1 Department of Nutritional
Sciences, Mass isotopomer
distribution analysis (MIDA) is a technique for measuring the synthesis
of biological polymers. First developed approximately eight years ago,
MIDA has been used for measuring the synthesis of lipids,
carbohydrates, and proteins. The technique involves quantifying by mass
spectrometry the relative abundances of molecular species of a polymer
differing only in mass (mass isotopomers), after introduction of a
stable isotope-labeled precursor. The mass isotopomer pattern, or
distribution, is analyzed according to a combinatorial probability
model by comparing measured abundances to theoretical distributions
predicted from the binomial or multinomial expansion. For combinatorial
probabilities to be applicable, a labeled precursor must therefore
combine with itself in the form of two or more repeating subunits. MIDA
allows dilution in the monomeric (precursor) and polymeric (product)
pools to be determined. Kinetic parameters can then be calculated
(e.g., replacement rate of the polymer, fractional contribution from
the endogenous biosynthetic pathway, absolute rate of biosynthesis).
Several issues remain unresolved, however. We consider here the impact
of various deviations from the simple combinatorial probability model
of biosynthesis and describe the analytic requirements for successful
use of MIDA. A formal mathematical algorithm is presented for
generating tables and equations
(APPENDIX), on the basis of which
effects of various confounding factors are simulated. These include
variations in natural isotope abundances, isotopic disequilibrium in
the precursor pool, more than one biosynthetic precursor pool,
incorrect values for number of subunits present, and concurrent
measurement of turnover from exogenously labeled polymers. We describe
a strategy for testing whether isotopic inhomogeneity (e.g., an
isotopic gradient or separate biosynthetic sites) is present in the
precursor pool by comparing higher-mass (multiply labeled) to
lower-mass (single- and double-labeled) isotopomer patterns. Also, an
algebraic correction is presented for calculating fractional synthesis
when an incomplete ion spectrum is monitored, and an approach for
assessing the sensitivity of biosynthetic parameters to measurement
error is described. The different calculation algorithms published for MIDA are compared; all share a common model, use overlapping solutions to computational problems, and generate identical results. Finally, we
discuss the major practical issue for using MIDA at present: quantitative inaccuracy of instruments. The nature and causes of
analytic inaccuracy, strategies for evaluating instrument performance, and guidelines for optimizing accuracy and reducing impact on biosynthetic parameters are suggested. Adherence to certain analytic guidelines, particularly attention to concentration effects on mass
isotopomer ratios and maximizing enrichments in the isotopomers of
interest, reduces error. Improving instrument accuracy for quantification of isotopomer ratios is perhaps the highest priority for
this field. In conclusion, MIDA remains the "equation for biosynthesis," but attention to potentially confounding factors and
analytic performance is required for optimal application.
THE ASSEMBLY AND DISASSEMBLY of polymers
synthesized from repeating monomeric units is a central theme in
biology. Such polymers may be as simple as fatty acids synthesized from
acetyl-CoA units or as complex as proteins synthesized from amino acids
or DNA made from nucleotides. Other examples include carbohydrates
(e.g., glucose from triose units, glycogen from glucose,
glycoproteins), porphyrins (e.g., chlorophyll, heme), and lipids (e.g.,
cholesterol, triacylglycerols). Biological polymers may be homonuclear
(defined as containing subunits that are identical), as in fatty acids, or heteronuclear (defined as containing more than one type of subunit),
as in proteins or polynucleotides. Despite the importance of polymers
in the chemistry of living systems, techniques for determining their
rates of synthesis or breakdown have historically been unsatisfactory
(1, 9, 18, 19). As a consequence, fields as wide ranging as lipid
biosynthesis, protein metabolism, carbohydrate metabolic
regulation, and control of cell proliferation have been severely constrained.
In this article, we will provide an update and eight-year perspective
on a technique that provides a fundamental solution to the problem of
measuring polymerization biosynthesis. Mass isotopomer distribution
analysis (MIDA) is a technique based on combinatorial probabilities and
the labeling patterns in intact polymers that can be said to provide a
fundamental "equation for biosynthesis." Although MIDA was first
presented as a systematic approach to polymerization biosynthesis only
a few years ago (13-15, 20), a number of refinements, alternative
calculation algorithms, and criticisms have been published since then
(4, 5, 22, 31, 32). We will review here the theoretical and practical factors that must be taken into account if MIDA and related techniques are to be applied successfully.
The principle of isotope incorporation techniques for measuring
polymerization biosynthesis is, on the surface, straightforward. In a
biological system, polymers that are newly synthesized mix into a pool
that also contains preexisting polymer molecules. The goal of an
isotope incorporation study is to quantify the fraction of molecules in
the mixture that were newly synthesized during the label incorporation
period (i.e., "what's new") and the rate at which the total pool
of polymers is turning over. To determine the newly synthesized
fraction (f) present in the mixture,
one must first establish exactly how much label is contained in the
population of newly synthesized polymers. Dilution of this labeled
population by the population of preexisting, unlabeled molecules can
then be determined, according to the precursor-product relationship
(15, 22, 39, 40).
The major practical difficulty has been establishing how much label is
contained in the newly synthesized population of molecules. There
exists no purely physical technique for identifying in a mixed
population of molecules which ones are new and which are not. No
classical extraction technique can reveal where different molecules in
a population came from or how long they have been present. The
biochemistry of the precursor-product relationship provides a possible
solution, however (Fig. 1), because the
precursor pool of subunits in a cell has a physical reality and can in
principle be isolated by extraction techniques.
ABSTRACT
INTRODUCTION
BIOLOGICAL BASIS OF MEASUREMENT OF POLYMERIZATION
BIOSYNTHESIS BY ISOTOPE INCORPORATION
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Fig. 1.
Mass isotopomer distribution analysis (MIDA) principle.
A: combinatorial probabilities
determine the mass isotopomer pattern in polymers. In this simulation,
natural abundance or 10% labeled pools of a subunit combine into a
polymer of eight subunits. The population of each of these pools will
contain a characteristic distribution of
M0,
M1,
M2, and so on,
molecular species (mass isotopomers). These proportions can be
represented as a frequency histogram of the mass isotopomer pattern in
the polymer and can be measured by mass spectrometry. After correction
for natural abundance, degree of enrichment of precursor pool can be
calculated by comparing measured patterns of mass isotopomer abundances
with those predicted from theoretical precursor pool enrichments.
B: simple numerical example of MIDA
principle. C: three-dimensional
representation of change in fractional abundance
( A1) of a
particular mass isotopomer (in this case,
M1 of methyl
palmitate) as a function of p and
f. A plane is extended at values of
M1 = 0.05, 0.10, 0.15, 0.20 and 0.25, demonstrating the family of solutions for all
combinations of p and
f that give this value of
A1.
Inset: a 2-dimensional projection of
p vs.
f in the plane
A1 = 0.15. Note linearity of
A1 vs.
f.
Serious problems arise when investigators have tried to use surrogate monomer pools to represent the isotopic content of the true precursor pool (p) (9, 19, 34, 37, 38), however: e.g., plasma amino acids or free intracellular amino acids to represent the tRNA-amino acid precursor pool for protein synthesis, or ketone bodies to represent the acetyl-CoA pool for lipogenesis. Complicating factors deriving from subcellular or intracellular biochemical organization have been shown to affect every class of polymer so far examined in detail, including proteins (38), lipids (8, 9), carbohydrates (19, 34), and nucleic acids (18).
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A SOLUTION TO THE PRECURSOR-PRODUCT PROBLEM: THE USE OF COMBINATORIAL PROBABILITIES |
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MIDA is based on a model of combinatorial probabilities. Polymerization
biosynthesis can be conceptualized as a combinatorial process, with
monomeric subunits from a precursor pool combining into a polymeric
collection or assemblage. If the monomeric subunits are of more than
one distinctive type, i.e., labeled and unlabeled, then the population
of assembled polymers will not be of uniform isotopic composition. The
polymers will exist as distinguishable species containing varying
numbers of the different types of subunits. Some species will include
no labeled subunits, some will include one labeled subunit, some will
contain two labeled subunits, and so on. The relative proportion of
each species of polymer is determined by and can be calculated from the
binomial (or multinomial) expansion (Fig.
1A). The binomial
expansion contains two variables, the number of subunits in the
collection (n) and the probability
(p) of each subunit being of a
particular type. Because the number of subunits in a biological polymer
is constant and known, the sole factor determining the relative
proportions of each polymeric combination (i.e., the quantitative
distribution of mass isotopomers) is
p, the labeling probability in the
precursor pool.
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The population of intact polymeric assemblages therefore contains information about the precursor pool that is not available by analysis of the monomeric units in isolation: the combinations of labeled and unlabeled subunits in the polymer population, which are manifested for statistical or mathematical analysis as the distribution of mass isotopomers. This is the central insight on which MIDA is based. Because each isotopomeric distribution is uniquely determined by p, each distribution is characteristic of and capable of revealing the unique value of p from which it was assembled. The distribution is, moreover, immutable; it is a fingerprint that will persist throughout the lifetime of the population, as long as there is no biological discrimination (no isotope effect) between species of the polymer and no remodeling of the polymer after its original assembly.
What is the effect of mixing a population of polymers assembled from a precursor pool of labeling probability p with a population of polymers assembled from an unlabeled precursor pool? Mixing of this sort (dilution of the polymer pool) is what happens in a biological system when a labeling experiment is performed: newly synthesized polymers from the labeled pool mix with polymers that were present before the experiment began. A key mathematical feature of MIDA is that the relationships among those polymeric species that contain labeled subunits (the internal pattern among isotopomers) are unchanged by dilution from an unlabeled population of polymers (Refs. 13-15; see CENTRAL FEATURES OF MIDA SUMMARIZED).
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CENTRAL FEATURES OF MIDA SUMMARIZED |
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The first rule of MIDA is that there must be combinations possible in the molecule analyzed. At least two repeats of a probabilistically identical subunit must be present. Metabolic pathways involving other kinds of chemical transformations but no polymerization are therefore not amenable to the combinatorial approach. Polymers studied must also be analyzed intact, or with at least two subunits present, because the distribution of isotopomeric species carries the essential information. Any maneuver that reduces the population to monomeric homogeneity, such as combustion to carbon dioxide for isotope ratio measurements or hydrolysis to monomeric subunits before analysis, loses the combinatorial information and precludes application of MIDA.
The second rule of MIDA is that subpopulations of molecules must be distinguishable and quantifiable. Indeed, it is the variations within a population of assembled polymers that carry the information crucial for MIDA. The notion that there is a homogenous precursor pool and a uniform product pool is replaced by the notion of subpopulations of precursors (some A, some B) and subpopulations of products (of characteristic isotopomeric composition in quantifiable proportions). Any analytic modality must therefore be capable of discriminating among different polymeric subpopulations (species) present within the population. This is why radioisotopic methods cannot be used: specific activity is measured from the total counts and total mass of material present, treated as a uniform population; and it is why average mass measurements by electrospray ionization-mass spectrometry also cannot be used: a "centroid" average mass collapses all of the population variability in the polymer pool into a single value.
The third essential concept underlying MIDA is that dilution of the monomeric (precursor) and polymeric (product) pools affects abundance distributions differently. Both sources of dilution can alter the relative proportion of polymeric species containing no labeled subunits vs. labeled subunits, but only dilution in the precursor pool can alter the internal quantitative relationships among labeled species. It is this differential effect on "amount" (proportion of the polymer population containing any labeled subunits) vs. "pattern" (relationships within the population of labeled polymers) that allows independent calculation of p and f, respectively.
The model just described involves some simplifying assumptions, which are discussed in THEORETICAL ISSUES FOR THE USE OF MIDA.
In addition to determining p directly,
MIDA offers several operational advantages over previous isotopic
techniques for measuring biosynthesis rates (Table
1). One analytic consequence of the need
for intact combinations is that sophisticated mass spectrometric techniques must be used in cases in which biosynthesis of
high-molecular-weight polymers, such as proteins or oligonucleotides,
is being measured.
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Definitions
It is useful to define terms to avoid ambiguity. The following definitions will be used here.Isotopes. Atoms with the same number of protons and hence of the same element but with different numbers of neutrons (e.g., H vs. D).
Exact mass. The mass calculated by summing the exact masses of all the isotopes in the formula of a molecule (e.g., 32.04847 for CH3NHD).
Nominal mass. The integer mass obtained by rounding the exact mass of a molecule.
Isotopomers. Isotopic isomers or species that have identical elemental compositions but are constitutionally and/or stereochemically isomeric because of isotopic substitution, as for CH3NH2, CH3NHD, and CH2DNH2.
Isotopologues. Isotopic homologues or molecular species that have identical elemental and chemical compositions but differ in isotopic content (e.g., CH3NH2 vs. CH3NHD in the example above) (36). Isotopologues are defined by their isotopic composition; therefore, each isotopologue has a unique exact mass but may not have a unique structure. An isotopologue is usually comprised of a family of isotopic isomers (isotopomers) that differ by the location of the isotopes on the molecule (e.g., CH3NHD and CH2DNH2 are the same isotopologue but are different isotopomers).
Mass isotopomer. A family of isotopic isomers that is grouped on the basis of nominal mass rather than isotopic composition. A mass isotopomer may comprise molecules of different isotopic compositions, unlike an isotopologue (e.g., CH3NHD, 13CH3NH2, CH315NH2 are part of the same mass isotopomer but are different isotopologues). In operational terms, a mass isotopomer is a family of isotopologues that are not resolved by a mass spectrometer. For quadrupole mass spectrometers, this typically means that mass isotopomers are families of isotopologues that share a nominal mass. Thus the isotopologues CH3NH2 and CH3NHD differ in nominal mass and are distinguished as being different mass isotopomers, but the isotopologues CH3NHD, CH2DNH2, 13CH3NH2, and CH315NH2 are all of the same nominal mass and hence are the same mass isotopomers. Each mass isotopomer is therefore typically composed of more than one isotopologue and has more than one exact mass. The distinction between isotopologues and mass isotopomers is useful in practice, because all individual isotopologues are not resolved using quadrupole mass spectrometers and may not be resolved even by using mass spectrometers that produce higher mass resolution, so that calculations from mass spectrometric data must be performed on the abundances of mass isotopomers rather than isotopologues. The mass isotopomer lowest in mass is represented as M0; for most organic molecules, this is the species containing all 12C, 1H, 16O, 14N, and the like. Other mass isotopomers are distinguished by their mass differences from M0 (M1, M2, etc.). For a given mass isotopomer, the location or position of isotopes within the molecule is not specified and may vary (i.e., "positional isotopomers" are not distinguished).
Mass isotopomer pattern. A histogram of the abundances of the mass isotopomers of a molecule. Traditionally, the pattern is presented as percent relative abundances, where all of the abundances are normalized to that of the most abundant mass isotopomer; the most abundant isotopomer is said to be 100%. The preferred form for applications involving probability analysis, such as MIDA, however, is proportion or fractional abundance, where the fraction that each species contributes to the total abundance is used (see ). The term isotope pattern is sometimes used in place of mass isotopomer pattern, although technically the former term applies only to the abundance pattern of isotopes in an element.
Monoisotopic mass. The exact mass of the molecular species that contains all 1H, 12C, 14N, 16O, 32S, and the like. For isotopologues composed of C, H, N, O, P, S, F, Cl, Br, and I, the isotopic composition of the isotopologue with the lowest mass is unique and unambiguous, because the most abundant isotopes of these elements are also the lowest in mass (23). The monoisotopic mass is abbreviated as m0, and the masses of other mass isotopomers are identified by their mass differences from m0 (m1, m2, etc.).
Fractional abundances. The abundances of individual isotopes (for elements) or mass isotopomers (for molecules) given as the fraction of the total abundance represented by that particular isotope or mass isotopomer. This is distinguished from relative abundance, wherein the most abundant species is given the value 100 and all other species are normalized relative to 100 and expressed as percent relative abundance. For a mass isotopomer Mx
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Isotopically perturbed.
The state of an element or molecule that results from the explicit
incorporation of an element or molecule with a distribution of isotopes
that differs from the distribution found in nature (Table
2), whether a naturally less abundant
isotope is present in excess (enriched) or in deficit (depleted).
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Monomer. A chemical unit that combines during the synthesis of a polymer and that is present two or more times in the polymer.
Polymer. A molecule synthesized from and containing two or more repeats of a monomer.
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CALCULATIONS |
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A tradition in mass spectrometric applications has often been to express quantitative results as relative abundances (each species normalized to the most abundant species, which is given the value 100). In contrast, fractional abundances or analogous expressions are generally preferable for MIDA, because the method is based on combinatorial probabilities, and probabilistic events are most directly represented as fractions of the total universe of choices possible.
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THEORETICAL ISSUES FOR USE OF MIDA |
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Every model is based on assumptions, which may or may not describe real biological systems accurately. It is useful to consider and ultimately to be able to evaluate or correct for potential deviations from the simple MIDA model. For all of the simulations performed here, calculations were carried out by use of the computer algorithms described in the APPENDIX.
Effect of Variations in Natural Abundance Values of the Isotopes of Elements
The contribution to mass isotopomer distributions in a polymer from natural abundance isotopes of the elements has to be subtracted, or otherwise taken into account, for labeled subunits to be quantified (13, 15, 20, 22). One of the most obvious questions that is asked is whether the theoretical natural abundance values selected, especially for 13C, could have significant effects on the calculations. We have done calculations for several polymers while varying natural 13C fractional abundance between 1.08 and 1.11%, the range that might be present in biological carbon in mammals (6, 33), in the calculation algorithm. The results are shown for palmitate-methyl ester (Fig. 3). There is very little effect on calculated values of f when p > 0.03. The same is true for glucose, cholesterol (15), and other molecules (not shown). Thus variations in natural abundance values of 13C do not have an important effect on calculated parameters.
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Effect of Isotope Discrimination
Isotope discrimination or fractionation at the level of the precursor pool is not a problem within a biosynthetic model based on analysis of combinatorial probabilities (MIDA). The MIDA calculation reveals the isotope content of the subunits that actually entered a polymer, regardless of their relation to the isotope content of biochemical intermediates leading to these subunits. If, for example, there were a 10% discrimination against [2H3]leucine by leucyl-tRNA synthase or a 10% discrimination against [2H3]leucyl-tRNA by the ribosomal protein synthesis machinery, it would not affect the calculations of f or true p; it is the 2H3 enrichment of the leucine subunits that actually entered the protein that determines the mass isotopomer abundance pattern. This pattern will reveal the true [2H3]leucine precursor subunit enrichment for biosynthesis, even if this value is different from the tRNA-leucine or free leucine enrichments, and the calculated fractional synthesis contribution would be correct. Measurements of p, f, and the like would then be accurate with MIDA but not if tRNA-leucine were used, in this example. Thus combinatorial probability analysis is unique among isotope kinetic approaches in that its validity is not altered by isotope discrimination during biosynthesis. In contrast, isotope effects on the metabolism of the polymer once synthesized (e.g., effects on clearance) will affect kinetic measurements, because the behavior of labeled polymers will not reflect that of the general pool.Effect of Incorrect Value for Expected Number of Monomeric Subunits
Lee et al. (22) demonstrated elegantly that n (the number of precursor subunits actually present in a polymer) can be determined experimentally by using the same principles of probability analysis that are used for determining f. Instead of a reference table for p vs. mass isotopomer pattern at a known value of n, one can generate a reference table for n vs. mass isotopomer pattern at a known value of p. The true value of n can then be inferred from the experimental data. This technique is possible only when there exists an independent method for determining p; the measurement of body water 2H enrichments during 2H2O incorporation experiments represents a unique situation that permitted this application (22).Calculation of p and f When the Complete Ion Spectrum is not Sampled
For any number of reasons, the mass spectrometrist may choose not to monitor all of the ions in a mass isotopomer envelope (e.g., for convenience, to maximize dwell time on the most abundant ions, or to avoid contaminating ions). An important property of combinatorial probabilities is that the calculation of p is not affected by the choice of ions selected for monitoring. The internal pattern and relationship among excess mass isotopomers are fixed and characteristic of p and n regardless of which particular masses are monitored. As long as the appropriate equation is used for the masses under consideration, the choice of masses monitored will not influence calculation of p. Surprisingly, this is not the case for calculation of f, which is affected by incomplete ion spectrum sampling. This is because of a somewhat unexpected mathematical feature of mixtures of numerical distributions (e.g., populations of mass isotopomers): dilution is not linear when the proportion of the total population monitored is different in the natural abundance and enriched populations. As noted in the APPENDIX (and see Fig. 1C), the mathematical object of solving for p in step-wise calculation algorithms is to linearize the relationship between abundance of a particular mass isotopomer (Ax) and the molar fraction of its associated molecular population in the mixture (f), so that f can be solved algebraically from Ax. When different proportions of the total ion envelope are monitored for different populations, for example, as occurs when a high p generates high mass isotopomers that are not monitored, the linear relationship between any Ax and f (fractions of the mass isotopomer and molecule in the population, respectively) is lost (Fig. 3). Stated in intuitive terms, when higher masses are not monitored, a mole of isotopically enriched molecules will contribute fewer ions to the total spectrum sampled than a mole of natural abundance molecules. The molecular mixture is thereby weighted in favor of the more completely sampled molecular population (the unlabeled population), and a correction has to be made to put equal weight on each molecular population in the mixture.A numerical example follows. If M1 theoretically represents 20% of the M0 through M2 ions in natural abundance molecules and 40% of the M0 through M2 ions at p = 0.10, but only 90% of the envelope is contained in M0 through M2 at p = 0.10 compared with 100% in M0 through M2 for the natural abundance molecules, what would be the effect of mixing these populations and monitoring only M0 through M2? It should be apparent that the enriched population will not contribute the theoretical 40 ions of M1 for every 20 ions of M1 from unlabeled molecules in an equimolar mixture when only M0 through M2 are measured, but will contribute only 36 (= 40% × 90% of the mole in the envelope monitored) for every 20 (= 20% × 100% of the mole of natural abundance isotopomers). It would therefore be a mistake to use percentages of the ions monitored to represent percentages of the entire population when mixing populations with different percentages of ions monitored, because f will be systematically underestimated. The solutions to this confounding factor are straightforward: either monitor an essentially complete ion spectrum for the molecules under consideration or include a mathematical correction for unequal ion spectrum sampling in the calculation algorithm.
An algebraic correction is derived and presented in the
APPENDIX (Eq. A9b) for instances of significantly incomplete ion
spectrum monitoring. This equation corrects for the proportion of ions monitored at the measured value of p
present relative to the proportion monitored in unlabeled molecules. By
use of this correction factor, mixtures of labeled and unlabeled
molecules are again reduced to linear combinations of mass isotopomers,
from which dilution of molecules can be calculated simply. This
correction is generally extremely small and has no practical impact on
most calculations (Fig. 4), because >98%
of the ions within an isotopomeric envelope are typically monitored for
most labeled molecules. Failure to consider the effects of incomplete
ion spectrum sampling can contribute to underestimation of values of
f in special cases, however, such as
very high values of p, if high masses
are not monitored. The impact of incomplete ion spectrum monitoring has
not to our knowledge been considered previously or corrected for in
other MIDA calculation algorithms.
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Effect of Analytic ArtifactsFragment Ions
Effect of Isotopic Disequilibrium in the Precursor Pool
Evaluating the theoretical impact of isotopic disequilibrium.
A biosynthetic system may or may not exhibit isotopic equilibrium among
different pools of a monomeric subunit from which a polymer is
synthesized. Accordingly, there may not always be a single value for
p. A physiologically relevant example
of a biosynthetic system that does not necessarily have a single value for p is gluconeogenesis. There are
actually two precursors comprising the gluconeogenic triose-phosphate
pool, dihydroxyacetone phosphate (DHAP) and glyceraldehyde-3-phosphate.
Isotopic equilibrium between the triose-phosphates may not always be
complete. One can simulate the effect of various degrees of isotopic
disequilibrium between DHAP and glyceraldehyde-3-phosphate and
determine the extent to which calculated values of
p and
f would be distorted if the standard MIDA reference table were applied to the fractional abundances generated (27). If we allow the average
p to range between 0.05 and 0.15 and
vary p in pool
2 from 1.0 to 2.0 times the pool
1 value, the consequences for the
f can be calculated. When
p in pool
1 = p in
pool 2 (i.e., when isotopic
equilibrium is present), the calculated value of
f is of course exactly as expected
from the MIDA tables (100%), whatever the value of
p. When
p in pool 2 is double that of pool
1, calculated f is
~12% higher than the true value for all values of
p; when pool
2 is made 50% above pool
1, f is within 4% of
the true value. An interesting general mathematical result to emerge
from this analysis is that f is always
overestimated (>100% the actual value) if isotopic disequilibrium exists within precursor subunit pools (27). The practical implication for measuring gluconeogenesis in particular is that isotopic
disequilibrium in the triose-phosphate precursor pool is in principle
unlikely to represent a major problem, because the MIDA calculations
will work well unless DHAP and glyceraldehyde-3-phosphate are
differentially enriched by a factor of >2 (27). Similar calculations
can be applied to other polymers of interest.
Correcting for documented isotopic disequilibrium.
If one is not satisfied with theoretical arguments discounting the
importance of isotopic disequilibrium within a precursor pool, it is
possible to modify the calculation algorithm to incorporate deviations
from isotopic equilibrium within precursor pools. Theoretical tables
can be generated by modifying the algorithm described above, if the
degree of isotopic disequilibrium is measurable. In the case of
gluconeogenesis, for example, mass spectrometric fragmentation of the
molecule into "top" (C-1 to C-3) and "bottom" (C-4 to C-6) halves can reveal whether labeling was equal in DHAP and
glyceraldehyde-3-phosphate, respectively (26). If enrichments differ by
a certain proportion, then this value can be incorporated into the
probability calculations to generate an appropriate, individualized
standard curve that adjusts asymptotic values appropriately. Thus
individualized standard curves can be generated for each experiment on
the basis of the observed degree of isotopic disequilibrium within
precursor pools, if the latter is significant and can be determined
experimentally. Because the mathematical approach that we have
described (see APPENDIX and Refs.
13-15) is based on empirical relationships between derived values
(fractional abundances) rather than expressions of the pure binomial
or multinomial expansion, deviations from the simple combinatorial
probability model can be accounted for relatively easily and without
compromising mathematical rigor.
Effect of Isotopic Inhomogeneity in the Precursor Pool (e.g., More Than One Biosynthetic Site, an Isotopic Gradient Across a Tissue, or Time Variations in p)
A potentially more important deviation from the simple MIDA model is if the polymer is made in more than one anatomic location and p is not equal in each site, or if the value of p changes over time. This situation differs from the situation of isotopic equilibrium within a precursor subunit pool (see Effect of Isotopic Disequilibrium in the Precursor Pool). Each of the polymer populations synthesized has a single precursor enrichment, but there is more than one pool of polymers present, whereas in the former case, each polymer molecule has more than one precursor enrichment but there is only a single pool of polymers. Examples of more than one anatomic location for biosynthesis might include extrahepatic and hepatic gluconeogenesis or cholesterogenesis, or labeling gradients within a precursor pool across a tissue. The same considerations would apply if p changed over time during an experiment; polymers made at different times would have different mass isotopomer patterns.The consequence of these scenarios is that, instead of a single binomial distribution, there will be a mixture of distributions from the different values of p in newly synthesized polymers. This mixture of distributions itself mixes with, and needs to be distinguished from, the natural abundance distribution that represents old molecules. Any attempt to model biosynthesis as two populations or two distributions, enriched and unenriched, will not be rigorously correct mathematically but will instead be an approximation, because binomial or multinomial expansions cannot themselves be averaged (i.e., are not linear) (21). The M2 isotopomer changes approximately as the power of 2 for changes in p, the M3 as the power of 3, etc., so that different expansions cannot be combined and averaged as if they were linear.
The practical questions are, how much does this matter? what impact on
estimated parameters will there be if
p is inconstant in time or space? and
can it be identified or corrected for when present? A simulation for
gluconeogenesis in two tissues or at two time points with different
p values has been presented elsewhere (26): f remains 0.8-0.85, even
when pool 2 enrichment is 2-3 times pool 1. Another example is a
gradient in precursor pool enrichment across a tissue (Fig.
5A). If
one models 10 pools contributing equally to gluconeogenesis with a
labeling gradient that spans an approximately twofold range
[e.g., 0.105-0.195 molar excess (ME)], the consequence
is minor (underestimation of true values of
f by a factor of <5%, Fig.
5A). Even for a fourfold gradient (0.06-0.24 ME), f is only
underestimated by ~15%; i.e., if the actual value of
f = 0.50, measured
f will be 0.425. Only at very large
gradients (e.g., 15-fold, from 0.02 to 0.29 ME) is even a 25%
underestimation observed. An analogous situation can be simulated for
lipogenesis, with an isotopic gradient of acetyl-CoA across a lipogenic
tissue such as liver. If 10 pools contribute equally to lipogenesis,
with a gradient from 0.03 to 0.30 ME (at intervals of 0.03),
f is 87.3% instead of 100% (i.e.,
underestimated by 12.7%). If a gradient from 0.02 to 0.10 ME is
simulated, with 100 pools contributing equally to lipogenesis, the
value of f calculated by MIDA by use
of M1 and
M2 isotopomers is
90.1%. Thus inconstancy in p over
time or space means that the simple binomial model becomes an
approximation rather than an exact description of biosynthesis, but the
practical impact varies according to physiological conditions and
typically is fairly small. An investigator is able to evaluate the
likelihood of significant error and the practical acceptability of this
degree of error by performing a simulation of this type.
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It is also possible to identify, and even correct for, isotopic gradients or variations in precursor pool enrichments by application of combinatorial principles. If a large isotopic gradient is present or two precursors of different enrichment contributed to biosynthesis, there will be a divergence between the isotopomer pattern in high-mass (multiply labeled) vs. low-mass (single- and double-labeled) polymers (Fig. 5, B and C). If a gradient exists within the precursor pool, high-mass species will be produced that would otherwise never be observed if the average value of p were uniformly present. The pattern of higher-mass isotopomers predicted by analyzing lower masses will not be observed; similarly, the pattern of low-mass isotopomers predicted by the higher masses will not be met (Fig. 5, B and C).
The occurrence of "inappropriate" multiply labeled species relative to the pattern among the less-labeled species (Fig. 5, B and C) can therefore be used diagnostically to confirm or exclude the existence of an isotopic gradient. One simple approach is to monitor higher-mass isotopomers and compare calculated values of p from higher- vs. lower-mass relationships. In the case of a labeling gradient across a lipogenic tissue spanning 0.03 to 0.30 (Fig. 5C), for example, the pattern of excess M3/M2 isotopomers in palmitate indicates p = 0.213; the ratio in M4/M3 indicates p = 0.226, whereas M2/M1 isotopomers reveal a lower p (0.166). The divergence is even greater for simple two-precursor-pool systems (Fig. 5B). If there were an equal mixture of a palmitate population derived from 0.30 and a 0.50 value of p, analysis of M1 and M2 would reveal p = 0.173, whereas analysis of M3 and M4 would indicate p = 0.29. In contrast, if a single, homogenous precursor pool is present, calculated values of p are identical whatever masses are used for its calculation (15). The finding of different p values by analysis of high- vs. low-mass isotopomer patterns represents a technique for identifying the presence of an isotopic gradient.
Conversion of Fractional Synthesis Values into Chemical Fluxes: Combining MIDA Calculations with Administration of Exogenous Stable Isotope-Labeled Polymers
Expression of synthesis as rates in chemical units (mass/time) requires an estimate of the turnover of the polymer pool being sampled in addition to the fraction of the polymer pool that came from endogenous synthesis during the time period studied. Probability considerations demonstrate that high-mass isotopomers are uniquely useful in the labeled-polymer decay phase, because problems from persistent isotope incorporation are avoided for multiply labeled species even if pulse/chase conditions do not exist (i.e., if precursor subunits continue to contain a low level of labeling because of isotope recycling or slow turnover of the precursor pool). This application of MIDA has been discussed in detail previously (15, 25). The turnover of the polymer can also be measured by analyzing the rate of rise toward plateau during the label incorporation phase, as discussed elsewhere (16). Alternatively, exogenously labeled polymers can be administered (to measure turnover by dilution) concurrently with a biosynthetic incorporation experiment. For this last approach, however, potential interference by the exogenous label with the isotope incorporated via biosynthesis has to be accounted for.For example, it is useful to measure the plasma glucose turnover concurrently with fractional gluconeogenesis to determine the absolute rate of gluconeogenesis. If [1-2H]glucose or [6,6-2H2]glucose is used for turnover, labeled species have the same nominal mass as the isotopomers analyzed for MIDA calculations (M1 and M2). Because quadrupole mass spectrometers do not have sufficient resolving power to distinguish between 2H and 13C exact masses, a technique for determining the contributions from [2H]glucose vs. [13C]triose-phosphate is required. This can be achieved by analyzing a derivative that is stripped of the labeled hydrogen (e.g., aldonitrile-pentaacetate or saccharic acid derivatives from which position 1 and 1,6 hydrogens are removed, respectively) in addition to a derivative that contains both inputs (e.g., pentaacetate). The MIDA calculation on the derivative stripped of 2H is routine. The problem, however, is how to "subtract" or correct the 13C contribution from the combined spectrum to establish the 2H labeling, by difference.
A calculation algorithm can be used to correct for the underlying
isotopomeric distribution from incorporation of
13C gluconeogenic precursors, for
example, to measure
[2H]glucose enrichment
(7). The glucose molecules present during a simultaneous measurement of
fractional gluconeogenesis and glucose turnover consist of a mixture of
three populations: gluconeogenic product molecules arising from the
labeled triose-phosphate precursor pool, labeled glucose molecules
infused exogenously as tracer, and unlabeled molecules with a natural
abundance distribution. The key is that the isotopomeric distribution
of each of these components is known. The infused tracer
([6,6-2H2]-
or [1-2H]glucose) has
an isotopomer distribution that is easy to calculate; natural abundance
glucose also has a known distribution; and the gluconeogenic population
has a distribution of isotopomers that is a function of
p and that is measurable from the
deuterium-stripped derivative. The distributions from each of these
three components of the mixture can therefore simply be added to
construct a theoretical standard curve, simulating the effect of adding
2H-labeled glucose to mixtures of
the other two populations at the measured
f. If gluconeogenesis
f = 0.33 and
p = 0.15, for example, the calculation
consists of adding 0.33 times the abundance of each isotopomer from
gluconeogenesis at p = 0.15, then
(0.67 z) times the abundance
of each isotopomer from natural abundance glucose, and
z times the abundance of each
isotopomer from the [2H]glucose, where
z is the fraction of
2H-labeled glucose added to
generate the theoretical standard curve. Two or more values of
z are simulated to construct a linear
standard curve, wherein the isotopomers of interest are plotted against z to generate a slope and intercept
for calculation of 2H enrichment
and dilution in the intact molecule (Fig.
6). This algorithm must be applied
separately for each time point sampled, because each sample will have a
unique p and
f (8, 36), and thus a unique slope and
intercept for the standard curve.
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Assessing the Sensitivity of MIDA-Calculated Biosynthetic Parameters to Measurement Error
To plan isotopic experiments and evaluate results, it is useful to know how sensitive the derived parameters are to analytic imprecision or inaccuracy. Error-sensitivity analysis can be performed by using the MIDA calculation algorithm presented here. An example with gluconeogenesis has been presented previously (26). This analysis reveals that an analytic coefficient of variation of 1% in estimates of the ratio of ![]() |
ALTERNATIVE CALCULATION ALGORITHMS |
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MIDA as we now understand it was developed from 1990 to 1992 by Hellerstein and co-workers (13-15, 17) and Kelleher et al. (20), working independently. MIDA is defined by its purpose, its method, and its calculations. The purpose or field of MIDA is to measure the synthesis of biological polymers, the isotopic labeling of the monomeric precursor pool from which the polymers were assembled, and related kinetic parameters. The method involves measurement and analysis of mass isotopomer abundance distributions in intact polymers according to a combinatorial probability model, after introduction of a stable isotopically labeled monomeric subunit. The calculation approach uses the binomial or multinomial expansion as a basis for interpreting incorporation of isotopically labeled repeating subunits in the intact polymer and for inferring dilution in the monomeric and polymeric (precursor and product) pools.
It is in the area of a calculation algorithm that modifications have been presented (1, 5, 22, 32) since the original approaches described by Hellerstein and co-workers (13-15, 17) and Kelleher et al. (21). All the calculation algorithms presented so far, however, share fundamental assumptions and postulate a common model of biosynthesis. All postulate a combinatorial (binomial/multinomial) precursor-product biosynthetic model, and all postulate two confounding factors that may then modify the simple binomial/multinomial distributions: first, the natural abundance isotopes in the molecule, which interact with label-derived isotopomers; and second, the fact that two sources of dilution exist in biosynthetic systems (in the product pool as well as the precursor pool) and that these two sources of dilution influence isotopomer abundances differently in the product.
Only two general solutions have been proposed for each of the problems just noted. The influence of natural abundance isotopes on label distributions is a strictly computational problem. The solution has been either to create a computational model that incorporates all sources of isotope from both labeled precursor and natural abundance isotopes, and thus does not conform to a simple binomial distribution (Hellerstein and Neese, Ref. 15, and Kelleher et al., Ref. 20), or to transform the data in a way that removes the influence of natural abundance isotopes and restores a pure binomial distribution from the labeled precursor (Lee et al., Ref. 22, and Chinkes et al., Ref. 5). The problem of two sources of dilution, in contrast, reflects a biological issue. Again, there have been two computational solutions proposed. Most methods (Hellerstein, Lee, and Chinkes) have used a step-wise approach. Ratios among natural abundance-corrected terms are first computed. Use of internal ratios of isotopomers in the polymer sample analyzed removes the effect of varying product dilution, because all isotopomers sampled in the labeled molecules are equally diluted by natural abundance molecules, so that precursor pool dilution can be calculated independently. Once this unknown (p) is solved, the second unknown (f) can be solved algebraically (Fig. 1C). Alternatively, the two sources of dilution (Fig. 1C) can be solved simultaneously, by best fit (nonlinear regression analysis) of multiple solution sets for the two unknowns taken together (21).
The most important point is that all the calculation algorithms presented to date give essentially identical results. Thus data of Byerley et al. (4), from 2H2O incorporation into cellular cholesterol in cultured cells, give identical values for p and f whether calculated by the method of Lee (22) or by our approach (unpublished results). Identical results are obtained when data are analyzed by the approach of Kelleher et al. (21) and ours (unpublished observations; and T. Masterson, personal communication, April 1994). Chinkes et al. (5) also compared calculation algorithms using simulated data and concluded that results were essentially identical.
It should be noted that all these approaches are of roughly equal computational complexity. They all require a computer program1, to calculate abundances and to generate either a model or algebraic correction factors, and a specific software package that has to be applied separately for each molecule analyzed.
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ANALYTIC AND EXPERIMENTAL DESIGN CONSIDERATIONS |
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The single most difficult problem facing the use of MIDA at present, both in theory and in practice, relates to quantitative accuracy of measurements, i.e., the analytic performance of mass spectrometers. This problem is widely recognized by workers in the field but has only rarely been noted in the literature (3, 10, 11, 23, 24, 26, 30). MIDA is based on analysis of numerical distributions in the context of a model of combinatorial probabilities. If the instrument generates inaccurate numbers, measured distributions will no longer reflect the actual isotopomeric distributions present. The actual effect on kinetic estimates (p, f) will depend on the nature and extent of the experimental inaccuracy. How then does one apply equations that are based on a model of combinatorial probabilities if the numbers do not fit the actual distributions generated? The best solution would be if the experimenter understood the cause and exact nature of instrumental inaccuracy: if one knew that the explanation was, for example, inadequate resolution of adjacent masses by the mass analyzer, a suitable correction algorithm might be applied. This is in essence what is done with liquid scintillation counting of radioisotopes, wherein 3H and 14C spillover is accounted for, so that each isotope can be independently measured. Unfortunately, the analytic basis of quantitative inaccuracy by current mass spectrometers is not understood in a sufficiently definitive way at present to allow simple correction (see Strategies for Evaluating Quantitative Instrument Performance and Data Acceptability). Another reasonable approach is to use standard curves, as one does when measuring dilution of an exogenous labeled product. There are problems also that make this difficult for biosynthetic MIDA methods, however. These we will discuss.
Several questions concerning mass spectrometric quantitative inaccuracy need to be addressed. We will not review these issues extensively here but will note some practical implications of each.
The Nature of Quantitative Inaccuracy in Mass Spectrometric Measurement of Isotope Ratios
Surprisingly little literature exists concerning the mass spectrometric causes of deviations between expected and measured abundances of mass isotopomers in organic analytes (10, 11, 30). The abundance of one mass relative to another might be overestimated by a fixed proportion, by a fixed amount, or by random error. Each type of error would have different implications for attempted correction algorithms. One also needs to know whether instruments drift over time, so that standards analyzed near to a sample in time will reveal the existence of error in the sample, or whether error occurs in an erratic, unpredictable way. Unfortunately, few data and no consensus exist on these questions, although several mechanistic possibilities can be considered.One potential cause of inaccuracy is incomplete resolution of adjacent ions in the ion envelope (peak tailing), resulting in contamination of adjacent mass channels. If the mass analyzer is operating at the limit of its mass-resolving capacity, the degree of misidentification of ions due to ion scattering and peak tailing (24) could vary from run to run. According to this explanation, mass analyzers that achieve significantly better resolution (e.g., magnetic sector compared with quadrupole mass analyzers) would be predicted to exhibit better accuracy. This prediction has not yet been systematically tested. Another prediction is that higher abundances in adjacent mass isotopomers should worsen resolution (increase peak tailing), resulting in worse concentration sensitivity of fractional isotopomer abundances. Abundance sensitivity (24), the observation that the most abundant ion in an envelope tends to be underestimated quantitatively, has been identified as a problem in the field of isotopic analysis of elements by use of isotope ratio mass spectrometers. The physical explanation and methods for instrumental correction continue to be debated, however. A second possible cause of inaccuracy is nonlinearity of the detector response at different abundances or for different ions. If the detector output at each mass does not faithfully and consistently reflect the number of ions that reach it, numerical distributions will be skewed (10). Detector nonlinearity might be correctable by use of suitable standards, if these could be synthesized, or by use of improved multiplier-detectors. Detector nonlinearity would also predispose to abundance-sensitivity effects: if abundances of different isotopomers span a large dynamic range, then the slope of detector output vs. injected material will be different for each. A third possibility is the occurrence of chemistry in the ion source (10, 11, 30). Chemical reactions such as hydrogen abstraction or addition could alter mass isotopomer abundances. This problem could be addressed by using derivatives that are unlikely to undergo these reactions (such as fluorinated molecules lacking exchangeable hydrogens) or by use of different ionization conditions (e.g., metastable atom bombardment). This problem might also explain concentration effects on isotope ratios (increased concentrations in the ion source lead to more chemical interactions, as postulated in Refs. 10, 11, and 30).
Regardless of the physical mechanisms involved, some empirical observations may be helpful operationally. First, concentration effects (relative abundances of isotopomers varying as a function of the total amount of material injected onto the mass spectrometer) are a problem for most molecules and tend to be more pronounced the greater the dynamic range among the masses monitored. With glucose-pentaacetate, for example, in natural abundance samples the ratio of the M0 (0.8396) isotopomer to the M1 (0.1348) and M2 (0.0256) isotopomer abundances spans almost two orders of magnitude. In contrast, at higher values of precursor enrichment (e.g., p = 0.24), the ion envelope is more evenly spread out (M0 = 0.3060, M1 = 0.4400 and M2 = 0.2550, for a span of less than twofold), and observed concentration sensitivity is in fact less of a problem (Neese, R. A., R. Bandsma, and M. K. Hellerstein, unpublished observations). Second, the highest abundance isotopomers tend to be relatively underestimated as total ion abundance increases (as has also been observed with inorganic elemental analyses using isotope ratio mass spectrometers, Ref. 24). Third, and counterintuitively, masses with very low baseline isotope abundances (i.e., higher masses with few or no natural isotope abundances) can be analytically undesirable when they have to be compared quantitatively with higher abundance masses. Although it may seem attractive to avoid having to subtract baseline values, the extremely large dynamic range maximizes the relative concentration sensitivity of different isotopomers and may thereby lead to concentration-sensitivity for isotopomer abundances.
In summary, a number of analytic factors influence the relative abundances of mass isotopomers measured in an envelope (Table 2). These factors range from chemical events in the ion source (abstraction of H) to performance of the mass analyzer (ion transmission efficiency, mass resolution, peak tailing), characteristics of the ion detector (velocity dependence of multiplier, nonlinearity due to threshold or saturation effects), or accuracy of the integration software (baseline value that is subtracted, peak-fitting algorithm used). Until basic mass spectrometry research identifies the causes of quantitative inaccuracy, it will not be possible to correct post hoc in a definitive manner for substantial deviations from expected isotopomer abundances. Other strategies are therefore required. The most important of these in practice involve assessment of instrument performance and analytic techniques for prevention of inaccuracy.
Strategies for Evaluating Quantitative Instrument Performance and Data Acceptability
In the absence of methods for salvaging inaccurate analyses, the practitioner can establish criteria for acceptable accuracy and reject data that fail to meet these criteria. Two general approaches can be used for evaluating instrument accuracy and data acceptability.Measurements on natural abundance standards. The theoretically expected mass isotopomer abundances can be calculated for any natural abundance molecule or ion fragment of known chemical composition (see APPENDIX). The impact of variations in natural isotope abundances is extremely small (Fig. 2), so that natural abundance distributions should reliably predict measurements from standards. The simplest test of instrument accuracy is therefore how closely the measured isotopomer abundances in a natural abundance sample match the theoretically expected values. Minimum accuracy criteria for data acceptability can be empirically established on the basis of statistical considerations (e.g., all isotopomers must be within 2% of their theoretical natural abundance values for the data to be included; thus 0.0025 for an M1 of palmitate-methyl ester or 0.0005 from M2 of palmitate-methyl-ester or glucose pentaacetate), taking into account the degree of accuracy required for a particular application, which in turn is influenced by the isotopomer enrichments achieved in the experiment. Obviously, accuracy needs to be at its best if the actual isotope enrichments present are low. One can formalize these criteria by simulating the effect of different types of errors, e.g., constant fraction or constant amount errors on calculated parameters (see Achievement of adequate enrichments of masses of interest).
Comparison of baseline measurements to theoretical abundances represents a simple strategy for establishing whether mass resolution, nonlinearity of detector response, or ion chemistry is a significant problem in a particular analysis. The main caveat is that analysis of natural abundance molecules cannot ensure that linearity is maintained as the relative abundances of different ions change, i.e., that accuracy will be maintained for labeled, biological samples. The latter may require use of labeled standards. Also, it should be noted that performance for mass isotopomers with essentially zero natural abundance values (e.g., M4 glucose) cannot be evaluated by this method, which makes it more difficult to assess quality of data if these masses are subsequently monitored in labeled molecules (32).Use of isotopically enriched mass standards to establish linearity of response for different isotopomers. One can use labeled standards to assess linearity and quantitative accuracy at various masses. [1-2H1]- and [6,6-2H2]glucose or [1-13C]- and [1,2-13C2]palmitate, for example, can be purchased and mixed with natural abundance molecules to generate mass standards. After correction for the isotopomeric envelopes actually present in labeled molecules (see APPENDIX), standard curves representing different values of p and f can be analyzed. Problems with this approach include the fact that standards are themselves not 100% isotopically enriched, so one has to use an instrumental measurement of enrichment at some point to evaluate instrument performance, which can lead to circularities of logic, and the fact that accuracy of pipetting, completeness and comparability of derivitization, and reproducibility of the injector can influence the standard curves observed. Moreover, this approach does not provide a definitive method of correcting for inaccuracies of abundance measurements, but only of evaluating whether inaccuracy is present and severe enough to invalidate results. Nevertheless, this approach is useful for evaluating quantitative linearity over a range of isotopomer abundances (3, 28) and is particularly useful when a mass isotopomer being monitored has insufficient natural abundances to be measurable in baseline samples.
Guidelines for Optimizing Quantitative Mass Spectrometric Analyses
There are some useful experimental guidelines that have proven helpful in preventing instrument inaccuracy and reducing the impact of instrument performance on kinetic parameters with the use of MIDA (26, 30).Attention to concentration effects. Publications that use MIDA should show the concordance of baseline isotopomer ratios with expected abundances (or show some other index of accuracy) and should demonstrate that concentration effects were considered and avoided. Failure to report these data makes technical evaluation of results difficult or impossible.
Achievement of adequate enrichments of masses of interest.
A second factor that is to some extent under the control of the
investigator is the enrichments achieved in mass isotopomers of
interest. Improving enrichment relative to background
abundances improves reliability of parameter estimates and reduces
sensitivity to analytic error, as we have discussed previously (26,
37). As an empirical rule, any isotopic enrichment <0.0050 (0.50 MPE) is problematic for MIDA calculations because of the large coefficient of variation that is unavoidable at such low enrichments (e.g., imprecision or inaccuracy of even ±0.0010-0.0020 represents a >20-40% coefficient of variation). A formal error analysis at 0.0050 M2
enrichment in a sample polymer (palmitate) is shown (Fig.
7). These guidelines are dependent on the
state of the technology, of course; if mass spectrometers improved
accuracy and precision by an order of magnitude, the lower limit of
acceptable incorporation would change accordingly.
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Use of standard curves. Most non-MIDA kinetic applications in stable isotope-mass spectrometry (e.g., dilution measurements of an infused tracer to determine metabolite flux) do not ultimately require instrument accuracy. Standard curves of the analyte can be made simply by mixing known amounts of labeled and unlabeled molecules in different proportions; the standard curve allows measured isotope enrichment to be converted to true proportions of labeled species present (tracer/tracee). The problem for biosynthetic measurements is that a simple standard curve cannot be easily made from available reagents, because there is no "standard" molecule for comparison. Each biological experiment results in a unique combination of p and f; thus a unique pattern of mass isotopomers are present in the population of molecules. At a minimum, one would have to establish the performance of the instrument by creating a standard curve of p vs. measured ion abundances. It would be better to mix enriched molecules with unlabeled molecules to simulate end-product dilution (f). Testing of three-dimensional standard curves in this manner requires substantial effort and analytic time, however, and does not correct for concentration effects (without imposition of another analytic dimension for the standards). Although mixtures of labeled standards can be useful for assessing instrument performance (3, 28 and previous discussion), the role of higher-dimensional standard curves in MIDA applications remains uncertain.
Does the MIDA Calculation Algorithm Used Affect the Final Parameter Estimates, in Practice?
As discussed above, the published algorithms for calculating biosynthetic parameters by MIDA from experimental data are similar in many respects and give essentially identical parameter estimates in the theoretical case (5). One potential difference is the capacity of different calculation approaches to adjust to instrument inaccuracy. Some calculation algorithms subtract measured baseline (natural abundance) data from enriched sample data before transforming sample data or fitting them to a model; other algorithms do not subtract measured baselines but correct for theoretical baselines or simply use the enriched sample data as they stand. In the former case, the goal is to account for instrument performance on a sample-to-sample basis; in the latter case, ideal instrument performance is assumed. The capacity of these two strategies to adapt to instrument inaccuracy can be simulated (Table 3). In this simulation, we considered several potential types of measurement inaccuracy: spillover between adjacent ions, constant contaminant at a particular mass-to-charge ratio (m/z), nonlinearity of the detector at different m/z values. The impact on parameter estimates of using theoretical values vs. measured baselines was modeled. It is clear that use of measured natural abundance values in all cases reduces the error in parameter estimates, although not completely. This conclusion was also reported by Chinkes et al. (5). Thus baseline corrections cannot substitute for accurate quantitation by mass spectrometers but may reduce error in the final calculated values.
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Is There Experimental Evidence Supporting or Contradicting the MIDA Model?
A general measurement technique such as MIDA needs to be tested under controlled conditions both in vitro and in vivo. Strong experimental evidence in support of the method has been generated in vitro. Lee et al. (22) synthesized glucose-pentaacetate from [13C]acetic-anhydride at known enrichments and then imposed dilutions by known amounts of unlabeled glucose-pentaacetate. The calculated values of p and f were nearly identical to the expected values. We (28) performed an analogous test by synthesizing an oligopeptide (SVVLLLR) from [2H3]leucine at known enrichments and imposing subsequent dilutions by unlabeled peptide. Again, observed values were extremely close to predicted values. The combinatorial probability-mass isotopomer quantification model is clearly an accurate theoretical description of polymerization biosynthesis under controlled conditions.Testing a method definitively in vivo is not as straightforward. Comparisons with alternate methods, e.g., the close similarity of lipogenic estimates by 2H2O and MIDA (reviewed in Ref. 16) or of cholesterogenesis by sterol balance and MIDA (25) are not definitive, because the comparison methods may be flawed as well. A useful result was presented by Kelleher et al. (20): cholesterogenesis approached the 100% value expected in exponentially growing cells in culture.
An important issue to discuss is the proper interpretation of apparently dissonant results with an in vivo method like MIDA. A recent example is the intriguing observation of Aarsland et al. (1) that total hepatic lipogenesis (based on MIDA on circulating very low density-triglyceride fatty acids) was less than 1/20th of the rate of net whole body lipogenesis (based on indirect calorimetry) during massive carbohydrate overfeeding in humans. Because net lipogenesis (synthesis minus oxidation) cannot be greater than unidirectional lipogenesis, is this evidence that MIDA failed to give a physiologically possible answer? This conclusion would be incorrect: the authors (1) instead concluded that lipogenesis occurred in tissues or sites not immediately communicating with circulating very low density lipoprotein triglycerides during an 8-h isotope infusion. Thus lipogenesis in adipose tissue or lipogenesis entering the hepatic cytosolic storage pool could account for the unmeasured lipogenesis in the whole body. Physiological explanations must be excluded when the validity of MIDA is evaluated in vivo.
Analytic factors must also be excluded, particularly those related to instrument accuracy and concentration effects on measured isotope abundances (10, 11, 30). In our view (7, 26), analytic and experimental design factors may to some extent explain recent discordant results (32) of the use of MIDA for gluconeogenesis. Although this particular question has not been resolved, in general it is essential for manuscripts testing MIDA to demonstrate accuracy, avoid abundance-sensitivity effects, and explicitly describe the measures used to do so. Claims that a biosynthetic system is not adequately described by a combinatorial model need to be carefully evaluated using criteria other than just dissonant final estimates.
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SOME FUTURE DIRECTIONS FOR MIDA |
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A number of future directions can be considered for combinatorial probability techniques. Applications with large, heteronuclear polymers (e.g., proteins, polynucleotides) represent a challenge but potentially include some of the most important molecules in biology. Special problems are introduced for heteronuclear polymers, such as proteins, for example, because their large size and composition (including 20 or more amino acid subunits) require the investigator to identify repeats of a particular homonuclear subunit and then isolate this subunit from the intact molecule (28). Although techniques such as electrospray ionization are able to introduce intact proteins into the gas phase for mass spectrometry, resolution of individual mass isotopomers is not generally possible with most mass analyzers, especially for the multiply charged species generated by electrospray ionization. We (28) have successfully used the strategy of enzymatically hydrolyzing proteins to proteolytic fragments, and then collecting a selected fragment that includes a homonuclear stretch (e.g., 3-5 leucines out of a 7- to 15-amino acid stretch). An analogous approach might be applicable to DNA or RNA samples, which have the advantage of containing only four different subunits.
Another potentially powerful direction for MIDA may be to exploit information about p, not just f. Establishing the timing of biosynthetic events (e.g., during embryonic development) might be possible by fingerprinting polymers according to their precursor pool enrichment after generating a time gradient within the precursor pool. Measuring the tissue location of a biosynthetic event (e.g., whether cholesterol in high-density lipoprotein was synthesized in peripheral tissues or the liver, representing reverse or forward cholesterol transport) might also be possible by analyzing nonoverlapping values of p within an isotopomeric envelope, if label can be delivered at different rates to different tissues. Testing or correcting for labeling gradients within a tissue may also be possible by analyzing different portions of an isotopomeric envelope for divergent values of p (Fig. 5C).
Conclusion
An algorithm (see APPENDIX) for calculating fractional abundances of mass isotopomers in complex mixtures of labeled and natural abundance polymers can be used to construct reference tables that allow inference of the biosynthetic parameters p and f. The consequences of deviations from various assumptions of the MIDA model and the practical limits of the technique can also be tested in this manner. MIDA appears to be robust in the face of a number of deviations from its central assumptions. The combinatorial-probability approach imposes minor or no constraints with regard to the isotope-labeled substrate that can be administered, the length of the polymer that can be studied, the presence of contaminating M ![]() |
APPENDIX |
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general calculation algorithm for measuring polymerization biosynthesis by MIDA2
Our previous descriptions of the MIDA method (13, 14, 16, 17) provided the underlying theoretical basis but presented only an overview of the mathematical approach. The actual computer-based calculation algorithm that we have used for the past several years has not been described since our original presentation of the technique. We will describe a systematic and general calculation algorithm that can be used with a personal computer to generate expected fractional abundances of mass isotopomers for polymers containing labeled subunits; we will then show how these theoretical fractional abundances can be made into a "reference table" from which one can convert experimental data on mixtures of natural abundance and isotopically enriched polymers into biosynthetic parameters (p and f); and finally, we will demonstrate how to perform a MIDA biosynthetic calculation from experimental data. How the algorithm can be used to evaluate limitations of the technique or deviations from the model, or to correct for certain deviations from the model, is described in the text of this article.
Calculation Algorithm
We first present a formal mathematical algorithm for calculating the fractional abundances of mass isotopomers resulting from mixing natural abundance molecules with molecules newly synthesized from a pool of labeled monomers characterized by the parameter p. A mixture of this type can be fully characterized by f, the fraction new, and p. This algorithm is presented in a step-wise fashion, beginning with the simplest calculation, a molecule synthesized from a single element containing isotopes with the same fractional abundances that occur in nature and not mixed with any other molecules. We then proceed to molecules containing more than one element with all isotopes at natural abundance; then to nonpolymeric molecules containing different elements, some of which are in groups whose isotope composition is not restricted to natural abundance but is variable; then to polymeric molecules containing combinations of repeating chemical units (monomers), wherein the monomers are either unlabeled (containing a natural abundance distribution of isotopes) or potentially labeled (containing an isotopically perturbed element group); and finally to mixtures of polymeric molecules, composed of both natural abundance polymers and potentially labeled polymers, the latter containing combinations of natural abundance and isotopically perturbed units. The last-named calculation addresses the condition generally present in a biological system, wherein polymers newly synthesized during the period of an isotope incorporation experiment are present along with preexisting natural abundance polymers, and the investigator is interested in determining the proportion of each that is present to infer synthesis rates or related parameters.Molecules containing only a single element at the fractional isotope abundances that occur in nature. A first step is to calculate the isotope pattern of a hypothetical molecule composed of the element I with the fractional abundances 0I = 0.989, 1I = 0.01, 2I = 0.001. In the limit the molecule is a single atom, and the isotope pattern in a collection of element I is obtained directly from the fractional abundances of the isotopes: A0 = 0.989, A1 = 0.01, and A2 = 0.001. However, for a molecule composed of N I atoms (IN), the mass isotopomer distribution (isotope pattern) is obtained from the multinomial distribution. This distribution is a function of two variables: N (the number of I atoms) and the fractional abundances of the isotopes, which in this case are not perturbed from natural abundances. The contribution at each mass unit is obtained by individually summing the fractional abundances of all the isotopologues with that particular nominal mass. In this fashion one obtains the fractional abundance that would be observed at that mass with a mass spectrometer operating at unit mass resolution, arising from the conglomerate of isotopologues with that nominal mass. The frequency (F) of any given isotopologue in the summed total abundance of all of the isotopologues is given by the multinomial distribution [as adapted from CRC Standard Mathematical Tables (26th ed., pg 519); see Eq. A1]. For example, the probability of observing the I8 molecule composed of 0I21I52I1 is calculated as follows
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Molecules containing more than one element at natural isotope abundances. Next, suppose that probability distribution calculations have been done for the element groups C2, H4, and O2 as if they were isolated molecules, each composed of a single element, as described in the previous section. How then is the mass isotopomer distribution for C2H4O2 (acetic acid) obtained? One way is to multiply the fractional abundances of the components of each element group together and then to sum the fractional abundances of the specific isotopologues according to their nominal mass. Accordingly, to obtain the M1 components of acetic acid, the M1 component of each element group is combined with the M0 components of the others: (13C12C, 1H4, 16O2), (12C2, 1H32H, 16O2), and (12C2, 1H4, 16O17O). Each of these unique combinations has a probability of occurring that can be calculated by using the multinomial distribution (Eq. A1); they are multiplied together to obtain the fractional abundances of the isotopologues (see Eq. A2). The fractional abundance (A1) of the M1 mass isotopomer of acetic acid is then the sum of these fractional abundances, representing the sum of all the isotopologue fractional abundances (Eq. A2d).
Although calculating the fractional abundances of individual isotopologues and summing them according to mass is a reasonable approach for obtaining a mass isotopomer distribution in simple molecules, a systematic, step-by-step algorithm is needed for more complex molecules. We now describe an algorithm, first in general terms and then by using acetic acid as an example. The strategy, alluded to in the previous example, is to disaggregate the molecule conceptually into element groups (e.g., C's, H's, O's), calculate the mass isotopomer distributions for each element group, and then multiply the appropriate components of each element group together in a systematic fashion to attain the final mass isotopomer distribution of the molecule. A computer algorithm can do this by exhaustively combining all of the components of the first two element groups until the mass isotopomer distribution corresponding to the hypothetical molecule composed of those two element groups is obtained, and then by recording these abundances in an array. The process is then repeated for the next element group by combining its fractional abundances with those in the array. The resulting fractional abundances in the new array are then combined with the fractional abundances of the components of the next element group, and so on. A key aspect of this procedure is specifying all the combinations that contribute to the fractional abundances at each nominal mass during each iteration of the algorithm. For example, only M0 values from the array and the element group contribute to the M0 values in the new array, so they are multiplied together; however, M1 and M0 values contribute to the new M1, so they must be multiplied each time. Likewise, M0, M1, and M2 values from the two element groups contribute to the new M2 values, so M0 values are cross multiplied with M2 values, and M1 values are multiplied together. When all of the element groups have been combined together, the final distribution of fractional abundances for the whole molecule is attained. In the computer subroutine, this multiplication and summing process is carried out by use of loops, one nested inside the other. Because each addition of an element group increases the number of mass isotopomers and because the fractional abundances of mass isotopomers greater than approximately M10 are typically extremely low, an arbitrary limit may be set so that abundance calculations are not performed beyond this or some other set limit. The example of acetic acid demonstrates how the computer algorithm is used (Table 4). The two element group distributions C2 and H4 are combined to obtain the mass isotopomer distribution of the intermediate C2H4 molecule. This new distribution is in turn combined with the O2 distribution to form the final mass isotopomer distribution for acetic acid. The M0 value for C2H4 (0.97771) is multiplied by the M0 value for O2 (0.99519) to yield the fractional abundance of the M0 mass isotopomer for acetic acid (A0 = 0.97300). Because only M0 mass isotopomers of the element groups contribute to that mass isotopomer for the final molecule, the calculations are complete for A0, and the routine moves on to the next one, the M1 mass isotopomer. In this manner A0 to A8 are calculated (Table 4).
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Nonpolymeric molecules containing an element group in which isotope
composition is perturbed from natural abundances and is variable.
Next, the calculation of mass isotopomer distributions is shown for
nonpolymeric molecules that contain an element group enriched in a
particular isotope, that is, perturbed from the natural fractional abundances of its isotopes. For a molecule
IxJy,
where a number (w) of the
I element group is enriched in
+1I, the
calculation is nearly the same as described already except that the
w atoms of
I must be considered as a separate
element group (*I) from the other
(x w) atoms of
I in the molecule. The molecule then
becomes
*IwIx
wJy,
with the appropriate distribution calculated for each element group and the element group distributions combined to generate the final distribution of fractional abundances of mass isotopomers in the whole
molecule. The first step operationally, as described in the previous
examples, is to break the molecule into element groups, calculating
Jy and
Ix
w
from the natural isotope distributions of elements
J and
I. It is important to emphasize that
Jy and
Ix
w
will have constant mass isotopomer abundance distributions even as the
enriched elemental group (*I) changes. This invariant portion will be referred to here as the constant or invariant mass isotopomer abundance distribution of the
molecule, and it can be treated as though it were a chemical derivatizing agent attached to the variable moiety. Dividing the isotopically perturbed molecule into constant and variable moities greatly simplifies the calculation algorithm and is the motivation for
dividing the elements in a molecule into element groups (one of which
may be constant while the other is variable).
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Polymeric molecules containing repeating monomeric subunits, with some of the monomeric subunits composed exclusively of element groups at natural isotope abundances while other monomeric subunits contain an isotopically perturbed element group. The next step is to calculate the fractional abundances of mass isotopomers in polymers containing combinations of monomers, which themselves are either unlabeled (containing only element groups at natural isotope abundances) or labeled (containing an isotopically perturbed element group). The calculation procedure is an extension of the principles described so far. A general discussion is presented first, followed by an example of a peptide containing repeated subunits of leucine, either at natural abundance or containing [2H3]leucine (see above).
Consider a polymer composed of IxJy subunits, i.e., (IxJy)z. If a number (w) of I atoms (w<x) in each IxJy subunit are enriched in +1I (*I), whereas all other atoms are at natural isotope abundances (I and J), the calculation for each subunit IxJy is as just described for a nonpolymeric molecule that contains an element group enriched in a particular isotope. The mass isotopomers of the polymer (IxJy)z then can be calculated and will depend upon p. Several mathematically interchangeable algorithms exist for calculating the distribution of mass isotopomer abundances for a polymer of this type. The calculation approach that we believe to be the simplest computationally is to treat the isotopically perturbed element group in the polymer as a single, discrete (inseparable) unit, with its own mass isotopomer abundance distribution that is then combined with the constant distribution of the remainder of the polymer. The first step, as with the described nonpolymeric leucine example, is to break the polymer into element groups. The I positions that can be enriched are treated as a separate polymer (*Iw)z. This is convenient because the mass isotopomer abundance distribution of (*Iw)z will vary as a function of p, whereas the remaining element groups Jyz and I(x
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Mixtures of polymers. Finally, one can consider mixtures of polymers, as might be present during a physiological isotope incorporation experiment in vivo, wherein newly synthesized polymers are being added to a preexisting pool of polymers as part of the process of turnover. This calculation consists simply of generating linear combinations of the fractional abundances of each mass isotopomer.4 Thus one multiplies the fractional abundances of mass isotopomers in each polymer population times the proportion of the polymer pool represented by each population, and one sums the results. In this manner, the fractional abundances of each mass isotopomer in the mixture are weighted for the proportion of each polymer present. The net result is a linear combination of mass isotopomer abundances (Eq. A5).
Generation of Reference Tables for Inferring Biosynthetic Parameters from Experimental Data
Rationale for use of fractional abundances in
reference tables.
As discussed in the text of this article and previously (13, 15, 20,
21), inference of the fractional biosynthetic contribution to a
polymeric pool (f) requires
knowledge of the proportion (p) of
precursor subunits that were isotopically labeled after introduction of
a labeled monomer. The mathematical reason why
p must be known to establish
f is evident by graphical analysis (see accompanying manuscript, Fig. 1C). The universe of
possible fractional abundances for any mass isotopomer in a polymer can be seen to depend on the two variables,
p and
f. By envisioning a plane drawn at the
fractional abundance value for any
Ax (i.e., 0.15, Fig. 1C), it is apparent that an
infinite number of solution pairs of p
and f could result in any given value
of Ax. In a
nonlinear system in which both p and
f are unknown and variable, such as an
in vivo biosynthetic system, it is therefore necessary to solve for
p to linearize the relationship
between fractional abundance Ax and
f. It is then possible to solve for
f by simple algebraic means.
Conversion of Experimental Data into Biosynthetic Parameters
The sequence followed in converting experimental data into biosynthetic parameters is as follows. The ratio (R) ofSample Calculations
A sample of experimental data will now be presented. The example described is of an oligopeptide fragment of human serum albumin (SVVLLLR, or serine-valine-valine-leucine-leucine-leucine-arginine), which can be produced by partial proteolytic degradation of human serum albumin by treatment with the enzymes trypsin and chymotrypsin (28). This oligopeptide contains three repeating leucine subunits and was synthesized in vitro from mixtures of natural abundance leucine and [2H3]leucine subunits. The reference table for this compound, establishing the relationship between p andExperimental data from a mixture of isotopically perturbed and natural
abundance SVVLLLR molecules can then be analyzed. The peak areas are
converted to fractional abundances, assuming measurements are made on
the complete ion spectrum (M0 M9). Baseline (natural abundance) experimental data
are subtracted to generate
fractional abundances. If, for example,
the value of
A3 (mixture) = 0.0941 and
A6
(mixture) = 0.0214, then the ratio
A6(mixture)/
A3(mixture) was 0.227. The reference table equation (Table 7) indicates that p = 0.165 and
A
3 = 0.2091. Next,
f is calculated as
A3(mixture)/
A
3 = 0.0941/0.2091, or 45%. In a biological experiment, the
half-time (t1/2) of
albumin could then be calculated (i.e.,
f = 1
ekst, and t1/2 = 0.69/ks).
Appendix Equations
Equation A1
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(A1) |
Equation A2a
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(A2a) |
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Equation A2b
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(A2b) |
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Equation A2c
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(A2c) |
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Equation A2d
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(A2d) |
Equation A3
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(A3) |
Equation A4
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(A4) |
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Equation A5a
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(A5a) |
Equation A5b
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(A5b) |
Equation A5c
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(A5c) |
Equation A5d
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(A5d) |
Equation A6
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(A6) |
Equation A7a
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(A7a) |
Equation A7b
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(A7b) |
Equation A7c
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(A7c) |
Equation A8
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(A8) |
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Equation A9a
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(A9a) |
Equation A9b
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(A9b) |
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
1 A computer program for calculating theoretical tables and spreadsheets is available and will be sent by the authors on request.
2 Richard A. Neese, Dennis Faix, Kenneth Caldwell, and Marc K. Hellerstein were the authors of the APPENDIX. Dr. Caldwell is deceased as of August 1997.
3 We will assume 100% isotopic labeling by +1I in the material. If the material is <100% +1I, the actual distribution of 1Iw is calculated by using Eq. A3.
4 This holds unless an incomplete ion spectrum is being monitored, in which case a correction must be applied to restore the molar combinations to linearity (see text and Eq. A9b).
Address for correspondence and reprint requests: M. K. Hellerstein, Dept. of Nutritional Sciences, Univ. of California, Berkeley, CA 94720 (E-mail: march{at}nature.berkeley.edu).
Received 1 September 1998; accepted in final form 19 February 1999.
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REFERENCES |
---|
1.
Aarsland, A.,
D. Chinkes,
and
R. R. Wolfe.
Contributions of de novo synthesis of fatty acids to total VLDL-triglyceride secretion during prolonged hyperglycemia/hyperinsulinemia in normal man.
J. Clin. Invest.
98:
2008-2017,
1996
2.
Benyon, J. H.
Mass Spectrometry and its Application to Organic Chemistry. New York: Elsevier, 1960.
3.
Bergner, E. A.,
and
W.-N. P. Lee.
Testing gas chromatographic/mass spectrometric systems for linearity of response.
J. Mass Spectrom.
30:
778-780,
1995.
4.
Byerley, L. O.,
S. Bassilian,
E. A. Bergner,
and
W. N. P. Lee.
Use of D2O to quantitate cholesterol and fatty acid synthesis in tumor-bearing rats.
FASEB J.
7:
A289,
1993.
5.
Chinkes, D. L.,
A. Aarsland,
J. Rosenblatt,
and
R. R. Wolfe.
Comparison of mass isotopomer dilution methods used to calculate VLDL production in vivo.
Am. J. Physiol.
271 (Endocrinol. Metab. 34):
E373-E383,
1996
6.
Deines, P.
The isotopic composition of reduced organic carbon.
In: Handbook of Environmental Isotope Geochemistry. The Terrestrial Environment, edited by P. Fritz,
and J. C. Fontes. Amsterdam: Elsevier, 1980, vol. 1, chapt. 9.
7.
Dekker, E.,
M. K. Hellerstein,
J. A. Romijn,
R. A. Neese,
N. Peshu,
E. Endert,
K. Marsh,
and
H. P. Sauerwein.
Glucose homeostasis in children with falciparum malaria: precursor supply limits gluconeogenesis and glucose production.
J. Clin. Endocrinol. Metab.
82:
2514-2521,
1997
8.
Des Rosiers, C.,
F. David,
M. Garneau,
and
H. Brunengraber.
Nonhomogenous labeling of liver mitochondrial acetyl-CoA.
J. Biol. Chem.
266:
1574-1578,
1991
9.
Dietschy, J. M.,
and
M. S. Brown.
Effect of alterations of the specific activity of intracellular acetyl-CoA pool on apparent rates of hepatic cholesterogenesis.
J. Lipid Res.
15:
508-516,
1974
10.
Fagerquist, C.,
and
J.-M. Schwarz.
Gas-phase acid-base chemistry and its effects on mass isotopomer abundance measurements of biomolecular ions.
J. Mass Spectrom.
33:
144-153,
1998.
11.
Fagerquist, C. K.,
R. A. Neese,
and
M. K. Hellerstein.
Molecular ion fragmentation and its effects on mass isotopomer abundances of fatty acid methyl esters ionized by electron impact.
J. Am. Soc. Mass Spectrom.
10:
430-439,
1999.[Medline]
12.
Faix, D.,
R. A. Neese,
C. Kletke,
S. Walden,
D. Cesar,
M. Coutlangus,
C. H. L. Shackleton,
and
M. K. Hellerstein.
Quantification of periodicities in menstrual and diurnal rates of cholesterol and fat synthesis in humans.
J. Lipid Res.
34:
2063-2075,
1993[Abstract].
13.
Hellerstein, M. K.
Relationship between precursor enrichment and ratio of excess M2/excess M1 isotopomer frequencies in a secreted polymer.
J. Biol. Chem.
266:
10920-10924,
1991
14.
Hellerstein, M. K.,
M. Christiansen,
S. Kaempfer,
C. Kletke,
K. Wu,
J. S. Reid,
N. S. Hellerstein,
and
C. H. L. Shackleton.
Measurement of de novo hepatic lipogenesis in humans using stable isotopes.
J. Clin. Invest.
87:
1841-1852,
1991[Medline].
15.
Hellerstein, M. K.,
and
R. Neese.
Mass isotopomer distribution analysis: a technique for measuring biosynthesis and turnover of polymers.
Am. J. Physiol.
263 (Endocrinol. Metab. 26):
E988-E1001,
1992.
16.
Hellerstein, M. K.,
J.-M. Schwarz,
and
R. A. Neese.
Regulation of hepatic de novo lipogenesis in humans.
Annu. Rev. Nutr.
16:
523-557,
1996[Medline].
17.
Hellerstein, M. K.,
K. Wu,
S. Kaempfer,
C. Kletke,
and
C. H. L. Shackleton.
Sampling the lipogenic hepatic acetyl-CoA pool in vivo in the rat. Comparison of xenobiotic probe to values predicted from isotopomeric distribution in circulating lipids and measurement of lipogenesis and acetyl-CoA dilution.
J. Biol. Chem.
266:
10912-10919,
1991
18.
Hentze, M. W.
Determinants and regulation of cytoplasmic mRNA stability in eucaryotic cells.
Biochim. Biophys. Acta
1090:
281-292,
1991[Medline].
19.
Hetenyi, G.
Correction for the metabolic exchange of 14C for 12C atoms in the pathway of gluconeogenesis in vivo (Abstract).
Federation Proc.
41:
109,
1982.
20.
Kelleher, J. K.,
A. T. Kharroubi,
T. A. Aldaghlas,
I. B. Shambat,
K. A. Kennedy,
A. L. Holleran,
and
T. M. Masterson.
Isotopomer spectral analysis of cholesterol synthesis: applications in human hepatoma cells.
Am. J. Physiol.
266 (Endocrinol. Metab. 29):
E384-E395,
1994
21.
Kelleher, J. K.,
and
T. M. Masterson.
Model equations for condensation biosynthesis using stable isotopes and radioisotopes.
Am. J. Physiol.
262 (Endocrinol. Metab. 25):
E118-E125,
1992
22.
Lee, W. N. P.,
E. A. Bergner,
and
Z. K. Guo.
Mass isotopomer pattern and precursor-product relationship.
Biol. Mass. Spectrom.
21:
114-122,
1992[Medline].
23.
Mills, M.,
J. Chen,
R. Neese,
M. Hellerstein,
and
J.-M. Schwarz.
Mass isotopomer distribution analysis (MIDA) for measurement of gluconeogenesis (GNG) under conditions of hyperglycemia in streptozotocin (stz) diabetic rats (Abstract).
Diabetes
47, Suppl. 1:
A287,
1998.
24.
Mook, W. G.,
and
P. M. Grootes.
The measuring procedure and corrections for the high-precision mass-spectrometric analysis of isotopic abundance ratios, especially referring to carbon, oxygen and nitrogen.
Int. J. Mass Spectrom. Ion Phys.
12:
273-298,
1973.
25.
Neese, R. A.,
D. Faix,
C. Kletke,
K. Wu,
A. C. Wang,
C. H. L. Shackleton,
and
M. K. Hellerstein.
Measurement of endogenous synthesis of plasma cholesterol in rats and humans using MIDA.
Am. J. Physiol.
264 (Endocrinol. Metab. 27):
E136-E147,
1993
26.
Neese, R. A.,
D. Faix,
J.-M. Schwarz,
S. M. Turner,
D. Vu,
and
M. K. Hellerstein.
Measurement of gluconeogenesis and rate of appearance of intrahepatic triose-phosphate and its regulation by substrates by mass isotopomer distribution analysis (MIDA). Testing of assumptions and potential problems.
J. Biol. Chem.
270:
14452-14463,
1995
27.
Neese, R. A.,
and
M. K. Hellerstein.
Appendix. Calculations for gluconeogenesis by MIDA.
J. Biol. Chem.
270:
14464-14466,
1995.
28.
Papageorgopoulos, C.,
K. Caldwell,
C. H. L. Shackleton,
H. Schweingruber,
and
M. K. Hellerstein.
Measuring of protein synthesis by mass isotopomer distribution analysis (MIDA).
Anal. Biochem.
267:
1-16,
1999[Medline].
29.
Park, O.-J.,
D. Cesar,
D. Faix,
K. Wu,
C. H. L. Shackleton,
and
M. K. Hellerstein.
Mechanisms of fructose-induced hypertriglyceridemia in the rat: activation of hepatic pyruvate dehydrogenase (PDH) through inhibition of PDH kinase.
Biochem. J.
282:
753-757,
1992[Medline].
30.
Patterson, B. W.,
and
R. R. Wolfe.
Concentration dependance of methyl-palmitate isotope ratios by electron impact ionization gas chromatography/mass spectrometry.
Biol. Mass Spectrom.
22:
481-486,
1993[Medline].
31.
Peroni, O.,
V. Large,
and
M. Beylot.
Measuring gluconeogenesis with [2-13C]glycerol and mass isotopomer distribution analysis of glucose.
Am. J. Physiol.
269 (Endocrinol. Metab. 32):
E516-E523,
1995
32.
Previs, S. F.,
C. A. Fernandez,
D. Yang,
M. V. Soloviev,
D. France,
and
H. Brunengraber.
Limitations of the mass isotopomer distribution analysis of glucose to study gluconeogenesis substrate cycling between glycerol and triose phosphates in liver.
J. Biol. Chem.
270:
19806-19815,
1995
33.
Sackett, W. M.
Stable carbon isotope studies on organic matter in the marine environment.
In: Handbook of Environmental Isotope Geochemistry. The Terrestrial Environment, edited by P. Fritz,
and J. C. Fontes. Amsterdam: Elsevier, 1980, vol. 1, chapt. 4, p. 141-178.
34.
Schumann, W. C.,
I. Magnusson,
V. Chandramouli,
K. Kumaran,
J. Wahren,
and
B. R. Landau.
Metabolism of [2-14C]acetate and its use in assessing hepatic Krebs cycle activity and gluconeogenesis.
J. Biol. Chem.
266:
6985-6990,
1991
35.
Seeman, J. I.,
H. V. Secor,
R. Disselkamp,
and
E. R. Bernstein.
Conformational analysis through selective isotopic substitution: supersonic jet spectroscopic determination of the minimum energy conformation of o-xylene.
J. Chem. Soc. Chem. Commun.
1992:
713-714,
1992.
36.
Siler, S. Q.,
R. A. Neese,
M. P. Christiansen,
and
M. K. Hellerstein.
The inhibition of gluconeogenesis following alcohol in humans.
Am. J. Physiol.
275 (Endocrinol. Metab. 38):
E897-E907,
1998
37.
Srere, P.
Complexities of metabolic regulation.
Trends Biochem. Sci.
19:
519-520,
1994[Medline].
38.
Waterlow, J. C.,
P. J. Garlick,
and
D. J. Millward
(Editors).
Protein Turnover in Mammalian Tissues and in the Whole Body. Amsterdam: North Holland, 1978Waterlow, J. C., P. J. Garlick, and D. J. Millward (Editors). Protein Turnover in
Mammalian Tissues and in the Whole Body. Amsterdam:
North Holland, 1978.
39.
Wolfe, R. R.
Tracers in Metabolic Research. Radio-Isotope and Stable Isotope/Mass Spectrometric Methods. New York: Liss, 1984, p. 119-144.
40.
Zilversmit, D. B.
The design and analysis of isotope experiments.
Am. J. Med.
29:
832-848,
1960[Medline].