The goal of this study was to investigate genetic effects on mechanical properties of the mouse femur. We found evidence for QTL on eight chromosomes that affect mechanical traits. Some of these QTL may have primary effects on body weight or femoral geometry, and others seem to affect bone quality directly.
Introduction: Previous studies have shown a dependence of fragility-related fracture risk on genetic background. Although many of these studies investigated the effect of genetics on BMD, basic measures of bone geometry and mechanical integrity may provide a more comprehensive characterization of the genetic effects on bone fragility. The purpose of this study was to identify quantitative trait loci (QTL) that affect mechanical and material properties of cortical bone in a genetically heterogeneous mouse population.
Materials and Methods: A total of 486 female UM-HET3 mice was used for this study. UM-HET3 mice are produced as the offspring of (BALB/cJ × C57BL/6J) F1 females and (C3H/HeJ × DBA/2J) F1 males. Femurs from 18-month-old mice were tested to failure in four-point bending to assess mechanical properties of cortical bone; these properties were compared with genotype data from 185 biallelic loci. A permutation-based test was used to detect significant associations between genetic markers and mechanical traits. This test generates p values that account for the effect of testing multiple hypotheses. Throughout the experiment, p ≤ 0.05 was considered statistically significant. Analysis of covariance was used to examine possible effects of body weight and femoral geometry.
Results: We found evidence for genes on maternal chromosomes 11 and 13 and paternal chromosomes 2, 4, 7, 10, 11, and 17 that affect mechanical and material properties of femoral bone. The total variance explained by genetic effects on each mechanical trait ranges from 2.9% to 15.4%. Most of the identified polymorphisms influence mechanical traits even after adjustment for body weight. Adjustment for femoral geometry reduces the effects of some of the QTL, but those on chromosomes 2 and 10 do not seem to be influenced by femoral geometry.
Conclusions:Many genes and chromosomes are involved in the genetic control over mechanical integrity of cortical bone. QTL on paternal chromosomes 4 and 11 may mediate mechanical properties, at least in part, by modulation of femoral geometry. Other QTL identified here may directly affect bone tissue quality.
THE NATIONAL OSTEOPOROSIS Foundation (NOF) estimates that 1.5 million fragility-related fractures occur annually in the United States. The direct costs of these fractures were an estimated $17 billion in 2001, and this figure is rising. In addition to the staggering economic impact, osteoporosis often causes devastation to the lives of its victims and their families. Only 15% of hip fracture patients can walk across a room unaided 6 months after a fracture. An estimated 24% of hip fracture patients ≥50 years of age die within 1 year of their fracture.(1)
The risk of fracture depends on factors such as the amount and structure of bone that is present and the mechanical integrity of the bone tissue. These factors may, in turn, be affected by the genetic background, hormonal milieu, age, disease status, and physical activity of the individual. At this time, the dependence of fracture risk on many of these factors is not well understood. A number of previous studies investigated the genetic control of fracture risk; however, most of these studies focused on BMD, because BMD is the primary factor used to predict fracture risk clinically. Twin and multigeneration family studies have estimated that 50-90% of the normal variability in BMD at various anatomical locations is genetically determined.(2–6) Inbred mouse strains have also been used to investigate the genetics of bone characteristics. Beamer et al.(7) showed differences in BMD among 11 inbred strains of mice. Other studies have similarly reported differences in BMD between various inbred strains.(8–11) A few studies have reported specific quantitative trait loci (QTL) that associate with BMD in mice.(12–17) Although the findings of these studies are important, BMD may not be the best outcome measure to predict fracture risk. We believe that a more complete understanding of the genetic control of fracture risk can be attained by determining the effects of genetic background on specific measures of bone size, structure, elasticity, strength, and other indices of mechanical integrity. This type of analysis is obviously not feasible in humans, but inbred mouse strains can be used to develop suitable models, because detailed geometric and mechanical analysis can be performed on their bones. In addition, the genetic backgrounds of these animals are known, and differences in bone properties exist between strains.
In a previous study, we identified 14 QTL that regulate various measures of femoral geometry in a genetically heterogeneous mouse population.(18) However, femoral geometry cannot completely predict fracture risk, because femoral strength depends on both the geometric and material properties of the bone. A few previous studies have begun to investigate the genetic determinants of cortical bone mechanical properties in mice. Differences in various mechanical properties have been shown between inbred strains.(9,11,19,20) Other studies have identified specific QTL that associate with femoral strength(21) and work to failure(22) in mice. The purpose of this study was to identify QTL that affect mechanical and material properties of cortical bone in a genetically heterogeneous mouse population to enhance our understanding of the genetic control of cortical bone. We hypothesized that we would discover some QTL whose effects on mechanical properties of cortical bone would be mediated by effects on femoral size and shape. We also predicted that other QTL would influence mechanical properties independently of femoral geometry, thus representing polymorphisms that directly affect the quality of cortical bone tissue in mice.
MATERIALS AND METHODS
Mice and husbandry
The animals used in this study are the same as those used in a previous report of genetic effects on geometric traits of cortical bone.(18) Briefly, the mouse population is of the UM-HET3 stock and is derived from a four-way breeding among four inbred strains: BALB/cJ (C), C57BL/6J (B6), C3H/HeJ (C3), and DBA/2J (D2). The experimental animals are the female progeny of (C × B6) F1 females and (C3 × D2) F1 males.
The F1 breeding animals were purchased from Jackson Laboratories (Bar Harbor, ME, USA) and were used to produce a total of 525 UM-HET3 mice. Animals were housed by sex in a single suite of specific-pathogen-free (SPF) rooms and were exposed to identical environmental conditions (12:12-h light/dark cycle, 23°C). Mice were given ad libitum access to water and laboratory mouse chow. The cages were covered with microisolator tops to minimize the spread of infectious agents. Sentinel mice were tested every 3 months to verify the pathogen-free status of the population. All such tests were negative throughout the course of the study. UM-HET3 mice were entered into the study in a staggered fashion at a rate of 25-35 mice/month. Animals were killed at 18 months of age, at which time right femurs were removed, dissected free of soft tissue, and frozen in a PBS solution. This work was approved by the Animal Care and Use Committee at the University of Michigan.
Genomic DNA was prepared from 1-cm sections of tail from 4-week-old animals using a standard phenol-extraction method.(23) Final DNA preparations were tested for concentration, ability to sustain PCR amplification under standard conditions, and electrophoretic size distribution. DNA was genotyped using an ALFexpress automated sequence analyzer (Pharmacia, Piscataway, NJ, USA); the details of this genotyping method have been described previously.(24) Primer pairs were purchased from MWG Biotech (High Point, NC, USA). In total, 185 markers were examined from 99 genetic loci. Of the 99 loci, 86 markers were informative for both the maternal- and paternal-derived alleles, and 13 loci were only informative for either maternal or paternal alleles. The selection of genetic loci is described previously in detail.(18) Chromosomal localization and order of markers were calculated using the MapMaker QTX program package (Whitehead Institute, MIT, Boston, MA, USA).
After the right femurs were scanned with μCT for a previous geometric analysis, they were mechanically tested in four-point bending. A servohydraulic system (858 Mini Bionix II; MTS, Eden Prairie, MN, USA) with a custom testing apparatus (Fig. 1A) was used to test the femurs to failure at a constant displacement rate of 0.5 mm/s. The femurs were loaded in the anterior-posterior direction so that the posterior side of the bone was in tension and the anterior side was in compression (Fig. 1B). All four loading points were placed in contact with the bone by adjusting the heights of the upper two points independently. A 50-lb load cell (Model 41; Sensotec, Columbus, OH, USA) was used to measure the load applied to the bone, and the mid-diaphyseal displacement was measured with a linear variable differential transducer (010 MHR; Schaevitz Engineering, Pennsauken, NJ, USA). Load and displacement data were acquired using the TestStar IIs system (version 2.4; MTS) at a sampling frequency of 2000 Hz. MATLAB (version 6.5; The Mathworks, Natick, MA, USA) was used with a custom analysis program to determine stiffness, yield load and displacement, ultimate load and displacement, postyield displacement and energy to failure from the load, and displacement data. The analysis program contained an algorithm that determined the linear region of the load-displacement curve; stiffness was measured as the slope of this linear region. The yield point was defined as the point at which the secant stiffness differed by 10% from the initial tangential stiffness. Ultimate load was the maximum load attained before failure, and ultimate displacement was the corresponding displacement. Postyield displacement was calculated as the displacement at failure minus the displacement at the yield point. Energy to failure was determined with numerical integration as the area under the load-displacement curve up to the fail point. A displacement ratio was calculated as the ratio of ultimate displacement to yield displacement to characterize the relative magnitudes of elastic and plastic deformation. Additionally, elastic modulus (E) and ultimate strength (σ) were estimated using these equations:
where S is the whole bone stiffness determined with four-point bending, I is the moment of inertia with respect to the medial-lateral axis of the bone, a and b relate to the spacing of the contact points and are defined as shown in Fig. 1C, M is the moment at maximum load, and C is the distance from the centroid of the bone to the periosteal surface in the posterior direction. I and C were determined for each femur from μCT data.
Testing was performed on 6 different days. Each day, a set of assays was preceded by tests of pieces of steel music wire (type 302/304 stainless steel spring wire, 0.020 in diameter, McMaster-Carr product 8908K21; Aurora, OH, USA) to evaluate the consistency of the assay system. This wire was chosen because it has a stiffness within the same range as the murine femurs. Six wire specimens were evaluated at the beginning of each day's work and every 2-3 h thereafter. ANOVA showed no significant differences across the series of assays (p = 0.22). The means and SD for the 6 testing days were 169.7 ± 2.6, 169.2 ± 3.0, 168.6 ± 2.3, 167.9 ± 3.1, 167.4 ± 1.7, and 169.7 ± 3.3, respectively, with an average CV of 1.62% (1.56%, 1.75%, 1.38%, 1.83%, 1.00%, and 1.97%, respectively).
A single-point, genome-wide search was performed for each trait to detect QTL that may be associated with the trait. To make the analysis consistent for all partially and fully informative markers, four-way informative markers were split into two sets of biallelic markers that were informative for either the maternally or paternally transmitted alleles. One-way ANOVA models, with a trait as the dependent variable and a biallelic marker as the factor with two levels, were used to perform genome-wide searches for all 185 biallelic markers. The strength of linkage associations between genetic markers and mechanical traits was evaluated using a permutation-based test of statistical significance. This test generates an “experiment-wise” acceptance criterion to take into account the multiple hypotheses that were tested in this search and to avoid type I error inflation.(25) A null distribution for permutation analysis was generated based on 1000 shuffles of original phenotype data. Throughout the experiment, p ≤ 0.05 was considered statistically significant. The percent of variance in each mechanical trait that can be explained by genetic effects was estimated in a standard way from corresponding regression models.
The animals used in this study were of various sizes and weights. To account for overall animal size, covariance analyses were performed with a trait as the dependent variable, a biallelic marker as the factor with two levels, and body weight at 3 or 18 months of age as the covariate. Permutation-based statistical tests were used to evaluate statistical significance as described above. Because whole bone mechanical properties are dependent on the geometry of the bone, a second set of covariance analyses was performed to account for variations in geometric properties of the femur. Femoral cross-sectional area, cortical thickness, and moment of inertia with respect to the medial/lateral axis of the bone were used simultaneously as covariates. These measures of femoral geometry were determined with μCT as described previously.(18)
Of the 525 mice used in this study, 38 died before 18 months of age and were not included in this analysis. Mechanical data could not be obtained on 1 additional mouse; therefore, the final population consisted of 486 UM-HET3 mice. On average, there were 4.5 marker loci per autosome, and the average distance between marker loci varied from 15 to 20 cM.
Ten variables were determined for each specimen from the four-point bending tests. These variables are shown in Table 1 with their means and SD among the UM-HET3 mice used in this study. Table 2 shows Spearman rank-order correlations among these mechanical traits and between the traits and body weight measured either at 3 or 18 months of age. Not surprisingly, many of these indices show significant correlations with one another, although the many correlations below r = 0.5 suggest that most of these measurements provide information about bone properties not fully captured by any other single variable. Body weight measures show weak correlations with the bone measurements other than predicted modulus and predicted ultimate strength, which are calculated using information about bone geometry likely to be modulated by overall body size and weight.
Table Table 1.. Summary of Mechanical Traits
Table Table 2.. Correlations Among Mechanical Factors, Including Body Weight at 3 and 18 Months
Table 3 shows significant linkage associations between mechanical traits and genetic markers that were determined from the permutation analysis. Because the maternal and paternal alleles were separated for the linkage analysis, the origin of each marker is indicated with an M or a P in Table 3. The chromosomal position of each marker is reported in centimorgans and millions of basepairs from the centromere. The estimated genetic effect for each significant association is given with the SE in parentheses. The estimated genetic effect is the difference between mean levels of the indicated trait in the two groups of mice differing at the indicated marker locus. Units of estimated effects are the same as the variable units shown in Table 1. The column labeled “Comparison” indicates the background allele at a particular marker that results in the larger value of the trait. The maternally inherited alleles were either C or B6 alleles, and the paternally inherited alleles were either C3 or D2 alleles. The genome survey thus indicated the presence of QTL on eight chromosomes, including maternal chromosomes 11 and 13 and paternal chromosomes 2, 4, 7, 10, 11, and 17.
Table Table 3.. Associations with Experimentwise Significance of p ≤ 0.05
The percent variance estimated in each mechanical trait that can be attributed to genetic effects was determined, and the results are shown in Table 4. The variance explained by individual chromosomes was determined, considering only the significant marker/trait associations shown in Table 3. The last row in Table 4 shows the total variance that can be attributed to all QTL that were significantly associated with each trait. The total variance explained by genetic effects ranges from 2.9% to 15.4%.
Table Table 4.. Variance Caused by Individual and Combined Genetic Effects
We conducted analyses of covariance to determine if the QTL of interest listed in Table 3 might directly affect body weight, and therefore, indirectly affect mechanical properties. Body weights at 3 and 18 months of age were used as covariates, and the results are shown in Table 5. The estimated genetic effects on the mechanical traits are shown before and after adjustment for body weight. Estimated effects are reported for all significant linkage associations shown in Table 3 as well as for a few associations (chromosomes 2, 4, 5, 7, and 11; Table 5, bold) that obtained significance only after adjustment for one of the weight measures. Genome scan-seeking QTL that modulate weight, per se, found no loci on any of these chromosomes that had a significant effect on body weight at 3 or 18 months.
Table Table 5.. Effect Sizes Before and After Adjustment for Body Weight
A similar analysis was conducted to determine if the effects presented in Table 3 were potentially mediated by the geometry of the femoral diaphysis. The results are shown in Table 6. Linkage associations involving predicted elastic modulus and predicted ultimate strength were not included in these analyses, because femoral geometry has already been accounted for in the calculation of these traits. The regression equation included cross-sectional area (CSA), cortical thickness (CT), and moment of inertia with respect to the medial-lateral axis of the bone (IML) as covariates.
Table Table 6.. Effect Sizes Before and After Adjustment for Geometry
We have shown evidence for QTL on maternal chromosomes 11 and 13 and paternal chromosomes 2, 4, 7, 10, 11, and 17 that affect whole bone mechanical and material properties of the femur. Together, these QTL account for 2.9-15.4% of the variance estimated in the mechanical traits. Paternal chromosomes 2, 4, 7, and 11 contained multiple markers associated with the mechanical properties. It should be noted that this does not necessarily prove the existence of multiple genes that affect mechanical traits on these chromosomes. Closely linked SSLP markers may show associations with traits because of linkage to a single effector gene locus. This initial QTL analysis does not allow for high-resolution mapping of the various markers to their chromosomal positions. Therefore, multiple markers on a chromosome may be linked to a single gene of interest. Additional genotyping using more closely spaced markers is now underway and will help to determine the chromosomes that contain more than one locus with effects on the mechanical properties of the femur. Although we have used a permutation-based significance test to control type I error rate and produce an “experiment-wise” p value for each genome scan, we have not adjusted the significance criterion with respect to the number of traits evaluated; thus, Table 3 may well contain a small proportion of false positive conclusions. In addition, we note that a study of 500-600 mice has only limited statistical power. Power analysis using a synthetic data set suggests that a population of this size will detect only 27% of the QTL with heritability of 0.10 and only 45% of QTL with heritability 0.15. Thus, there is a good likelihood that our compilation (Table 3) has missed many QTL with substantial effects on the bone traits we have measured.
The mechanical properties studied here (stiffness, yield load and displacement, ultimate load and displacement, postyield displacement, displacement ratio, and energy to failure) depend on material properties of the bone tissue (such as modulus and ultimate strength that we have estimated in this study) and the size and cross-sectional shape of the bone. Our previous geometric analysis revealed QTL that strongly associate with various measures of femoral size and shape on maternal chromosomes 1, 5, 6, 7, 11, 12, 15, and 17 and paternal chromosomes 1, 3, 4, 8, 9, 11, 14, and 15.(18) A direct comparison of these results with the current mechanical trait results (not including material properties like modulus and ultimate strength) reveals two areas of overlap: paternal chromosomes 4 and 11 have QTL that associate with both femoral geometry and mechanical properties. It is possible that one or more genes on these chromosomes actually affect the geometry of the femur, which in turn affects mechanical properties. Because the remaining QTL that associate with mechanical properties are not strongly associated with geometric properties, they may instead directly affect bone tissue quality or they may affect bones indirectly (e.g., through the alteration of a hormone that in turn influences bone quality).
Material properties of femoral diaphyseal cortical bone in the UM-HET3 mice were estimated by calculating elastic modulus and ultimate strength according to Eqs. 1 and 2, respectively. These estimated material properties were significantly associated with markers on maternal chromosomes 11 and 13 and paternal chromosomes 7, 11, and 17, indicating that genes on these chromosomes affect the material properties of cortical bone, independent of the femoral geometry. However, it is noteworthy that one of these markers, D11Mit83 on the maternal chromosome 11, is also strongly associated with various femoral geometry traits. True material properties should be independent of geometry. It is possible that the elastic modulus and ultimate strength values used here may not completely account for femoral geometry, because they are estimates based on beam theory. Another possibility is that a gene near the D11Mit83 marker affects some other factor, such as calcium metabolism or osteoblast regulation, that could indirectly affect both geometry and material properties. Future plans include producing uniform microbeams from femoral cortical tissue of the same animals and testing the beams in micro-four-point bending to determine the material properties of femoral cortical tissue more directly.
There are a relatively small number of previous studies that have identified QTL and associate it with femoral mechanical properties and BMD in mice. In 1999, Beamer et al.(13) identified four QTL on chromosomes 1, 5, 13, and 15 that were strongly linked with femoral BMD in an F2 cross between C57BL/6J and CAST/EiJ strains. Using a different mouse model (F2 cross between C57BL/6J and C3H/HeJ), Beamer et al.(15) performed a similar study in 2001 and found QTL on chromosomes 1, 4, 6, 11, 13, 14, and 18 that strongly associate with femoral BMD. Klein et al.(16) measured whole body BMD in mice derived from C57BL/6 and DBA/2 strains in 2001. The results showed links with QTL on chromosomes 1, 2, 4, and 11.(16) Comparing our current results with these previous BMD studies, we find commonalities on chromosomes 2, 4, 11, and 13. Inconsistencies among other significant QTL may reflect differences in outcome measures or in the specific genetic crosses used; these inconsistencies could also reflect type II errors in one or more of these studies.
Li et al.(21,22) used an F2 cross between MRL/MpJ and SJL/J strains to identify QTL-affecting femoral failure load and energy to failure. The results identified markers on chromosomes 1, 2, 8, 9, 10, and 17 that associated with failure load and markers on chromosomes 2, 7, 8, 9, and X that associated with energy to failure. We found no QTL that strongly associated with energy to failure and only one on chromosome 4 that associated with ultimate load; this is similar to failure load in the UM-HET3 mice. The lack of consistency between our results and the findings of Li et al.(21,22) are most likely attributable the different mouse models used in the studies.
We considered the possibility that some of the genetic effects listed in Table 3 might act primarily on body weight, with only secondary effects on mechanical properties. To test this idea, we conducted analyses of covariance using body weight at either 3 or 18 months of age as the covariates. The results shown in Table 5 show that, in most cases, the genetic effects have similar magnitudes before and after adjustment for body weight. However, there are a few exceptions. First, the associations between the paternal alleles of D10Mit40 and ultimate displacement and postyield displacement were reduced after adjustment for 18-month body weight. It is possible that the linkage association of this QTL with displacement measures is mediated indirectly through an effect on body weight throughout midlife. It is also possible that some third factor, perhaps hormones, modulates both bone properties and body weight and is under control of a locus on paternal chromosome 10. Similarly, the association between displacement ratio and the paternal allele at D2Mit285 is diminished in calculations involving 18-month body weight. It is interesting to note that the relationship between D2Mit434 and displacement ratio is not similarly affected by 18-month weight. This difference may suggest that chromosome 2 harbors two different loci with effects on displacement ratio—one that is associated with body weight dependence, and one that is not. Further studies involving a higher density of markers on chromosome 2 are required to confirm this.
Table 5 displays six linkage associations (bold) in which QTL had significant increases in effect size only after adjustment for body weight. Three of these associations involve D4Mit84, D7Mit25, and D11Mit156, which were already noted in Table 3 because of their associations with other mechanical traits. Two other loci, however, are new. The estimated genetic effect of the gene associated with D2Mit58 on energy to failure increased only after adjustment for body weight at 18 months. It is possible that this maternal QTL modulates the process by which bone properties adjust to differences in body weight or to physiological factors, perhaps hormonal, that modulate both body weight and bone fragility. The other new QTL modulates predicted ultimate strength of the bone and is associated with the paternal alleles at D5Mit292. Here, the effect size increases after adjustment for weight at 3 months. However, the effect size increase is much less dramatic after adjustment for weight at 18 months.
A second set of covariance analyses were conducted to determine if effects noted in Table 3 were potentially mediated by genetic influences on the geometry of the femoral diaphysis. These results are presented in Table 6. For associations involving markers on paternal chromosomes 4 and 11, the estimated genetic effect is reduced after adjustment for femoral geometry. These results are consistent with the fact that paternal chromosomes 4 and 11 contained markers that were significantly associated with both femoral geometry and mechanical properties. These genetic markers may represent QTL whose effects on mechanical properties are mediated, at least in part, by modulation of femoral geometry. However, the associations shown in Table 6, involving markers on paternal chromosomes 2 and 10, do not seem to be affected by femoral geometry and presumably reflect modulation of bone quality. Only one new locus, D1Nds2, was found to have a stronger association after adjustment for geometry. In this case, mice inheriting the B6 allele were found to show greater stiffness in calculations adjusted for bone geometrical traits, suggesting that this QTL might modulate compensation of bone mechanical properties to bone size or shape.
In conclusion, we have shown the complex nature of the genetic control of cortical bone in mice that is caused by the multiple QTL that were found to associate with various measures of femoral mechanical and material properties. We found evidence for QTL on paternal chromosomes 4 and 11 whose effects on mechanical properties may be mediated, at least in part, by modulation of femoral geometry. Other genetic markers identified in this survey may be linked to QTL that directly affect bone tissue quality and material properties, but further studies are needed to clarify the role of these QTL in the modulation of femoral mechanical integrity. Although the results of this study do not allow us to positively identify candidate genes that affect femoral mechanical properties in mice, we now have an appropriate starting point from which we can begin the search to find specific genes. In addition, further analysis of this four-way cross-population should help to delineate interactions among bone traits, underlying hormonal and biochemical differences among mice, and the genes that modulate bones both during and after developmental maturation. Finally, the results of this study may have important implications with respect to fragility or fracture risk in humans. The data in this study relate to 10-15 QTL, each of which corresponds to one or two human syntenic regions with 200-500 known genes. Testing or review of these genes is beyond the scope of this study, but focused searches for human alleles at the same (syntenic) positions of the mouse genes may provide additional insight (beyond BMD) into fracture risk prediction. In addition, identification of the true effector genes and their function in regulating bone extracellular matrix properties in the mouse may support the development of new therapeutic strategies for treating or preventing fragility in humans.
The authors thank Gretchen Buehner, Maggie Vergara, Steve Pinkosky, Shu Chen, and Zhihong Shao for contributions to this study. This work was supported by National Institutes of Health Grants P01-AG16699, AG08808, and P30-AR46024.