Assessing Protein Synthesis and Degradation Rates in Arabidopsis thaliana Using Amino Acid Analysis

Plants continually synthesize and degrade proteins, for example, to adjust protein content during development or during adaptation to new environments. In order to estimate global protein synthesis and degradation rates in plants, we developed a relatively simple and inexpensive method using a combination of 13CO2 labeling and mass spectrometry–based analyses. Arabidopsis thaliana plants are subjected to a 24‐hr 13CO2 pulse followed by a 4‐day 12CO2 chase. Soluble alanine and serine from total protein and glucose from cell wall material are analyzed by gas chromatography time‐of‐flight mass spectrometry (GC‐TOF‐MS) and their 13C enrichment (%) is estimated. The rate of protein synthesis during the 13CO2 pulse experiment is defined as the rate of incorporation of labeled amino acids into proteins normalized by a correction factor for incomplete enrichment in free amino acid pools. The rate of protein degradation is estimated as the difference between the rate of protein synthesis and the relative growth rate calculated using the 13C enrichment of glucose from cell wall material. Degradation rates are also estimated from the 12CO2 pulse experiment. The following method description includes setting up and performing labeling experiments, preparation and measurement of samples, and calculation steps. In addition, an R script is provided for the calculations. © 2021 The Authors. Current Protocols published by Wiley Periodicals LLC.


INTRODUCTION
Synthesis and degradation of proteins represent fundamental processes during development, growth, and adjustment to the environment (Nelson & Millar, 2015). Due to the high energy cost of amino acid synthesis (∼5 ATP per amino acid when synthesized for nitrate) and formation of peptide bonds (also ∼5 ATP per amino acid), protein turnover represents a large part of the total energy budget (Amthor et al., 2000;Penning de Vries, 1975). These costs are increased by the need to invest heavily in ribosomes; these large machines have a relatively slow rate of peptide bond formation and can represent 40% or more of total protein content in rapidly growing cells (Warner, 1999; see Pal et al., 2013, for further literature).
Although plant research has made significant advances into understanding the complex networks that regulate protein synthesis and degradation, measurement of protein synthesis and degradation rates remains challenging. In microbial and animal systems, this is done by supplying exogenous label, often as amino acids. In plants, this was done in the last century using 14 C-, 35 S-, or 15 N-labeled amino acids or amino acid precursors, and more recently using 13 C-labeled amino acids or amino acid precursors. The use of radioisotopes has the advantage that very small amounts can be supplied with a high specific activity, but assignment of label to specific metabolites can be challenging. This is much easier using stable isotopes linked with mass spectrometry, but with the potential disadvantage that large amounts of exogenous compounds must be applied to obtain a clear signal. This is feasible in microbial or animal systems in which cells are supplied with exogenous medium that can be easily switched between unlabeled and labeled metabolites. It is much more challenging with most plant tissues, as the internal transport pathways are far more complicated with the exception of studies in isolated cells or organelles, or in certain tissues such as developing seeds, which receive nutrients from over the apoplast (Allen, Laclair, Ohlrogge, & Shachar-Hill, 2012). It should be noted that a large supply of external amino acids or precursors like sugars can result in a perturbation of metabolism and, in all likelihood, the rates of protein synthesis and degradation. Further problems are raised by mixing of the labeled metabolite with the internal pool, which leads to dilution of the label and underestimation of flux to protein (see below).
In plants, all carbon is derived directly or indirectly from photosynthetically fixed CO 2 . We have developed a relatively simple approach to quantify the rates of protein synthesis (K S ) and degradation (K D ) in Arabidopsis thaliana using 13 CO 2 labeling experiments (Ishihara, Obata, Sulpice, Fernie, & Stitt, 2015;Ishihara et al., 2017). This approach has three potential advantages over other methods using different stable isotopes or radioisotopes. First, 13 CO 2 is incorporated via photosynthetic CO 2 fixation, allowing introduction of the isotope without perturbation of metabolism or growth. Second, 12 CO 2 and 13 CO 2 can be rapidly interchanged in the gas mixture supplied to the plant or leaf, allowing rapid start of the pulse and rapid and complete removal of external label at the start of a chase. Third, 13 CO 2 should label all amino acids and the extent of labeling can be measured using gas chromatography time-of-flight mass spectrometry (GC-TOF-MS).
We define K S as the rate of 13 C-labeled amino acid incorporation into proteins. Note that the enrichment of 13 C differs among amino acids. This could be due to differences in the various amino acid synthesis pathways. For example, in A. thaliana, amino acids that are directly synthesized from central carbon metabolism (by amino transferase) show higher 13 C enrichment values than those whose synthesis requires multiple steps (Ishihara et al., 2015;Szecowka et al., 2013). It can also reflect compartmentation, for example, the sequestration of part of the amino acid pool in the vacuole that is not immediately involved in metabolism and is labeled only slowly. Furthermore, slow exchange between compartmented pools and the cytoplasmic pool used for protein synthesis can lead to decreased labeling in the latter in a manner that is difficult to predict. Compartmentation is much more prevalent in plants than microbes and animals, posing an especially large challenge to determination of fluxes to protein in plant systems. Therefore, information regarding 13 C enrichment values from amino acids in soluble fractions are used to correct for incomplete 13 C enrichment of free amino acid pools for accurate estimation of K S .
It has been shown that protein abundance does not vary much within a single diel cycle (Sulpice et al., 2009). Thus, K D can be assessed based on enrichment and decay of 13 C-labeled amino acids in the protein fraction in a pulse and chase, respectively, and is estimated with the assumption that proteins that are not used for growth are degraded (Ishihara et al., 2015(Ishihara et al., , 2017. Depletion of 13 C enrichment in the protein fraction is due not only to protein degradation but also to dilution of labeled amino acids by tissue growth. Therefore, determination of K D requires information about the relative growth rate (RGR), which can be estimated in various ways, including measuring fresh weigh, dry weight, and size of rosette leaves for at least 3 days and estimating the slope of a log plot over this time (Poorter & Nagel, 2000). In our protocol, the 13 C enrichment of glucose in the cell wall fraction is used to estimate structural RGR (RGR STR ) (Ishihara et al., 2015(Ishihara et al., , 2017. We describe here the procedures for estimating K D based on the difference between K S and RGR STR . The work flow for estimating the rates of protein synthesis and degradation is divided into six protocols (Fig. 1). Basic Protocol 1 focuses on setting up of the 13 CO 2 labeling system and the labeling experiment. Basic Protocols 2-4 describe how to obtain soluble (free) amino acids, amino acids from total protein, and sugars from cell wall for GC-TOF-MS analysis. Basic Protocol 5 briefly explains how to obtain, organize, and analyze GC-TOF-MS data to calculate 13 C enrichment (%) in compounds obtained using Basic Protocols 2-4. Basic Protocol 6 presents stepwise calculations of K S and K D . Stepwise calculations using R language are also available on the open-source GitHub repository (https:// github.com/ thiagomaf/ Kd_Ks_RGRstr).

STRATEGIC PLANNING
It should be decided whether to perform a 13 CO 2 pulse experiment alone or a 13 CO 2 pulse followed by a 12 CO 2 chase experiment. In general, a 13 CO 2 pulse experiment is sufficient to obtain K S , K D , and RGR STR . The advantage of performing a 13 CO 2 pulse/ 12 CO 2 chase experiment is the estimation of these parameters from two different datasets instead of one.
The temporal distribution of harvest time points and the number of samples per time point needs to be carefully planned in order to obtain robust results. It is recommended to have at least three biological replicates per time point. We use five A. thaliana plants per replicate to reduce biological noise. When using younger and/or smaller plants, it is recommended to grow more plants per pot in order to increase the amount of material harvested. If only a 13 CO 2 pulse experiment is performed, the number of replicates and time points can be increased, leading to increased statistical power and increased understanding of labeling kinetics in a timely manner.
During a 13 CO 2 pulse experiment, the first time point is typically at the beginning of the light period (ZT0) and is used to estimate the natural abundance of 13 C. A second time point can be taken at the end of a 24-hr 13 CO 2 pulse (ZT24). If possible, however, it is encouraged to take a few time points during the light period (including at the end of the light period) and a few during the dark period to obtain better temporal information about 13 C incorporation into protein and increased precision in the correction for enrichment in free amino acids. It should be noted that 13 C enrichment of soluble free amino acids rises in the first 30-60 min after illumination and decreases slightly between the end of Ishihara et al.

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Figure 1 Work flow for protocols. Basic Protocol 1: Setting up the 13 CO 2 labeling system and stable isotope labeling of A. thaliana rosette leaves. Basic Protocol 2: Extraction of soluble amino acids for GC-TOF-MS analysis. Basic Protocol 3: Preparation of amino acids from total protein for GC-TOF-MS analysis. Basic Protocol 4: Preparation of sugars from cell wall material for GC-TOF-MS analysis. Basic Protocol 5: GC-TOF-MS analysis of 13 C-labeled samples and estimation of 13 C enrichment (%). Basic Protocol 6: Estimation of protein synthesis and degradation rates.
the light period and the end of the dark period (Ishihara et al., 2015). Thus, for example, if free amino acids were only measured at ZT24 (corresponding in our case to the end of the dark period), their 13 C enrichment values at ZT24 need to be adjusted by considering the decay during the night based on changes previously reported (Ishihara et al., 2017). Generally, we perform a 12 CO 2 chase for 96 hr and harvest samples at the end of the chase. At this time point, 13 C enrichment of alanine, for example, is reduced from 25% to 10%. Figure 2 13 CO 2 labeling setup for a 13 CO 2 feeding experiment using A. thaliana growing in soil. (A) Outside the growth chamber, stationary gas mixer (1) is used to mix N 2 and O 2 gases. The gas mixture is humidified using a gas washing bottle (2) filled with water. A mass flow controller (4) is used to control the 13 CO 2 flow rate from a gas cylinder with a pressure regulator (3). A tee gas mixer (5) is used to mix 4.5 ml/min 13 CO 2 gas with 10 L/min N 2 /O 2 gas mixture. Inside the growth chamber, glass tube rotameters (6) are used to distribute equal flow (5 L/min) of labeled gas mixture to each labeling chamber (7). Two labeling chambers are shown. Labeling chambers are made of Plexiglass (internal dimensions: 60 × 31 × 17.4 cm) and can contain up to eighteen 10-cm pots. Holes (red dots) in the labeling chambers function as gas inlet/outlet and are fitted with 6-mm PVC tubes. The inlet is located on the upper part of one Plexiglass panel, and the outlet on the lower part of the opposite panel. 13 CO 2 exiting the labeling chamber is directed to a gas washing bottle filled with soda lime (8). (B) Labeling chambers containing A. thaliana plants inside a growth chamber. (C) Tee gas mixer.
In order to estimate K D , it is necessary to have an accurate RGR. We have shown that RGR values estimated from rosette size, fresh weight, and 13 C labeling are very similar (Ishihara et al., 2015). If RGR will be determined based on fresh weight, dry weight, or rosette size, extra plants should be grown in the same conditions and at the same time as the plants used for the labeling experiment and harvested 1 day before the start of the experiment (ZT-24), at the beginning of the experiment (ZT0), and 1 day after the start of the experiment (ZT24).

SETTING UP THE 13 CO 2 LABELING SYSTEM AND STABLE ISOTOPE LABELING OF ARABIDOPSIS THALIANA ROSETTE LEAVES
A schematic representation of the labeling system is presented in Figure 2A. Stable isotope labeling of A. thaliana rosette leaves is typically done using transparent Plexiglass labeling chambers that can contain up to eighteen 10-cm pots (Fig. 2B). To reduce biological noise, we recommend growing five plants per pot. The labeling chambers are placed inside a plant growth chamber with a controlled environment (Fig. 2B). 13 CO 2 Ishihara et al.

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gas is mixed with a N 2 /O 2 gas mixture using a custom-made tee gas mixer (Fig. 2C). The 13 CO 2 flow (i.e., concentration) is adjusted and controlled using a mass flow controller. The labeled gas mixture is directed to each labeling chamber at a flow rate of 5 L/min, which is sufficient to completely replace the air in each labeling chamber in 15 min.
It has been reported that metabolite and transcript levels change when plants are transferred to different growth conditions (Moraes et al., 2019). In order for plants to be adapted to the experimental conditions, they should be transferred to labeling chambers 3 days prior to the labeling experiment. The labeling chambers are not closed with a lid until the start of the experiment.

Set up labeling system
1. Three days prior to the labeling experiment, place labeling chambers in the growth chamber.
2. Connect each component of the labeling system as illustrated ( Fig. 2A) using 6-mm PVC tubes except between the MFC (4) and tee gas mixer (5). For this connection, use a ⅛-in. PVC tube to increase the gas pressure (Fig. 2C).
Numbers in parentheses refer to the apparatus diagram in Figure 2.
As an alternative to the tee gas mixer, a small-gauge syringe needle can be placed at the end of the ⅛-in. PVC tube exiting the MFC and used to puncture the N 2 /O 2 gas tube.
3. Inside the growth chamber, divide the tube exiting the tee gas mixer using a Y-shaped hose connector and connect each outlet to a glass tube rotameter (6).

Connect the rotameters to the gas inlets of the labeling chambers (7)
Ishihara et al.

5.
Connect the PVC tubes exiting the labeling chambers using a Y-shaped hose connector. Connect the resulting single PVC tube to a LICOR LI850 CO 2 analyzer connected to a CO 2 trap (8).
The CO 2 trap is a gas washing bottle filled with soda lime pellets with indicator (Merck Millipore) to prevent release of 12/13 CO 2 into the atmosphere, which would otherwise affect the natural 13 C abundance in other plants growing in the vicinity.
Set up 13 CO 2 gas mixture 6. Mix 79% N 2 and 21% O 2 at a flow rate of 10 L/min using a stationary gas mixer (1).
It is important that the gas mixture entering the labeling chambers be humidified using a gas washing bottle (2) containing water. Humidification is done with the N 2 /O 2 gas mixture because humidifying the final gas mixture can lead to gas backflow.
7. Set the 12 CO 2 flow rate at 4.5 ml/min using the MFC.
If you can measure 13 CO 2 concentration directly, it is not necessary to use this indirect method. You can then use the 13 CO 2 cylinder from the start.
8. Adjust the rotameters to a flow rate of 5 L/min. 9. Close the lids of the labeling chambers.
10. Check the 12 CO 2 concentration in the gas mixture using a CO 2 analyzer. If necessary, adjust the concentration using the MFC.
In our work space, the atmospheric CO 2 concentration is ∼450 ppm, so the concentration in the gas mixture is set to this value.
11. Replace the 12 CO 2 cylinder with the 13 CO 2 cylinder.
12. Stop the gas flow, remove the CO 2 analyzer from the system, and place the plants in the labeling chambers without lids.
Label rosette leaves 13. Remove unlabeled control plants from the growth chamber 15 min before the start of the light period.
For this first harvest, we keep the lights off in the room where the growth chamber is located and use a green light.
14. As soon as the control plants have been removed, place the lids on the labeling chambers and start the gas flow with the 13 CO 2 mix.
This will replace all the 12 CO 2 in the labeling chambers before the start of the light period.
15. Immediately harvest rosette leaves from the unlabeled control plants and immediately freeze in liquid nitrogen. Transfer frozen material to pre-cooled scintillation vials in liquid nitrogen. This is done in the dark using a green light.
16. For each harvesting time point, slightly open the lids of the labeling chambers, quickly remove the pots, close the lids, and immediately harvest rosette leaves.
The opening and closing of the lids should be completed within 10 s.
If plants are left for long in air with 12 CO 2 , and also in undefined light conditions, there may be a decrease in the enrichment of some free amino acids.
17. After performing the 13 CO 2 pulse for 24 hr, stop the gas flow, replace the 13 CO 2 cylinder with the 12 CO 2 cylinder, and restart the gas flow.

Current Protocols
Opening and closing of the chambers during the chase does not have to be done as quickly as during the pulse.
19. Grind frozen leaves to a fine powder using a mixer mill with steel balls. Store ground frozen material at −80°C until use.
It is important to ensure that all liquid nitrogen is removed from the vials before grinding, and that the material is not allowed to thaw during this process.
The protocol requires at least 30 mg frozen plant tissue powder per sample.

EXTRACTION OF SOLUBLE AMINO ACIDS FOR GC-TOF-MS ANALYSIS
GC-TOF-MS can identify and quantify a few hundred metabolites in a single plant extract, including sugars, sugar alcohols, phosphorylated intermediates, lipophilic compounds, and organic and amino acids (Lisec, Schauer, Kopka, Willmitzer, & Fernie, 2006). The following sample preparation protocol is relatively simple, established for different plant species such as A. thaliana, cassava, maize, and tomato (Lisec et al., 2006;Obata et al., 2015;Rosado-Souza et al., 2019;Schauer et al., 2006), and adapted for a lower amount of starting material (Ishihara et al., 2015(Ishihara et al., , 2017.
Make sure to not thaw the plant material while aliquoting. Also make sure that there is no liquid nitrogen inside the tube before closing it, as this could cause material to be violently extruded when the tube is opened.
2. Mix 280 μl of 100% methanol and 12 μl of 0.2 mg/ml ribitol per sample and cool the mixture on ice.
Prepare an adequate volume based on the number of samples.
3. Add 292 μl cold methanol/ribitol to each sample and shake at 100 rpm for 15 min at 70°C using a Thermomixer.

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Current Protocols 9. Transfer 150 μl of the upper polar phase to a 2-ml Safe-Lock tube. As a backup, transfer 300 μl to another 2-ml Safe-Lock tube.
10. Dry overnight in a vacuum concentrator without heat.
11. Optional: Fill tubes with argon gas for long-term storage at −80°C.

PREPARATION OF AMINO ACIDS FROM TOTAL PROTEIN FOR GC-TOF-MS ANALYSIS
Protein solubilization is considered the most problematic step during sample preparation for proteomic studies. A protein extraction buffer including a combination of urea and thiourea was shown to solubilize proteins efficiently (Chan, Lo, & Hodgkiss, 2002). Once the proteins are extracted, amino acids are released from peptides using classical acid hydrolysis with 6 M HCl at 110°C for 24 hr. Neutralization and cleaning of the samples for GC-TOF-MS analysis are carried out by liquid-phase extraction using dioctylamine/chloroform and chloroform.

Extract and quantify protein
1. Carefully wash the pellet containing protein and cell wall material three times with 500 μl of 100% methanol to remove potential amino acid contamination from leftover supernatant.
2. Add 200 μl protein extraction buffer and vortex vigorously at room temperature.
3. Centrifuge at 20,000 × g for 10 min at room temperature. Transfer supernatant to a 1.5-ml screw-cap tube. Keep the pellet at −20°C for cell wall preparation.
Prepare an adequate volume based on the number of samples. 17. Repeat neutralization two more times and then check that the pH of the aqueous phase is neutral using pH indicator paper.
If the pH is not neutral, repeat until it becomes neutral.
19. Transfer the upper polar phase to a 2-ml Safe-Lock tube without taking any chloroform.
20. Dry samples overnight in a vacuum concentrator without heat.
21. Fill tubes with argon gas and store at −80°C to avoid oxidation of metabolites.

PREPARATION OF SUGARS FROM CELL WALL MATERIAL FOR GC-TOF-MS ANALYSIS
The A. thaliana cell wall is composed of polysaccharides, proteins, and lignin, with polysaccharides accounting for 80% (Zablackis, Huang, Muller, Darvill, & Albersheim, 1995). The polysaccharides are cellulose, hemicellulose, and pectin. Cellulose and the hemicellulose backbone are linear β(1-4) linked d-glucose polymers synthesized from UDP-glucose. On the assumption that there is little or no turnover of these polymers, the 13 C enrichment of glucose in the cell wall can be used to estimate how fast plants are growing (RGR). However, the pellet obtained in Basic Protocol 3 contains starch as well as cell wall material. Starch is a polysaccharide composed of d-glucose joined by α1,4-glycoside linkages. In the growth and labeling conditions of our protocol, starch is labeled rapidly and to high enrichment by 13 CO 2 . Starch must therefore be completely removed by repeated incubations with α-amylase and amyloglucosidase before cell wall samples can be used to prepare sugars. Hydrolysis of cell wall material (polysaccharides) is carried out by pre-hydrolysis with 72% (v/v) H 2 SO 4 followed by hydrolysis with 1 M H 2 SO 4 (Saeman, Moore, Mitchell, & Millett, 1954). Neutralization and cleaning of samples for GC-TOF-MS analysis are carried out by liquid-phase extraction using dioctylamine/chloroform and chloroform.

Remove starch
1. Add 700 μl ultrapure water to the pellet containing cell wall material and vortex. Centrifuge at 20,000 × g for 10 min at room temperature and discard supernatant. Repeat at least three more times.
2. Resuspend pellet in 400 μl of 0.1 M NaOH, shake vigorously, and heat at 100°C for 30 min using a Thermomixer.

This will loosen starch crystals so that the enzymes in the starch degradation buffer can access the starch granules for digestion.
3. Neutralize by adding 80 μl neutralization buffer and vortex. Check that the pH is neutral using pH indicator paper.

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Current Protocols 8. When the optical density (OD) is stable (15-20 min), remove the plate from the reader, add 1 μl hexokinase to each well, vortex lightly, and return the plate to the plate reader.
Keep the reader running during this step.
9. When the OD is stable again (20-30 min), stop the plate reader and record the OD.
Because 1 mol glucose uses 1 mol NADP to make 1 mol NADPH, the amount of glucose can be estimated using NADPH formation and the extinction coefficient of NADPH (6.22 mM −1 cm −1 ).
11. Repeat steps 1-10 with the pellet in step 5 two more times or until no starch remains.
More exhaustive incubations may be needed when analyzing plant material where starch synthesis is rapid but growth rates are slow.
12. Add 700 μl ultrapure water to the pellet, vortex, and centrifuge at 20,000 × g for 10 min at room temperature. Discard the supernatant and air-dry the pellet for 2 hr.

Hydrolyze polysaccharides and neutralize sugars
13. To disrupt the crystallinity of the cellulose, add 63 μl of 72% (v/v) H 2 SO 4 to the pellet, vortex vigorously, and incubate at room temperature for 1 hr.
14. Add 690 μl ultrapure water to dilute the H 2 SO 4 to 1 M and incubate 3 hr at 100°C using a Thermomixer.
15. Neutralize hydrolysate by adding 1 ml of 20% (v/v) dioctylamine in chloroform, vortexing thoroughly, and centrifuging at 20,000 × g for 1 min at room temperature. Discard the organic phase.
16. Repeat neutralization two more times and then check that the pH of the aqueous phase is neutral using pH indicator paper.
If the pH is not neutral, repeat until it becomes neutral.
17. Remove excess dioctylamine by adding 1 ml of 100% chloroform, vortexing thoroughly, and centrifuging at 20,000 × for 2 min at room temperature. Transfer the upper polar phase to a 2-ml Safe-Lock tube and repeat two more times.
A volume of 70 μl is generally enough to measure glucose and other cell wall sugars.
19. Dry samples overnight in a vacuum concentrator without heat.
20. Fill tubes with argon gas and store at −80°C to avoid oxidation of metabolites. Lisec et al. (2006) published a detailed protocol on how to profile and quantify metabolites from A. thaliana using GC-TOF-MS. This protocol describes in great detail the processing of samples, including derivatization, and the settings for GC-TOF-MS. Heise et al. (2014) provide a protocol describing how to process GC-TOF-MS data to estimate 13 C enrichment (%) using CORRECTOR software.

Materials
Samples containing soluble amino acids, amino acids from total protein, and sugars from cell wall (see Basic Protocols 2-4) 1. Process samples and perform GC-TOF-MS analysis as described (Lisec et al., 2006).
2. Select peak areas of the fragment mass of amino acids and sugars from the GC-TOF-MS chromatograph .cdf file, based on Supplemental Data S1 (Lisec et al., 2006).
We recommend analyzing alanine and serine in the amino acid-containing samples and glucose in the sugar-containing samples (Ishihara et al., 2015).
3. Generate an input.txt file (see the exemplary file in Supplemental Data S2; also see Heise et al., 2014) 4. Estimate 13 C enrichment (%) of amino acids and glucose using CORRECTOR software as described in Heise et al. (2014).

ESTIMATION OF PROTEIN SYNTHESIS AND DEGRADATION RATES
The absolute rate of protein synthesis in a pulse, K S(pulse) , is calculated from the labeling kinetics of amino acids in total protein after correcting for incomplete enrichment in soluble (free) amino acid pools. Many amino acid pools show very low enrichment in the light and decrease rapidly in the dark, and cannot be used to estimate K S(pulse) (Ishihara et al., 2015). Instead, K S(pulse) is calculated using the labeling kinetics of alanine and serine, both of which are rapidly labeled to high enrichment in the day and whose enrichment stays high during the night (Ishihara et al., 2015). The 13 C enrichment in the amino acids from protein in a given time interval is corrected by the average enrichment in free amino acids over the time internal. Without 13 C enrichment data from the light period, K S(pulse) will be overestimated due to the slight decrease in enrichment between the end of day (ED) and the end of night (EN) (Ishihara et al., 2015). Therefore, we recommend that ED and EN values be obtained. In addition, K S can be estimated from the decay of the enrichment of serine and alanine in a protein during the chase period, K S(chase) . The rate of protein degradation during pulse (K D(pulse) ) and chase (K D(chase) ) periods can be estimated as the difference between the rate of protein synthesis and the relative growth rate (K D = K S − RGR). Since K S , K D , RGR are estimated from descriptive statistics on replicate sample data, we describe here how to estimate rates using Gaussian error propagation with the widely used R language.

Materials
Spreadsheet editor (e.g.; excel) R (https:// www.r-project.org/ ), optional R studio (https:// rstudio.com/ ), optional 13 C enrichment (%) of soluble amino acids, amino acids from total protein, and glucose from cell wall material 13 C enrichment exemplary data (Supplemental Data S3): 13 C enrichment (%) of alanine, serine, and glucose from three independent replicate experiments containing data from thirteen A. thaliana accessions at ZT0, ZT24, and ZT120 (Ishihara et al., 2017) Estimate protein synthesis rate The rate of protein synthesis in a 13 CO 2 pulse experiment, K S(pulse) , is defined as the rate of incorporation of labeled amino acids into proteins normalized by a correction factor for incomplete enrichment in the free amino acid pool (Pocrnjic, Mathews, Ishihara et al.

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Current Protocols Rappaport, & Haschemeyer, 1983). It is calculated over the time interval from t 1 and t 2 using Equation 1: where S B(t) represents the average labeled amino acids in protein at time t, and S A(t2-t1) represents the average labeled free amino acids in the interval between t 1 and t 2 . Results are expressed as mg protein/mg protein/day. Exemplary results can be found in Supplemental Data S3 and S4. In step form: 1. Calculate the mean and standard error of the 13 C enrichment (%) of free amino acids (S A ) and of amino acids in total protein (S B ) from samples harvested at time points t 1 and t 2 (Supplemental Data S3).
2. Subtract the mean 13 C enrichment of amino acids in proteins at time t 1 from time t 2 (S B(t 2 ) -S B(t 1 ) ).
3. Calculate the average 13 C enrichment of free amino acids in the time interval between t 1 and t 2 (S A(t 2 −t 1 ) ).
When t 1 corresponds to ZT0, the 13 C enrichment of free amino acids at t 1 should not be used for the calculation, as this would lead to overestimation of K S .
4. Divide the result from step 2 by the result from step 3.
5. Divide the result by the time interval between t 1 and t 2 expressed as days (in our case, 1 day).
The standard error of the mean is then used for Gaussian error propagation.

Estimate relative structural biomass growth rate (RGR STR )
We estimate RGR STR based on the labeling kinetics of glucose in cell walls (see Ishihara et al., 2015Ishihara et al., , 2017 for more details) during a 13 CO 2 pulse experiment RGR STR(pulse) . The first time point in a 13 CO 2 pulse experiment (t 1 = 0) corresponds to unlabeled material with no glucose labeling (Glc (t 1 ) = 0). In this case, RGR STR(pulse) is linearly estimated as the total 13 C enrichment (%) in glucose at the end of the pulse period. This is done by subtracting the mean 13 C enrichment at t 1 from that at t 2 (Glc (t 2 ) -Glc (t 1 ) ) and dividing by the time interval between t 1 and t 2 (in our case, 1 day). Exemplary results can be found in Supplemental Data S3 and S5.
Alternatively, estimation of RGR STR can be done during a 12 CO 2 chase, assuming that there is negligible dilution of glucose in cell wall polysaccharides during the analyzed period. RGR STR(chase) can be estimated considering exponential growth using Equation 2:

Equation 2
where t 1 and t 2 are the start and end of the chase, respectively; t is the time interval from t 1 to t 2 (in our case, 4 days); and Glc (t) represents the average 13 C enrichment of glucose in the cell wall material. Exemplary results can be found in Supplemental Data S3 and S8. The unit of RGR STR (chase) is mg 13 C glucose per mg total glucose in cell wall per day.
6. Calculate the mean and standard error of the mean using measurements of glucose 13 C enrichment in cell wall fractions collected at the start and end of the chase (t 1 and t 2 ).

The standard error is used for Gaussian error propagation across all calculation steps.
7. Divide mean 13 C enrichment at t 2 by mean 13 C enrichment at t 1 and calculate the t th root of the result.
A simple way to perform the latter step is to power the quotient to 1/t.

Estimate protein degradation rate
The rate of protein degradation during a 13 CO 2 pulse experiment, K D(pulse) , can be estimated as the difference between the rate of protein synthesis (K S(pulse) ) and the relative growth rate (RGR STR(pulse) ) using Equation 3:

Equation 3
The unit for K D(pulse) is mg protein/mg protein/day. Exemplary results can be found in Supplemental Data S3 and S6.
The rate of protein degradation during a 12 CO 2 chase experiment, K D(chase) , can be estimated as the difference between the rate of decay in 13 C enrichment of amino acids in proteins (K S(chase) ) and the rate of amino acid enrichment dilution due to tissue growth (RGR STR(chase) ) using Equations 4 and 5:

Equation 5
where S B(t) represents the average labeled amino acids in protein at time t. The unit for K S(chase) and K D(chase) is mg protein/mg protein/day. Exemplary results can be found in Supplemental Data S3, S7, and S9.
9. Calculate the mean and standard error of the 13 C enrichment (%) of amino acids in total protein from samples harvested at time points t 1 and t 2 .
The standard error is used for Gaussian error propagation across all calculation steps.
10. Calculate the natural logarithm of the mean 13 C enrichments at t 1 and t 2 and subtract the latter from the former.
11. Divide the result by the time interval (in our case, 4 days).

Prepare data and estimate RGR STR , K S , and K D using R language
As previously mentioned, Supplemental Data S3 from Ishihara et al. (2017) is used to illustrate the analysis of a 13 CO 2 pulse/ 12 CO 2 chase experiment. Data analyses were done manually (for Supplemental Data S3) or using R language (https:// www.r-project.org/ ; Supplemental Data S4-S9).

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Current Protocols Calculations for RGR STR(pulse) in the pulse experiment involved comparison between ZT0 and ZT24. For the chase experiment, ZT24 and ZT120 were used.
In this example from Ishihara et al. (2017), K S(pulse) was estimated using alanine and serine from a pulse experiment (ZT0 to ZT24; t 2t 1 = 1 day) and is expressed as mg protein/mg protein/day.
In this experiment, at ZT0 (t 1 = 0), enrichment of labeled free amino acids is taken as zero (S A(t 1 ) = 0). The correction factor S A(t 2 −t 1 ) was then defined as the enrichment of free labeled alanine or serine at ZT24. The latter assumes that labeling of free amino acids is roughly constant during the diel cycle, which might not always be true in plants and could lead to under-or overestimation of K S (for more details, see Ishihara et al., 2015). Therefore, Equation 1 is simplified as:

Background Information
Plants constantly synthesize and degrade proteins to replace damaged proteins, remobilize resources, and change protein content during development or adaptation to new environments (Nelson & Millar, 2015). The rate of protein turnover varies between A. thaliana accessions, and this has a negative impact on growth rate in standard lab conditions. It has been hypothesized that faster protein turnover may aid adjustment to changes in environmental conditions (Ishihara et al., 2017).
Protein synthesis and degradation rates can be measured using stable or radioisotopes. Although the use of radioisotopes has the advantage that very small amounts can be supplied with a high specific activity, it also requires dedicated analytical instruments for accurate determination of isotope incorporation in proteins and the precursor pool (Huffaker & Peterson, 1974). Alternatively, proteins can be labeled by supplying organisms with labeled amino acids or labeled basic elements present in proteins (S, P, C, N, O, H). Cell cultures supplied with labeled amino acids such as [ 2 H4]-lysine and [ 13 C6]-arginine displayed lower enrichment of proteins in the light than in the dark (Gruhler, Schulze, Matthiesen, Mann, & Jensen, 2005;Schütz, Hausmann, Krug, Hampp, & Macek, 2011). However, this method presents several disadvantages, especially when performing experiments in plants. Plants produce amino acids using carbon skeletons that derive from photosynthesis, which in the light will dilute the pool of supplied labeled amino acids (Schütz et al., 2011). Another drawback is that biosynthesis of most amino acids is subject to feedback regulation, meaning that supplying plants with external amino acids in excess will inhibit amino acid biosynthesis (Galili, 1995). Altogether, feeding experiments with labeled amino acids are not suitable for plants (Schütz et al., 2011).
Several studies have used labeled basic elements present in proteins to estimate protein turnover rates. For example, labeling of plant proteins using two different water isotopes ( 2 H 2 O or H 2 18 O) was shown to have a low efficiency due to inhibition of growth (Yang et al., 2010) and a slower incorporation of 18 O in proteins (Zhou et al., 2012). N can be incorporated in proteins through inorganic 15 N salts such as ammonia and nitrate. 15 N is the most common stable isotope used to measure protein synthesis and degradation rates in plant tissues, such as A. thaliana leaf, root, and cell culture (Fan et al., 2016;Li et al., 2017;Nelson, Li, Jacoby, & Millar, 2013), barley (Nelson, Li, & Millar, 2014), and Medicago truncatula (Lyon et al., 2016). Unlike labeled water, 15 N salts do not inhibit plant growth. Another advantage of 15 N salts is that they are inexpensive compared to labeled amino acids and can be fed to plants grown in liquid medium, solid medium, or black sand (Masclaux-Daubresse & Chardon, 2011;Nelson & Millar, 2015). The major disadvantage of using 15 N salts is that they are taken up and moved through the plant quite slowly, with the consequences that the start of the pulse is rather undefined, the isotope is significantly diluted by internal pools, and the isotope is difficult to remove completely from the growth medium and therefore is not suitable for chase experiments.
Since plants are photoautotrophs, 13 C can be supplied as 13 CO 2 and is rapidly incorporated into the plant's metabolism through photosynthesis. To perform a chase experiment, 13 CO 2 can be easily replaced with 12 CO 2 . As a result, 13 CO 2 is widely used in plants to measure flux of plant metabolites (Huege et al., 2007;Szecowka et al., 2013;Williams et al., 2010), turnover of specific proteins (Chen et al., 2011), and synthesis of total protein (Ishihara et al., 2015(Ishihara et al., , 2017Pal et al., 2013). The bottleneck of using 13 CO 2 is the varying incorporation rates of 13 C in different amino acids (Ishihara et al., 2015;Szecowka et al., 2013). This is partially due to the compartmentation of metabolites in plants. GC-TOF-MS analysis, for example, can be used to measure all possible amino acids in order to find the most suitable ones for estimation of protein synthesis and degradation rates. In general, amino acids such as alanine and serine, which are synthesized in the central metabolism by amino transferase, show higher 13 C enrichment compared to amino acids requiring multiple biosynthesis steps (Ishihara et al., 2015). Since estimation of protein degradation rates requires the plant growth rate, another advantage of using 13 CO 2 is that the growth rate can be measured using the same labeled material by quantifying 13 C enrichment of glucose in the cell wall (Ishihara et al., 2015(Ishihara et al., , 2017. Here, we present a relatively simple and inexpensive method to determine the rates of protein synthesis, degradation, and plant growth using 13 CO 2 labeling experiments in A. thaliana.

Critical Parameters and Troubleshooting
Planning of the experiment. It should be decided whether to perform a 13 CO 2 pulse experiment or a 13 CO 2 pulse/ 12 CO 2 chase experiment. In addition, the temporal distribution of harvest time points and the number of samples per time point need to be carefully planned in order to obtain robust results. If RGR will be calculated by measuring rosette size or fresh Ishihara et al. weight, extra plants must be grown in parallel to those used in the labeling experiment and in the same conditions. For a more detailed discussion of these points, see Strategic Planning.
Difficulty in mixing CO 2 . The flow rate (pressure) of the CO 2 gas is 200 times lower than that of the N 2 /O 2 gas mixture, which can make it difficult to obtain the desired CO 2 concentration in the final gas mixture. The CO 2 pressure can be improved by reducing the length and diameter of the tube connecting the MFC to the tee gas mixer. It is important this tube not be bent, as this could cause a backflow.
Amount of starting material. This protocol requires 30 mg frozen plant powder, but the amount of material used could vary. For example, young actively growing leaves contain substantially higher metabolites and protein compared to older slow-growing leaves (Sulpice et al., 2014). Therefore, the amount of starting material can be adjusted depending on the plant material.
Estimation of RGR from cell wall polysaccharide. This estimation is based on 13 C enrichment of glucose and is heavily influenced by contamination of cell wall material by starch. Therefore, we recommend digesting starch at least four times and checking that there is no glucose detected before hydrolysis of the cell wall pellets. Plants grown in different growth conditions may contain different amounts of starch, and may need more or less starch hydrolysis.
Unexpectedly high or low 13 C enrichment of glucose from cell wall material. Unusually high 13 C enrichment levels, especially in samples harvested during the light period, could be due to contamination of cell wall material by starch. As mentioned above, it is important check that starch is completely removed before hydrolyzing cell wall pellets. Unusually high 13 C enrichment of glucose could also result from a peak saturation of glucose during GC-TOF-MS analysis. This can lead to overor even underestimation of 13 C enrichment. In this case, we recommend analyzing a dilution series of the sample to determine the best dilution and/or using different split ratios of sample during GC-TOF-MS analysis.
Loss of GC-TOF-MS sensitivity. If sensitivity decreases over the course of the measurement run of amino acids obtained from total protein, it is most likely due to contamination by urea/thiourea from the protein extraction buffer, which will overload the GC column. In this case, the samples should be washed more thoroughly.

Understanding Results
This method provides a quantification of the rates of protein synthesis and degradation. The estimation of protein degradation makes two important assumptions: (1) that plant growth has a dilution effect on the amount of proteins synthesized per day, and (2) that proteins that are not used for growth are degraded.

Time Considerations
The time needed to complete the experiment and analyses varies depending on many factors, such as personal experience, number of samples, and availability of equipment.
Basic Protocol 1. We grow A. thaliana plants (five plants per pot) under an 8-hr photoperiod for 3 weeks in order to obtain enough plant material. If lower light intensities are used, more time will be needed for plant growth; if higher light intensities or longer photoperiods are used, less time is needed for growth. When growing plants in long photoperiods to study vegetative growth, experiments should be performed before the initiation of flowering. Three days before the start of the labeling experiment, the system is set up and the plants placed in the labeling chambers to adapt to the experimental conditions. The 13 CO 2 pulse/ 12 CO 2 chase experiment is done in 5 days. Grinding and aliquoting the plant material takes 1-2 days, depending on experience.
Basic Protocol 2. A set of 48 samples can be prepared in 1 day and be ready on day 2 following an overnight drying step.
Basic Protocol 3. A set of 48 samples can be processed in 2 days and be ready on day 3. Protein extraction and precipitation are done on day 1, followed by acid hydrolysis over 24 hr. On day 2, the hydrolyzed samples are neutralized, cleaned, and dried overnight.
Basic Protocol 4. A set of 48 samples can be processed in 5 days. It takes 3 days to completely remove starch from the samples. It takes another 2 days for hydrolysis and neutralization.
Basic Protocol 5. It is recommended to derivatize a maximum of 30 samples per day, including standards, for GC-TOF-MS analysis (Rosado-Souza et al., 2019). The number of samples that can be processed and the measurement time frame are dependent on the availability of the GC-TOF-MS (Rosado-Souza et al., 2019). Analysis of chromatograms is done in a few hours.
Basic Protocol 6. With the R script provided, it is possible to analyze many data sets at once within a few hours.