Abstract
Metabolic flux analysis (MFA) is a powerful approach for quantifying plant central carbon metabolism based upon a combination of extracellular flux measurements and intracellular isotope labeling measurements. In this chapter, we present the method of isotopically nonstationary 13C MFA (INST-MFA), which is applicable to autotrophic systems that are at metabolic steady state but are sampled during the transient period prior to achieving isotopic steady state following the introduction of 13CO2. We describe protocols for performing the necessary isotope labeling experiments, sample collection and quenching, nonaqueous fractionation and extraction of intracellular metabolites, and mass spectrometry (MS) analysis of metabolite labeling. We also outline the steps required to perform computational flux estimation using INST-MFA. By combining several recently developed experimental and computational techniques, INST-MFA provides an important new platform for mapping carbon fluxes that is especially applicable to autotrophic organisms, which are not amenable to steady-state 13C MFA experiments.
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Acknowledgements
This work was supported by NSF EF-1105249 and DOE DE-SC0008118. LJJ was supported by DOE SCGF DE-AC05-06OR23100 and GAANN P200A090323.
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Appendix: Simple Network Example for INST-MFA Calculations
Appendix: Simple Network Example for INST-MFA Calculations
A simple metabolic network appears in Fig. 6 as an example of how to construct the stoichiometric matrix S, identify the set of EMUs required to simulate MIDs of measured metabolites, and set up dynamic isotopomer balances on these EMUs. Table 3 delineates the atom transitions for the network. In this network example, metabolite A is the sole substrate and metabolite G is the only final product. The intermediary metabolites B, C, D, E, and F are assumed to be at metabolic steady state but isotopically nonstationary.
The stoichiometric matrix S is shown below, which has k = 5 intermediary metabolites and j = 8 fluxes, resulting in a 5 × 8 matrix:
Therefore, S∙v = 0 is expressed in vector form as
A systematic method of EMU network decoupling in which metabolite units are grouped into mutually dependent blocks is described through this simple network example. For this example, we will set up the simplest possible model to simulate the MID of metabolite C, i.e., EMU C123. First, we need to identify all the possible EMUs that contribute to the formation of C123—in this reaction model, C123 is formed from the condensation of B12 + E1 and D12 + F1 in reactions 2 and 4, respectively. This is recorded and the process is then repeated for all new EMUs, starting with the largest EMU in size; in this case, all EMUs of size 3 have already been identified. Next, the process is repeated to determine all the EMUs of size 2 that were previously identified, starting with D12. D12 is formed from two different reactions—from B12 in reaction 5 and from C23 in reaction 3. Following this, we determine which reactions form C23; C23 is formed from D12 in reaction 4 and B2 + E1 in reaction 2. Finally, we need to determine which reactions form B12. B12 is formed from A12 and D12 in reactions 1 and 6, respectively. A12 is a network substrate and is not produced by any other reactions and D12 has already been considered in the previous step. Therefore, all EMU reactions of size 2 have been identified. The process is repeated once again for EMUs of size 1, until all the EMUs have been traced back to network substrates or previously identified EMUs. Table 4 shows the complete EMU decomposition of this system, which involves 24 EMU reactions connecting 16 EMUs.
After EMU decomposition, the reaction network can be further decoupled into blocks, which group together minimal sets of mutually dependent metabolite units that must be solved simultaneously. Figure 7 shows the EMU network decomposition for the simple network example after block decoupling. The blocks are arranged so that each one is a self-contained subproblem, which will depend on the outputs of the previously solved blocks. Therefore, EMUs in block 1 should first be solved, then block 2, etc.
The EMU reactions obtained from network decomposition and block decoupling form the new basis for generating system equations. The decoupled blocks can be arranged into a cascaded system of ODEs with the following form, as described in Subheading 3.9:
The concentration matrix C n is a diagonal matrix whose elements are pool sizes corresponding to EMUs represented in X n . X n comprises row vectors that represent the MIDs of each EMU and dX n /dt is the time derivative of X n . Analogously, the input matrix Y n also comprises row vectors that represent MIDs of EMUs that have been previously calculated. The system matrices A n and B n come from calculating the “true” flux vectors (v) based on the chosen free fluxes (u) and null space matrix (N). Furthermore, in the decoupled blocks, the full MID of products formed from condensation reactions can be obtained from the convolution (or Cauchy product, denoted by “×”) of MIDs of preceding EMUs. In the case of C123, these MIDs are B12 and E1 or D12 and F1, i.e., C123 = B12 × E1 or C123 = D12 × F1. The following equations represent the system of ODEs for the simple network example:
Solving this system of ODEs will simulate the EMU labeling trajectories needed to calculate the time-dependent MID of metabolite C. The flux and pool size parameters can then be adjusted iteratively using an optimization search algorithm to converge on parameter values that minimize the lack of fit with experimental mass isotopomer data.
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Jazmin, L.J., O’Grady, J.P., Ma, F., Allen, D.K., Morgan, J.A., Young, J.D. (2014). Isotopically Nonstationary MFA (INST-MFA) of Autotrophic Metabolism. In: Dieuaide-Noubhani, M., Alonso, A. (eds) Plant Metabolic Flux Analysis. Methods in Molecular Biology, vol 1090. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-688-7_12
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