Figure 3.

## 5. Extracting information from isotopomeric data

^{13}C enrichment probability.

#### 5.1. Inclusion of metabolic pool sizes

^{13}C

_{1,2}isotopomer of citrate. With this in mind, transient data that is able to capture the shape and timing of major transient curves like this one are useful for constraining not only the net fluxes and bi-directionality of the metabolic network, but also metabolic pool sizes. If the pool size found by optimization does not match that measured during the experiment, it could be a clue that this metabolic pool is compartmentalized. Other clues in the shape of these transients also aid in identifying compartmentalization.

#### 5.2. Compartmentalization is revealed in the dynamics

_{i}with B

_{j}and their pool sizes. ATP exhibits compartmentalization in cardiomyocytes and astrocytes, as evidenced by a

^{31}P NMR saturation and inversion analysis of the creatine kinase reaction[60]:

#### 5.3. Example optimization of the TCA cycle in yeast

^{13}C NMR absolute and conditional enrichments from the carbon skeleton of proteinogenic amino acids harvested and hydrolyzed at isotopic steady state. This excludes the optimization of pool sizes so they have all been set to be equal to simplify simulation, and all comparisons to measured data were made at the last time point simulated after all isotopic dynamics reached steady state.

## 6. Conclusions

## Acknowledgments

## References and Notes

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**Figure 1.**Metabolic scheme with atom mapping and bi-directional compartmentalization between mitochondria (shaded green) and cytosol. Carbon numbers correspond to chemical nomenclature and the arrows between them indicate bi-directionality. Each reaction label is given above the red arrows that indicate the assumed net positive reaction flux. Pyruvate (PYx) derived from extracellular glucose and acetate (ACx) are inflows to the system (blue), and CO

_{2}and amino acids are outflows(red). Metabolite abbreviations are given in Table 1. Green carbons indicate biomass precursor metabolites with mappings to the amino acids they produce. Carbons of the same color are equivalent due to molecular symmetry.

**Figure 2.**The isotopic transient of the metabolic system given in Figure 1 was simulated with two different sets of metabolic pool sizes chosen at random over three orders of magnitude. All other parameters are the same between the two simulations. For clarity, only the isotopomers of mitochondrial citrate reaching the highest enrichment are included with their nomenclature explained in the text.

**Figure 3.**Three simulations of isotopic dynamics in the metabolic system given in Figure 1 were performed with identical net flux, exchange flux, and metabolic pool sizes. Isotopic transients of mitochondrial citrate are given following a switch to: (1) fully labeled acetate, (2) fully labeled pyruvate, and (3) both fully labeled acetate and pyruvate. For clarity, only the isotopomers of mitochondrial citrate reaching the highest enrichment are included.

**Figure 4.**Optimization of example system with absolute and conditional

^{13}C NMR data. Simulated points are marked with stars and measured data are marked with circles. Absolute enrichments are written with one carbon label, and conditional enrichments have a second carbon label. Conditional enrichment is the probability of

^{13}C enrichment in the first carbon when the second carbon is a

^{13}C.

**Figure 5.**Simulated steady state isotopomer distribution of mitochondrial and cytosolic oxaloacetate. Since the isotopomers differ between compartments comparing the simulation with measured data can help determine the functional location of biosynthesis reactions.

Metabolite | Abbreviation | |
---|---|---|

Cytosolic | Mitochondrial | |

acetate | ACo | |

acetyl-CoA | AcCoAo | AcCoAm |

pyruvate | PYo | PYm |

PY biomass precursor | PBm | |

citrate/isocitrate | CIm | |

oxaloacetate | OAo | OAm |

succinate | SUm | |

malate | MAm | |

2-oxoglutarate | OGm |

© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

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**MDPI and ACS Style**

Schryer, D.W.; Peterson, P.; Paalme, T.; Vendelin, M.
Bidirectionality and Compartmentation of Metabolic Fluxes Are Revealed in the Dynamics of Isotopomer Networks. *Int. J. Mol. Sci.* **2009**, *10*, 1697-1718.
https://doi.org/10.3390/ijms10041697

**AMA Style**

Schryer DW, Peterson P, Paalme T, Vendelin M.
Bidirectionality and Compartmentation of Metabolic Fluxes Are Revealed in the Dynamics of Isotopomer Networks. *International Journal of Molecular Sciences*. 2009; 10(4):1697-1718.
https://doi.org/10.3390/ijms10041697

**Chicago/Turabian Style**

Schryer, David W., Pearu Peterson, Toomas Paalme, and Marko Vendelin.
2009. "Bidirectionality and Compartmentation of Metabolic Fluxes Are Revealed in the Dynamics of Isotopomer Networks" *International Journal of Molecular Sciences* 10, no. 4: 1697-1718.
https://doi.org/10.3390/ijms10041697