Quantifying conversion of linoleic to arachidonic and other n-6 polyunsaturated fatty acids in unanesthetized rats.

Isotope feeding studies report a wide range of conversion fractions of dietary shorter-chain polyunsaturated fatty acids (PUFAs) to long-chain PUFAs, which limits assessing nutritional requirements and organ effects of arachidonic (AA, 20:4n-6) and docosahexaenoic (DHA, 22:6n-3) acids. In this study, whole-body (largely liver) steady-state conversion coefficients and rates of circulating unesterified linoleic acid (LA, 18:2n-6) to esterified AA and other elongated n-6 PUFAs were quantified directly using operational equations, in unanesthetized adult rats on a high-DHA but AA-free diet, using 2 h of intravenous [U-(13)C]LA infusion. Unesterified LA was converted to esterified LA in plasma at a greater rate than to esterified gamma-linolenic (gamma-LNA, 18:3n-6), eicosatrienoic acid (ETA, 20:3n-6), or AA. The steady-state whole-body synthesis-secretion (conversion) coefficient k*(i) to AA equaled 5.4 x 10(-3) min(-1), while the conversion rate (coefficient x concentration) equaled 16.1 micromol/day. This rate exceeds the reported brain AA consumption rate by 27-fold. As brain and heart cannot synthesize significant AA from circulating LA, liver synthesis is necessary to maintain their homeostatic AA concentrations in the absence of dietary AA. The heavy-isotope intravenous infusion method could be used to quantify steady-state liver synthesis-secretion of AA from LA under different conditions in rodents and in humans.

were HPLC-grade and were purchased from Fisher Scientifi c (Fair Lawn, NJ) or Sigma-Aldrich.

Animals
This protocol was approved by the Animal Care and Use Committee of the Eunice Kennedy Schriver National Institute of Child Health and Human Development and followed the National Institutes of Health Guide for the Care and Use of Laboratory Animals (NIH Publication 80-23). Adult male Fischer-344 (CDF) rats (4 months old) were purchased from Charles River Laboratories (Portage, MI) and housed in a facility with regulated temperature, humidity, and a 12 h light/12 h dark cycle. They were acclimated for one week before surgery in this facility and had free access to water and rodent chow (NIH-31 Auto18-4). The chow contained soybean oil and fi shmeal; it had 4% by weight crude fat. Its fatty acid composition has been reported ( 27 ). Of n-3 PUFAs, ␣ -LNA, EPA, and DHA contributed 5.1%, 2.0%, and 2.3% of total fatty acid, respectively, whereas n-6 PUFAs LA and AA contributed 47.9% and 0.02%, respectively. The surgery and infusion procedures have been described in detail ( 11 ). The rats were provided food the night before surgery. During the surgery, recovery from anesthesia (3-4 h), and the 2 h infusion period, they did not have access to food.
A rat was anesthetized with 1-3% halothane, and polyethylene catheters (PE 50, Clay Adams, Becton Dickinson, Sparks, MD) fi lled with heparinized isotonic saline (100 IU/ml) were surgically implanted in the right femoral artery and vein. After it had recovered from anesthesia, the rat was infused via the femoral vein catheter with 3 mol/100 g body weight [U- 13 C]LA, dissolved in 5 mM 4-(2-hydroxy-methyl)-1-piperazineethanesulfonic acid (HEPES) buffer (pH 7.4) containing 50 mg/ml fatty acidfree bovine serum albumin, at a constant rate of 0.021 ml/min. During the 2 h, body temperature was maintained at 36-38°C using a feedback-heating element (YSI Indicating Temperature Controller, Yellow Springs Instruments, Yellow Springs, OH), and 2 ml of normal saline was injected subcutaneously to prevent dehydration. Arterial blood (130 l) was collected in centrifuge tubes (polyethylene-heparin lithium fl uoride-coated; Beckman) at 0, 0.5, 1.0, 2.0, 3.0, 5.0, 8.0, 10.0, 20, 30, 60, and 90 min of infusion. At 120 min, 500 l blood was removed, and the rat was euthanized by an overdose of sodium pentobarbital (100 mg/kg iv). The blood samples were centrifuged at 13,000 rpm for 1 min, and plasma was collected and kept at Ϫ 80°C until use.

Lipid extraction and PFB derivatization
Plasma lipid extraction and pentafl uorobenzyl (PFB) derivatization procedures have been reported ( 11 ). Appropriate amounts of internal standards (di-17:0 PC and free 17:0) were added to plasma, and then KOH solution was added. "Stable" lipids (phospholipids, triacylglycerol, and cholesteryl ester) containing esterifi ed fatty acids were extracted with hexane twice. The remaining lower phase was acidifi ed with HCl, and unesterifi ed fatty acids were extracted with hexane twice. The extracted esterifi ed fatty acids in stable lipids were hydrolyzed (10% KOH in methanol) at 70°C to release their free fatty acids, which were extracted with hexane and dried under N 2 . A freshly made PFB derivatizing reagent (PFB: diisopropylamine: acetonitrile, 10:100:1000) was added to the sample residue of hexane extraction and shaken for 15 min at room temperature. The sample was evaporated again to dryness under N 2 and redissolved in 100 l of hexane.

GC/MS analysis of fatty acid PFB esters
The fatty acid PFB esters from the plasma samples were analyzed by GC/MS as described ( 11 ). Nonlabeled and labeled n-6 PUFAs were monitored by selected ion mode (SIM) of the base PUFAs in the VLDLs may be recycled back into the liver via lipoprotein receptors, hydrolyzed by lipoprotein lipases within plasma and adipose tissue, and then recycled, or they may be lost to other organs and undergo ␤ -oxidation ( 13,16,17 ). The brain, kidney, and testes, as well as liver, can synthesize AA and DHA from their shorter-chain precursors, since they, like the liver, express the enzymes for a complete synthesis (18)(19)(20). However, they do so at much lower rates, because their enzyme activities are at lower levels (21)(22)(23)(24). Rat heart and brain have low capacities of synthesizing DHA and possibly AA from circulating unesterifi ed ␣ -LNA or LA, respectively, due to their low expression of synthesizing enzymes ( 23,(25)(26)(27).
It is not clear whether the liver has a higher effi ciency of conversion of ␣ -LNA to DHA than of LA to AA, but data suggest this to be the case (28)(29)(30)(31)(32). Exact rates of synthesis in the intact organism are not known, yet knowing them would help to estimate daily dietary requirements of ␣ -LNA and LA compared with their elongated products and would provide a fi rmer basis for making nutritional recommendations ( 8,9 ).
To address this issue, we developed a heavy-isotope intravenous infusion method to determine rates of wholebody, steady-state DHA synthesis from circulating unesterifi ed ␣ -LNA and eicosapentaenoic acid (EPA, 20:5n-3) in the unanesthetized rat ( 11,12 ); this method might be extended for human studies. Briefl y, the method involves infusing the isotopically labeled precursor intravenously at a constant rate, sampling arterial plasma concentrations of unesterifi ed and esterifi ed labeled precursor and elongation products as a function of time, and then applying operational equations to calculate steady-state synthesis-secretion coeffi cients and rates of the esterifi ed products when taking plasma volume into account. With this method, we reported that whole-body steady-state rate of conversion of unesterifi ed ␣ -LNA to esterifi ed DHA, in rats fed a high DHA-containing diet, equaled 9.84 mol/day.
To compare this rate to the rate of AA synthesis from LA in rats fed the same diet, in the present study we infused [U-13 C]LA intravenously for 2 h and determined rates of appearance of esterifi ed AA in arterial plasma, as well as of other n-6 PUFA elongation products, ␥ -LNA and ETA. We applied our operational equations to estimate steady-state synthesis coeffi cients and rates, and plasma turnovers and half-lives ( 11,12 ).

Materials
[U- 13 C]LA was purchased from Cambridge Isotope Laboratories (Andover, MA), and was purifi ed by high-performance liquid chromatography (HPLC) (Agilent, Palo Alto, CA) with a Sym-metry® C18 column (9.2 × 250 mm, 5 m, Agilent) before use. Purity was determined to be >95% by HPLC, and the concentration of purifi ed [U- Because plasma concentration C i,es (nmol/ml) of esterifi ed PUFA i was constant during the study, turnover F i (min Ϫ 1 ) and half-life t 1/2,i (min) of esterifi ed plasma PUFA i due explicitly to conversion from unesterifi ed LA equal, respectively, Steady-state synthesis-secretion rates J i and plasma turnover and half-lives were calculated for i = LA, ␥ -LNA, ETA, and AA by equations 1-6.
Data are given as means ± SD.

Plasma n-6 PUFA concentrations
Concentrations and ratios of unlabeled esterifi ed and unesterifi ed n-6 PUFAs in arterial plasma were determined before the 2 h [U-13 C]LA infusion ( Table 1 ) and agree peak (M-PFB). The concentration of each n-6 PUFA was quantifi ed by relating its peak area to the area of the internal standard, using an experimentally determined response factor for each fatty acid.

Calculations
Steady-state conversion rates of circulating unesterifi ed LA to esterifi ed AA and other elongated n-6 PUFAs were calculated by the method of Gao et al. ( 11,12 ). At steady-state secretion, the rate of change of labeled esterifi ed n-6 PUFA i ( i = LA, ␥ -LNA, ETA, or AA) in plasma is the sum of its rates of appearance and loss according to the following differential equation with constant coeffi cients, ; k 1, i is the synthesis-secretion rate coeffi cient (ml/min) of conversion of unesterifi ed labeled LA to esterifi ed labeled PUFA i [which relates the esterifi ed plasma PUFA concentration to the unesterifi ed LA concentration times plasma volume]; and k -1 ,i is the disappearance rate coeffi cient (ml/min) of esterifi ed labeled PUFA i from plasma. There is no isotope effect, so that k 1, i and k -1 ,i are valid for unlabeled as well as labeled PUFAs.
As reported ( 11,12 ), esterifi ed labeled PUFAs during intravenous labeled precursor infusion start to appear in rat plasma after a 30-60 min delay, after which their concentrations rapidly rise but later tend to rise more slowly due to the loss from plasma (see Fig. 2 ). To estimate their steady-state rates of secretion, we fi t the following sigmoidal equation using nonlinear least squares (Origin 7.0 software, Originlab, Northhampton, MA) to esterifi ed concentration × plasma volume data plotted against time, for each esterifi ed n-6 PUFA i (see Fig. 2 ), where A, B, C are best-fi t constants, and t 0 = 0 is time (min) at the beginning of infusion and t is time of infusion.
The fi rst derivative of equation 2 was determined for each esterifi ed PUFA i in each rat as a function of time. Its maximum value, S max,i nmol/min, occurs when steady-state liver secretion is best approximated and was taken to represent the left-hand side of equation 1. A steady-state synthesis-secretion coeffi cient, k is proportional to the net rate of the elongation and desaturation reactions, and unlike k 1, I , is independent of plasma volume; thus, it is a marker for evaluating net effi ciency of synthesis.
a Indicates the 13 C-labeled n-6 PUFA.  Table  1 ). The unesterifi ed LA concentration was used to calculate J i for each esterifi ed PUFA i by equation 4, and J i was used to calculate respective plasma half-lives and turnovers by equations 5 and 6.

[ 13 C]labeled unesterifi ed n-6 PUFA concentrations in plasma
A constant unesterifi ed arterial plasma concentration was achieved within 10 min after the start of intravenous [U-13 C]LA infusion ( Fig. 1 ). No other labeled unesterifi ed fatty acid was detected in plasma during the 2 h infusion. The mean concentration of unesterifi ed [U- 13 C]LA, * , LA unes C , equaled 1.10 ± 0.10 nmol/ml. Esterifi ed [ 13 C]LA was detected in plasma 30 min after infusion had started. Esterifi ed longer-chain n-6 PUFAs could be detected at 30-60 min, after which their concentrations increased rapidly with time but then began to plateau. At all times, esterifi ed plasma [ 13 C]LA was higher than the concentration of each of its three esterifi ed labeled elongation products ( Table 2 ).

W I T H D R A W N
A p r i l 1 0 , 2 0 1 4

N-6 PUFA synthesis-secretion coeffi cients and rates, turnovers, and half-lives
Synthesis-secretion coeffi cients and rates, turnovers, and half-lives of esterifi ed LA, ␥ -LNA, ETA, and AA were calculated from experimental measurements using equations 1-6. V plasma was taken as 26.9 ml/kg body weight, based on prior measurements under the same experimental conditions ( 11 ). Mean body weight equaled 305.3 ± 1.8 g. Rates of change (fi rst derivatives) of concentration × plasma volume curves were plotted as a function of time for the elongated products, and their maximal values S max,i were determined ( Fig. 3 ) . Because the curve for esterifi ed [ 13 C]LA did not start to level off during the 120 min infusion ( Fig. 2 ), we estimated S max,LA from the slope of its linear plot in the fi gure. Mean values of S max,i, from fi ve experiments are summarized in Table 3 .
Values of S max,i as determined from the fi rst derivatives of the labeled esterifi ed LA, ␥ -LNA, ETA, and AA curves were used to calculate synthesis-secretion coeffi cients * i k by equation 3

DISCUSSION
Whole-body (largely liver) steady-state synthesis-secretion coeffi cients and rates of conversion of circulating unesterifi ed LA to esterifi ed n-6 PUFAs were estimated by infusing unesterifi ed [U-13 C]LA intravenously for 2 h in unanesthetized 4-5-month-old male rats. The rats had been fed a diet enriched in DHA (2.3% of total fatty acid), with minimal AA (0.02%) and with LA as 47.9% of the total fatty acid concentration. Esterifi ed [ 13 C]LA and longerchain labeled n-6 PUFA products appeared in plasma after about 30 min. Their concentrations increased rapidly after 60 min, but later started to plateau due to loss from the vascular compartment. Unesterifi ed labeled ␥ -LNA, ETA, and AA could not be detected in plasma during [U-13 C]LA infusion, suggesting that any free labeled longer-chain n-6 PUFA that had been hydrolyzed from plasma VLDLs disappeared rapidly from blood, consistent with plasma half-lives of <1 min for circulating unesterifi ed fatty acids in the unanesthetized rat ( 33 ). Of the esterifi ed PUFAs converted from LA, 81% was esterifi ed LA, whereas 19% consisted of its elongated n-6 products. Only 3.4% became esterifi ed AA, indicating a relative ineffi ciency of conversion.

W I T H D R A W N
A p r i l 1 0 , 2 0 1 4 capacity to synthesize the elongation products from the precursors ( 25 ). Some secreted esterifi ed n-6 PUFAs within VLDLs will be returned over time to the liver via lipoprotein receptors or be hydrolyzed in blood or adipose tissue by lipoprotein lipases to their unesterifi ed forms and then be taken up again ( 13,16,34 ). Thus, the net rate of hepatic secretion of AA derived using [U-13 C]LA infusion may approach the sum of the secretion rates in Table 3 for ␥ -LNA, ETA, and AA, 88.3 mol/day, which is 3.6-fold higher than the calculated net rate of secretion of longer chain n-3 PUFAs from ␣ -LNA under the same conditions ( 11 ).
The calculated turnovers in this study ( Table 3 ) refl ect the contributions of conversion from unesterifi ed circulating LA, but exclude contributions from diet or synthesis from other precursors. Thus they are lower bounds, while the respective calculated half-lives t 1/2 are overestimates. The turnovers, furthermore, correlated roughly with the ratios of the unesterifi ed to esterifi ed PUFA concentrations ( Table 1 ), particularly for AA. While this issue should be explored further, it may be related to differential selectivities of the esterifi ed PUFAs for circulating or organ esterases, or to a lesser tendency of AA than of the other PUFAs for ␤ -oxidation in tissue mitochondria (39)(40)(41)(42)(43)(44)(45).
The brain incorporates unesterifi ed AA from plasma at a rate of 0.30-0.60 mol/day in unanesthetized rats not consuming AA ( 46,47 ). This rate approximates the rate of AA metabolic loss from brain, as AA cannot be synthesized de novo and is converted minimally (<0.2%) from the LA that enters from plasma ( 26 ). Thus, the AA synthesis-secretion rate from circulating shorter term precursors is у 16.1/0.60 = 27 times the brain AA consumption rate. As newly synthesized AA can get into brain after being hydrolyzed from circulating lipoproteins ( 11,14,48 ), hepatic synthesis from circulating LA has the potential of maintaining AA homeostasis in brain and other organs.
In summary, whole-body (largely liver) synthesis-secretion coeffi cients and rates of esterifi ed n-6 PUFAs from circulating unesterifi ed LA were quantifi ed by infusing [U-13 C]LA intravenously for 2 h in unanesthetized rats fed a DHAenriched, AA-defi cient diet. In the future, the heavy isotopic infusion method and model might be used to quantify liver synthesis-secretion of AA in relation to health, disease, and diet in humans as well as rodents.
The authors thank Dr. Edmund Reese for his helpful comments. time to reach a peak secretion rate (considered to approximate the steady-state rate), likely refl ected the time needed for the labeled PUFAs to be elongated and desaturated within different liver compartments, esterifi ed within triacylglycerols, phospholipids, and cholesteryl esters in those compartments, and then packaged and secreted within VLDLs ( 11,13,34,35 ). Because of these "lag times," it was not possible to simply apply the steady-state differential equation 1 to the concentration × plasma volume data over the period of study.
However, by applying the sigmoidal equation 2 to the data, we could represent the substantial delay, the slow then rapid rise in concentration, and the later tendency to plateau as material disappeared from plasma to calculate useful kinetic parameters. By taking the peak fi rst derivative of the best-fi t curves (e.g. Fig. 3), we calculated an S max,i to estimate the maximum rate of synthesis-conversion. This maximum, when referenced to the constant input function of unesterifi ed [U- 13 C]LA, provided steady-state synthesis coeffi cients and rates.
The synthesis-secretion coeffi cient k i * (equation 3) for conversion of unesterifi ed LA to esterifi ed AA equaled 5.4 × 10 Ϫ 3 min Ϫ 1 (  ( 11 ). Thus, liver synthesis-secretion is more selective for PUFAs of the n-3 than n-6 series, consistent with previous observations (28)(29)(30)(31)(32). In this regard, mRNA and protein levels of liver synthetic enzymes were upregulated, as were synthesis coeffi cients, for unesterifi ed ␣ -LNA conversion to DHA in rats on a diet with low compared to high ␣ -LNA, neither containing DHA ( 23 ), whereas enzyme expression was not changed in rats fed a diet with low-LA compared with high-LA, both free of AA (M. Igarashi et al., unpublished observations). This indicates more control of liver enzyme transcription by circulating n-3 than n-6 PUFAs and perhaps an evolutionary need for such differential control ( 6,(36)(37)(38). Steady-state synthesis-secretion rates J i of longer chain PUFAs from their 18-carbon precursors are calculated by multiplying S max,i, by the inverse of plasma specifi c activity of the unesterifi ed precursor (equation 4). Mean plasma unesterifi ed LA and ␣ -LNA concentrations were 219 nmol/ml and 13.9 nmol/ml, respectively, whereas the synthesis-secretion rate of esterifi ed AA from LA was 16.1 mol/day, only 1.6 times the rate of esterifi ed DHA synthesis from ␣ -LNA, 9.84 mol/day. Thus, a balanced synthesis-secretion of AA and DHA results from a relatively low conversion coeffi cient * i k of AA from LA with a high plasma unesterifi ed LA concentration , plasma unes C , but a comparatively high conversion coeffi cient DHA from ␣ -LNA with a low unesterifi ed plasma ␣ -LNA concentration.
Hepatic regulation of plasma AA and DHA availability is critical for brain and heart function. The high concentrations of AA and DHA that are maintained within membrane phospholipids of these organs are controlled largely by their plasma concentrations, as circulating unesterifi ed LA and ␣ -LNA precursors are almost completely ␤ -oxidized after entering brain ( 26,27 ), and the rat heart has a low