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1 Departments of Pathobiology and Nutritional Sciences, 2 Department of Biostatistics, and 3 Department of Medicine, University of Washington, Seattle, Washington 98195
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ABSTRACT |
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The aim of this study was to
determine whether phenotypes associated with type 2 diabetes are
altered in dyslipidemic obese mice. C57BL/6 wild-type, low-density
lipoprotein (LDL) receptor-deficient (LDLR
/
), and
apolipoprotein E-deficient (apoE
/
) mice were fed a high-fat,
high-carbohydrate diet (diabetogenic diet), and the development of
obesity, diabetes, and hypertriglyceridemia was examined. Wild-type
mice became obese and developed hyperglycemia, but not
hypertriglyceridemia, in response to this diet. LDLR
/
mice fed the
diabetogenic diet became more obese than wild-type mice and developed
severe hypertriglyceridemia and hyperleptinemia. Surprisingly, glucose
levels were only modestly higher and insulin levels and
insulin-to-glucose ratios were not strikingly different from those of
wild-type mice. In contrast, diabetogenic diet-fed apoE
/
mice were
resistant to changes in glucose and lipid homeostasis despite becoming
obese. These data suggest that modifications in lipoprotein profiles
associated with loss of the LDL receptor or apoE function have profound
and unique consequences on susceptibility to diet-induced obesity and
type 2 diabetic phenotypes.
obesity; type 2 diabetes; triglycerides; leptin; lipoproteins
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INTRODUCTION |
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TYPE 2 DIABETES has become an international epidemic and is expected to affect 300 million people within the next 25 years (15). Obesity is observed in over 46% of type 2 diabetic patients and is a positive risk factor for the development of this disease (31, 33, 35, 38). In conjunction with obesity, hypertriglyceridemia is also often observed in type 2 diabetics (5, 16), demonstrating an important role of fat metabolism in determining disease susceptibility. The use of animal models that exhibit differences in lipoprotein metabolism allows us to examine how factors that regulate lipid metabolism influence the development of type 2 diabetes.
C57BL/6 mice fed diets rich in fat and sucrose (diabetogenic diet) become obese and insulin resistant and develop moderate hyperglycemia (36, 40, 41). To test the hypothesis that particular lipoprotein patterns are associated with susceptibility to obesity and diabetic phenotypes, we fed the diabetogenic diet to C57BL/6 mice carrying mutations at loci for the low-density lipoprotein (LDL) receptor or apolipoprotein E (apoE). Mutations at these genes result in dyslipidemic states because of impaired lipoprotein production and metabolism (3, 20, 32, 47). The low-density lipoprotein receptor (LDLR) is involved with clearing LDL and lipoprotein remnants containing apoE (4, 17) and may also play a role in regulating hepatic lipoprotein production (45). ApoE is a structural component of all lipoprotein particles except LDL, and it serves as a high-affinity ligand for both the apoB and remnant receptor (11, 19). This allows for the specific uptake of apoE containing lipoproteins by the liver (7, 11). In addition, apoE is involved with promoting hepatic very low-density lipoprotein (VLDL) secretion (27). Thus both of these proteins play an integral role in the efficient production and clearance of lipoproteins.
Compared with wild-type C57BL/6 mice fed the diabetogenic diet,
LDLR-deficient (LDLR
/
) mice showed the greatest gains in adiposity
and hypertriglyceridemia. This strain also demonstrated increased
glucose levels compared with the other strains, demonstrating that
dyslipidemia induced by the LDLR mutation is associated with impaired
glucose metabolism. Remarkably, apoE-deficient (apoE
/
) mice were
resistant to diet-induced hypertriglyceridemia or hyperglycemia despite
significant weight gain. Thus diet in conjunction with distinct
lipoprotein profiles, as induced by the mutations in LDLR and apoE
genes, contribute to determining susceptibility to diabetes and
dyslipidemia. Our results demonstrate that alleles of the LDLR and apoE
should be considered as candidates for identifying diabetes
susceptibility and severity among individuals.
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METHODS |
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Mice and diets.
Male C57BL/6 wild-type, LDLR
/
, and apoE
/
mice, 6 wk of age,
were obtained from The Jackson Laboratory (Bar Harbor, ME). LDLR
/
and apoE
/
mice are maintained on the C57BL/6 background strain.
Mice were fed either rodent chow (Wayne Rodent BLOX 8604, Teklad,
Madison, WI) or a diabetogenic diet (no. F1850, Bioserve, Frenchtown,
NJ), with 20 mice per group. Rodent chow contains 4% fat (wt/wt) and
72% carbohydrate. The diabetogenic diet contains 35.5% fat (primarily
lard) and 36.6% carbohydrate (primarily sucrose) and contains no
cholesterol. The diabetogenic diet has been previously described and
demonstrated to induce obesity and type 2 diabetes in C57BL/6 mice
(36, 37, 40, 41). Mice were maintained in a
temperature-controlled (25°C) facility with a strict 12:12-h light-dark cycle and given free access to food and water. Blood was
collected after a 4-h fast from the retroorbital sinus into tubes
containing 1 mM EDTA, and plasma was stored at
70°C before analysis. The Animal Care and Use Committee of the University of
Washington approved this project.
Adiposity measurements using magnetic resonance spectroscopy.
To determine murine whole body fat mass, magnetic resonance
spectroscopy (MRS) was performed as described by Mystkowski et al.
(30). This technique exploits the differential behavior of
protons associated with water vs. lipid when placed in a magnetic field
and allows the precise quantitation of murine body fat. Mice were
anesthetized with intraperitoneal ketamine (100 mg/kg)-xylazine (6 mg/kg), lightly secured within a radio-frequency coil transceiving the
resonant proton signal at 200.1 MHz, and scanned using a 4.7 T research
magnet (Bruker/GE Omega CSI-II, Fremont, CA) at the University of
Washington Department of Radiology. Shimming (which corrects for
magnetic field inhomogeneities) was performed before each spectral
acquisition, and two acquisitions were obtained per animal. Care was
taken to center the mouse within the coil and to place the coil at
exactly the same longitudinal and rotational position for each reading.
Areas under the curve (AUC) for individual spectral peaks were obtained
using line integrals (GE Omega version 6.0.2 Fremont, CA), with the AUC
for the water peak (AUCH2O) demarcated by the region from
8.0 ppm to the relative minimum transformed signal between the water
and lipid peak. The AUC for the lipid peak (AUClipid) was
demarcated by the same relative minimum value between peaks and
1.5
ppm. Body fat percentage by MRS was defined as
%FATMRS = AUClipid/(0.38 × AUCH2O + AUCH2O + AUClipid),
and the value for each animal was determined by averaging the
%FATMRS calculated per spectrum.
Analytical procedures. Plasma insulin and leptin levels were measured using radioimmunoassay kits (nos. RI-13K and ML-82K, Linco, St. Louis, MO), with rat insulin and mouse leptin as the respective standards (36). Plasma glucose levels were determined colorimetrically (cat. no. 315-100, Sigma, St. Louis, MO). Plasma triglyceride concentrations were assessed colorimetrically after the removal of free glycerol (diagnostic kit no. 450032, Boehringer Mannheim, Indianapolis, IN). Plasma free fatty acids (FFA) were determined colorimetrically (diagnostic kit no. 99075401, Wako, Dallas, TX) with oleic acid as the standard.
Fat absorption. Fat absorption was measured in mice by modifying the procedure described by Ishibashi et al. (21). Mice were fed the diets for 12 wk, fasted overnight, and then gavaged with 1 µCi [3H]retinol (cat. no. NET 927, NEN Life Science Products, Boston, MA) in 200 µl corn oil. Plasma samples were obtained at 1, 2, 5, 8, 12, and 24 h after gavage, and plasma radioactivity was quantified. Total plasma radioactivity was determined by multiplying the disintegrations per minute per microliter by total plasma volume, which was estimated at 5.77% of body weight (2).
Statistics. Values are reported as means ± SE. To compare the longitudinal relationship between body weight and leptin levels across strains, a generalized estimating equation (GEE) approach was used (24). The GEE approach corrects for the dependence of multiple measurements taken within a single mouse across successive time points. ANOVA analyses were used to determine interactions, and Bonferonni post hoc tests were applied to determine differences between means. In some cases, the Student's t-test was used to compare independent means. P < 0.05 was accepted as statistically significant.
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RESULTS |
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Diabetogenic diet-fed LDLR
/
mice are heavier than wild-type or
apoE
/
mice.
Mice at the age of 6 wk were fed either the chow or diabetogenic diet
for a total of 16 wk. At the beginning of the diet study, wild-type
C57BL/6 mice were heavier (24.0 ± 0.2 g) than LDLR
/
(21.0 ± 0.3 g; P < 0.001) or apoE
/
(21.0 ± 0.3 g; P < 0.001) mice. Mice fed
rodent chow for 16 wk had final body weights of ~27-30 g. After
16 wk of the diabetogenic diet, body weights for wild-type, LDLR
/
,
and apoE
/
mice were 44.9 ± 2.1, 49.3 ± 1.3, and
35.2 ± 2.6 g (P < 0.001 vs. wild type),
respectively. Weights for wild-type and apoE
/
mice were 1.8-fold
higher than initial values, whereas LDLR
/
mice had weight increases
of 2.4-fold after 16 wk (P < 0.001 vs. wild-type, Fig.
1A). Thus diabetogenic diet-fed LDLR
/
mice gained significantly more weight than either wild-type or apoE
/
mice.
|
/
mice were singular in the early
and marked increase in plasma leptin levels when fed the diabetogenic diet (Fig. 1B). By 4 wk, leptin levels were 2.3-fold higher
in LDLR
/
mice than in the other strains. Between 8 and 16 wk,
leptin levels were 20-fold higher than for rodent chow-fed LDLR
/
mice. In contrast, wild-type mice experienced a 10-fold increase, and diabetogenic diet-fed apoE
/
mice had only a 3.7-fold increase in
leptin over their chow-fed counterparts. To determine whether leptin
expression is disproportional to body weight in LDLR
/
mice, the
body weight vs. leptin values for mice fed the diabetogenic diet for
4-16 wk were examined using GEEs (Fig. 1C; see
METHODS). For all mice, body weights correlated
significantly with leptin values (P < 0.0001). The
relationship between leptin and mouse weight for C57BL/6 was not
significantly different from that observed for apoE
/
mice
(P = 0.56), with a regression line described by
leptin = 2.04 × (body weight)
56. However, this
relationship was significantly different in LDLR
/
mice
(P < 0.0001 compared with either C57BL/6 or apoE
/
mice), with a regression line described by leptin = 2.83 × (body weight)
68. Thus leptin levels were consistently higher
in the LDLR
/
mice as reflected by the 38% increase in the slope of
the regression line for this strain.
Because body weight and leptin levels were highest for LDLR
/
mice
fed the diabetogenic diet, we expected food intake to be greatest for
this strain. However, as shown in Fig.
2A, diabetogenic diet-fed
wild-type mice and LDLR
/
mice had similar food consumption profiles
throughout the study. When averaged throughout the study, apoE
/
mice showed greater food intake (19.3 ± 0.7 calories per mouse
per day) than wild-type or LDLR
/
mice (17.7 ± 0.6 calories per mouse per day; P = 0.05). Therefore, increased food
intake does not account for increased weight gain in the LDLR
/
mice. To determine whether fat absorption was altered in either the LDLR
/
or the apoE
/
mice, radiolabeled retinol was gavaged into
mice fed the diabetogenic diet for 12 wk, and the plasma radioactivity
was followed for the subsequent 24 h (Fig. 2B). Results
demonstrate that retinol was readily absorbed by all strains, with
maximum plasma values obtained between 5 and 8 h after gavage treatment. Therefore, fat absorption was not different between strains
and cannot account for the increased weight gain in diabetogenic diet-fed LDLR
/
mice. We conclude that caloric intake or fat absorption does not account for variation in body weights between the
strains.
|
1.5
ppm cutoff) represents the lipid percentage. The areas under such peaks
were used to calculate the percent adiposity for each mouse (Fig.
3B).
|
/
and apoE
/
mice were 30% leaner than wild-type mice at 16 wk (P < 0.05). All mice had significant increases in
adiposity when fed the diabetogenic diet (P < 0.001, Fig. 3B). Both wild-type and apoE
/
mice showed a twofold
increase in adiposity (17.2 ± 1.3 to 32.5 ± 1.5% for
wild-type; 12.4 ± 0.9 to 23.5 ± 3.1% for apoE
/
),
demonstrating that loss of apoE does not alter the extent of obesity
compared with diabetogenic diet-fed wild-type mice. In contrast,
adiposity increased 3.6-fold for LDLR
/
mice (11.1 ± 0.9% to
39.5 ± 1.5%), showing that LDL receptor deficiency results in
increased diet-induced obesity. For diabetogenic diet-fed but not
chow-fed mice, adiposity positively correlated with body weight
(r = 0.79-0.95, P < 0.007). These results also suggest that the increased leptin levels in the LDLR
/
mice (Fig. 1C) are at least partially resulting from the
increased adiposity observed in this strain.
To examine how adiposity was distributed, liver, inguinal, and
epididymal adipose fat pads were removed from chow or diabetogenic diet-fed mice and weighed (Fig. 4). For
chow-fed mice, the percent body weight of these two fat depots
(%adipose weights) were significantly lower in apoE
/
mice compared
with wild-type mice (P < 0.03). This result is
consistent with the MRS analysis showing decreased adiposity in this
strain. Inguinal adipose was moderately higher in chow-fed LDLR
/
mice compared with wild-type mice (P < 0.05). Adipose
weights increased significantly for all strains fed the diabetogenic diet (P = 0.004-0.00001). Compared
with diabetogenic diet-fed wild-type mice, LDLR
/
mice showed
significantly increased inguinal but not epididymal %adipose weights
(Fig. 4B). Thus loss of the LDLR results in increased
adiposity that was due, in part, to increased subcutaneous adipose
accumulation.
|
/
mice
compared with wild-type mice, whereas %liver weights were increased
(Fig. 4). Liver lipid content was measured to determine whether hepatic
lipid storage was increased in apoE
/
mice. For mice fed the chow
diet, apoE
/
mice had moderately higher hepatic triglyceride (TG)
content (1.6 ± 0.4 mg TG/g liver) compared with wild-type mice
(1.1 ± 0.3 mg TG/g liver), although differences did not achieve
statistical significance. When wild-type or LDLR
/
mice were fed the
diabetogenic diet, hepatic TG levels increased twofold to 2.3 ± 0.4 mg TG/g liver (P < 0.01 vs. chow-fed mice). However, apoE
/
mice were resistant to any changes in hepatic TG
content in response to this diet, with a final hepatic lipid content of
1.7 ± 0.2 mg TG/g liver.
Hyperlipidemia occurs in LDLR
/
mice fed the diabetogenic diet.
The increase in adiposity in LDLR
/
mice could result from increased
TG availability from circulating lipoproteins. To test this
possibility, plasma TG levels were measured in mice fed the chow or
diabetogenic diet. Chow-fed LDLR
/
and apoE
/
mice had consistently higher TG levels than wild-type mice (Fig.
5A). During the course of the
diabetogenic diet feeding study, LDLR
/
mice showed a marked and
rapid elevation in plasma TG levels (Fig. 5B). In contrast,
TG levels were reduced by 30% in wild-type and apoE
/
mice in
response to dietary treatment (P = 0.01). Plasma FFA
were also highest for LDLR
/
mice fed the diabetogenic diet (0.41 ± 0.04 meq/l for wild-type; 0.99 ± 0.14 meq/l for
LDLR
/
, P < 0.05). ApoE
/
mice showed FFA levels
of ~0.80 meq/l regardless of dietary treatment.
|
LDLR
/
, but not apoE
/
mice, develop hyperglycemia and
hyperinsulinemia in response to the diabetogenic diet.
The association between obesity, hypertriglyceridemia, and type 2 diabetes is well documented (6, 12, 33, 34). To test for
the development of insulin resistance and diabetes, plasma levels of
glucose and insulin, and insulin-to-glucose ratios, were determined in
chow- and diabetogenic diet-fed mice (Fig. 6).
|
/
mice increased consistently with time, and final values were 247 ± 19 mg/dl, a level corresponding to frank diabetes (40). During the first 12 wk of feeding the
apoE
/
mice the diabetogenic diet, glucose levels remained
consistently lower than in the other strains. However, after 16 wk of
feeding the diabetogenic diet, glucose levels for this strain were not different from those observed for wild-type mice.
Insulin levels for mice fed rodent chow remained constant at ~0.8
ng/ml. Plasma insulin levels increased significantly for diabetogenic
diet-fed wild-type and LDLR
/
mice, but not for apoE
/
mice (Fig.
6B). Final insulin values for diabetogenic diet-fed mice
were 4.2-fold higher in wild-type and 5.3-fold higher in LDLR
/
mice
compared with chow-fed counterparts (P < 0.02). Overall, insulin levels were highest for diabetogenic diet-fed LDLR
/
mice, but differences were only statistically significant at
the 8-wk time point (P < 0.003). A measure of insulin
resistance is the ratio of insulin to glucose (I/G). This ratio
increases as insulin resistance develops, indicating that more insulin
is needed to maintain normal glucose levels. All chow-fed mice showed similar I/G ratios (Fig. 6C). Evidence of insulin resistance
was seen for wild-type and LDLR
/
mice, because I/G ratios increased two- to threefold compared with chow-fed mice (P < 0.03). Despite the greater obesity and hypertriglyceridemia observed in
the LDLR
/
mice, I/G ratios were similar to those of diabetogenic
diet-fed wild-type mice. ApoE
/
mice showed no diet-induced changes
in I/G, demonstrating maintenance of low glucose and insulin levels despite the dietary challenge.
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DISCUSSION |
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This report explores the role of genes involved with lipid
metabolism in the susceptibility to obesity and complications
associated with obesity. Loss of the LDLR increases susceptibility to
diet-induced obesity, hyperleptinemia, and hypertriglyceridemia and
influences the sites of lipid deposition, demonstrating an important
role of LDLR function in regulating adipose lipid storage and leptin secretion. However, despite the profound hypertriglyceridemia observed in the LDLR
/
mice, glucose and insulin levels were only modestly increased compared with wild-type mice, and I/G ratios
were comparable to those of wild-type mice. Therefore, severe
hypertriglyceridemia did not exacerbate insulin resistance beyond that
induced by the diabetogenic diet. ApoE deficiency did not alter
susceptibility to diet-induced obesity from wild-type values but
resulted in resistance to diet-induced hyperglycemia and
hyperinsulinemia. Taken together, these findings help link the factors
that regulate lipid metabolism with the development of obesity and diabetes.
The direct role of the LDLR on obesity has not been well studied. In
humans, LDLR polymorphisms have been associated with obesity
(26), suggesting a link between LDLR function and
peripheral lipid deposition. In our study, loss of the LDL receptor
increased adipose deposition, especially in subcutaneous adipose
depots. This suggests either that the loss of adipose LDLR expression directly contributes to increased TG uptake in adipose or, more likely,
that loss of hepatic LDLR expression increases circulating lipoproteins, providing increased TG substrate for uptake by
adipocytes. Alternatively, loss of the LDLR may have indirect effects
on reducing lipolysis in fat cells or altering thermogenesis, which
would also increase lipid storage in adipose tissue. LDLR deficiency in
mice and humans results in increased levels of circulating apoB-100
particles due to both increased hepatic lipoprotein production and
impaired clearance (21, 39, 42, 45). Furthermore, LDLR
/
mice are highly susceptible to high-fat diet-induced
hypertriglyceridemia (28, 43). The TG-enriched lipoprotein
particles may then be preferentially cleared by nonhepatic tissues,
such as adipose, resulting in increased obesity. Interestingly, male
LDLR
/
mice appear to be more susceptible than female mice to
obesity associated with hypertriglyceridemia (23). We have
also observed that male C57BL/6 mice are more susceptible to
diabetogenic diet-induced obesity [(36) and unpublished
observations]. Therefore, increased diet-induced obesity may
be dependent on both LDLR activity and gender-dependent factors.
Increased lipid accumulation in adipose would be expected to increase
leptin production. Circulating leptin levels are known to reflect whole
body adiposity in humans and rodents (10, 25). The
temporal change and magnitude of leptin increases were distinct for
LDLR
/
mice. The LDLR
/
mice as a group were the heaviest and
showed the highest leptin levels of all three strains, increasing 3.8-fold over wild-type and apoE
/
by 8 wk. Interestingly,
subcutaneous adipose was preferentially increased in diabetogenic
diet-fed LDLR
/
mice. Subcutaneous adipose is more responsive in
producing leptin than visceral adipose (13, 29). It is
likely that the increased subcutaneous adipose in the LDLR
/
mice is
contributing to the increased leptin levels observed in this strain.
However, regression analysis demonstrated that, even between
weight-matched mice of the three strains, leptin levels were
significantly higher for the LDLR
/
mice. Therefore, it is also
possible that LDL receptor deficiency results in overproduction of
leptin by adipose tissue. Whether this results from LDLR deficiency
within the adipocyte itself or from indirect effects through hepatic
LDL receptor deficiency remains to be determined.
The overproduction of leptin in LDLR
/
mice was not reflected in the
food intake by this strain. Leptin is produced only in adipose tissue
and elicits satiety responses by binding to leptin receptors in the
brain (9, 22, 48). On the basis of increased leptin levels
that we observed in the LDLR
/
mice, we hypothesized that food
intake would be decreased. However, results from our food intake and
fat absorption studies clearly showed that this was not the case.
Therefore, these mice are likely becoming leptin resistant, a disorder
observed in human obesity (18, 49). Studies evaluating
leptin production and signaling responses in the obese LDLR
/
mice
should help us understand the relationship between leptin production
and responsiveness, which may open new avenues of leptin therapy
treatment in obese individuals.
The response of apoE
/
mice to the diabetogenic diet was quite
different from that observed for the LDLR
/
mice. Several possibilities for this observation exist. First, we considered whether
loss of apoE
/
impaired fat absorption. Our fat absorption studies
showed that there were no apparent defects in gut fat absorption
compared with wild-type mice. Also, apoE
/
mice fed the diabetogenic
diet gained weight, demonstrating a positive energy balance. Second, a
study demonstrated that apoE deficiency reduced hepatic VLDL secretion
by >60% and increased hepatic TG content threefold (27).
No increases in hepatic TG levels were observed in diabetogenic diet-
vs. chow-fed apoE
/
mice, suggesting that hepatic TG were being
shunted away from lipid storage or VLDL production. We suggest that
fatty acid oxidation is accelerated in these mice to remove hepatic TG
stores. Triscari et al. (44) showed that in high fat-fed
rodents,
-oxidation is increased compared with chow diet-fed
controls. Furthermore, several studies have demonstrated that, in
livers from obese mice, uncoupling protein 2 (UCP2) mRNA and protein
levels are increased (14, 46). UCP2 uncouples respiration
from oxidative phosphorylation, resulting in ATP depletion and energy
release in the form of heat. Our data suggest that apoE may be an
important toggle that directs hepatic fatty acids away from fatty acid
oxidation and into TG production for lipoprotein secretion. In this
scenario, apoE deficiency would promote
-oxidation, possibly
providing more substrate for UCP while preventing fatty liver
formation. This concept is currently under investigation.
In addition to effects on hepatic tissue, we must consider whether
dietary lipids are being preferentially stored in adipose or muscle
from apoE
/
mice. This seems unlikely, because the apoE
/
mice
did not exhibit extraordinary increases in adiposity. However, the
ability of these tissues to activate UCPs in response to this diet has
not been studied in apoE
/
mice. It is quite possible that one or
more members of the UCP family are activated, resulting in increased
thermogenesis in the diabetogenic diet-fed apoE
/
mice.
Overall, our findings demonstrate that loss of the LDLR increases the susceptibility to obesity and disorders associated with obesity. In contrast, loss of apoE did not alter obesity but reduced some of the complications associated with obesity, including hyperglycemia and hyperinsulinemia. The use of these mice will therefore provide us with important tools to understand how metabolic and genetic factors control the distribution of lipoprotein-derived lipids in obesity and how this distribution contributes to complications associated with obesity. Finally, alleles at loci coding for the LDLR and apoE should be included in the list of candidate genes determining susceptibility to complications associated with obesity in human populations.
| |
ACKNOWLEDGEMENTS |
|---|
We are grateful for insightful discussions with Dr. Alan D. Attie and Dr. John F. Oram concerning this research.
| |
FOOTNOTES |
|---|
This work was supported by National Heart, Lung, and Blood Institute Grant HL-52848.
Address for reprint requests and other correspondence: R. C. LeBoeuf, Dept. of Pathobiology, Raitt Hall Rm. 305, Box 353410, Univ. of Washington, Seattle, WA 98195 (E-mail: leboeuf{at}u.washington.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.
Received 27 March 2001; accepted in final form 31 August 2001.
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