Calculation of the Protein Turnover Rate Using the Number of Incorporated ²H Atoms and Proteomics Analysis of a Single Labelled Sample.

Abstract

Rate constant estimation with heavy water requires a long-term experiment with data collection at multiple time points (3-4 weeks for mitochondrial proteome dynamics in mice and much longer in other species). When tissue proteins are analyzed, this approach requires euthanizing animals at each time point or multiple tissue biopsies in humans. Although short-term protocols are available, they require knowledge of the maximum number of isotope labels (N) and accurate quantification of observed ²H-enrichment in the peptide. The high-resolution accurate mass spectrometers used for proteome dynamics studies are characterized by a systematic spectral error that compromises these measurements. To circumvent these issues, we developed a simple algorithm for the rate constant calculation based on a single labeled sample and comparable unlabeled (time 0) sample. The algorithm determines N for all proteogenic amino acids from a long-term experiment to calculate the predicted plateau ²H-labeling of peptides for a short-term protocol and estimates the rate constant based on the measured baseline and the predicted plateau ²H-labeling of peptides. The method was validated based on the rate constant estimation in a long-term experiment in mice and dogs. The improved 2 time-point method enables the rate constant calculation with less than 10% relative error compared to the bench-marked multi-point method in mice and dogs and allows us to detect diet-induced subtle changes in ApoAI turnover in mice. In conclusion, we have developed and validated a new algorithm for protein rate constant calculation based on 2-time point measurements that could also be applied to other biomolecules.

Graphical Abstract

Introduction

Stable isotopes coupled with high-resolution mass spectrometry have become a critical tool in protein turnover studies ¹. A standard protocol for protein turnover studies involves steady-state administration of a pre-labeled amino acid precursor tracer and the time course measurement of amino acid incorporation into a protein product ². Deuterated water (²H₂O)-based metabolic labeling has been used as an alternative to more traditional methods to study biosynthesis of proteins and other biomolecules ³. It consists stable incorporation of deuterium, contained in the media solvent (water) for cell cultures or in the body water in living organisms, with carbon-bound hydrogen atoms of proteogenic amino acids. Their time-dependent incorporation of labeled amino acids into proteins allows for the calculation of the turnover rate of these macromolecules.

Two protocols, long-term and short-term labeling, have been used to study protein turnover. Both methods rely on steady-state metabolic and precursor tracer labeling assumptions ⁴. The long-term protocol enables the measurement of protein turnover rate constants based on the first order kinetic modeling of the time-course labeling of analyzed peptides. While this approach enables accurate quantifications of turnover rates, it requires the collection of multiple samples and long-term tracer exposure to achieve (or project) a plateau labeling of a product. Although it is possible to study protein turnover with ²H₂O (administered in drinking water) in free living subjects without the need for in-patient intravenous tracer infusion, it is difficult to apply the multi-point sampling approach to human studies, especially for muscle turnover measurements that require multiple sampling via invasive biopsy. Although small blood samples can be collected from a single mouse⁵, multiple tissue sampling in a long-term protocol is also costly, in that it requires sacrificing many animals at each time point⁶.

The short-term protocol requires a bolus load of deuterated water and peptide enrichment measurements during the early hours, i.e. those corresponding to the semi-linear segment of the exponential rise curve in the long-term protocol. While the optimal design requires several data points for linear regression analysis, a single time-point sampling after ²H₂O administration is also feasible^7-8. Thus, sample collections only before and after tracer administration are sufficient for rate constant measurements and render the short-term protocol with a single labeled sample an attractive option for tracer-based studies. However, accurate rate constant calculations require the knowledge of the exact stoichiometric relationship between the deuterated water tracer precursor and its product at the plateau⁹, thus it is imperative to determine the precise number of incorporated ²H label (N) into each biomolecule of interest. This has been reported for biomolecules including fatty acids, glucose, cholesterol, alanine, and tripeptide glutathione analyzed in different organisms^10-13. The number of metabolically labeled ²H atoms in tissue amino acids has been determined experimentally using radioactive counting and GC-MS assays^{4, 14-15}. These estimates are useful in the calculation of the rate constant based ²H-labeling of protein-bound amino acids measurements. However, as a metric of the biosynthetic pathway, the number of ²H in individual amino acid may vary between species, organs, and cells. Therefore, it is critical to estimate the N values based on the proteins originated from different organs and cell compartments.

Since ²H-labeling of a biosynthetic product is a function of precursor water enrichment and number of isotope label (N), the plateau enrichment can be calculated using mass isotopomer distribution analysis (MIDA). According to MIDA, in an ideal situation with accurate measurement of isotope distribution, the corrected observed spectral intensities (for the baseline natural enrichment) can be described based on binomial distribution of N and fraction of deuterium in water¹⁶. Often corrections for the baseline enrichment were performed only for ¹³C isotope¹⁷, although attempts were made to correct for other natural isotopes including ¹⁸O, ¹⁵N, and ³⁴S in metabolites^18-19. In addition, this approach requires high spectral accuracy of mass spectrometric analysis, which is compromised in current instruments for high-resolution accurate mass measurements, including mass spectrometers with Fourier transform-ion cyclotron resonance (FT-ICR) and Orbitrap detectors^20-21.

Here, we chose an alternative approach for the calculation of the fractional synthesis rate of proteins without correction for the natural enrichment of the analyzed peptides. For this purpose, first, we used a combinatorial method and estimated the maximum number of incorporated label (N) in tryptic peptides based on their plateau labeling. To account for the spectral error measurements, we quantified the isotopomer distribution in peptides at the baseline and plateau with the Q Exactive Orbitrap Plus mass spectrometer. Then, using data on multiple peptides, we determined the apparent number of incorporated ²H atoms in individual amino acids (N_aa). Once N_aa is determined for all proteogenic amino acids from an experiment with a long-term ²H₂O-labeling protocol, the maximum number of incorporated ²H atoms can be calculated for any peptide measured on the same mass spectrometer and used for a short-term labeling protocol. The turnover rate constant of the peptide is estimated based on 2 time-point measurements of total labeling at baseline and at the selected time point with stable isotope enrichment. We validated this 2 time-point method using results from a multi-point labeling experiment in mice and dogs. We showed that not only does our approach provides accurate values for rate constants calculations, but its high accuracy also enables us to detect small differences in the rate constants due to the high fat diet (HFD) induced changes in protein turnover in wild type mice. While we employed this method to calculate the turnover rate constants for proteins, it could also be applied to other biomolecules including carbohydrates, lipids, DNA, and RNA.

Experimental section

Mouse experiment:

Animal procedures were approved by the Institutional Animal Care and Use Committee at the Northeast Ohio Medical University (NEOMED) and were performed in accordance with National Institutes of Health (NIH) guidelines. Twelve eight-week-old male C57BL/6 mice were purchased from Jackson Laboratories and housed in the animal care facility of NEOMED. The animals were accommodated with a 12-hour light-dark cycle, chow diet (20% kcal from protein, 70% kcal from carbohydrate and 10% kcal from fat, Harlan Teklad), and water. Mice (n=6/group) were fed either a normal chow diet (ND) or HFD (D12492, 20% kcal from protein, 20% kcal from carbohydrate and 60% kcal from fat, Research Diets) for 4 weeks. ²H₂O-based turnover experiments were performed during the last week of dietary regimen. Two days after taking baseline blood samples from the lateral saphenous vein, animals received a loading dose, via intraperitoneal injection of ²H₂O (25 μl of 99.9% ²H-labeled saline per gram body weight) and then they had free access to drinking water enriched with 8% ²H₂O and food. Saphenous vein blood samples (60-80 μl) were collected at 8-hours, 1, 2 and 3 days after a bolus dose of ²H₂O and placed in potassium EDTA containing tubes (Fig. 1). The animals were euthanized 7 days after ²H₂O exposure, and the terminal blood sample was collected through cardiac puncture. Plasma was separated immediately and stored at −80 °C for later analyses. The ²H₂O labeling protocol results in a steady state 4.7±0.3% ²H-labeling of body water in mice.

Fig.1.

Schematic representation of the protocol for metabolic ²H₂O labeling of plasma proteins in mice. Mice were loaded with a bolus injection of 25 μl ²H₂O/g body weight, followed by free access to 8% ²H₂O in drinking water. Small blood samples were collected at different time points for one week. The turnover rate constants of plasma proteins were determined based on ²H-incorporation into tryptic peptides using 2-point and multi-point approaches.

Dog experiment:

The protocol was approved by the Institutional Animal Care and Use Committee (IACUC) of the Temple University and conformed to the guiding principles for the care and use of laboratory animals published by the NIH. Three male mongrel dogs (age: 9–13 months; weight: 21–24 kg) were instrumented as previously described²². After taking the baseline samples dogs were given an intravenous bolus of 99.9% ²H₂O with 0.9% NaCl dissolved in it at the dose of 18 μl per gram body weight and then animals had free access to drinking water enriched with 5% ²H₂O to achieve ~2.5% body water enrichment. Arterial blood samples (~3 ml) were taken at 8-hours, 1, 2, 3 and 7 days after the ²H₂O bolus, placed in potassium EDTA containing tubes and immediately spun for plasma separation.

Total body water enrichment measurements.

²H-enrichment of total body water was measured using a modification of the acetone exchange method as described²³. After the exchange between plasma water and acetone was complete, acetone vapor from the headspace was directly injected for gas chromatography-mass spectrometry (GC-MS) analysis. Isotopic enrichment of acetone was determined using electron impact ionization and selected ion monitoring. Acetone isotopomers were monitored at m/z 58 (M₀), 59 (M₁), and 60 (M₂). Biological samples were analyzed in parallel with a set of calibration curve samples containing 0 to 5% ²H₂O. The regression equation of the calibration curve was used for ²H₂O enrichment measurement in the biological sample.

Tryptic digestion of proteins:

After precipitation of proteins from 20 μl plasma with 1 mL of cold acetone (−20 °C), the pellets were centrifuged at 2000 g for 5 minutes and dried under a nitrogen gas flow. The residue was then dissolved in 200 μl of 50 mM ammonium bicarbonate solution and the fraction of the above protein solution corresponding to 50 μg protein was taken from each sample followed by reduction with 2.5 μl of 0.1 M dithiothreitol (DTT) at 60°C for 30 minutes. The sample was then alkylated with 2.5 μl of 0.2 M iodoacetamide at room temperature for 60 minutes. Tryptic digestion was performed by addition of 10 μl of 0.1 μg/μl Promega sequencing grade modified porcine trypsin (20 μg lyophilized trypsin in 200 μl 50 mM ammonium bicarbonate solution). The samples were incubated at 37 °C overnight. Tryptic digestion was stopped by adding 4 μl of 20% formic acid. Protein digests were cleaned up through C18 solid phase extraction using the Pierce Pepclean C18 spin columns.

LC-MS/MS analysis:

A solution containing the tryptic peptides was analyzed by Ultimate 3000 UHPLC (Thermo Scientific, CA) coupled online to Q Exactive™ Plus Hybrid Quadrupole-Orbitrap™ Mass Spectrometer (Thermo Scientific, CA). After desalting samples on an Acclaim PepMap100 precolumn (300 μm x 5 mm, C18, 5 μm, 100Å, Thermo Fisher Scientific), peptides were separated on an Acclaim PepMap RSLC reverse phase nanocolumn (75 μm x 15 cm, C18, 2 μm, 100Å, Thermo Fisher Scientific) at 300 nL/min with a mobile phase A (0.1% formic acid in water) and B (20% water in acetonitrile with 0.1% formic acid). A stepwise gradient was employed with an initial 2% of mobile phase B. After 4 min of de-salting, mobile phase B was linearly increased to 40% in 100 min. Mobile phase B was then ramped to 90% in 5 min and then held at 90% B for 10 min. Subsequently, mobile phase B was decreased to 2% for 2 min and equilibrated for 13 min with 2% of phase B.

Mass spectrometry analysis was performed in data-dependent acquisition mode with a full profile MS scans at 70000 resolution (200 m/z) between 380 and 1300 m/z. MS/MS spectra were collected in data-dependent acquisition mode for the 12 most abundant precursor ions with an isolation window of 1.5 and offset of 0.4 m/z and 17,500 resolution (at 200 m/z). Higher-energy collisional dissociation (HCD) was performed at a normalized collision energy of 25%. The precursor ion masses were dynamically excluded from MS/MS analyses for a duration of 17 s. MS and MS/MS spectra were acquired for 100 ms with the automatic gain control (AGC) target set at 1.0 x 10⁶ and 2.0 x 10⁴ ions for MS and MS/MS scans, respectively.

Data analysis:

For protein identification, all the spectra obtained from the mass spectrometer were transformed into mzML file format using ProteoWizard MSconvert Version 3.0.18116 (http://proteowizard.sourceforge.net/tools), and the MZML files were searched using Mascot software (Matrix Science, London, UK) version 2.3 against the mouse subset of the UniProt protein database released on June 29^th, 2016 (containing 149,730 entries) with cysteine carbamidomethylation as fixed and methionine oxidation as variable modifications and trypsin digestion with a maximum of two missed cleavages per peptide. The intensities of peptide’s isotopomers in the proteins of interest at each time-point were extracted from high-resolution full scan (MS1) spectra of analyzed peptides using d2Ome software²⁴. The ²H- enrichment values were calculated using a script written in Python.

The results were summarized using means and standard deviations and were compared between groups using two-sample t-tests. Mean differences between groups with 95%-confidence intervals were presented. To assess correlations between methods, Pearson correlations were used. All calculations assume a 0.05 significance level. Statistical analysis was performed using Prism (GraphPad, La Jolla, CA) software (version 5).

Theoretical considerations

Equations for the rate constant calculations:

In the metabolic labeling experiment with stable isotopes including ²H₂O, the kinetic information is obtained from a time-course change in the mass isotopomer distribution of a molecule. The observed mass isotopomer distribution represents the combination of the natural abundances of atoms in the molecule and deuterium atoms incorporated into this molecule. Two different approaches have been used to interpret the data from metabolic labeling experiments. The first approach corrects the observed spectral intensities of the ion cluster of an analyzed molecule for the contributions of natural abundances. Often the background corrections result in overcorrection when applied to the higher molecular weight peptides due to consistent underestimation of heavy isotopomers in liquid chromatography coupled high-resolution mass spectrometers (LC-MS). In the second approach, the background enrichment (natural abundances of heavy isotopomers) is subtracted from the observed molar fraction of an isotopomer or total labeling of all isotopomers. This method yields “excess enrichment” without any knowledge of ²H-distribution in different isotopomers. Here, we used the peak intensities of mass isotopomers without correction for the natural abundances of elements. We assume that the change in the relative isotope abundance of the monoisotopic peak reflects the deuterium incorporation due to protein synthesis ²². Thus, the relative isotope abundance for the monoisotopic peak (M₀) at a given time point t (I₀(t)) is calculated by the ratio of M₀ intensity to the summation of peak intensities of all isotopomers:

$$Io(t)={}^{M_0(t)}∕_{{\sum }_{j=0}^n{M}_j(t)}$$ (1)

Since the increase in heavy isotopomers due to ²H-incorporation is related to the decline in monoisotopic peak, the total ²H-labeling (I(t)) can be expressed as:

$$I(t)=1-Io(t)={\sum }_{j=1}^n{M}_j(t)∕{\sum }_{j=0}^n{M}_j(t)$$ (2)

In a long-term experiment, the rate constant (k) is determined using a single compartmental model by fitting a time course ²H-labeling (I (t)) of peptides, to an exponential rise curve equation (Eq. 3) after the removal of statistical outliers using the Prism software⁴:

$$\mathrm{I}(t)=\mathrm{I}(0)+(\mathrm{I}(plateau)-\mathrm{I}(0))\mathrm{x}(1{\text{-e}}^{\text{-}kt})$$ (3)

where I(0) and I(plateau) are the total labelings before heavy water exposure (t=0) and at infinite time, respectively. Although this method allows for the accurate calculation of the rate constant, it requires multiple sample collection at different time points and necessitates the long-term labeling protocol to measure a peptide enrichment at the asymptote.

To calculate the rate constant using 2-time point measurements, we solve Eq. 3 for k:

$$\text{ln}[\mathrm{I}(\mathrm{p}lateau)-\mathrm{I}(\mathrm{t})]=\text{-}\mathit{k}t+\text{ln}[\mathrm{I}(\mathrm{p}lateau)-\mathrm{I}(0)]$$ (4)

After simple rearrangement, the rate constant (k) can be calculated as:

$$\mathit{k}=\text{-}1∕\mathrm{t}\times \text{ln}[1\text{-}(\mathrm{I}(t)\text{-}\mathrm{I}(0))∕(\mathrm{I}(Plateau)\text{-}\mathrm{I}(0))]$$ (4a)

where the I(t) and I(0) represent observed total labeling at the baseline and at time t which are measured experimentally, while I(plateau) is the value at the asymptote which could be measured or calculated theoretically based on the binomial model that includes molecular composition of chemical elements, their natural abundances, the tracer precursor water enrichment, and the maximum number of ²H atoms (N) that are incorporated during metabolic labeling experiment. When kt<<1, the exponent can be linearized and the expression of the rate constant becomes:

$$\mathit{k}=(\mathrm{I}(t)\text{-}\mathrm{I}(0))∕(\mathrm{I}(plateau)\text{-}\mathrm{I}(0))∕\mathrm{t}$$ (4b)

Estimation of N:

Current methods use the number of metabolically exchangeable carbon bound hydrogens (N_aa) in individual amino acids to calculate the total number of ²H atoms incorporated into peptides N ^{1, 25-26}. N_aa has been determined based on the ²H enrichments or the ³H specific activities of free amino acids determined by GC-MS or radioactivity counting after metabolic labeling with ²H₂O or ³H₂O, respectively ^{14-15, 27} However, the calculation of the plateau isotopic enrichment based on the literature results in erroneous estimation of the rate constants due to the following reasons: (i) N_aa for each amino acid is estimated approximately and may depend on the isotopic equilibrium in each system, (ii) Since the high-resolution mass spectrometers consistently underestimate the isotope ratio measurements compared to the predicted values, the use of a theoretically calculated plateau value (I(plateau)) based on N from literature would underestimate the rate constant value. Therefore, we propose a new approach that calculates N_aa and total N for a peptide based on only experimentally measured parameters on the Orbitrap mass spectrometer.

To model N estimation, we use the fractional abundances of isotopomers in an analyzed peptide at the plateau from a long-term labeling experiment. For this purpose, the fractions of isotopomers are determined by binomial formulas, as previously described ²⁸. The details of isotope distribution simulation have been described by us and others in previous publications^{4, 16}. First, for simplicity, we consider only M₀ and M₁ isotopomers. The probability of the M₀ isotopomer for the molecular ion C_cH_hN_nO_oS_s is:

$${\mathrm{M}}_0=({\mathrm{X}}_{12}{)}^{\mathrm{c}}•({\mathrm{X}}^1{)}^{\mathrm{h}}•({\mathrm{X}}_{14}{)}^{\mathrm{n}}•({\mathrm{X}}_{16}{)}^{\mathrm{o}}•({\mathrm{X}}_{32}{)}^{\mathrm{s}}$$ (6)

Where X₁₂, X₁, X₁₄, X₁₆, and X₃₂ are the natural abundances of ¹²C, ¹H, ¹⁴N, ¹⁶O, and ³²S, and superscripts (c, h, n, o, and s) are the number of carbons, hydrogen, nitrogen, oxygen, and sulfur atoms in the molecule. To calculate the probability of heavy isotopomers, ²H is considered as “a separate element” with the abundance corresponding to heavy water enrichment (²H₂O). So, there are two classes of ²H atoms: ²H_h and ²H_N, representing the natural abundance of deuterium and sites that are labeled by metabolic labeling with ²H₂O, respectively ¹⁰. The expressions for the higher isotopomers including all natural heavy isotopomers and ²H_N are shown in the Supplementary material (SM 1). Thus, for a peptide with the molecular formula C_c¹H_h1N_nO_oS_s²H_N, the probability of M₁ isotopomer normalized on M₀ is determined as ²⁸:

$${\mathrm{M}}_1∕{\mathrm{M}}_0={\mathrm{M}}_{10}={\mathrm{h}}_1{\mathrm{Y}}_{20}+\mathrm{c}{\mathrm{Y}}_{13}+\mathrm{n}{\mathrm{Y}}_{15}+\mathrm{o}{\mathrm{Y}}_{17}+\mathrm{s}{\mathrm{Y}}_{33}+\mathit{N}{\mathrm{Y}}_{21}$$ (7)

Where X₁₃, X₂, X₁₅, X₁₇, and X₃₃ are the natural abundances of heavy isotopes ¹³C, ²H, ¹⁵N, ¹⁷O, and ³³S, respectively and the ratios Y₁₃=X₁₃/X₁₂, Y₁₅=X₁₅/X₁₄, Y₁₇=X₁₇/X₁₆, Y₃₃=X₃₃/X₃₂, represent their fractions normalized relative to the light isotope, h=h₁+N. Since we separated newly incorporated ²H (as a result of metabolic labeling) from the natural ²H background, Y₂₀ and Y₂₁ represent the relative fractions of ²H before and after metabolic labeling. In this case, Y₂₁=²H/¹H also represents the ²H enrichment of water normalized to an unlabeled fraction. For example, when ²H enrichment of water is 5%, the ratio is 5/95. N represents the total number of carbon-bound deuterium incorporated into a peptide sequence. Thus, the term N•Y₂₁ reflects the contribution of metabolic ²H-labeling to total labeling of a peptide, while all other terms together represent the contribution of other elements, except deuterium, to M₁ isotopomer. By combining all background natural enrichments under term α, the ratio M₁/M₀ can be simplified as:

$${\mathrm{M}}_1∕{\mathrm{M}}_0=\alpha +N•{\mathrm{Y}}_{21}$$ (7a)

$$\text{where}\alpha ={\mathrm{h}}_1{\mathrm{Y}}_{20}+\mathrm{c}{\mathrm{Y}}_{13}+\mathrm{n}{\mathrm{Y}}_{15}+\mathrm{o}{\mathrm{Y}}_{17}+\mathrm{s}{\mathrm{Y}}_{33}$$ (7b)

Thus, in Eq. 7a, M₁ isotopomer is presented as a composite of the background natural enrichment of a peptide (term α) and contribution of ²H from hypothetical metabolic labeling experiments with ²H₂O (the term N•Y₂₁). This simplified expression for M₁/M₀ ratio (Eq. 7a) allows us to derive the baseline (t=0) and plateau (t=∞) total labeling based on M₀ and M₁ isotopomers using Eq. 2:

$$\mathrm{I}(0)=\left[\frac{\text{M1}}{\text{M0}+\text{M1}}\right]baseline=1-\frac{1}{1+\alpha +N\ast \mathrm{Y}20}$$ (8a)

$$I(plateau)=[\frac{\text{M1}}{\text{M0}+\text{M1}}]plateau=1-\frac{1}{1+\alpha +N\ast \mathrm{Y}21}$$ (8b)

As shown in Eqs 8a and 8b, at the baseline (t=0), N•Y₂₁ = N•Y₂₀. It should be emphasized that α does not depend on metabolic deuterium labeling, while N represents the total number of deuterium incorporated into peptide during the biosynthesis of protein. At the baseline (Eq. 8a), total labeling includes only natural enrichment of heavy isotopes including ²H, thus N denotes the potential number of deuterium to be incorporated during the metabolic labeling.

The Eqs 8a and 8b, allows us to find the difference I(plateau)-I(0) and calculate the rate constant using Eq. 4b:

$$\mathrm{I}(plateau)\text{-}\mathrm{I}(0)=\frac{N(Y21-Y20)}{(1+\alpha +N\ast \mathrm{Y}21)(1+\alpha +N\ast \mathrm{Y}20)}$$ (9)

$$\mathit{k}=\frac{(\mathrm{I}(\mathrm{t})-\mathrm{I}(0)(1+\alpha +\mathrm{N}\ast \mathrm{Y}21)(1+\alpha +\mathrm{N}\ast \mathrm{Y}20)}{N(Y21-Y20)t}$$ (4c)

If the molecular weight of a biomolecule is too small, the contribution of natural enrichment of heavy isotopes can be neglected (α<<1). This is because for small molecules, including amino acids and small peptides, the fraction of heavy isotopes is negligible. Furthermore, at lower body water enrichments, a small number of isotopic label (N) is incorporated into the biosynthetic molecule, and therefore N * Y21 and N * Y20 terms could be neglected (N * Y21 ≪ 1, N * Y20 ≪ 1, Y20 ≪ Y21). In these circumstances and when kt<<1 (the main assumption for the linearization of Eq. 4a), the expression of the turnover rate constant transforms to a conventional simplified expression ⁹:

$$\mathit{k}=\frac{\mathrm{I}(t)-\mathrm{I}(0)}{N\ast Y21\ast t}$$ (4d)

Note that Eqs. 4c and 4d are applicable to data generated on mass spectrometers with an ideal spectral accuracy, i.e. the ability to accurately measure the fractional abundances of isotopomers, while the high-resolution FT-ICR and Orbitrap mass spectrometers are characterized by the systemic error in the isotopic distribution patterns ^{20, 29}. The absolute spectral error, the difference between theoretically predicted and measured values, for the several unlabeled ApoAI peptides analyzed in Q Exactive Orbitrap is presented in the Supplementary Table S1. Therefore, one needs to take into account the instrumental isotopic spectral error to perform the kinetic analysis.

When applied to the experimentally measured isotopic distribution, α is considered as an experimental parameter that depends on the mass analyzer type and peptide composition. Defining α from Eq. 8a and substituting it in Eq. 8b allows us to calculate the predicted plateau labeling for each peptide:

$$I(plateau)=1-\frac{1}{\frac{1}{1-\mathrm{I}(0)}-N\ast \mathrm{Y}20+N\ast \mathrm{Y}21}=1-\frac{1}{\frac{1}{1-\mathrm{I}(0)}+N(\mathrm{Y}21-\mathrm{Y}20)}$$ (10a)

Since Eq. 10 (in addition to water enrichment and the number of exchanged hydrogen atoms) includes the experimentally measured baseline (I(0)) and the calculated I(plateau) labeling, therefore it takes into account the instrumental spectral error in the baseline natural enrichment measurements. It should be noted, that the total number of incorporated ²H (N) needs to be estimated independently. Here, we determined N from the preliminary long-term experiment based on the measured plateau labeling of peptides. In order to calculate N, we use the system of Eqs. 8 again but solve it this time for N in Eq. 8b after defining α from Eq. 8a:

$$\alpha =\frac{1}{1-I(0)}-N^{\ast }\mathrm{Y}20-1$$ (11a)

$$N=(\frac{1}{1-I(plateau)}-\frac{1}{1-I(0)})∕(\mathrm{Y}21-\mathrm{Y}20)$$ (11b)

Since α is an experimental parameter and it depends on the spectral accuracy of mass spectrometer used for data acquisition, α could be considered as a correction factor for the isotopic distribution measurements that is included in the rate constant and N calculations. Thus, using this formula (Eq. 11b), N can be calculated based on the precursor water enrichment (²H₂O expressed as Y21), and the experimentally measured I(0) and I(plateau) values from a long-term experiment. Table 1 contains calculated N for different tryptic mouse ApoAI peptides (more examples are presented in the Supplementary Table S2). The data are from a metabolic labeling experiment in wild type mice on a normal chow diet exposed to ²H₂O for 168 hours (7 days). This long-term protocol allows to reach the plateau labeling of many plasma proteins, including ApoAI in mice that enables the accurate calculation of N. To improve the accuracy of N calculation, we chose proteins with shorter half-lives (1-2 days) and use the peptides with the high-quality fitting to an exponential rise curve equation (R²> 0.99). To further improve the accuracy of N calculation, instead of measured plateau and baseline values, we used the projected values obtained from the fitting of multi-points data to Eq. 3.

Table 1.

Calculated asymptotic number of incorporated deuterium atoms (N) in tryptic peptides from wild type mouse ApoAI. The total labeling values at the baseline (I(0)) and asymptote (I(Plateau)) were determined based on the multi-point fitting of the experimentally measured total labeling values to Eq. 1 which also allows for the calculation of the turnover rate constant.

Parameters	ARPALEDLR	QKLQELQGR	AKTHLKTLGEK	LSPVAEEFRDR
Experimental I(0)	0.347	0.358	0.390	0.409
Experimental I(Plateau)	0.585	0.584	0.555	0.619
Rate Constant (pool/hour)	0.028	0.027	0.030	0.028
Calculated N	16.784	16.093	11.547	17.784

Since the main goal is to determine the rate constant using the short-term labeling experiment based on any tryptic peptide (Eq. 4a), one needs to determine N_aa for each amino acid based on the plateau labeling of peptides from a long-term experiment. Once N_aa is accurately determined, N for any peptide can be calculated by summing N_aa for amino acids in a peptide sequence. To calculate N_aa for each amino acid, we determine N for multiple (60-80) peptides containing all 20 proteogenic amino acids. These peptides were derived from several proteins that reached plateau enrichment in mice after 7 days of ²H₂O metabolic labeling. The set of linear equations with 20 unknown N_aa were constructed (Equations 12a-), where the right side of the equilibrium represents N for each peptide, and each letter on the left side of the equilibrium denotes the number of exchanged hydrogen atoms (Naa) in a specific amino acid. For example, in accordance with one letter description of amino acids, A and R represent the number of ²H incorporated into alanine (A) and arginine (R), respectively (similarly, for other amino acids the initial letter indicates the number of exchangeable hydrogens in that amino acid).

$$\text{A+R+P+A+L+E+D+L+R}=\text{2A + 2R + 2L + E + P + D}=16.784$$ (12a)

$$\text{Q+K+L+Q+E+L+Q+G+R}=\text{3Q + K + 2L E + G + R}=16.093$$ (12b)

$$\text{A+K+T+H+L+K+T+L+G+E+K}=\text{A+3K+2T+H+2L+G+E}=11.546$$ (12c)

$$\text{L+S+P+V+A+E+E+F+R+D+R}=\text{L+S+P+V+A+2E+F+2R+D}=17.784$$ (12d)

Since the Naa calculation is based on the experimental data, the system of equations can’t be solved exactly. However, it can be resolved using the least squares method. Briefly, during the 1^st cycle of calculations N_aa for an individual amino acid varied by the small steps, so that the left sides in the expressions (12a−) reach a local minimum and then this was repeated for each 20 amino acids. This procedure was repeated multiple cycles until a minimum error was found. Thus, the solution of this system of equations yields N_aa for each amino acid. The calculated N_aa values for all 20 amino acids are presented in Table 2.

Table 2.

The number of incorporated hydrogen atoms in individual amino acids determined based on M₀-M₁ isotopomers in analyzed tryptic peptides from plasma proteins in wild type mice on a normal chow diet exposed to ²H₂O for one week.

Essential amino acids		Non-essential amino acids
Amino acid	Naa	Amino acid	Naa
Histidine (H)	1.372	Alanine (A)	3.471
Isoleucine (I)	0.592	Arginine (R)	1.326
Leucine (L)	0.634	Aspartic acid (D)	2.490
Lysine (K)	0.121	Asparagine (N)	0.674
Methionine (M)	0.994	Cysteine (C)	1.496
Phenylalanine (F)	0.418	Glutamic acid (E)	3.580
Threonine (T)	0.097	Glutamine (Q)	3.517
Tryptophan (W)	0.003	Glycine (G)	1.844
Valine (V)	0.591	Serine (S)	1.574
		Proline (P)	0.780
		Tyrosine (Y)	0.740

The accuracy of N_aa estimates depend on the accuracy of the mass isotopomer distribution measurements, therefore, we also estimated N_aa for individual amino acids based on a different set of isotopomers, i.e. M₀-M₁, M₀-M₂, M₀-M₃, and M₀-M₄ (Supplementary Table S3a). Since the modified cysteine and methionine have different mass signatures, we also determined N_aa for their modified forms. The relative change due to modifications of cysteine and methionine were <10% within the accuracy of our measurements (±22%), indicating that modified forms of these amino acids are duplicate measures of their unmodified forms. While we observed some differences in N_aa values calculated based on different set of isotopomers, we failed to evaluate any relationship between N_aa values and measured number of mass isotopomers, suggesting that the differences were related to the variabilities in the N_aa value calculation.

To assess whether the number of incorporated ²H atoms is sensitive to diet, we also calculated N_aa for the individual amino acids in high fat diet fed wild type mice. As shown in the Supplementary Table S3b, a high fat diet resulted in a similar number of N_aa for all 20 proteogenic amino acids suggesting that the diet doesn’t have any measurable effect on the metabolic labeling of amino acids. To further evaluate whether the source of analyzed proteins has any effect on estimated N_aa values, we also calculated these parameters based on the peptides derived from mice liver proteins at the plateau. In these calculations, we used the proteomics data from our published study on hepatic proteome dynamics in LDLR^−/− mice liver and demonstrated that many proteins in mice liver reach plateau ²H-enrichment after 21 days of ~3% ²H₂O exposure ²⁴. As shown in Supplementary Table 3SC, N_aa values calculated using the liver proteins in LDLR^−/− mice are also similar to those calculated from plasma proteins in wild type mice. This could be related to the fact that our algorithm is based on a single compartmental model which assumes rapid labeling of all amino acids in all organs and cells. Future studies involving multi-compartmental modeling may determine the role of different diet and diseases on N_aa values in different tissues and cellular/subcellular compartments.

Finally, since we also identified post-translational acetylation in multiple hepatic proteins, we also estimated the number of ²H atoms in acetyl moiety of acetylated peptide. Proteins are acetylated on their lysine residues with the acetyl-CoA which is derived from glucose and fatty acids ²H-labeled during gluconeogenesis and lipogenesis, respectively. Therefore, acetyl-CoA could potentially be labeled with ²H. These results show that the N value for acetyl-lysine is 2.5, while for lysine itself, it is 0.1, indicating N=~2.4 deuterium incorporation into the acetyl moiety of acetyl peptide.

Next, we use N_aa values for each amino acid to calculate the maximum number N for peptides analyzed in the short-term ²H₂O-labeling experiment. This allows us to calculate the predicted plateau ²H labeling of these peptides from Eq. 10 based on the measured background labeling value, the maximum number of incorporated ²H atoms and body water enrichment. These parameters enable us to calculate the rate constant based on the experimental measured I(0), I(t) and the body water enrichment values using Eq. 4a:

$$k=-\frac{1}{t}\ast \text{ln}[1-\frac{\mathrm{I}(t)-\mathrm{I}(0)}{1-\mathrm{I}(0)}\ast \frac{1+N(1-\mathrm{I}(0))(\mathrm{Y}21-\mathrm{Y}20)}{\mathrm{N}(1-\mathrm{I}(0))(\mathrm{Y}21-\mathrm{Y}20)}]$$ (4e)

As mentioned above, for the sake of simplicity, this equation of the rate constant is based on M₀-M₁ isotopomers. For the higher order isotopomers, the plateau labeling including M_0-j isotopomers could be expressed as:

$$I(plateau{)}_{\text{M0-j}}=1\text{-}\frac{1}{\frac{1}{1-\mathrm{I}(0)}+N(\mathrm{Y}21-\mathrm{Y}20)\ast \theta j}$$ (10b)

Where additional factor θ_j depends on the number of isotopomers included in calculations. When only M_0-1, factor θ₁ = 1. The derivations of the θ_j for higher order M₂, M₃, and M₄ isotopomers are shown in the Supplementary material SM2. The Supplementary Table S3 contains Naa values calculated based on different sets of isotopomers. Note that in contrast to previous methods of rate constant calculations ¹⁶, our method doesn’t correct the experimentally measured peptide enrichment (I(t)) for natural enrichment. The predicted plateau ²H-enrichment and the rate constant values were calculated using scripts written in Python. The scripts of 2-point algorithm are freely available from GitHub, https://github.com/saIlchenko/2pointGrowth

Results and Discussion.

The turnover rate constant measurements with heavy water-based short-term metabolic labeling protocol require the accurate determination of the observed ²H-labeling of a product and the asymptotic number of ²H atoms incorporated into a fully substituted product. Based on this information and precursor water ²H-enrichment, fractional synthesis rate is determined according to the conventional Eq. 4d that compares the observed and predicted molar enrichments (N * Y21 term). This simplified equation is widely used in the metabolic flux studies employing instruments with high isotopic accuracy, including isotope-ratio mass spectrometry (IRMS) and gas chromatography-mass spectrometry (GC-MS)^{13, 30}. In our study, we modified this equation by incorporating a new parameter representing the spectral error of Orbitrap mass spectrometers ²⁹.

We and others have shown that despite the high mass resolving power and mass accuracy of high-resolution mass spectrometers, the isotopomer ratios measured by these instruments are consistently lower than predicted. The systematic error in these instruments has been attributed to time-dependent trap overfilling (space-charge-effect) and ion motion damping¹³. Therefore, the observed mass isotopomer distribution requires the correction of the observed spectral ratio error prior to use in the kinetic calculations. Although the spectral accuracy could be improved by decreasing resolution, measurements at a low-resolution compromise the data quality because of the presence of interfering signals in a complex mixture. In the past, we improved the accuracy of spectral measurements on high- resolution FT-ICR mass spectrometer by performing scans of different duration and extrapolation of the data to the initial moment of ion rotation³. Recently, Su and co-authors applied discrete mass scan ranges (by dividing the total scan into several scan events) that enhanced the spectral accuracy of Q-Exactive Orbitrap instrument for the analysis of singly charged metabolites ¹⁸. Even though these approaches allow for the accurate measurement of mass isotopomer distribution of metabolites and selected peptides, they are not applicable to global proteome dynamics studies that require multiple mass spectrometry runs and complex data analyses.

Here, we developed a novel, improved a single labeled sample approach to estimate the rate constant based on 2 time-point measurements. According to this approach, the rate constant calculation using Eq. 4a is based on estimation of both observed and predicted ²H-labeling of a peptide using previously described isotope distribution simulations ¹². However, in contrast to existing methods of probability calculations, here, we present an improved method for an accurate estimation of the predicted ²H-labeling of a peptide that takes into account the spectral error of the mass analyzer. This approach assumes a similar error for all isotope distribution measurements (including the baseline natural labeling before the tracer exposure (t=0) and observed enrichment at the sampling time-point) and corrects the predicted theoretical ²H-labeling of a peptide based on the spectral error measurements at the baseline. We show that when the molecular weight of analyzed biomolecule and water enrichment are small, this equation transforms to a conventional short Eq. 4d used in metabolic studies. However, the application of Eq. 4d for the higher molecular weight peptides may result in a substantial error even for the isotopic enrichment measured on an ideal instrument with good spectral accuracy. To demonstrate this, we performed a simulation study for the rate constant calculations using the conventional method and our new approach. First, to mimic the conditions similar to human ²H₂O studies^{11, 31}, we simulated the ²H-labeling of different peptides for a given lower water enrichment (0.5%) and a smaller protein rate constant (0.01 pool/hour). For this purpose, we calculated the total labeling of several peptides at the baseline and asymptote, then simulated the total labeling at any time point using Eq. 3 for the selected turnover rate constant (Supplementary Table S4). The predicted total labeling for each peptide at 8 h was then used to calculate the rate constants using both the short (conventional) (Eq. 4d) and full versions of this equation (Eq. 4e) based on 2-data points. As seen in Figure 2A, the rate constants calculated using the conventional equation are consistently lower than the expected rate constant (the horizontal line). We also performed a simulation using the higher water enrichment (5%) and rate constant (0.03 pool/hour) values to mimic protein turnover in mice³². As shown in Figure 2B, the discrepancy between rate constants calculated using the conventional equation and expected rate constant values are markedly higher for the fast turnover proteins at higher body water enrichment. This is because the linearized expression of the rate constant assumes kt<<1, which is the main assumption for the transition from the logarithmic equation (Eq 4a) to its linear form (Eq 4b). Furthermore, Eq. 4d used in the conventional method neglects the contribution of natural enrichment of heavy isotopes (term α) and assumes minuscule label incorporation at low body water enrichment (terms N•Y21 and N•Y20). However, the contribution of the heavy isotopomers for higher molecular weight molecules at higher body water enrichment is substantially higher and can’t be ignored. In contrast, the calculation of the rate constant using the full version of a 2 time-point equation with the inclusion of an estimated α parameter (Eq. 10a) yields results that are almost identical with the expected values for all peptides with a wide range of mass, body water enrichment, and turnover rates. Note that these simulations assumed accurate measurements of isotope ratios. When the spectral accuracy of mass isotopomeric measurements is compromised, the differences between the expected and calculated rate constants might be much larger.

Fig.2.

Dependence of 2-time point rate constants estimations on the molecular weight of analyzed peptides. The rate constant for each peptide with different molecular weights was calculated based on 8-hour labeling using Eq 4c or Eq 4d. In both equations, we used N values from literature¹⁵. The dashed lines show the expected rate constant values used for each simulation. While the calculation of k with conventional short formula is applicable only to a low molecular weight amino acid such as glycine, the calculation of k with the newly developed formula coincides well for all peptides.

A: The predicted total labeling of peptides simulated based on body water enrichment (0.5%) and rate constant (0.01 pool/hour) values.

B: The predicted total labeling of peptides simulated based on body water enrichment (5%) and rate constant (0.03 pool/hour) values.

The time course incorporation of ²H into peptides provides qualitative information about their turnover rates, however the quantitative interpretation of these data requires the knowledge of the stoichiometric relationship between tracer precursor (²H₂O) and product (a peptide). It has been challenging to calculate the label number (N) in proteolytic peptides due to the complexity introduced by 20 different amino acid precursors. Furthermore, the PTMs of proteins further complicates the situation because groups attached to peptides are derived from ²H-labeled metabolites. Thus, the total number of incorporated N into a modified peptide is the sum of N in the PTM and peptide backbone moieties. The asymptotic number of deuterium (N) transferred from water into an individual peptide is generally calculated by summing the number of deuterium in the free amino acids (N_aa) that build the peptide. While predicted N_aa in each amino acid can be determined based on metabolic pathways involved in the synthesis of non-essential amino acids and transamination reaction for both essential and non-essential amino acids, the experimental values depend on equilibrium constants, which are generally lower than 1. Previously, we have calculated the total asymptotic number of deuterium (N) in individual peptide based on the measured enrichments of both the peptide and water⁴. Here, we expanded this approach to calculate the number of incorporated ²H atoms into individual amino acids (N_aa) and acetyl group in acetylated lysine based on the measured ²H-enrichments in multiple peptides consisting of all 20 proteogenic amino acids and acetylated lysine at the plateau using a simple mathematical algorithm. Since the accurate estimation of the ²H-enrichment of a peptide depends on the spectral accuracy on a mass spectrometer, these parameters must be evaluated for each type of instrument used for the isotope ratio measurements. It is important to note that the calculated N_aa are lower than those reported previously ¹⁵, which may reflect an underestimation of heavy isotopomers of peptides in the Orbitrap mass spectrometer.

To validate our new algorithm, we estimated the turnover rate constant of albumin in wild type mice after 24 hours of ²H₂O exposure and compared to those obtained using the bench-marked multi-point method. The predicted I(plateau) labeling was calculated using Eq. 10b based on body water enrichment and the total numbers of exchanged H atoms for each peptide (calculated using Naa values listed in Table 1). The rate constant was determined using Eq. 4e based on the experimentally measured labeling values for I(0) and I(t). The results obtained analyzing selected peptides are presented in Table 3. The full data from all 67 peptides are shown in Supplementary Table S5.

Table 3.

Validation of 2-time point method based on a multi-point (six time points) experiment. The turnover rate constant of albumin in a mouse was calculated based on the M₁ labeling of tryptic peptides at 24 h (2-point method) and time-course labeling during 7 days of ²H₂O exposure (multipoint method). The maximum number of incorporated ²H in each peptide was determined based on N_aa values presented in Table 2. In the 2-point method, the turnover rate constant was calculated in a single mouse for each peptide. In the multi-point method, nonlinear regression analysis with 0.95 confidence interval was used to calculate the rate constant based on ²H-labeling of each peptide at six time-points. R² represents the curve fitting regression coefficient.

Rate Constant (pool/hour)	FGERAF K	QTALA ELVK	EKAL VSSVR	ALVSS VRQR	SLHTL FGDK	AFKAW AVAR	KQTALA ELVK
Multi-point method (R2)	0.0119 (0.995)	0.0096 (0.999)	0.0092 (0.999)	0.00916 (0.999)	0.0103 (0.998)	0.00921 (0.999)	0.00968 (0.999)
2- point method	0.0096	0.0087	0.00962	0.00863	0.0091	0.0080	0.00867

As shown in Table 3, our 2-point method usually slightly underestimates the rate constant values compared to a multi-point method, however, the discrepancy between 2 methods is less than 10 %, indicating that the presented method allows accurate estimation of the rate constant using 2-time point measurement.

Effect of the number of quantified mass isotopomers on the rate constant estimates

This method was validated based on only M₀-M₁ isotopomers. However, in metabolic labeling experiment with ²H₂O, the amount of ²H-incorporated per molecule is distributed among all heavy isotopomers (M₁….M_n). To assess the role of the number of quantified mass isotopomers on the rate constant estimations, we calculated the turnover rate constant of ApoAI in mice using different sets of isotopomers to determine the optimal number of isotopomer measurements for the kinetic studies. As shown in Figure 3, when the intensity of all isotopomers could be quantified with certainty, the estimated value of the rate constant gradually increased with the inclusion of more isotopomers (from M₀-M₁ to M₀-M₄) using both traditional multi-point and newly developed 2-point methods. The reason for these differences is related to the fact that for the higher mass molecules like proteolytic peptides, the contribution of heavy isotopomers to the total mass is significant and the inclusion of heavy isotopomers into total labeling of newly synthesized protein (I(t) in Equations 4c and 4d) results in higher rate constant values. However, since the differences in the rate constant measurements using M₀-M₃ and M₀-M₄ isotopomers are less than 3%, we conclude that for the peptides with m/z 500-3000, it may be appropriate to calculate the rate constant based on M₀-M₃ isotopomers. Since the measurements of higher mass isotopomers with lower intensity are associated with poor spectral accuracy this decision needs to be made based on the ion intensity and other circumstances. Similar results were obtained for mice albumin: the rate constant values for different sets of isotopomers using a 2-time point method are in a good agreement with the multipoint fittings (Supplementary Tables S6, S7, and S8). The discrepancy between the two methods was ≤9%.

Fig. 3.

The effect of different heavy isotopomer measurements on the rate constant estimation in wild type mice. A: Time course labeling of selected ApoAI WKEDVELYR peptide measured using a different set of isotopomers: M₀-M₁, M₀-M₂, M₀-M₃, and M₀-M₄. B: Calculated turnover rate constant of ApoAI using the multi-point and 2-point methods. Mean ± SD. White and black bar graphs represent multi-point and 2-point corrected methods, respectively.

Effect of sampling time-point on the rate constant estimates

Another critical parameter in a short-term experiment with 2 time-point measurements is the sampling time. To determine the optimal sampling time, we estimated the rate constant of ApoAI in wild type mice (t_1/2=22 h from multi-point experiment) using the observed ²H-labeling of multiple peptides at different time points. Figure 4a shows that a more accurate turnover rate constant value was obtained at 24 h. As expected, the estimated rate constant values decrease gradually with increasing sampling time. The accuracy of the rate constant measurement can be evaluated by partial derivatives of k (Eq. 4a) relative to observed ²H-labeling (I(t)) and time (t):

$$\Delta \mathit{k}=\Delta \mathrm{I}(t)∕(\mathrm{I}(\mathrm{p}lateau)\text{-}\mathrm{I}(t))∕\mathrm{t}+\Delta {\text{t/t}}^{2\ast }\text{ln}\frac{I(plateau)-I(t)}{I(plateau)-I(0)}$$ (13a)

Fig. 4.

The effect of ²H₂0 labeling duration on the accuracy of the rate constant measurement. A: The turnover rate constant of ApoAI in wild type mice was evaluated using the standard multi-point approach (dashed line) and the newly developed 2-time point method using ²H-labeling data. All values represent mean ± SD, n= 6. B: The accuracy of the rate constant is measured at different time points. The relative errors in rate constant measurements were determined by partial differentiating the rate constant expression relative to observed ²H-labeling of a peptide and time using Eq. 13b.

The relative error in the rate constant measurements (Eq. 4a) can be calculated as:

$$\Delta \mathit{k}∕\mathit{k}=\Delta \mathrm{I}(\mathrm{t})∕(\mathrm{I}(\mathrm{p}lateau)\text{-}\mathrm{I}(t))∕\text{ln}\frac{I(plateau)-I(t)}{I(plateau)-I(0)}+\Delta \text{t/t}$$ (13b)

We used simulated ²H-labeling data at different time points to calculate the error for the mice ApoAI turnover rate constant values in a wide range of sampling time periods. Figure 4A shows that the minimum error in the 2-time point method (compared to the multi-point method) corresponds to 24 h sampling time: 0.004 absolute error (9 % relative error). These results are in agreement with the minimum of predicted relative error, estimated using Eq. 13b (Figure 4b). The low accuracy of enrichment measurements explains the higher error at the beginning of the experiment, while the decrease in term (I(plateau) -I(t)) leads to error arising at the end of the experiment. Therefore, the optimal sampling time should be selected based on the half-life of a protein and lower limit of ²H-enrichment measurement by a mass spectrometer.

Application of single labeled method to animal studies

After optimizing our method, we applied it to assess the effect of 4-week HFD on ApoAI turnover in wild type mice with body water enrichment of ~5%. The rate constant of ApoAI based on a single labeled sample was calculated using the conventional Eq. 4d with N_aa values from literature¹⁵ and newly developed Eq. 4e using and N_aa values from Table 2 and compared to the benchmarked multipoint method. As shown in Figure 5, the HFD results in an increased turnover rate of ApoAI as measured by the multi-point standard method (P=0.006). The rate constant calculation using a conventional 2-time point approach (t=24 h) yields 3-fold lower values for the rate constant for both mice on ND and HFD groups without any differences between groups. In contrast, the rate constant calculation using our new method yields k values similar to those obtained by a multi-point approach and shows significant differences between ND and HFD groups (P=0.012), suggesting that the accuracy of the new method may allow detecting subtle changes in protein turnover.

Fig.5.

The effect of a high fat diet in ApoAI turnover in mice. The rate constant measurements using conventional and newly developed 2-point methods were evaluated using the multi-point approach. All values represent mean ± SD, n= 6/group.

To validate our new algorithm in larger animals with relatively lower body water enrichment, we quantified the kinetics of ApoAI in healthy dogs loaded with a bolus of pure ²H₂O/NaCl followed by 5% ²H₂O in drinking water for one week. This protocol allowed the animal to reach ~2.5% labeling of body water at the steady state. Although, due to the long half-life of dog ApoAI (~3.5 day), one-week ²H₂O exposure doesn’t allow the asymptotic labeling of ApoAI peptides to be achieved, the rate constant of ApoAI was accurately calculated based on the projected plateau labeling using the multi-point method (Fig. 6A). We used the N_aa values determined from plateau labeling of peptides in mice (Table 2) to calculate the total number of incorporated ²H atoms in dog peptides. The rate constant calculation based on the new 2-point method was in good agreement with the results from the multi-point method (Fig. 6B), suggesting that N calculation does not depend on biological species, but rather on accurate measurements of plateau enrichment.

Fig. 6.

Validation of the 2-point method based on a multi-point approach in healthy dogs (n=3) with body water ²H enrichment of ~2.5%. The turnover rate constant of plasma ApoAI was measured based on the labeling of an ApoAI peptide (AQLAPYSDDLR) at 24 h (2-point method) and time-course labeling during 7 days of ²H₂O exposure. A: Time-course labeling of AQLAPYSDDLR in multi-point experiment. B: Calculated turnover rate constant using 2-point and multi-point (from Panel A) methods.

Finally, to further evaluate our new algorithm, we compared the rate constant values calculated by the 2 time-point and multi-point approaches using the data set for several mice plasma proteins. We quantified the kinetics of 16 proteins with total numbers of 130 and 170 peptides in ND and HFD, respectively. Figure 7 shows the scatter plot of rate constant results obtained using multi-point curve fitting and our new 2-point algorithm. The correlation coefficient (R²) between the two methods was 0.97, suggesting compatibility of the rate constant calculations based on a single labeled sample and multi-point sample method. The slope and intercepts of the linear regression of rate constants were 0.9 and 0.0007, respectively. These results show that our new method measures the rate constant within 10% accuracy of benchmark multi-point method for different proteins with wide-range turnover rates.

Fig.7.

The scatter plot of rate constant calculations in wild type mice based on multi-point curve fitting and 2-point methods. Each data point represents one peptide. The rate constants in the multipoint method were calculated based on six time-points measurements during a one-week ²H₂O labeling experiment (X coordinate). In the 2-point method, the rate constants were calculated based on the baseline labeling (t=0) and after 24 hours of ²H₂O exposure (Y coordinate). Quantified proteins: ApoAI, ApoAII, ApoC3, ApoH, CFAB, CFAD, FETUA, FETUB, KNG1, MUG1, PLMN, PZP, THRB, TRFE, VTDB and albumin, with total number of 130 and 170 peptides from ND and HFD, respectively.

Conclusion

We have developed a general approach for protein turnover determination with short-term heavy water labeling and 2-time point measurements. This approach considers the spectral error of mass spectrometric analysis and enables accurate rate constant calculations. We implemented an algorithm to estimate the rate constant using isotope distribution data quantified by d2Ome software. We validated this method using the gold-standard multi-point approach. We tested its utility to study the effect of HFD on ApoAI turnover in wild type mice and found that like multi-point approach, this new method allows detection of the HFD-induced alterations in ApoAI turnover. Most importantly, this algorithm allows us to accurately quantify the rate constant of a plasma protein in dogs with body water enrichment of ~2.5%, suggesting its potential use for human studies. While the utility of this method was tested for plasma proteins in mice and dogs, it also should be applicable to a wide range of in vivo and in vitro metabolic labeling studies involving other bio molecules. Particularly, this method would allow for the estimation of the number of incorporated isotopes for any biosynthetic molecule and its rate constant.