Insulin stimulation of glucose uptake fails to decrease palmitate oxidation in muscle if AMPK is activated

W. W. Winder, B. F. Holmes

Abstract

Fatty acid oxidation in muscle has been reported to be diminished when insulin and glucose levels are elevated. This study was designed to determine whether activation of AMP-activated protein kinase (AMPK) will prevent inhibitory effects of insulin and glucose on the rate of fatty acid oxidation. Rat hindlimbs were perfused with medium containing 0, 0.3, or 60 nM insulin with or without 2 mM 5-aminoimidazole-4-carboxamide-1-β-d-ribofuranoside (AICAR). Glucose uptake was stimulated four- to fivefold by inclusion of insulin in the medium. Insulin attenuated the increase in AMPK caused by AICAR both in perfused hindlimbs and in isolated epitrochlearis muscles. The activation constant for citrate activation of acetyl-CoA carboxylase (ACC) was significantly increased in response to AICAR, and the increase was slightly attenuated if insulin was present in the perfusion medium. Insulin stimulated an increase in malonyl-CoA content of the muscles in the absence of AICAR. Malonyl-CoA was decreased to approximately the same value in AICAR-perfused muscle, regardless of insulin concentration. Muscle glucose 6-phosphate and citrate were significantly increased in response to AICAR and insulin. The rate of palmitate oxidation tended to decrease in response to insulin and in the absence of AICAR. AICAR increased palmitate oxidation to approximately the same level regardless of the insulin concentration or the rate of glucose uptake into the muscle. The rate of palmitate oxidation showed a curvilinear relationship as a function of muscle malonyl-CoA content, with half-maximal inhibition at ∼0.6 nmol/g. We conclude that AMPK activation can prevent high rates of glucose uptake and glycolytic flux from inhibiting palmitate oxidation in predominantly fast-twitch muscle under these conditions.

  • AMP-activated protein kinase
  • acetyl-coenzyme A carboxylase
  • malonyl-coenzyme A
  • muscle citrate

amp-activated protein kinase (AMPK) has recently been implicated as having important actions in skeletal muscle (35), including regulation of fatty acid oxidation (1, 14, 21, 23, 32), stimulation of glucose uptake (3, 11, 15, 21), and regulation of transcription of GLUT-4, hexokinase, and some of the oxidative enzymes (12, 36). Muscle AMPK has been demonstrated to be activated in rats during treadmill running or in response to contraction induced by electrical stimulation (28, 32, 34,35). The isolated enzyme is activated by 5′-AMP and inhibited by creatine phosphate (27). The increase in free 5′-AMP and the decrease in creatine phosphate observed during muscle contraction are thought to be responsible for activation of this kinase. It is activated by phosphorylation by an upstream kinase, AMPK kinase, which is also activated allosterically by 5′-AMP (8, 9, 35). The AMPK can be activated chemically in resting muscle by use of an adenosine analog, 5-aminoimidazole-4-carboxamide-1-β-d-ribofurano side(AICAR), which can be taken up by the muscle and phosphorylated to form ZMP, the monophosphorylated form of AICAR. ZMP can activate AMPK similarly to 5′-AMP (8, 21, 35).

Although the phosphorylation targets for AMPK are yet undefined for control of GLUT-4 transcription and glucose transport, the effect on enhancement of fatty acid oxidation appears to be mediated by the phosphorylation of acetyl-CoA carboxylase (ACC; Refs. 8,9, 34, 35). AMPK phosphorylation of the purified muscle isoform of ACC results in a marked decline in activity at physiological citrate concentrations and in specific changes in the citrate activation curve [increase in the activation constant (K a) and decrease inV max] (34).

In perfused rat hindlimbs and in incubated soleus muscle, activation of AMPK with AICAR results in a decline in malonyl-CoA and an increase in fatty acid oxidation (1, 21-23). Malonyl-CoA is a potent inhibitor of carnitine palmitoyltransferase-1 (CPT-1), the rate-limiting enzyme of fatty acid oxidation (17, 29).

Previous studies have indicated that insulin has inhibitory effects on the rate of fatty acid oxidation in cultured hepatoma cells, in perfused heart and cultured myocytes, and in incubated soleus muscle (1, 2, 6, 23, 37). This experiment was designed to determine the effect of insulin on the signaling processes involved in enhancement of fatty acid oxidation in isolated perfused hindlimbs by AMPK. To attain this goal, we asked the following questions: Does increased glucose uptake induced by insulin have a negative effect on fatty acid oxidation in skeletal muscle when AMPK is activated? Will malonyl-CoA content of the muscle be reduced when AMPK is activated by AICAR, even in muscles taking up glucose at a high rate? By using combinations of insulin and AICAR in the perfusion medium, a wide range of malonyl-CoA concentrations can be generated. What is the relationship between intramuscular malonyl-CoA content and the rate of fatty acid oxidation?

METHODS

Animals.

Male Sprague-Dawley rats (Charles River, Wilmington, MA) were housed in individual cages in a temperature- (20–22°C) and light- (12:12-h light-dark cycle) controlled room. Rats were fed ad libitum with Harlan Teklad rodent diet (Madison, WI). The protocols for these experiments were approved by the Institutional Animal Care and Use Committee.

Hindlimb perfusion.

Rats in this study weighed 293 ± 2 g. Rats were anesthetized with pentobarbital sodium (60 mg/kg). Catheters were inserted into the abdominal aorta and inferior vena cava. Vessels to the tail and to the abdominal muscle were ligated. After vessels were flushed with warm Krebs-Henseleit bicarbonate (KHB), both hindlimbs were perfused with medium (37°C) composed of washed bovine erythrocytes and KHB containing 4 g/100 ml bovine serum albumin (Sigma Chemical, St. Louis, MO), 8 mM glucose, and 0.5 mM palmitate. Insulin was diluted in medium to a final perfusate concentration of 0.3 or 60 nM in different rats. Other rats were perfused with medium containing no insulin. At each insulin concentration, rats were also perfused with and without addition of 2 mM AICAR.

The perfusions were done in a Plexiglas perfusion chamber (37°C) as described previously (21, 22). The medium was oxygenated as it traversed a Silastic tubing coil (6 m, 0.16 cm ID, 0.24 cm OD) in a 1-liter chamber equilibrated with 95% O2-5% CO2. Rats were given an overdose of pentobarbital sodium once the perfusion started. Hindlimbs were perfused at a rate of 8–10 ml/min. Medium was not recirculated. The hindlimbs were perfused with medium for 25 min. At this time, referred to as the0 min time point, AICAR or vehicle (KHB, albumin) was then added, and the perfusion was continued for 45 min.

For determination of the rate of palmitate oxidation, 1.6 μCi of [1-14C]palmitic acid (in KHB, albumin) were added per 100 ml perfusate medium at the beginning of the perfusion. Samples of medium were collected from a port between the oxygenation chamber and the arterial catheter (referred to as the arterial sample) and from the venous catheter (referred to as the venous sample).14CO2 was quantitated in arterial and venous samples at the end of a 25-min washout period and at 15, 30, and 45 min by the method described previously (21, 22). A filter paper wick (1 × 2 cm) was glued to a cap from a 20-ml glass liquid scintillation vial. The wick was saturated with 2-aminoethanol (0.075 ml) immediately before sample collection. Samples (5 ml) of media were added to the vials containing 1 ml of 4.5 M lactic acid. Vials were immediately capped and incubated 20–24 h to allow the14CO2 to be absorbed on the wick. The wicks were then quickly transferred to another scintillation vial. Ecolite (ICN, Irvine, CA) was added immediately, and the vials were kept in the dark for 2 days before quantitation of radioactivity.

Arterial and venous samples were also taken for determination of oxygen consumption, glucose uptake, and lactate production. A 0.5-ml sample of medium was added to 2 ml 10% perchloric acid for glucose and lactate determinations.

Epitrochlearis incubation.

Epitrochlearis muscles from rats weighing 191 ± 2 g were incubated in 5 ml continuously oxygenated KHB, 5 mM glucose with 60 nM insulin or 2 mM AICAR, or the combination, for a total of 60 min. The muscles were then quickly trimmed and frozen in liquid nitrogen. Muscles were analyzed for AMPK activity and ACC activity at 0.2 mM citrate.

Analytical methods.

Glucose (4) and lactate (7) were determined on neutralized (by use of 2 M KOH, 0.4 M KCl, 0.4 M imidazole) perchloric acid extracts of the medium. Cell-free perfusate was collected by centrifugation and used for measurement of free fatty acid concentration (24) and for determination of fractional extraction of labeled palmitate in the oxidation study. Perfusate samples were kept at −20°C until analyzed. Oxygen saturation of hemoglobin was determined on arterial and venous samples with an OSM 2 hemoximeter (Radiometer, Copenhagen, Denmark) for calculation of oxygen consumption.

Muscles were kept under liquid nitrogen until time of analysis. They were first ground to powder under liquid nitrogen. Perchloric acid extracts (400 mg muscle powder added to 2 ml of 6% perchloric acid) were prepared and neutralized for determination of malonyl-CoA (20), glucose-6-phosphate (16), and citrate (26). Muscle glycogen was determined on the freeze-clamped muscle samples by the anthrone method (10).

AMPK activity and citrate-dependence curves for ACC activity were determined with use of ammonium sulfate precipitates from homogenates prepared from the powdered (under liquid nitrogen) muscles as described previously (34). Curves were analyzed and fitted to the Hill equation by using Grafit (Sigma Chemical).

CPT-1 activity.

CPT-1 activity was determined in mitochondria isolated from rat gastrocnemius and quadriceps muscles by the method of McGarry et al. (18) with addition of proteolytic enzyme inhibitors to the homogenizing medium (antitrypsin, 0.01 mg/ml; leupeptin, 0.01 mg/ml; aprotinin, 0.1 trypsin-inactivating unit/ml). CPT-1 was determined by measuring the rate of incorporation ofl-[methyl-14C]carnitine into palmitoyl-carnitine, using palmitoyl-CoA as the other substrate (18). Malonyl-CoA was added to the incubation medium at concentrations of 0, 0.2, 1.0, 2.5, and 100 mM. Malonyl-CoA inhibition of CPT-1 was studied at three different albumin concentrations: 2, 5, and 10 mg/ml. Only curves for 2 and 5 mg/ml are shown. Results are means of two separate measurements at each point. Each of the two measurements were made on different mitochondrial isolates.

Statistical analyses.

Values are expressed as means ± SE. Results were analyzed by two-way analysis of variance followed by Fisher's least significant difference test for multiple comparisons.

RESULTS

Hindlimb perfusion study.

Mean values for hemoglobin for the medium were 14.4–14.9 g/100 ml and were not different in the six treatment groups (Table1). Oxygen consumption of the perfused hindlimb was significantly increased in response to insulin, but was not influenced by the presence of AICAR in the medium (Table 1).

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Table 1.

Hemoglobin concentration of medium and oxygen consumption of hindlimbs perfused with medium containing different combinations of insulin and AICAR

AMPK activity was significantly increased in response to perfusion of the muscles with AICAR (Fig. 1). Insulin at physiological and maximal concentrations attenuated the increase in AMPK caused by AICAR. The citrate-dependence curves of ACC activity of the perfused gastrocnemius muscles showed marked changes when AICAR was included in the perfusion medium, with decreases in theV max (Table 2) and increases in the K a for citrate (Fig.2). The increase inK a in response to AICAR was attenuated to a small extent when insulin was present at either concentration, but theV˙max was not changed. The activity in the physiological range of citrate (0.2 mM) was approximately sixfold higher in the absence of AICAR vs. when AICAR was present in the perfusion medium (Table 2). Gastrocnemius muscle content of malonyl-CoA was increased in response to insulin in the absence of AICAR (Table3). At all insulin concentrations, the malonyl-CoA content of the muscle was reduced to approximately the same level when 2 mM AICAR was included in the medium (Table 3).

Fig. 1.

Effect of insulin and aminoimidazole-4-carboxamide-1-β-d-ribofuranoside (AICAR) on AMP-activated protein kinase (AMPK) activity in perfused rat hindlimb muscles. Values are means ± SE (n = 8–9). Square brackets indicate concentration. *Significantly different from AICAR-infused muscles with 0 insulin, P < 0.05.

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Table 2.

ACC activity at 0.2 mM citrate and ACC Vmax in muscle of rats perfused with medium containing different concentrations of insulin and AICAR

Fig. 2.

Effect of insulin and AICAR on acetyl-CoA carboxylase (ACC) activity of ammonium sulfate precipitates of muscle homogenates from perfused hindlimbs. Values are means ± SE (n= 8–10). Standard errors for each point were determined but are not shown. The differences in V max between No AICAR (○) and AICAR-treated muscles (●) were all significant (P < 0.05). *Activation constant (K a) significantly different from muscles perfused with medium containing no insulin, P < 0.05.

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Table 3.

Effects of insulin and AICAR on metabolite contents of perfused rat gastrocnemius muscle

Palmitate oxidation was reasonably stable between 15 and 45 min of perfusion in the absence of AICAR at all insulin concentrations (Fig.3). Palmitate oxidation increased in response to perfusion of the muscles with AICAR to approximately the same extent at all insulin concentrations. The presence of insulin tended to inhibit fatty acid oxidation when no AICAR was present in the medium (P < 0.09). This effect was completely abolished when AMPK was activated. The fractional extraction of palmitate was in the range of 0.18–0.25. The hindlimbs perfused without insulin and without AICAR had a significantly lower fractional extraction than all other groups. None of the other groups were statistically different from one another.

Fig. 3.

Effect of insulin (Ins) and AICAR on rate of palmitate oxidation by perfused rat hindlimb muscles. Values are means ± SE (n = 8–10). KHB, Krebs-Henseleit bicarbonate. After 30 min, palmitate oxidation by all AICAR-perfused muscles was significantly increased compared with No AICAR muscles (P < 0.05). The presence of insulin did not significantly influence the rate of palmitate oxidation when AICAR was present.

Glucose uptake and lactate production during the last 15 min of perfusion are shown in Fig. 4. AICAR and insulin both stimulated a significant increase in glucose uptake and an increase in lactate production. In response to both insulin and AICAR, an increase in muscle content of glucose 6-phosphate was noted (Table3). Glycogen content was not influenced by AICAR infusion but significantly increased in response to insulin (Table 3). Muscle citrate significantly increased in response to AICAR at all insulin concentrations and increased in response to 0.3 nM insulin (P < 0.05; Table 3).

Fig. 4.

Effect of insulin and AICAR on glucose uptake and lactate production by perfused rat hindlimb muscles. Values are means ± SE (n = 8–10 for glucose and 4–8 for lactate). *Significantly different from No AICAR at same insulin concentration (P < 0.05). Insulin stimulated a significant increase in glucose uptake at both concentrations (P < 0.05).

Palmitate oxidation rate as a function of muscle malonyl-CoA content is shown in Fig. 5. There appeared to be near-maximal inhibition of palmitate oxidation at a muscle malonyl-CoA content of ∼1.5 nmol/g. The line of best fit was determined by using the Grafit program (Sigma Chemical) for determination of concentration of malonyl-CoA producing 50% of maximal inhibition (IC50). Although it is impossible to determine the rate of palmitate oxidation in the absence of malonyl-CoA under these conditions, the IC50 appears to be in the range of 0.6–0.8 nmol/g, depending on the extrapolation to 0 nmol/g malonyl-CoA.

Fig. 5.

Palmitate oxidation by rat hindlimbs vs. malonyl-CoA content of muscle at the end of a 45-min perfusion (after a 25-min washout period). The variable malonyl-CoA and palmitate oxidation values were generated by perfusing muscles with medium containing three different insulin concentrations (0, 0.3, and 60 nM) and two different AICAR concentrations (0 and 2 mM). Parameters for the concentration of malonyl-CoA producing 50% of maximal inhibition (IC50; Grafit, Sigma Chemical, St. Louis, MO) were manipulated to produce the best fit by eye. This produced an IC50 of 0.6 nmol/g.

Epitrochlearis incubation.

In the isolated epitrochlearis muscle, AMPK activity was also increased in response to inclusion of 2 mM AICAR in the incubation medium (Fig.6). This increase was attenuated when 60 nM insulin was included in the medium along with AICAR. This had no effect on the decline of ACC activity at 0.2 mM citrate, however (Fig.6).

Fig. 6.

AMPK and ACC activity (at 0.2 mM citrate) in ammonium sulfate precipitates of epitrochlearis muscles incubated in vitro with 60 nM insulin, 2 mM AICAR, and the combination. Values are means ± SE (n = 6). * The changes in response to AICAR are significant (P < 0.05). † Inclusion of insulin with AICAR significantly attenuated the AMPK response to AICAR, but not the ACC response (P < 0.05).

Isolated mitochondria studies.

Figure 7 demonstrates that, in isolated mitochondria, the CPT-1 activity is dramatically influenced by the incubation conditions. Simply altering the albumin concentration produces marked differences in the shape of the inhibition curve and the values of IC50. The IC50 was 0.03 μM malonyl-CoA when the albumin concentration was 5 mg/ml in the incubation medium vs. 0.28 μM malonyl-CoA when the albumin concentration was 2 mg/ml. The curve at an albumin concentration of 10 mg/ml was similar to that seen at 5 mg/ml.

Fig. 7.

Influence of albumin concentration on malonyl-CoA inhibition of carnitine palmitoyltransferase-1 (CPT-1). Values are means of two separate determinations on two mitochondrial preparations. The y-axis represents the radioactivity incorporated into palmitoyl carnitine from labeled carnitine and palmitoyl-CoA in a 6-min period. Curve fitting was done with the Grafit Program for IC50 (Sigma Chemical).

DISCUSSION

The rate of fatty acid oxidation by skeletal muscle has been demonstrated to be influenced by several factors, including malonyl-CoA content, the concentration of fatty acids, carbohydrate availability as determined by glucose and insulin concentrations, and availability of other substrates such as ketone bodies (1, 21-23,28). Malonyl-CoA, a key player in regulation of fatty acid oxidation, is synthesized in muscle by ACC, a cytosolic enzyme (17, 29). Malonyl-CoA is a potent inhibitor of CPT-1, the rate-limiting enzyme of fatty acid oxidation.

The rate of synthesis of malonyl-CoA is dependent on cytosolic concentration of long-chain acyl-CoA, cytosolic concentration of citrate, availability of ACC substrates, and phosphorylation state of ACC (28, 29, 35). Palmitoyl-CoA has been demonstrated to inhibit the muscle isoform of ACC (see Ref. 35). Acetyl-CoA, synthesized in the mitochondria, may be transferred to the cytosol by condensing with oxaloacetate, forming citrate. The citrate may then move into the cytoplasm, where it is cleaved by citrate lyase to form acetyl-CoA, a substrate for ACC (29). In addition to being regulated by substrate supply and allosteric activators, the muscle isoform of ACC can also be phosphorylated and inactivated by AMPK (34). ACC becomes much less sensitive to activation by citrate after AMPK phosphorylation (29, 34, 35).

The present study confirms earlier studies in heart and incubated soleus muscle that show an increase in malonyl-CoA and a decrease in fatty acid oxidation in response to inclusion of glucose and insulin in the incubation medium (1, 6, 13, 23). In isolated perfused hearts, this resulted in a decrease in AMPK activity and an increase in ACC activity as well (6). To our knowledge, this is the first demonstration that physiological and maximal concentrations of insulin can acutely reduce AMPK activity in muscle. This was observed in two different experimental models, the isolated perfused hindlimb and the epitrochlearis incubated in vitro. Although little is known regarding the mechanisms of reversal of AMPK activation in skeletal muscle, it appears that phosphatases are involved (32).

The shape of the citrate activation curve has been utilized previously as an indicator of the phosphorylation state of ACC (21, 22, 32,34). Phosphorylation of the purified muscle isoform of ACC with purified AMPK results in an increase in the K aand a decrease in the V max for the citrate activation curve. This is accompanied by a shift in the mobility of ACC in SDS-PAGE (32). The insulin-induced reduction in AMPK activation with AICAR did not result in significant changes in theV max for citrate activation of ACC, but it did cause significant differences in the shape of the citrate activation curve, shifting it to the left, which resulted in attenuation of the increase in K a in response to AICAR. This subtle change in properties of ACC was apparently insufficient to significantly alter the muscle malonyl-CoA content, however.

It seems clear from the present study that when ACC is phosphorylated by AMPK (as seen in the AICAR-perfused muscles), synthesis of malonyl-CoA is dramatically reduced even in the face of elevated citrate, increased availability of insulin and glucose, and increased glycolytic flux. In the physiological range of citrate (0.2 mM), the activity of ACC isolated from AICAR-perfused muscle was reduced to approximately one-sixth the value seen in the corresponding controls. The presence of insulin appeared to have no effect on increasing malonyl-CoA and decreasing fatty acid oxidation when AMPK was activated by perfusion of the muscles with AICAR.

The muscle isoform of CPT-1 has been reported to be much more sensitive to inhibition by malonyl-CoA than is the liver isoform (19,31). The muscle isoform has been reported to have an IC50 of 0.03 μM compared with the liver value of 2.7 μM for malonyl-CoA (19). Even after prolonged exercise, the malonyl-CoA content of muscle does not fall below ∼0.2 nmol/g (33). These observations together have led some to question whether malonyl-CoA is actually involved in control of fatty acid oxidation in muscle (see Ref. 29). Theoretically, CPT-1 would always be inhibited near maximally by the full range of concentrations of malonyl-CoA seen in intact muscle. The design of the present study allowed generation of a wide range of malonyl-CoA concentrations in the perfused muscle, which could then be correlated with the measured rates of palmitate oxidation. It is apparent in Fig.6 that the relationship is curvilinear, with half-maximal inhibition occurring somewhere in the range of 0.6–0.8 nmol/g, much higher than that reported previously for CPT-1 measurements in isolated mitochondria.

The measurement of the IC50 for malonyl-CoA in isolated mitochondria does not necessarily reproduce the conditions seen inside the muscle fiber. Figure 7 demonstrates that a tenfold increase in the measured IC50 was observed simply by decreasing the albumin concentration of the assay medium from 5 to 2 mg/ml. It apparently is difficult to precisely mimic the intracellular conditions of CPT-1 in the mitochondria when quantitating the inhibitory effects of malonyl-CoA in the test tube. The approach of correlating malonyl-CoA content of the muscle with the rate of fatty acid oxidation may produce more accurate estimates of the in vivo IC50. It should also be remembered that the rate of fatty acid oxidation is determined by several other factors besides malonyl-CoA that could influence the shape of the malonyl-CoA-vs.-palmitate oxidation curve.

Human muscle malonyl-CoA content has been reported to be ∼0.1 the concentration that reported in rat muscle (5, 25, 29). In general, the muscle content of malonyl-CoA has not been found to decline in response to exercise in humans to the extent seen in rat muscle (5, 25). This may be due in part to the difficulty in obtaining homogenous muscle fiber populations from human muscle biopsies, but currently the role of malonyl-CoA in human muscle is not clear. ACC activity of human muscle declines in response to contraction (5). This is accompanied by small decreases in muscle malonyl-CoA at higher work rates (5), thus suggesting that this control system is operative in humans. A recent report indicates CPT-1 in isolated human skeletal muscle mitochondria to be sensitive to malonyl-CoA inhibition, particularly in endurance-trained muscle (30). In that study, CPT-1 activity was decreased by incubation at pH 6.8 vs. 7.0 in the presence of 0.7 μM malonyl-CoA. The decline in muscle pH may therefore play a role in the reduction in fatty acid oxidation by muscle at very high work rates (30).

The present results have implications for determination of the rate of fatty acid oxidation during exercise. It is clear that the rate of fatty acid oxidation increases during the course of long-term exercise. Activation of AMPK in the muscle during exercise may be important for allowing this increased rate of fat oxidation even before a drop in plasma insulin. In fact, the activation of AMPK has been postulated to be the signal for coupling muscle contraction with the increased fatty acid oxidation and increased glucose uptake that occur during exercise (21, 35). The increased glucose uptake and increased fatty acid oxidation then supply the ATP required for driving the contractile process.

In summary, physiological and supraphysiological concentrations of insulin tend to inhibit fatty acid oxidation across the rat hindlimb muscles, which consist predominantly of fast-twitch muscle fibers. When AMPK is activated with AICAR, the rate of fatty acid oxidation in the rat hindlimb preparation increases to about the same level, regardless of the insulin concentration and in the face of a four- to fivefold increase in glucose uptake and a twofold increase in muscle citrate. A curvilinear relationship was noted between the gastrocnemius-plantaris muscle malonyl-CoA concentration and the rate of fatty acid oxidation with half-maximal inhibition at ∼0.6 nmol/g.

Acknowledgments

Technical assistance was provided by A. Perry.

Footnotes

  • This work was supported by the National Institute of Arthritis and Musculo-skeletal and Skin Diseases Grant AR-41438.

  • Address for reprint requests and other correspondence: W. W. Winder, Dept. of Zoology, Brigham Young Univ., Provo, UT 84602 (E-mail: william_winder{at}byu.edu).

  • The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

REFERENCES

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