Jeffry R. Alger^{1,2,3}, Gaurav Sharma^{1}, A. Dean Sherry^{1,4}, and Craig R. Malloy^{1,5}

^{1}Advanced Imaging Research Center, University of Texas, Southwestern Medical Center, Dallas, TX, United States, ^{2}Neurology, University of California, Los Angeles, Los Angeles, CA, United States, ^{3}NeuroSpectroScopics LLC, Sherman Oaks, CA, United States, ^{4}Department of Chemistry, Universiy of Texas at Dallas, Richardson, TX, United States, ^{5}Department of Internal Medicine, University of Texas-Southwestern Medical Center, Dallas, TX, United States

### Synopsis

tcaCALC has been developed as a MATLAB tool that facilitates the
quantitative analysis of metabolic tracing experiments that use ^{13}C
enriched tracers. The most recent version of tcaCALC facilitates analysis by
incorporating spectral fitting of J-coupled ^{13}C NMR multiplets and modeling complex metabolic situations in which specific metabolic fluxes may be
active or inactive. The MATLAB source code and a compiled version are available
for sharing to interested research teams.

### Introduction

tcaCALC is a MATLAB software tool for quantitative analyses of studies that use ^{13}C-enriched tracers to estimate flux through the tricarboxylic acid (TCA) cycle
and interconnected pathways (Figure 1). Analysis by ^{13}C-NMR spectroscopy is more informative than by radiotracing or mass spectrometry (MS). However there have been two limitations: 1) analysis of ^{13}C-NMR multiplets (from ^{13}C-^{13}C J-coupling) requires experience and 2) how to select which of the Figure 1 metabolic models best represents the potential biological complexity has been unclear. tcaCALC has been revised to address both issues.

tcaCALC can model experiments that use
combinations of all commercially available ^{13}C-enriched substrates. It uses non-linear-least-squares fitting to determine
the relative steady state fluxes through Pyruvate dehydrogenase (PDH), Pyruvate
Carboxylase (Ypc), Pyruvate Kinase (PK), and four-carbon anaplerosis (Ys). Each is expressed as a ratio with respect
to the TCA cycle rate. It fits measured metabolic product ^{13}C-enrichment,
to the metabolic models shown in Figure 1. Model01 is a generalized
model that potentially has nonzero values for each of the unknowns. The
12 additional candidate metabolic models (Model02 – Model16) are derived by
turning off (setting to zero and not fitting) all combinations of PDH, Ypc,
PK and Ys. Model06, Model10 and Model15 are not present in Figure 1 because these models
violate the steady state assumption. To facilitate ^{13}C-NMR analysis, tcaCALC can read spectra generated by Bruker and Agilent NMR systems.
After point/click identification of key ^{13}C signals in the
spectrum, a nonlinear least squares spectral-model based approach is used to estimate
the relative intensities of all user-requested metabolic product ^{13}C-NMR multiplets.### Methods

tcaCALC was developed using MATLAB 2017b. The software represents measured
and simulated ^{13}C-NMR multiplet and/or MS data together with metabolic models as MATLAB
structures that contain all relevant quantitative information, which
parameters are to be fit and the conditions for fit convergence. tcaCALC uses a
recently developed MATLAB version of tcaSIM (1) to simulate ^{13}C-enrichment of all relevant TCA cycle intermediates and products. It then generates simulated ^{13}C-NMR multiplet and/or MS intensities from the ^{13}C-enrichments. Metabolic model
fitting is performed by simultaneous non-linear-least-squares optimization of PDH, Ypc, Ys, PK and substrate enrichment (if necessary) driven by least squares agreement between simulated and measured ^{13}C-NMR multiplet and/or MS intensities.

Spectral fitting was validated against that performed with a commonly-used spectral fitting software package – ACD/NMR
Processor v 12.01 (Advanced Chemistry Development Inc).

Metabolic fitting was validated by simulating (with
tcaSIM) glutamate ^{13}C-NMR multiplet intensities over a range of metabolic conditions and
then fitting the simulated data with tcaCALC.### Results

Figure 2 provides an example of spectral fitting of the
glutamate C3 doublet and pseudo-triplet with tcaCALC. Detailed illustrations of
the spectral fitting module’s performance will be given at the formal
presentation.

Figure 3 illustrates the performance of tcaCALC's metabolic
model fitting module. Glutamate ^{13}C-NMR multiplets were used for this illustration
because isotopic metabolic tracing experiments typically produce substantial amounts of this ^{13}C-enriched product. For this illustration tcaSIM was used to simulate 8745 ^{13}C
glutamate spectra (15 glutamate multiplets per spectrum) that would be produced
in hypothetical experiments in which uniformly ^{13}C-enriched lactate having an
exactly known enrichment of 0.9 was provided as a substrate to metabolic systems operating over a range of metabolic conditions (0.0 < PDH < 1.0, 0.0 < Ypc, Ys,
PK < 5.0). The resulting simulated glutamate ^{13}C-NMR multiplets were then fitted to
each of candidate metabolic models using tcaCALC’s metabolic fitting module to produce estimates PDH, Ypc, Ys and PK. The Figure 3 plots show the distribution of PDH error
(PDH_{GroundTruth} – PDH_{BestFit}) as colored ‘clouds’ for
each of the ground truth metabolic models. The plots illustrate results when
fitting with only Model01, only Model02, only Model05, and only Model07 (bottom
to top). These results simulate the common practice of assuming that PK and/or
Ys are insignificant when lactate is used as a substrate and the primary study goal is to estimate PDH. Figure 3 (top) also illustrates the results of fitting
all 13 models and selecting which metabolic model best fits the glutamate ^{13}C-NMR multiplets. The
results illustrate that fitting to all candidate models and selecting
the best fit model shows superior performance (smaller and less frequent errors) with
regard to PDH estimation in comparison with arbitrary fitting with any
particular metabolic model. Further, it illustrates that use of fitting models
that have Ys and PK turned off can lead to significant error/bias in PDH
estimation in metabolic situations in which Ys and PK are actually active.
Further illustrations of error performance for Ypc, Ys and PK will be given at
the formal presentation.### Conclusion

tcaCALC has been developed as a tool that facilitates the
quantitative analysis of metabolic tracing studies that use ^{13}C
enriched substrate. The most recent version of tcaCALC includes novel features of 1) incorporating spectral fitting of J-coupled ^{13}C-NMR multiplets and 2) accommodating
possibility of complex metabolic situations in which PDH, Ypc, Ys and PK may be
active or inactive. The MATLAB source code and a compiled version is available to interested research teams.### Acknowledgements

Financial support from NIH/NIBIB P41 EB015908### References

Alger JR, Sherry AD, Malloy CR. tcaSIM: A simulation program for optimal design of 13C tracer experiments for analysis of metabolic flux by NMR and mass spectroscopy. Current Metabolomics 2018;6:176-187.