Important syntheses in living systems occur by condensation reactions of the type nA----1B (where n is the number of A molecules needed to synthesize 1 molecule of B). Quantitative relationships for estimating the rate of synthesis of B from radioactive and stable isotope tracers are compared. With radioisotope tracers, only a single quantity is detected, the amount of radioactivity in B. In contrast, isotopes of varying mass produce multiple mass isotopomers B that are detected using mass spectrometry. The analysis demonstrates that the rate of synthesis of B is identifiable from stable isotope data but not from radioisotope data. This results because the isotopomer distribution of B at any time after tracer addition is a function of only the multinomial distribution representing the synthesis of B from n molecules of A and two parameters representing the fractional fluxes of isotopically enriched molecules to the sampled compartment of B. The model considers the possibility that the sampled compartment of B may not reach isotopic steady state during the experiment. A graphical method for obtaining initial estimates of the two parameters is presented.
A new analysis of stable isotope data for biosynthesis reaction, isotopomer spectral analysis (ISA), is demonstrated. ISA is theoretically applicable for polymerization biosynthesis where data are collected using selected ion-monitoring gas chromatography-mass spectrometry. ISA utilizes the discrete spectrum of isotopomer abundances and the multinomial distribution to estimate two key parameters related to the biosynthesis. These parameters are 1) the dilution of the precursor immediately before biosynthesis and 2) the dilution of the newly synthesized product in the sampled compartment. Differentiated 3T3-L1 cells incorporated 2 mM [1,2-13C]acetate into triglyceride palmitate, yielding a spectrum of mass isotopomers of palmitate. The set of equations for the first nine isotopomers were solved for the two parameters using nonlinear regression. We found that precursor dilutions for acetate and glucose were constant over time, whereas the product dilution parameter increased with time, as expected for cells accumulating triglyceride palmitate. Mathematical procedures are presented for calculating 1) the predicted isotopomer fractional abundance values and 2) the correction for atoms other than the tracer atom in the mass ion.
Cholesterol synthesis from 13C-labeled precursors produces a discrete spectrum of mass isotopomers detectable using gas chromatography-mass spectrometry. The isotopomer spectral analysis (ISA) method matches the observed spectrum of cholesterol isotopomers with a mathematical model to obtain the best fit of model spectrum to data spectrum. The model was based on multinomial probability expressions that simulate cholesterol synthesis as a condensation of mevalonate fragments. As many as four unknown parameters, representing fluxes between compartments, were included in the model. Models were developed to assess cholesterol synthesis from 13C-enriched precursors including mevalonate, acetate, acetoacetate or octanoate. Models were tested in the human hepatoma cell line, Hep G2, which readily incorporated the 13C substrates into cholesterol. The ISA approach was used to estimate the fractional amount of the cholesterol precursors derived from the 13C substrate and the fraction of total cellular cholesterol synthesized in the presence of the 13C substrate. The study demonstrated the feasibility of the ISA approach for a condensation biosynthesis that is not a simple polymerization and for models with more than two unknown parameters.
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