Laboratory inbred mouse strains show a broad range of variation in phenotypes, such as body composition, bone mineral density (BMD), plasma leptin, and insulin-like growth factor I (IGF-I), and thus provide a basis for the study of associations among them. We analyzed these phenotypes in male and female mice from 43 inbred strains fed on a high-fat (30% caloric content) diet and from 30 inbred strains fed on a low-fat (6%) diet. Structural equation modeling of these data reveals that the relationship of body fat content and areal BMD is altered by dietary factors and genotypes. Sex has no net effect on areal BMD, but after accounting for body mass difference females have higher areal BMD. Leptin is affected by relative fat mass and has no net effect on areal BMD. IGF-I has a direct effect on areal BMD.
- structural equation models
- insulin-like growth factor I
osteoporosis and related fractures represent major public health problems that are expected to increase dramatically in importance as the population ages (43), and low bone mineral density (BMD) is a well-established risk factor for osteoporotic fractures (2, 9). Genetic studies have shown that BMD is affected by multiple genetic variants of modest effect size and by gene-environment interactions (9, 33). Diet is a complex environmental factor that interacts with these genetic factors in their effects on BMD (43). The importance of dietary components such as calcium and vitamin D on the regulation of bone metabolism has been well documented, and the mechanisms are complex (8, 9). In addition, the effects of the intake of protein, fruit and vegetables, soy products, carbonated beverages, mineral water, dietary fiber, alcohol, and caffeine have also been examined (42, 43). Dietary fat may play a role in bone acquisition and maintenance, because fatty acids in food can activate peroxisome proliferator-activated receptor-γ, which in turn can affect the process of osteoblast formation (19, 30). However, in most cases, the mechanisms that relate dietary components to BMD are unknown.
The relationship between body composition and BMD is also complex. Body mass (BM), acting as a mechanical load, can have a significant effect on BMD (9, 34). Lean mass (LM) and fat mass (FM) are two major components of body soft tissue, and their relative contributions to the BM-BMD relationship present an interesting but challenging question. Conflicting results regarding the effects of FM on BMD have been reported in human studies (12, 14, 18, 34, 35). These may be due to variation in methods of bone density measurement or to confounding effects of age, sex, and diet. A recent study using a congenic mouse strain (B6.C3H-6T) indicated that higher FM is associated with reduced peak BMD (36), suggesting that FM may be inversely correlated with bone acquisition. The negative correlation of FM and BMD has also been documented in humans (13, 15).
The relationship among body composition, BMD, and physiological traits such as plasma leptin and insulin-like growth factor I (IGF-I) levels is complex and remains unresolved. IGF-I is an anabolic peptide that affects bone turnover (16, 26, 29, 45). Leptin, a hormone secreted by adipocytes, is involved in the regulation of food intake and energy expenditure (31). Leptin and BMD are involved in a complex system that includes both feedforward and feedback regulations (10, 11, 21). These relationships are also influenced by environmental factors such as dietary fat intake.
Understanding the effects of dietary fat intake and body composition on BMD has important implications for the prevention and treatment of osteoporosis. Here we use data collected on laboratory mouse inbred strain panels to investigate the roles of diet and sex as potential modulators of these relationships. Mouse strain panels display significant and continuous variation in body composition and BMD (41), and data are readily available through public resources such as the Mouse Phenome Database (MPD; http://phenome.jax.org/).
Structural equation modeling (SEM) is a generalization of multiple regression analyses that can be applied to gain insights into the causal relationships among many variables (40). SEM works by modeling causal relationships that give rise to the observed covariance structure (40). Unlike a multiple regression model, a variable in SEM can be both a predictor and a response. In SEM, path coefficients indicate the relative strength of effects along different paths in a causal model, an idea that traces back to the original work on path analysis by Wright (44). The relative effects of multiple paths can be calculated and compared. Additional insight into the relationship between specific factors can be obtained by comparing SEMs developed with the same population of inbred strains under different conditions. In this work, we use the SEM approach to analyze populations of inbred mouse strains in order to elucidate interactions between body composition variables and BMD and the effects of diet on these interactions. SEM of these data reveals that the relationship of body fat content and areal BMD is altered by dietary factors and genotypes. Sex has no net effect on areal BMD, but after accounting for BM difference females have higher areal BMD. Leptin is affected by relative FM and has no net effect on areal BMD. IGF-I has a direct effect on areal BMD.
MATERIALS AND METHODS
Mice and Diets
We analyzed data from two studies (MPD-143 and MPD-115), and all data were obtained from the MPD.
The Center for Mouse Models of Heart, Lung, Blood, and Sleep, a large-scale phenotyping program at The Jackson Laboratory, has characterized body composition and areal BMD on male and female mice from 43 inbred strains fed a high-fat diet (28) for 17 wk starting at 8 wk of age (41). Additional physiological data obtained on these same animals include serum leptin, insulin, glucose, and HDL cholesterol levels. We focus on the 25-wk data in this study.
Males and females of 30 inbred strains fed on a low-fat diet (LabDiet 5K52, Hudson, NH; 6% fat) were characterized for body composition, BMD, and IGF-I at 16 wk of age.
In both studies BMD was measured by PIXImus (GE Lunar, Madison, WI). Although the BMD data in MPD-143 and MPD-115 were measured at different ages, all mice had passed the peak bone acquisition age of 16 wk when the measurements were taken. For each data set, 8–10 mice of each strain and each sex were used for phenotyping. We used the strain- and sex-specific mean values (units) of each phenotype for analysis. Among the inbred strains surveyed in both studies, 22 strains are shared in common (Fig. 1 and Supplemental Table S1).1 Unless otherwise stated, all analyses were carried out on the 22 common strains, in which only two units from the MPD-143 have missing values for variables analyzed. We performed complete case analysis in the comparison of MPD-143 and MPD-115.
BM and FM are obtained by direct measurement of X-ray absorption with the PIXImus. LM is computed by the subtraction LM = BM − FM and represents the component of total BM that is not attributable to fat. In the analysis below we consider this additive breakdown, but we also consider the relative amount of fat in mice that differ in their overall size. Preliminary exploration of the data suggested that the logarithmic ratio of FM to LM, log(FM/LM), was the most appropriate representation. Clearly the absolute and relative fat measurements cannot both be linearly related to other variables in this study. However, we have confirmed that for the range of values observed here approximate linearity is observed on the logarithmic scale. This allowed us to explore the contributions of absolute and relative fat content on parameters such as BMD and leptin.
Structural Equation Modeling
The SEM approach in animal population genetics was described previously (23). We standardized each variable by subtracting its mean so that the SEM analysis focused on variances and covariances between variables. Exploratory SEM involves a model search and selection strategy that ideally considers all possible relationships among the variables (23). Prior knowledge is helpful in ruling out unlikely models. For example, factors such as sex and diet are never influenced by other factors; they are causally “upstream.” A model that best fits the observed data can be derived based on model selection statistics such as the Bayesian information criterion (BIC) (38). We use confirmatory SEM to test specific hypotheses based on maximum likelihood goodness-of-fit tests (3, 17).
Sample size limits the number of variables that can be included in a model. An observed covariance matrix among multiple variables is the foundation of structural modeling (40). Significant (P = 0.05) correlation (r = 0.30) between variables can be detected in a sample size of 44 at a type II error of 0.54 (1). Like other multivariate analysis methods, we have a reasonable power to derive a structural model when the ratio of the sample size to the number of variables included in model fitting is larger than five (4). In the 22-strain subset shared by MPD-143 and MPD-115, we have 44 units. Therefore, we have a reasonable power to model the relationship of at most eight variables with this subset of data.
The modeling analyses were conducted with R (http://www.r-project.org/) and the SAS software package (SAS, Cary, NC). Data were log transformed to obtain approximate linearity for all pairs of traits.
An SEM is a graphical model with directed edges. The graph provides an intuitive visual representation of an underlying system of linear equations, and the estimated coefficients of this linear system are called path coefficients. The path coefficients are standardized with reference to the variance of residuals, and the effects mediated by different paths can be decomposed and compared (22, 44). The effect of a direct path, where two variables are connected by a single directed edge, is the path coefficient. The effect of an indirect path, where two variables are connected by a series of directed edges in the same direction, is the product of all path coefficients along that path. The total effect of multiple paths on a variable is determined by the sum of effects across all incoming paths.
Multiple Regression Analysis
We also carry out multiple regression analysis to fit linear models using variables involved in SEM. Thus we can compare the results obtained from the two approaches.
Diet Alters Relationship Between Body Composition and BMD
The relationship between body composition and BMD is affected by diet, in addition to genotypes. BM consists of two major components, LM and FM. Fat content can be expressed as absolute FM or as relative FM-to-LM ratio (FM/LM). Scatter plots of FM and FM/LM against BMD stratified by diet indicate that the relationship of body fat content to BMD is different when the two diets are considered here (Fig. 2).
To further clarify the relationships among LM, FM, and BMD under different dietary fat conditions, we fit separate structural models to male and female data from the 22 inbred strains common to MPD-143 and MPD-115. On the basis of our previous studies (23), we know that there exist causal relationships from LM to BMD and from LM to FM. We contrast two models to assess the effect from FM to BMD (Fig. 3). The difference in log-likelihood (Δχ2) follows a χ2 distribution with one degree of freedom, and a value of Δχ2 >3.8 indicates that the addition of the path from FM to BMD will significantly (P < 0.05) improve the model fit. Under the high-fat diet condition there is strong evidence for a direct effect of FM on BMD in both males (Δχ2 = 7.21, P < 0.0001) and females (Δχ2 = 6.61, P < 0.0001) (Table 1). Conversely, there is no statistical evidence for a direct effect of FM on BMD for either sex under the low-fat diet condition (Δχ2 = 0.02, P = 0.99 and Δχ2 = 0, P = 1.0 for males and females, respectively). Thus the relationship of FM to BMD is affected by the diet.
We finally fit multiple regression models using the same data from the 22 common inbred strains. Under the high-fat diet condition both LM and FM have significant effects on BMD (Table 2). Under the low-fat diet condition, LM significantly impacts BMD, but FM does not. These results are consistent with those obtained from SEM.
In addition to the absolute fat-BMD relationship, we also investigated the relationship of relative fat and BMD by fitting a structural model including BM, FM/LM, and BMD. We consider a model where BM has causal relationships to respective BMD and FM/LM and FM/LM has a causal relationship to BMD. We then use four subsets of the data from the 22 common strains to fit the same model. These subsets include data from respective males and females on a low-fat diet and from respective males and females on a high-fat diet. Significance of the effect sizes along different paths can be tested with the t-test. Our interest here is the direction of effects from FM/LM to BMD as significance tests may be under the power for each subset of the data because of small sample sizes. Interestingly, the effect of FM/LM to BMD is positive for both males and females under the high-fat diet condition and negative for both sexes under the low-fat diet condition, as indicated by the signs of t-values (Supplemental Table S2). These results indicate that the relationship of FM/LM and BMD is altered by the diet.
Effects of Sex on BMD
We investigated the effect of sex on BMD by introducing sex as a variable in the structural models. Models relating LM, FM, BMD, and sex under each of the diet conditions are shown in Fig. 4. Both models fit the respective data (χ2, df, and P values are 0.0784, 1, and 0.78, respectively, for model A and 0.0002, 2, and 0.99, respectively, for model B). The effect size of each path in these models is significantly different from zero (Supplemental Table S3). These two models indicate the same relationships between body composition variables and BMD in response to dietary fat as shown in Tables 1 and 2. Sex has both direct and indirect effects on BMD. These two components of effects have different directions. The indirect effect is mediated through LM. Male mice have higher LM, and this in turn has a positive effect on BMD. The direct effect on BMD is higher for females, but the net effect is minor compared with the direct or indirect effect components (Table 3). On the other hand, evidence from both SEM and multiple regression analyses indicates that after accounting for the effect of LM sex has a significant effect on BMD (Table 2 and Fig. 4).
Roles of Plasma Leptin Levels
We applied structural modeling analysis to investigate the role of leptin with all 43 strains in the MPD-143. Using model fitting and assessment, we arrive at two structural models (Fig. 5). These two models contrast the effects of relative and absolute fat content on BMD and leptin. Both models fit the data well (χ2, df, and P values are 0.94, 3, and 0.82, respectively, for model A and 0.91, 2, and 0.64, respectively, for model B).
Model A in Fig. 5 delineates the relationship among sex, BM, FM/LM, and plasma leptin levels in the MPD-143 data. We further investigated the BM-leptin relationship by first-order correlation analysis, which is obtained by conditioning on every other variable one at a time (24). Results of first-order correlations (Supplemental Table S4) indicate that FM/LM, rather than FM or LM, is a mediator for the BM-leptin relationship. In addition, BMD is also a mediator for this relationship. A scatter plot of BM and leptin stratified by FM/LM is shown in Fig. 6. For the relative fat strains on the high-fat diet, BM and plasma leptin levels are significantly correlated, but they are not correlated for the relative thin strains on the same diet. These lines of statistical evidence support the idea that FM/LM is a mediator for the relationship between BM and plasma leptin levels under a high-fat diet.
In both models (Fig. 5), plasma leptin levels do not have a direct net effect on BMD, but there is an indirect relationship of leptin and BMD because both of them are affected by FM or FM/LM. The effect of fat content on the leptin-BMD relationship is illustrated in Fig. 7, where the relative or absolute fat content is stratified in terms of the population means. Leptin and BMD are significantly correlated in relative fat strains challenged with a high-fat diet, while there is no correlation between them for relative lean strains under the same diet condition. Thus FM and FM/LM are mediators for the leptin-BMD relationship under the high-fat diet condition.
We finally fit multiple regression models for BMD to confirm that leptin-BMD relationship (Table 4). After accounting for effects of other variables including FM or FM/LM, plasma leptin levels do not have a significant direct effect on BMD. In addition, none of the pairwise interactions among the variables shown in Table 4 has a significant effect on BMD (data not shown).
Roles of Plasma IGF-I Levels
We applied structural modeling analysis to investigate the role of IGF-I, using 30 strains in the MPD-115. We identified two structural models that fit the data (Fig. 8), as suggested by the goodness-of-fit statistics (χ2, df, and P values are 6.23, 4, and 0.18, respectively for model A and 1.45, 4, and 0.84, respectively, for model B). In both models, IGF-I has a direct effect on BMD. The relationship of IGF-I and BMD is further illustrated in Fig. 9. Here we note a strain-specific effect on this relationship. These two groups of strains differ in body size on the average, and strain group 1 consists of wild-derived strains with smaller body sizes except for the strains A/J and SM/J (Supplemental Table S1).
Results from fitting multiple regression models indicate that the binary strain group variable has a significant effect on BMD, after accounting for the effects of IGF-I, BM (or LM), and sex (Table 5). However, none of the pairwise interactions among IGF-I, BM (or LM), sex, and strain group is detected to have a significant effect on BMD (data not shown).
SEM provides an approach to developing causal models that accurately describe correlation structure among phenotypes in a reference population. Compared with multiple regression analysis, SEM has the advantage that it can reveal the hieratical relationships among multiple variables. However, interactions between variables in SEM remain a challenge. Results from SEM can be used to generate hypotheses for further experimental tests. For example, results from our modeling indicate that FM/LM is an important mediator for the relationship between BM and plasma leptin levels under the high-fat diet condition. Mouse models showing reduced plasma leptin levels (21, 32, 39) may be used to test the functional mediation of FM/LM in the BM-leptin relationship.
The across-strain correlations studied here are driven by genetic effects that may be different from within-strain correlations that are driven by physiological variation among individual animals within an inbred strain. Indeed, each strain may have its own physiological characteristics that could result in different correlation patterns among the variables. This is a dimension of analysis that we have not explored. The nature of the data precludes us from investigating multivariate relationships at individual animal levels, because of the incomplete records at this level. Our objective here is to identify relationships that arise because of variation in genetic background. In human populations both physiological and genetic correlations are likely to play a role in shaping the relationships among phenotypes.
The relationship of body composition to BMD is difficult to study in human populations because of uncontrolled genetic and environmental heterogeneity. Inbred mouse strains provide a set of fixed genetic backgrounds that can be studied under controlled conditions. They display a wide range of phenotypic diversity (41). Data obtained by phenotyping panels of inbred mouse strains are available in the Mouse Phenome Database. Multiple individuals of any given strain and sex can be measured to increase precision, but the unit in this study is strain-sex combinations and the numbers of available strains limit the complexity of the models that can fit. Data sets collected at different times or under different dietary conditions can be combined, but the overlapping strains and phenotypes may be fewer in number. To study both dietary fat conditions with available data, we were limited to only 22 strains and 4 variables. These concerns could be addressed by the development of larger reference populations of strains (5). Nonetheless, it was possible to develop insights into the roles that genotypes and diet play in modifying the relationship of body composition to BMD even with this limited sample size.
The relationship between body composition and BMD is complex and involves the interaction of multiple genetic and environmental factors. Our modeling approach provides insight into this relationship by investigating two panels of inbred strains under high-fat and low-fat diet conditions, and by systematic modeling of the relationship among LM, FM, and BMD. These results indicate that FM contributes to high BMD under the high-fat diet condition, consistent with previous studies showing that obesity protects osteoporosis in humans (6, 7). It is not clear what component(s) of the high-fat diet is responsible for this effect. We note, however, that the diet used in this study is also known as an atherogenic diet (28). This diet contains cholic acid, which has been shown to stimulate the vitamin D receptor (27). Most importantly, our modeling results indicate that high BMD can be achieved by increasing LM coupled with a low-fat diet (Fig. 4B), suggesting a beneficial effect of physical exercise as well as dietary fat and cholesterol intervention on the human skeleton.
Studies have documented that fat tissue is the storage of energy and muscle is the energy-consuming tissue, and that the BM-leptin axis is involved in energy metabolism (37). Plasma leptin is produced by adipocytes and affects bone remodeling (10). A recent study indicated that bone may exert a feedback control of energy homeostasis, which in turn impacts FM (21, 25). Our studies indicate that BMD, in addition to FM/LM, also mediates the relationship between BM and plasma leptin levels (Supplemental Table S4), suggesting that bone may be involved in the regulation of energy metabolism. Furthermore, our modeling results indicate that FM has a net effect on BMD under the high-fat diet condition, while the effect of FM on BMD might be balanced by feedback regulation under the low-fat diet condition. It seems plausible that the shared developmental pathways between adipocytes and osteoblasts (20) might be affected by dietary fat, which could provide a mechanistic explanation for our findings.
Further investigations are needed to reveal the genetic determinants that interact with diet and sex to regulate these phenotypic relationships, and to understand the physiological interactions among IGF-I, leptin, insulin, and other hormones in mice under both high-fat and low-fat conditions.
This research was supported by National Institutes of Health Grants HL-066611 and GM-070683, as well as by the Department of the Army DAMD17-03-1-0773.
We thank Drs. C. J. Rosen and W. G. Beamer at The Jackson Laboratory of the US and Dr. G. Brockman in the Institute of Animal Sciences, Humboldt-Universität zu Berlin, Germany, for their valuable comments and suggestions.
↵1 The online version of this article contains supplemental material.
Address for reprint requests and other correspondence: R. Li, The Jackson Laboratory, 600 Main St., Bar Harbor, ME 04609 (e-mail:).
Article published online before print. See web site for date of publication (http://physiolgenomics.physiology.org).
- Copyright © 2008 the American Physiological Society