Abstract
Low-density-lipoprotein receptor-related protein 5 (Lrp5) is a co-receptor in Wnt signaling, which plays a critical role in development and maintenance of bone. Osteoporosis-pseudoglioma syndrome, for instance, arises from loss-of- function mutations in Lrp5, and global deletion of Lrp5 in mice results in significantly lower bone mineral density. Since osteocytes are proposed to act as a mechanosensor in bone, we addressed a question whether a conditional loss-of-function mutation of Lrp5 selective to osteocytes (Dmp1-Cre; Lrp5f/f) would alter responses to ulna loading. Loading was applied to the right ulna for 3 min (360 cycles at 2 Hz) at a peak force of 2.65 N for 3 consecutive days, and the contralateral ulna was used as a non-loaded control. Young’s modulus was determined using a midshaft section of the femur. The results showed that compared to age-matched littermate controls, mice lacking Lrp5 in osteocytes exhibited smaller skeletal size with reduced bone mineral density and content. Compared to controls, Lrp5 deletion in osteocytes also led to a 4.6-fold reduction in Young’s modulus. In response to ulna loading, mineralizing surface, mineral apposition rate, and bone formation rate were diminished in mice lacking Lrp5 in osteocytes by 52%, 85%, and 69%, respectively. Collectively, the results support the notion that the loss-of-function mutation of Lrp5 in osteocytes causes suppression of mechanoresponsiveness and reduces bone mass and Young’s modulus. In summary, Lrp5-mediated Wnt signaling significantly contributes to maintenance of mechanical properties and bone mass.
Keywords: Lrp5, osteocytes, mechanotransduction, Young’s modulus, osteoporosis
Introduction
Genetic factors are critical determinants of health and the risk of bone diseases. Extensive genetic and functional data have suggested that a class of secreted morphogenic ligands [1], Wnt proteins, is linked to cellular proliferation and differentiation in numerous tissues [2][3][4], including bone [5][6]. Wnt signaling is regulated by binding of Wnt ligands to a receptor complex including a low-density-lipoprotein receptor-related protein 5 (Lrp5) [7]. Lrp5 is one of co-receptors for Wnt ligands [8] and genetic mutation involving excess or deficiency in Lrp5 signaling is known to affect bone mass and to increase the risk of bone disorder. A gain-of-function of Lrp5 increases bone mass accrual and strength [9], while null mutations in the receptor reduce bone mineral density [10]. Lrp5 is expressed in many tissues with the highest expression level in the liver [11]. Thus a specific role for Lrp5 in bone tissue is difficult to pinpoint solely based on clinical data or animal models in which its expression is augmented in all tissues [12]. The main aim of this study was to determine the skeletal consequences of Lrp5 deletion selectively in osteocytes and mature osteoblasts.
Skeletal adaptations to weight-bearing activity significantly affect bone’s mechanical properties and mass. The removal of regular activity, such as bed rest and microgravity, results in bone loss, commonly referred to as disuse osteoporosis [13]. Postmenopausal osteoporosis and bone fractures are major problems in elderly women, and physical exercise is often recommended to prevent skeletal fragility in age-related osteoporosis [14]. As mechanical signals are able to act as anabolic agents in bone [15] [16], much attention is drawn to an effective use of mechanotransduction or how bone cells transduce physical stimuli to promote new bone formation as a non-drug based intervention for osteoporosis. Although the skeletal consequences of global loss-of-function mutations in Lrp5 are linked to low bone mass [12] [17] [18], the effect of osteocyte-specific deletion of Lrp5 on mechano-responsiveness remains undetermined. In the present study, we investigated the role of Lrp5 in load-driven bone formation by establishing a conditional loss-of-function of Lrp5 selectively in osteocytes.
Two specific questions are addressed in this study: Does osteocytic deletion of Lrp5 alter skeletal size, bone mineral density (BMD), bone mineral content (BMC), and bone material properties (e.g., Young’s modulus)? Does osteocytic deletion of Lrp5 suppress responsiveness to load-driven bone formation? To address these questions, we constructed conditional Lrp5 knockout (KO) mutants by breeding dentin matrix acidic phosphoprotein 1 (Dmp1)-Cre mice to Lrp5 floxed mice. We hypothesized that a loss-of-function of Lrp5 in osteocytes would reduce bone size, BMD, BMC, and Young’s modulus in adult skeleton, and decrease load-driven bone formation. To evaluate bone size, three-dimensional microstructure, BMD, and BMC, we conducted X-ray imaging using DXA, CT, and pQCT. Young’s modulus was determined using dynamic compressive loading to the femur. To test responsiveness to mechanical loading, we employed an ulna loading modality and conducted bone histomorphometry.
Materials and Methods
Animals and genotyping
All procedures performed in this study were in accordance with the Institutional Animal Care and Use Committee (IACUC) guidelines. Mice lacking Lrp5 in osteocytes (Dmp1-Cre;Lrp5f/f; conditional Lrp5 KO mice) were created by breeding Dmp1-Cre transgenic mice with Lrp5 floxed mice both of which have been described earlier [17] [19]. Briefly, Dmp1 is a transcription factor, expressed predominantly in osteocytes and some latestage osteoblasts [20]. Dmp1-Cre transgenic mice contained a 10 kb fragment of the Dmp1 promoter, which was linked to the coding sequence of Cre recombinase [19]. Lrp5 floxed mice were engineered to harbor a pair of loxP sequences flanking exon 2 of the Lrp5 gene. Recombination of the floxed allele results in no detectable mRNA. Genotyping was performed using PCR with DNA isolated from tail samples. The primers for detecting Dmp1-Cre (534 bp product) were: 5’-CCC GCA GAA CCT GAA GAT G-3’, and 5’-GAC CCG GCA AAA CAG GTA G-3’. The primers for testing the presence of an Lrp5-floxed region were: 5’-TCT TGT AGC ACC CAG GAC CAT C-3’ (forward 1), 5’-TGC TCT TTC ATG CCC TCA GTG TA-3’ (forward 2), and 5’-CAC CAC AGC CAA CAG TCA CAG A-3’ (reverse for both forwards 1 and 2). Note that the forward primer 1 generated 404-bp PCR products (Lrp5f/f) and 282-bp PCR products (wild type control), while the forward primer 2 produced 534-bp cDNA fragments (Dmp1-Cre;Lrp5f/f) and 3,435 bp cDNA fragments including exon 2 of Lrp5 (wild type).
RNA isolation and real-time PCR
Total RNA was isolated from the femora of 4 week-old mice. In brief, the femora were stripped of surrounding tissues and periosteum. Their distal and proximal ends were cut off, and medullary cavities were rinsed with a saline solution. The femur samples were homogenized by a tissue homogenizer, and total RNA was isolated using TRIzol reagent (Life Technologies, Grand Island, NY, USA) and purified using Qiagen RNeasy mini kit. Using ~ 2 µg of total RNA, reverse transcription was conducted with a high-capacity cDNA reverse transcription kit (Life Technologies, Grand Island, NY, USA). For evaluation of the Lrp5 mRNA levels corresponding to the boundary of exons 1 and 2, quantitative real-time PCR was performed using a TaqMan gene expression master mix kit. The Lrp5 mRNA level at the boundary of exons 1 and 2 was normalized using the level of GAPDH mRNA.
Western Blot Analysis
Femur samples were dissociated with a mortar and pestle in a RIPA lysis buffer containing protease inhibitors (Calbiochem). Isolated proteins were fractionated using 10% SDS gels, and wet- and semidry-transferred to Immobilon-P membranes (Millipore) for Lrp5 and β actin, respectively. Membranes were incubated with primary antibodies specific to Lrp5 (Cell Signaling) or β-actin (Sigma), followed by secondary antibodies conjugated with HRP. Signals were detected with ECL chemiluminescence, and images were captured using an image analyzer (LAS-3000, Fuji Photo Film).
Longitudinal radiography
Radiographs of 16-week-old mice were obtained using a highresolution digital X-ray machine (piXarray100, Tucson, AZ, USA). Mice were anesthetized via inhalation of 2.5% isoflurane (IsoFlo; Abbott Lab, North Chicago, IL, USA) mixed with O2 (1.5 L/min), and they were placed in a prone position (facing to an X-ray sensor). The lateral and posterior images were acquired at 45 kV and 1 sec exposure time, and lengths of the femur and spine (L1 to S5) were measured manually from the digital radiographs using piXarray software.
Micro computed tomography (µCT)
The femoral mid-diaphysis bone was analyzed using images taken with a high-resolution µCT imaging system (µCT-20; Scanco Medical AG, Basserdorf, Switzerland). From the mid-diaphysis (i.e., 50 % of the total femur length from the tip of femoral condyle to the femur head), 20 transverse slices (6 mm thickness in total) were taken at 60 kV.
Determination of BMD and BMC
Using peripheral dual-energy X-ray absorptiometry (pDXA; PIXImus II; GE-Lunar Co., Madison, WI, USA), BMD and BMC of a whole body (excluding a head), a section of spine (L1 to L5), and a femur were determined. During scanning, mice (16-week-old) were anesthetized with isoflurane. Using XCT Research SA+ pQCT (Stratec Electronics, Pforzheim, Germany), volumetric BMD (vBMD) and volumetric BMC (vBMC) of femora were also determined. In brief, bone samples were stored in plastic tubes filled with 70% ethanol, and were positioned in the center of the CT gantry. Using a collimation of 0.26 mm and a voxel size of 0.07 mm, a single slice through each midshaft was imaged. Bone areas and densities were obtained at a threshold of 600 mg/cm3.
Ulna loading
Mechanical loading was carried out using the ulna loading modality, which has been described previously [12] [21]. In brief, under isoflurane-induced anesthesia, the right ulna was loaded for 3 min (360 cycles at 2 Hz) at a peak force of 2.65 N for 3 consecutive days using an electro actuator (Bose ElectroForce 3200; EnduraTEC, Minnetonka, MN, USA). The left ulna was not loaded and served as an internal control. Intraperitoneal injections of calcein (30 mg/kg body weight; Sigma, Saint Louis, MO, USA) and alizarin (50 mg/kg body weight; Sigma) were administered 5 and 11 days after the first loading day, respectively. Animals were sacrificed 18 days after the first loading day for bone histomorphometry. For strain measurement of the ulna, the previously described method [12] was used. Briefly, the strain gauge was mounted on the lateral face of the ulna, approximately 100 µm from the neutral bending axis of the bone.
Determination of BMD ratio
Micro CT images of the midshaft of femurs isolated from the control and KO mice were produced using a Skyscan 1172 high-resolution µCT (SkyScan, Kontich, Belgium) at 6-µm resolution. Average density of a 0.05 mm3 rectangular box of cortical bone in each femur was determined using MIMICS 13.1 software (Materialise, Inc., Plymouth, MI, USA). A BMD ratio was created by comparing the average BMD of the KO samples to the average BMD of the controls.
Determination of Young’s modulus
Sections of approximately 5 mm in length were prepared from the femoral midshaft, and dynamic compressive loading was imposed using an ElectroForce 3100 actuator. The loading condition consisted of a ramp function applied at 0.5 N/s to a peak compressive force of 6 N. The maximum load of 6 N was chosen to impart a physiologically relevant strain (~1500 – 2000 µstrain) to the control samples. A loading rate of 0.5 N/s was utilized in order to perform a non-destructive test. Young’s modulus was determined using the resulting force-displacement relationship and the physical dimensions of each sample [22].
Bone histomorphometry
Bone specimens from ulnae were immersed in 10% neutral buffered formalin for 48 h, dehydrated in graded alcohols, cleared in xylene, and embedded in methyl methacrylate. Using a diamond-embedded wire saw (Histo-saw; Delaware Diamond Knives, Wilmington, DE, USA), transverse sections (40 µm) were cut from the midshaft and ground to a final thickness of 20 µm. The slice sections were mounted on slides, and two sections per limb were analyzed using a Bioquant digitizing system (R&M Biometrics, Nashville, TN, USA). The following primary data were collected: total perimeter (B.Pm); single label perimeter (sL.Pm); double label perimeter (dL.Pm); and double label area (dL.Ar). From primary data, we derived mineralizing surface (MS/BS = [1/2sL.Pm+dL.Pm]/B.Pm ×100; %); mineral apposition rate (MAR = dL.Ar/dL.Pm/6 days; µm/day) and bone formation rate (BFR/BS = MAR × MS/BS × 3.65; µm3/µm2 per year). A set of relative values such as rMS/BS, rMAR, and rBFR/BS was derived from the differences between the loaded and nonloaded samples.
Statistical analysis
Data were expressed as mean ± s.e.m. (standard error of the mean). Differences between the loaded and non-loaded limbs were evaluated using paired t-test. Differences between groups were examined using Student’s t test for statistical significance at p < 0.05.
Results
Construction and characterization of Lrp5 mutant mice
Mice lacking Lrp5 in osteocytes (KO mice) had both positive Dmp1-Cre and homozygous flox allele. To examine whether the genetic engineering strategy was successful in recombining exon 2 of Lrp5 in osteocytes, we conducted PCR-based genotyping for wild type, Lrp5 floxed, and Cre-excised alleles. In the presence of the loxP site in Lrp5f/f mice, we detected 404-bp DNA fragments, which was larger than 282-bp fragments in Lrp5+/+ wild type mice in the absence of the loxP site (Fig. 1A, 1B and 1C). Mice lacking Lrp5 in osteocytes (Dmp1-Cre;Lrp5f/f) by breeding Dmp1-Cre mice with Lrp5f/f mice yielded 534-bp cDNA products, while their littermate controls generated significantly larger fragments (3,435 bp) including the exon 2 region (Fig. 1B). In the resultant KO mice (Fig. 1C), the Lrp5 mRNA expression at the boundary of exons 1 and 2 in the femurs was significantly diminished (96 % reduction) than that of the littermate controls (Fig. 1D). Immunoblots revealed that the Lrp5 protein level was significantly lower in the femur of KO mice than that of the control (Fig. 1E).
Shortening of bone length and cortical thickness in the KO mice
The KO mice exhibited an osteopenic skeletal phenotype (Fig. 2A–2B). There was significant reduction in femoral length among KO mice (15.33 ± 0.13 mm; mean ± s.e.m.) as compared controls (15.99 ± 0.23 mm) (p = 0.044) (Fig. 2C). Shortening of the spine length (L1 to S5) was also observed (37.34 ± 0.67 mm in control, and 35.44 ± 0.51 mm in KO) (p = 0.03) (Fig. 2D). Image analysis exhibited that cortical bone was thinner and more porous in the KO mice than that of the littermate controls (Fig. 3A–3F). Furthermore, the femur of the KO mice showed 21 % reduction in the cross-sectional area compared to Cre-negative littermate controls (p < 0.01) (Fig. 3G).
Reduced BMD and BMC in the KO mice
Compared to the littermate controls, the KO mice exhibited significant reduction in total body BMD (0.052 ± 0.001 g/cm2 in control, and 0.045 ± 0.001 g/cm2 in KO; 15 % decrease) (p = 0.0005), femur BMD (0.073 ± 0.002 g/cm2 in control, and 0.061 ± 0.001 g/cm2 in KO; 17 % decrease) (p = 0.002), and spine BMD (0.061 ± 0.002 g/cm2 in control, and 0.048 ± 0.002 g/cm2 in KO; 21 % decrease) (p = 0.0001) (Fig. 4A–C). Similar effects were noted for total body BMC. The femoral vBMD among KO mice (1096 ± 7 mg/cm3) was significantly lower than that of controls (1169 ± 9 mg/cm3) (p = 0.0006). Femoral BMC was likewise reduced among KO mice (0.027 ± 0.0008 mg in control, and 0.018 ± 0.0013 mg in KO) (p = 0.02) (Fig. 4D).
Reduction in Young’s modulus in the KO mice
Deletion of Lrp5 in the osteocyte population resulted in altered mechanical properties. The BMD of the KO mice was significantly decreased compared to that of controls, as confirmed by the BMD ratio (less than one), comparing the average BMD of the KO samples to the average BMD of the controls (p < 0.01) (Fig. 5A). Also, Young’s modulus was reduced from 6.55 ± 0.38 GPa (control) to 1.42 ± 0.24 GPa (KO) (p = 0.004) (Fig. 5B). In response to the same bout of cyclic loads, the ulna of the KO mice showed significantly higher strain (3,762 ± 69.6 µε) than the littermate control mice (703 ± 34.6 µε) (p < 0.05) (Fig. 5C).
Suppression of mechanoresponsiveness in the KO mice
In response to in vivo ulna loading, the loaded ulnae of the Cre-negative (control) mice showed fluorescent labeling corresponding to bone formation on the periosteal and endocortical surfaces. However, the ulna of the KO mice presented reduction in fluorescent label incorporation (Fig. 6B). Periosteal mineralizing surface was significantly reduced in the KO mice (31.6 ± 3.1% in control, and 15.2 ± 7.1% in KO) (p = 0.04), and mineral apposition rate was decreased significantly (0.74 ± 0.15 µm/day in control, and 0.11 ± 0.12 µm/day in KO) (p = 0.02). The relative bone formation rate was 266.8 ± 43.8 µm3/ µm2 per year in control and 82.2 ± 55.2 µm3/ µm2 per year in KO (p = 0.03) (Fig. 6C). The KO mice also showed a significant decrease in geometric properties. The ulna cortical area was decreased by 10 % (0.253 ± 0.007 AU in control, and 0.228 ± 0.008 AU in KO) (p < 0.05), and the minimum cross-sectional moment of inertia was reduced by 16 % (0.0032 ± 0.0001 in control, and 0.0027 ± 0.00009 AU in KO) (p < 0.05) (Fig. 6D).
In the periosteal surface, the relative bone formation of the KO mutants was diminished by 27% (227 µm3/ µm2/yr in control, and 166 µm3/ µm2/yr in KO) (Fig. 7A). The relationship between relative bone formation rate (y) and strain (x) for the control mice was best-fitted with y = 0.99x – 466 (R2 = 0.49) on the periosteal surface.
In the endosteal surface, the relative bone formation rate of the KO mutants was decreased by 66% (196 µm3/ µm2/yr in control, and 66 µm3/ µm2/yr in KO) (Fig. 7B). The relationship between relative bone formation rate (y) and strain (x) for the control mice was best-fitted with y = 1.03x – 528 (R2 = 0.55) on the endosteum.
The KO mice hardly demonstrated strain-dependent anabolic responses on both periosteum and endosteum, and thus the square of the correlation coefficient was estimated to be 0.11 on the periosteal surface and 0.06 on the endosteal surface (Fig. 7).
Discussion
We demonstrate in this paper that inactivation of Lrp5 in osteocytes impairs bone mass and size, mechanical properties, and responses to mechanical loading. Compared to the Cre-negative Lrp5f/f/ littermates, the conditional Lrp5 KO mice (cre-positive Lrp5f/f mice) lacking functional Lrp5 in osteocytes presented lower BMD and BMC in the whole body, femur and spine. They also presented shorter length of the femur and spine. In response to dynamic loads of 2.65 N to the ulna, the conditional Lrp5 KO mice induced 3,500 to 4,000 strain to the midshaft of the ulna while the littermate controls 500 to 800 µstrain. Although induced strain was significantly higher in response to dynamic loading, bone formation rate was substantially lower both on the periosteal and endosteal surfaces in the conditional Lrp5 KO mice than the littermate controls. These results strongly suggest that Lrp5-mediated Wnt signaling is critical in load-driven bone formation, and maintenance of bone mass and size as well as mechanical properties.
In Wnt-mediated mechanotransduction of bone, the interactions of sclerostin, a negative regulator of bone formation [23], to Lrp5 have been considered to be a key regulatory step [24]. In this mechanism, mechanical loading induces bone formation by repressing transcription of sclerostin, which inhibits Wnt signaling. This hypothesis is in agreement with high bone mass phenotypes in human Lrp5 gain-of-function mutants, in which sclerostin binds less strongly to mutated Lrp5 co-receptors than to wild-type receptors [25]. To further examine the Lrp5-linked mechanism of load-driven bone formation, we developed conditional Lrp5 mutations in the osteocyte pool of mice. Osteocytes reside in lacunae in the bone cortex and are terminally differentiated osteoblasts. In response to mechanical loading, they suppress transcription of sclerostin [26] and elevate synthesis of Dmp1 for bone mineralization [27]. In the described loss-of-function mutation in Lrp5 gene, the exon 2 was deleted by Cre recombinases driven by a Dmp1-promoter. Dmp1 is essential for mineralization of the skeleton and calcium/phosphate metabolism [28]. It is highly expressed in mature osteoblasts and osteocytes, and Dmp1-Cre mice are reported to activate Cre recombinases predominantly in osteocytes and late stage osteoblasts [29], though a small degree of recombination can also be detected in skeletal muscle in these mice [17]. Together with exons 3 and 4, the exon 2 encodes a YWTD-type β-propeller 1 motif. Lrp5 consists of 4 β-propeller motifs together with 4 epidermal growth factor-like repeats in its extracellular domain [30]. Thus, the described mutation apparently disrupted at least in part binding sites for extracellular Wnt ligands.
The estimation of Young’s modulus in the femur by dynamic compressive loading was consistent with the measured strain in the ulna. The proximity to the neutral axis is a major reason why the measured strain was below 1,000 microstrain. Strain of the midshaft of long bone is determined by multiple factors including Young’s modulus, cross-sectional area, cross-sectional moment of inertia, and bone curvature. Compared to the littermate controls, the conditional Lrp5 KO mice presented 4.6-times smaller Young’s modulus, together with 10% reduction in cross-sectional area and 16% decrease in cross-sectional moment of inertia. Bone curvature was not significantly different between the conditional KO and control mice. These geometric and mechanical properties are in good agreement with the induction of significantly higher strain in the conditional KO mice than the littermate control.
The conditional Lrp5 KO mice exhibited similarities and differences to global Lrp5 KO mice that lacked functional Lrp5 throughout the skeletal and non-skeletal system [31]. Since Wnt signaling is involved in morphogenesis of various tissues, impacts on bone shape and stiffness are considered more severe in the global KO mice than the conditional KO mice. However, changes in Young’s modulus might be primarily governed by osteocytes through mechanotransduction and thus differences between these two KO strains may differ to a lesser extent [12]. Both global and conditional inactivation of Lrp5 show low bone mass and decreased bone strength. The anabolic response to ulna loading was reduced by ~94% (global KO) and ~78% (conditional KO in this study). Cortical area and cross-sectional moment of inertia in the femur was reduced in both KO mice but the global KO mice to a larger extent (30 to 50%) than the conditional KO mice (10 to 20%).
There are a few limitations in the current study including the design of floxed mice, the target of DMP1 driven Cre mice, and the other receptor in Wnt signaling. First, the described conditional KO strategy aimed to disrupt a part of the extracellular domain in Lrp5 with an intact peptide sequence for the other three -propeller motifs [8][32]. It is thus important to evaluate potential effects of Wnt ligands whose binding to Lrp5 might not be affected by this loss-of-function mutation [33]. Second, Dmp1 driven Cre-recombinase might be activated in mature osteoblasts besides osteocytes. Generating transgenic mice with Cre recombinase driven by, for instance, a type I collagen promoter might be useful [34]. Third, the other known co-receptor, Lrp6, may participate to Wnt signaling and load-driven bone formation. It is yet to be investigated the contributions of Lrp5/6 [8][35]. Last, Wnt signaling has been suggested a therapeutic target for bone diseases [36]. Dickkopf 1 (DKK1), for instance, is known to suppress Wnt signaling by forming a complex with Lrp5/6. Further studies addressing interactions of DKK1 and other Wnt-linked molecules are necessary. In summary, conditional Lrp5 KO mice presented significant decreases in cortical area and cross-sectional moment of inertia, Young’s modulus, and mechanosensitivity to load-driven bone formation. The results support the notion that enhancing bone formation by increasing Lrp5-induced signaling may be beneficial to the treatment of osteopenia and osteoporosis.
Highlights.
Selective inactivation of Lrp5 in osteocytes in mice shows reduced bone mass.
Inactivation of Lrp5 in osteocytes leads to 4.6 times lower Young’s modulus in the femur.
Mice lacking Lrp5 in osteocytes present significantly diminished load-driven bone formation.
Acknowledgements
We dedicate this paper to Charles Turner who provided invaluable guidance and advice throughout this study. We appreciate Bart Williams for providing Lrp5 floxed mice. The study was in part supported from National Institute of Arthritis and Musculoskeletal and Skin Diseases Grant AR53237 (AR) and AR52144 (HY).
Abbreviations
- Lrp5
low-density-lipoprotein receptor-related protein 5
- Dmp1
dentin matrix acidic phosphoprotein 1
- Cre
Cre recombinase
- BMD
bone mineral density
- BMC
bone mineral content
Footnotes
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Contributor Information
Liming Zhao, Email: lizhao@iupui.edu.
Joon W. Shim, Email: shimjoon@iupui.edu.
Todd R. Dodge, Email: trdodge@iupui.edu.
Alexander G. Robling, Email: arobling@iupui.edu.
Hiroki Yokota, Email: hyokota@iupui.edu.
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