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Hum Mol Genet. Dec 1, 2010; 19(23): 4560–4572.
Published online Sep 15, 2010. doi:  10.1093/hmg/ddq384
PMCID: PMC2972692
Functional interactions between the LRP6 WNT co-receptor and folate supplementation
Jason D. Gray,1,2 Ghunwa Nakouzi,3 Bozena Slowinska-Castaldo,1 Jean-Eudes Dazard,4,5 J. Sunil Rao,4 Joseph H. Nadeau,3,5 and M. Elizabeth Ross1,2*
1Laboratory of Neurogenetics and Development,
2Graduate Program in Neuroscience, Weill Medical College of Cornell University, New York, NY 10021, USA,
3Department of Genetics,
4Department of Epidemiology and Biostatistics, and
5Center for Proteomics and Bioinformatics, Case Western Reserve University, Cleveland, OH 44106, USA
*To whom correspondence should be addressed at: Weill Cornell Medical College, 1300 York Avenue, PO Box 239, New York, NY 10065, USA. Tel: +Phone: 1 2127465550; Fax: +1 2127468226; Email: mer2005/at/med.cornell.edu
Contributed by These authors contributed equally to the work.
Contributed by Present address: Division of Biostatistics, Department of Epidemiology and Public Health, University of Miami Miller School of Medicine, Miami, FL 33136, USA.
Contributed by Present address: Institute for Systems Biology, Seattle, WA 98103, USA.
Received July 26, 2010; Revised September 3, 2010; Accepted September 3, 2010.
Crooked tail (Cd) mice bear a gain-of-function mutation in Lrp6, a co-receptor for canonical WNT signaling, and are a model of neural tube defects (NTDs), preventable with dietary folic acid (FA) supplementation. Whether the FA response reflects a direct influence of FA on LRP6 function was tested with prenatal supplementation in LRP6-deficient embryos. The enriched FA (10 ppm) diet reduced the occurrence of birth defects among all litters compared with the control (2 ppm FA) diet, but did so by increasing early lethality of Lrp6−/− embryos while actually increasing NTDs among nulls alive at embryonic days 10–13 (E10–13). Proliferation in cranial neural folds was reduced in homozygous Lrp6−/− mutants versus wild-type embryos at E10, and FA supplementation increased proliferation in wild-type but not mutant neuroepithelia. Canonical WNT activity was reduced in LRP6-deficient midbrain–hindbrain at E9.5, demonstrated in vivo by a TCF/LEF-reporter transgene. FA levels in media modulated the canonical WNT response in NIH3T3 cells, suggesting that although FA was required for optimal WNT signaling, even modest FA elevations attenuated LRP5/6-dependent canonical WNT responses. Gene expression analysis in embryos and adults showed striking interactions between targeted Lrp6 deficiency and FA supplementation, especially for mitochondrial function, folate and methionine metabolism, WNT signaling and cytoskeletal regulation that together implicate relevant signaling and metabolic pathways supporting cell proliferation, morphology and differentiation. We propose that FA supplementation rescues Lrp6Cd/Cd fetuses by normalizing hyperactive WNT activity, whereas in LRP6-deficient embryos, added FA further attenuates reduced WNT activity, thereby compromising development.
Of the more than 190 genetic mouse models of neural tube defects (NTDs) (13), remarkably few have been tested for responsiveness to prenatal folic acid (FA) supplementation and fewer still show a beneficial response (13). Mice with the naturally occurring Crooked tail (Cd) mutation are an example of a folate-responsive model of rostral NTDs (exencephaly) (4). Cd results from a single-nucleotide substitution in the low-density lipoprotein receptor-related protein 6 (Lrp6) gene (5). Lrp6 (arrow in Drosophila) encodes a single-pass transmembrane receptor that, like its paralog Lrp5, is a co-receptor with Frizzled in the canonical wingless (WNT) signaling pathway to activate β-catenin-dependent TCF/LEF-regulated transcription (6). The Lrp6Cd mutation replaces a highly conserved amino acid in the extracellular domain of LRP6 and interferes with the ability of dickkopf-1 (Dkk1) to inhibit canonical WNT signaling, resulting in sustained elevation of cytosolic β-catenin levels in the presence of WNT. Loss of Lrp6 function produces several birth defects including caudal axis truncation and limb deformities as well as exencephaly and spina bifida (7). Moreover, a hypomorphic allele of Lrp6, caused by the ringelschwanz point mutation, is associated with spina bifida in otherwise viable homozygous pups (8). Thus, both gain-of-function (GOF) and loss-of-function (LOF) Lrp6 mutations can result in NTDs.
Prenatal dietary FA supplementation reduces the incidence of NTDs in Lrp6Cd/Cd mice (4). Vitamin treatments result in a true rescue of Cd mice from NTDs as there was a normal Mendelian distribution of genotypes at all supplementation levels, and phenotypes in homozygous animals were shifted to increased embryonic viability and decreased NTD occurrence with FA supplementation. Moreover, analyses of gene expression profiles and biochemical markers of FA/HCY metabolism indicate a defect in intracellular FA utilization associated with homozygosity for the Lrp6Cd mutation (9). However, it is not yet known whether this effect is specific to the Lrp6Cd allele, the Cd mouse strain background, or whether FA supplementation influences the action of LRP6 itself. In this study, the response of LRP6-deficient mice to FA supplementation was examined in fetal outcomes, in biochemical and transcriptional activity in vitro and by gene expression in vivo, in order to characterize the impact of FA on NTD incidence, LRP6 function and WNT canonical signaling.
Folate supplementation and birth defect occurrence in Lrp6 null mice
Two hundred and eighty-seven embryos collected from dams that were fed diets containing 2 ppm FA (130 embryos, 29 resorptions) or 10 ppm FA (157 embryos, 29 resorptions) were examined and genotyped. Most deformities were observed in Lrp6−/− embryos with only two instances of spina bifida occurring in heterozygotes, one from each diet group. No instances of exencephaly, limb defects or axis truncation were found in any wild-type or heterozygous embryos. All Lrp6 homozygous null embryos exhibited at least two defects and several displayed three or more defects. For example, two Lrp6−/− embryos from the 2 ppm FA diet group at E12.5–13 displayed axis truncation and limb defects, in addition to coloboma of the eye and spina bifida in one embryo and exencephaly in another (Fig. 1A).
Figure 1.
Figure 1.
Incidence of NTD and morphogenic defects in pregnancies of FA-supplemented Lrp6+/− mice. Observed implantations were scored as resorptions, embryo dead at harvest (early lethality) or live embryo with open cranial folds (exencephalic), open caudal (more ...)
When expressed as a percent of conceptions, fewer cases of exencephaly, spina bifida, limb malformations and axis truncations were encountered in the litters maintained on the 10 ppm compared with the 2 ppm FA diet (Fig. 1B). Taken as a group, these deformities were found with significantly lower frequency in the higher FA diet cohort than in the 2 ppm FA-fed controls (P < 0.05). However, this was not a true rescue effect, because the number of Lrp6−/− genotypes recovered in the 2 ppm FA and especially in the 10 ppm diet cohort deviated significantly from the Mendelian expectations for a Lrp6+/− × Lrp6+/− intercross (Fig. 1C). Even when all resorptions above a baseline 10% (see below) are assumed to represent nulls, the recovery of Lrp6−/− embryos was significantly lower than expected in the 10 ppm FA diet group (Fig. 1C), suggesting that FA supplementation increased the severity of embryopathy occurring before implantation in Lrp6−/− mice.
Tables 113 further highlight these FA effects, with resorptions set aside as a separate group, as DNA could not be systematically recovered from necrotic tissue. In contrast to the expected equal numbers of homozygous wild-types and mutants among all progeny, mice displaying early embryonic or later lethality that genotyped as Lrp6−/− accounted for 46% fewer homozygous nulls than expected (P = 0.04) in the 2 ppm FA diet group and more severe deviation from expected in the 10 ppm FA cohort, with 71% fewer nulls observed (P = 0.0001) (Table 1). Interestingly, the deficit of recovered null embryos did not affect overall litter size, as there were no significant differences between diet groups in the average number or in the range of embryos per litter. Nevertheless, a significant shift toward early lethality was found in Lrp6−/− embryos in the FA-supplemented diet relative to control (Table 2). While on the 2 ppm FA diet, nearly all (90%) observed embryos were viable at E13, only slightly over a third (38%) of the Lrp6 null embryos on the 10 ppm FA diet were viable to that gestational age (P = 0.003).
Table 1.
Table 1.
Genotype distribution of embryos from Lrp6+/− × Lrp6+/− intercrosses
Table 2.
Table 2.
Early lethality of Lrp6−/− embryos
Table 3.
Table 3.
Resorption frequencies by FA diet in heterozygous (Lrp6+/− × Lrp6+/−) versus wild-type (Lrp6+/+ × Lrp6+/+) intercrosses
Despite the lower than expected number of nulls in the 10 ppm diet group, the number of resorptions was equivalent between the 2 ppm diet (18% of implantations) and the 10 ppm diet (16% of implantations) (Table 3, P = 5.1). The comparable resorption rates of wild-type embryos from Lrp6+/+ ×Lrp6+/+ crosses on the 2 versus 10 ppm FA diets ruled out the possibility that the 10 ppm FA diet reduced fetal viability on the wild-type background (Table 3). The 10 ppm group from Lrp6+/− × Lrp6+/− parents displayed a higher rate of resorption than was observed for Lrp6+/+ ×Lrp6+/+ intercrosses (9.3% at 10 ppm for Lrp6+/+ versus 15.6% for Lrp6+/− intercrosses), suggesting that resorptions above 10% on the high folate diet were genotype-dependent. Not all resorptions could be genotyped, but those from which DNA could be recovered genotyped as nulls. These results suggest that some embryonic loss in the 10 ppm FA group occurred prior to implantation or too early in embryogenesis to be detected at E13.
Together, these data indicate that FA supplementation reduced the frequency of birth defects as a group (exencephaly and spina bifida, limb malformation and axis truncation) observed at E13 and associated with LRP6 deficiency when compared with all embryos maintained on 2 ppm FA. However, increasing dietary FA reduced these rates by shifting outcomes to earlier embryonic lethality.
FA supplementation increases occurrence of NTDs in Lrp6 null mutants
The initial cohort of embryos screened at E13 showed a trend suggesting a higher proportion of viable nulls display NTD when receiving the 10 ppm FA diet (6/6 nulls on 10 ppm FA had NTDs compared with 12/18 nulls on the 2 ppm FA diet). However, the shift to early embryonic lethality of Lrp6−/− embryos on the supplemented FA diet reduced the number of viable nulls in that group, impeding evaluation of statistical significance. To further explore the effect of FA on neurulation in LRP6-deficient mice, additional embryos on either diet were scored specifically for NTDs at a slightly earlier stage (E10). In these litters, all wild-type siblings displayed closed neural tubes and mutants that were scored were viable and stage appropriate. Among viable Lrp6−/− embryos from dams fed with the control diet, 68% displayed NTDs while 100% of viable null embryos on the 10 ppm FA diet had NTDs (P = 0.03) (Table 4). Thus, increasing prenatal FA exacerbates embryopathy and increases NTD occurrence in LRP6-deficient mice.
Table 4.
Table 4.
Effect of maternal FA supplementation on incidence of NTDs in Lrp6−/− embryos
Effect of FA on cell proliferation and apoptosis in the LRP6-deficient neural tube
A hypothesized influence of FA supplementation on NTD mechanisms is that added FA enhances cell division in the neural folds and perhaps underlying mesenchyme to promote neural tube closure (10,11). This could potentially correlate with altered WNT signaling, because this developmentally crucial pathway is known to promote patterning and cell proliferation (12,13). We therefore examined cell proliferation in the cranial neural tube of Lrp6 wild-type, heterozygous and homozygous null embryos by quantifying the number of anti-phosphohistone 3 (PH3) labeled cells in M-phase per unit length along the cranial neural folds of E10 mice (Fig. 2). In Lrp6+/+ embryos, FA supplementation significantly increased cell proliferation. Interestingly, this FA effect was abolished in heterozygous and homozygous mutant embryos, in which proliferation on either the 2 or 10 ppm FA diet was unchanged or reduced relative to wild-type embryos on the 2 ppm control diet, indicating an interaction between gene dosage and FA supplementation.
Figure 2.
Figure 2.
FA diet supplementation fails to promote proliferation in the neural tube of E10 Lrp6-deficient embryos. Panels compare the dorsal midbrain of wild-type (WT), heterozygous (+/−) and homozygous (−/−) E10 embryos from each diet group. (more ...)
Changes in WNT activity could also have an impact on cell survival (1416). We therefore examined TUNEL labeling of apoptotic cells in E10 siblings (Fig. 3). There was no difference in the distribution or amounts of programmed cell death among genotype or diet conditions. While these assays sample a rapidly dynamic process at this stage making cell counts inherently inaccurate (and so counts were not performed), nevertheless it can be said that there were no qualitative genotype/diet-dependent differences in apoptosis as evaluated by TUNEL. Obviously, embryo survival overall is affected since earlier death ensues. However, increased apoptosis does not appear to be a central reason that neurulation fails in Lrp6−/− animals that are viable past E10.
Figure 3.
Figure 3.
FA diet supplementation does not alter the pattern of apoptosis in the E10 rostral neural tube of Lrp6-deficient embryos. Panels compare the dorsal midbrain of wild-type (WT), heterozygous (+/−) and homozygous (−/−) E10 embryos (more ...)
Canonical WNT signaling in the presence of defined FA levels
We next explored whether FA supplementation modulates canonical responses to recombinant WNT3a stimulation of NIH3T3 cells in vitro. The accumulation of cytosolic β-catenin was examined in cells treated with FA concentrations ranging from 0 to 100 μg FA/ml DMEM (Fig. 4A and B). Inclusion of FA in the defined medium did not alter the basal levels of cytosolic β-catenin. Significantly, FA depletion suppressed responses to WNT stimulation, with optimal response observed at 4 μg/ml FA. In contrast, 10 μg/ml FA or higher concentrations attenuated WNT responses. To distinguish the cytosolic and nuclear consequences of stabilized β-catenin, WNT-stimulated transcriptional activity was examined using NIH3T3 cells transfected with the TopFlash reporter plasmid (Fig. 4C). A similar sensitivity of WNT activity to FA levels was found. These data indicate that FA levels can modulate cellular responses to WNT stimulation by influencing cytosolic accumulation of β-catenin and TCF/LEF transcriptional activity. The importance of Lrp6 gene dosage to canonical WNT activity in the rostral neural tube was confirmed using the TCF/LEF-LacZ reporter mouse on the Lrp6−/− background, which showed a substantial decrease in the in situ β-galactosidase reaction product in the midbrain–hindbrain of LRP6-deficient embryos (Fig. 4D). Thus, continued Lrp5 gene expression does not fully compensate for LRP6 loss in the region of cranial neural tube closure point 2, which is a common location of neurulation failure in these mutants.
Figure 4.
Figure 4.
Impact of FA on the canonical WNT signaling pathway in vitro and demonstration of reduced WNT activity in situ of E9.5 Lrp6−/− embryos. (A) Western blot of cytosolic β-catenin levels in NIH3T3 cells that were cultured for 3 days (more ...)
Gene and diet effects on mRNA profiles
The observation of FA influence on WNT-mediated transcription led us to examine which transcriptional pathways are associated with these FA effects on neurualtion in LRP6-deficient embryos. In particular, cranial tissue from wild-type and Lrp6+/− E9.5 female embryos was examined to gain insight into the effects of maternal FA supplementation on molecular mechanisms leading to NTDs at a key developmental stage. In parallel, liver samples from adult female mice were used for several reasons. First, liver is the tissue where FA/homocysteine metabolism has been most comprehensively studied (1719). Second, gene expression in adult heterozygous females is relevant to maternal–fetal interactions, because certain maternal metabolic features are established risk factors in the pathogenesis of NTDs (2022). Third, gene expression patterns identified in adult tissues from Lrp6+/− heterozygotes may be relevant for screening assays designed to evaluate NTD risk and response to FA supplementation. Finally, Lrp6+/− heterozygotes rather than Lrp6−/− homozygotes were used as the test group to focus on subtle primary molecular features that lead to pathological changes and to avoid secondary effects of severely compromised development in homozygous mutants (23).
Of the nearly 40 000 sequences covering the mouse transcriptome that were interrogated, we focused on the curated consensus list of 1650 genes for embryos and 960 genes for liver that showed evidence for statistical significance in the genotype–diet interaction test (co-variance) and that appeared in at least one ingenuity pathway analysis (IPA) metabolic or signaling pathway. For metabolic pathways, significant over-representation was found for 6 of the 35 pathways in embryonic cranial tissue (Supplementary Material, Table S1) and for 36 of 67 pathways in adult liver (Supplementary Material, Table S2), whereas for signaling pathways, significant over-representation was found for 67 of 160 pathways in embryonic cranial tissues (Supplementary Material, Table S3) and for 23 of 139 pathways in adult liver (Supplementary Material, Table S4). Then we examined the ‘intersection’ set, where IPA was conducted for differentially expressed genes that were found in both embryonic cranial tissue and adult liver. Four of the 28 total metabolic pathways showed statistical significance in this intersection set (Supplementary Material, Table S5), whereas 28 of the 129 signaling pathways showed statistical significance in the same intersection set (Supplementary Material, Table S6). The ways in which selected genes co-varied in wild-type and heterozygous Lrp6+/− mice on the 2 and 10 ppm levels of dietary FA are illustrated in Figure 5 (also see Supplementary Material, Figs S1 and S2 for graphics of all interaction effects, and Supplementary Material, Tables S7 and S8 for gene lists and gene names).
Figure 5.
Figure 5.
Examples of gene–diet interactions. Genetic factors are shown for wild-type (WT) and mutant heterozygotes (KO), and dietary factors are shown for diets that were 2 (dashed lines) and 10 ppm (solid lines) in folate. Normalized means are indicated (more ...)
We identified the three highest-ranking metabolic and signaling pathways and highlighted several other significant pathways based on prior knowledge. Several observations are relevant. At least five groups of functionally related pathways were found (Table 5). These include (with IPA pathway designations provided in parentheses): methionine and folate metabolism (purine metabolism, methionine metabolism, one carbon pool by folate, polyamine regulation), WNT and ubiquitination (protein ubiquitination, WNT/β-catenin signaling), mitochondrial dysfunction (oxidative phosphorylation, ubiquinone biosynthesis, mitochondrial dysfunction), translation control (regulation of eIF2 and p70S6K signaling, eIF2 signaling) and cytoskeletal regulation (breast cancer regulation, CCR3 signaling in eosinophils and actin cytoskeleton signaling). Collectively, these pathways affect aspects of cell proliferation, cell morphology and oxidative stress, and implicate specific molecular and biochemical functions that corroborate the in vivo and in vitro results for WNT signaling and cell proliferation. We also note that inositol metabolism was significantly altered in adult liver; inositol supplementation has been shown to reduce NTD risk in curly-tail mutant mice (24).
Table 5.
Table 5.
Pathways most significantly associated with diet–genotype interaction
We show that the occurrence of birth defects associated with a LOF mutation in Lrp6 is reduced among all conceptions by moderate supplementation of FA in the prenatal diet. However, in contrast to our studies in the Cd mouse line that bears a GOF mutation, the same level of FA supplementation that rescued Lrp6Cd/Cd embryos did not rescue LRP6-deficient embryos. Instead, FA supplementation of Lrp6−/− embryos shifted an already severe phenotype to earlier embryonic lethality, so that LRP6-deficient embryos responded, but with an adverse reaction, to elevated FA levels. The fact that FA levels influence WNT signaling was evident in the effect of FA supplementation on gene expression profiles in Lrp6+/− embryos and adults. In fact, of the hundreds of pathways and networks that are traceable with IPA algorithms, it is highly significant that cell cycle regulatory and WNT pathways displayed a strong gene–diet interaction. The relevance of WNT signaling was validated using two in vitro assays of the WNT canonical pathway. In these assays, FA deficiency blunted pathway responses to WNT signaling, reflecting the importance of FA metabolism for early development (3,25). However, these assays also indicate that FA supplementation, even to a modestly elevated level, attenuates WNT signaling. These data suggest that added dietary FA likely rescued the Lrp6Cd defect by countering this net hyperactive Cd allele, whereas FA supplementation further suppressed WNT signaling to exacerbate the LOF in the Lrp6 knockout line. This indicates a direct relationship between FA supplementation and the LRP6/WNT signaling pathway. Such a direct relationship would be consistent with our previous studies indicating that the Lrp6Cd allele also impacts intracellular FA utilization (9).
The mitotic index of PH3 labeling in neuroepithelial cells around the time of cranial neural tube closure (E9.5–10) showed that raising dietary levels of FA promotes proliferation in wild-type mice. However, Lrp6 LOF mutant embryos displayed an impaired proliferative response to FA supplementation. While these results could explain the failure of added FA to rescue NTDs in Lrp6−/− embryos, they could not explain the increased loss of heterozygous mice, since there was no statistical difference in mitoses of heterozygotes compared with wild-type on the control diet or between diets in the heterozygous cranial neural folds. Moreover, Lrp6 null embryos of equivalent stage did not display a statistically significant difference in mitoses on the two diets, undermining the possibility that a proliferation defect was the sole reason for earlier embryonic loss in Lrp6 nulls receiving the 10 ppm FA diet. Similarly, TUNEL labeling ruled out an increase in apoptosis upon FA supplementation to account for the observed increase in NTD in nulls and fetal loss of heterozygous LOF mutants.
Involvement of LRP6 in canonical WNT signaling suggested that FA effects on neurulation could entail transcriptional influences on embryogenesis. Indeed canonical WNT signaling in the cranial neural folds and midbrain of E9.5 embryos was diminished as assessed by the comparison of in situ β-galactosidase activity in the Lrp6+/+::TCF-LacZ versus Lrp6−/−::TCF-LacZ double mutants, when sibling embryos were processed in parallel. Therefore, the loss of LRP6 in null embryo cranial folds was not fully compensated by continued LRP5 expression.
In vitro assessment of WNT canonical pathway stimulation in the presence of varied FA levels revealed a bimodal relationship between WNT signaling and FA concentration, in which FA excess was as deleterious to WNT signaling as FA deficiency. Particularly striking was that relatively modest FA increases of 2.5-fold or more above the optimal level can attenuate WNT signaling in vitro. There was no effect of FA alone on the basal levels of cytosolic β-catenin or TopFlash transcriptional reporter activity in NIH3T3 fibroblast cultures. Interestingly, the level of FA that provided optimal WNT activation in vitro, 4 μg/ml, is the same concentration used in the complete Dulbecco's modified Eagle's medium that was previously optimized for growth and maintenance of cell lines (26). FA concentrations of 10 μg/ml or higher blunted the cellular response to recombinant WNT3a in both β-catenin stabilization and TopFlash reporter assays. Therefore, FA supplementation has an impact on transcriptional activation by the canonical WNT signaling pathway.
We examined gene–diet interactions because of our interest in the impact of dietary folate supplementation on NTDs and expression profiles in wild-type and Lrp6 heterozygous mutants in two key tissues at different life stages. Our expression studies were focused on E9.5 crania because NTDs arise in embryonic cranial folds where key aspects of folate metabolism in mitochondria take place (27) and on adult liver where most of the methylation reactions and 50% of all methionine metabolism occurs (28). In addition, liver function in both embryos and adults depends on WNT signaling (29,30), and methionine metabolism in liver can be adversely affected in mice that have mutations in WNT signaling pathway genes (9,23). The statistical analysis used here is a new application of Bayesian hierarchical selection and interaction testing that provides a robust and highly reproducible result. Our interrogation of gene–diet interactions revealed several metabolic and signaling pathways that are significantly affected by Lrp6 mutation and FA supplementation in cranial development during embryogenesis, in liver function in adults or in both. Understanding the gene- and diet-dependent interplay among these physiological pathways may lead to general strategies for preventing NTDs, regardless of their responsiveness to folate. We propose that mutations in WNT signaling genes such as Lrp6 not only adversely affect methionine metabolism, but also secondarily affect methylation reactions, DNA synthesis (purine and pyrimidine metabolism), translation control and, through polyamine metabolism, the balance of cell proliferation, mitochondrial functions and perhaps metabolism of alternative methyl donors (Table 5). This proposal nicely integrates our molecular and pathway studies with known functions of these pathways.
Pathway analysis of gene–diet interactions suggests a central role for methionine and polyamine metabolism in these developmental and physiological processes. In particular, S-adenosylmethionine (AdoMet, also known as SAM) is used for methylating a wide variety of molecules such as DNA, RNA, lipids and proteins, for polyamine synthesis, a source of AdoMet radicals and a component of riboswitches that control transcription and translation (31). Availability of AdoMet for these reactions depends heavily on dietary folate. Polyamines (putrescine, cadaverine, spermidine and spermine), which are DNA-binding organic molecules with at least two amino groups, are ubiquitous in rapidly dividing cells (32). AdoMet decarboxylase converts AdoMet to dcAdoMet, which then is used to make spermine and spermidine. Although cell growth is retarded or blocked when polyamine pools are depleted, cells rigorously maintain polyamine levels at the expense of methionine metabolism, which in turn leads to imbalanced AdoMet and nucleotide pools, thereby adversely affecting methylation as well as purine and pyrimidine metabolism (33). The interdependency between methionine metabolism and polyamine biosynthesis exacerbates the functional consequences of folate deficiency, with ramifications for DNA synthesis, cell proliferation and mitochondrial functions.
Degradation of polyamines links methionine metabolism with mitochondrial function and alternative methyl donors. Degradation of spermine and spermidine uses acetyl-CoA and, under the action of succinate dehydrogenase (SDH1), leads to production of succinate, which is essential for complex II functions in mitochondria. Thus, demands of polyamine metabolism impact methionine metabolism in two ways, first by preferentially using AdoMet for polyamine synthesis rather than for methylation reactions, and second by using acetyl-CoA for polyamine degradation rather than for choline metabolism, which could affect availability of betaine, an alternative methyl donor. Together, these results and observations suggest that disruption of methionine metabolism in WNT mutant mice leads to diverse metabolic consequences that are remediated or exacerbated, depending on genetic conditions, with supplementary folate.
These studies provide a novel perspective to the gene–environment interactions that contribute to NTD formation. With respect to developmental signaling pathways, not only FA deficit but also elevated FA levels can impair WNT pathway function. Depending on individual genotype, FA supplementation can be deleterious to neurulation and embryogenesis. In the Lrp6 LOF mutants, the effects of supplementation on proliferation did not explain the negative impact of added FA on the heterozygous and homozygous mutants. Similarly, we did not detect an enhancement of apoptotic cell death in mutant embryos compared with wild-type. Thus, the impact of the detected pathway changes related to genotype and diet likely rests not in cell proliferation or cell death but in cell function and possibly cell morphology (oxidative stress and cytoskeletal regulation). Finally, these data in Lrp6 mutant mice also demonstrate that the mechanism of birth defect prevention by FA supplementation (reduction of NTD occurrence by amelioration versus increased embryonic loss) can vary not only with the genes associated with increased risk, but also with the type of mutation within those genes (i.e. LOF versus GOF). Clearly, a detailed understanding of genetic risk and interactions between folate metabolism and other developmentally important pathways will be required to optimize birth defect prevention strategies for individual families.
Animals
All procedures involving animals were carried out in accordance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals and were approved by the Institutional Animal Care and Use Committee at Weill Medical College of Cornell University. Gene-trap mice in which the Lrp6 locus was inactivated (7) have been backcrossed more than 12 generations to the C3H/HeJ background. Mice were housed in climate-controlled Thoren units with a 12 h light–dark cycle.
NTD phenotyping
Mating pairs of Lrp6+/− mice were maintained on a defined diet containing 10 or 2 ppm FA (Research Diets Inc., New Brunswick, NJ, USA) for two generations prior to tissue or embryo collection. Embryos from timed pregnant females were harvested at or near E13 and fixed in 4% paraformaldehyde to preserve embryos for phenotyping. Implantations were scored by visual inspection as undergoing resorption, early lethality (dead at harvest with development halted at least 24–48 h earlier) or as live embryos that displayed developmental staging comparable with wild-type littermates and signs of active cardiovascular circulation at the time of collection. Embryos were further scored as having one or more defects including spina bifida (open caudal neural tube), exencephaly (open cranial folds), caudal axis truncation and/or limb deformities. Genotyping of embryos and postnatal pups was performed by PCR as previously described using tissue from the embryonic yolk sac or tail snips, respectively (7). Statistical comparisons using chi-square analysis and Fisher's exact or Student's t-tests (two-tailed) were performed with Microsoft Excel and GraphPad QuickCalcs (http://graphpad.com/quickcalcs/chisquared1.cfm; http://graphpad.com/quickcalcs/contingency1.cfm, accessed April 2009). The threshold for significance was P < 0.05.
Immunohistochemistry and TUNEL labeling
Heterozygous pairs were placed in a mating cage in the evening and were separated the following morning, which was designated embryonic day 0.5 (E0.5). Embryos from Lrp6+/− × Lrp6+/− intercrosses within each diet group were harvested on E10 and yolk sacs were collected for genotyping. Embryos were fixed in 4% paraformaldehyde overnight at 4°C, and then transferred to 0.1 m PBS prior to paraffin processing (Tissue Tek 2000, Miles Laboratories). Embedded tissues were sectioned coronally at 6 µm, mounted on adhesive-coated slides (Fisher Scientific), deparaffinized and rehydrated. Antigen retrieval was performed with Reveal (BioCare Medical) and quenched in 3% hydrogen peroxide. Tissues were blocked in SNIPER (BioCare Medical) for 30 min at room temperature prior to incubation in anti-PH3 antibody (Upstate Biotechnology, 16-189, 1:1000) overnight at 4°C, to specifically label dividing cells in M-phase. Immunolabeling was visualized using a secondary antibody conjugated to a fluorophore (Alexa Fluor 488, Molecular Probes, A-11070, 1:500). Slides were cover slipped with DAPI mounting media (Vectastatin) and photographed on a Nikon Optiphot-2 compound microscope fitted with a Spot Insight CCD camera (Diagnostic Instruments). For TUNEL labeling, rehydrated sections were permeabilized with 20 μg/ml proteinase K for 15 min at room temperature and quenched with 3% hydrogen peroxide. The ApoTag Plus Apoptosis Detection kit (Millipore, S7101) was used per the manufacturer's instructions to label dying cells using the immunoperoxidase reaction. Slides were briefly (two dips) counterstained with hemotoxylin before they were dehydrated and cover slipped for imaging.
β-catenin stabilization assay
The levels of cytosolic β-catenin in WNT-stimulated cultured cells were measured as previously detailed (5,34), with the following modifications. Briefly, FA powder (Sigma) was dissolved in DMEM without FA (Specialty Media, Phillipsburg, NJ, USA) and culture media were prepared with 10% calf serum + DMEM with specific FA concentrations (0, 1, 4, 10, 50 or 100 µg FA/ml DMEM). Two hours after NIH3T3 cells were seeded in a six-well plate, growth media containing 10% calf serum+DMEM were replaced with culture media of specific FA concentrations. Cells were cultured for 72h in folate-specific media prior to assays, which were run as previously described (34). Cultures were incubated in vehicle with or without 40 ng recombinant WNT3a (R&D Systems, 1324-WN) for 2 h. Following collection of the cytosolic fraction, cell lysates were normalized for protein concentration using the BCA Assay (Pierce) and western transferred to nitrocellulose membranes. Blots were blocked at room temperature with 1% non-fat dairy milk for 1 h before incubation at 4°C overnight in primary antibody, either anti-β-catenin (Santa Cruz, sc-7963, 1:1000) or anti-Erk2 (Santa Cruz, sc-154, 1:5000) diluted in block solution. Blots were washed 2 × 15 min in TBS w/0.05% Tween-20 before incubation with horseradish peroxidase-conjugated secondary antibodies for 1 h at room temperature. Chemiluminescence reagents (Pierce, pico-34078 or femto-34096) were use for immunolabeled band detection. X-ray film exposures were scanned with an optical densitometer and analyzed using Quantity One software (Bio-Rad). Band densities of β-catenin were normalized for protein loading to the amount of Erk2 present in each lane.
Transfection and TopFlash reporter assay
A TCF/LEF in vitro reporter assay was used to examine the effect of FA on WNT-induced transcriptional activity. NIH3T3 cells (100 000 cells per well of a 24-well plate) were plated in DMEM containing 0, 1, 4, 10, 50 or 100 μg/ml FA. After 3 days, cells were transfected with 80 ng of TopFlash or FopFlash reporter plasmids using Lipofectamine according to the manufacturer's protocol (BioRad, #170-3350). Cells were allowed to recover 36 h in the FA-defined medium after which, either 0 or 200 ng of recombinant WNT3a (R&D Systems, 1324-WN) was added per well. Cultures were incubated another 8 h prior to collection and lysis of cells for luciferase reporter assay using a Microlumat Plus luminometer with automated sample injection (EG&G Berthold, LB96V). WNT activity (TopFlash) was normalized to a WNT-insensitive luciferase control (FopFlash) plasmid.
In situ assessment of canonical WNT activity
A TCF/LEF-LacZ reporter mouse line (35) was crossed with Lrp6 mutants and the progeny of Lpr6+/−::TCF-LacZ double-heterozygous parents were evaluated for canonical WNT activity in the cranial folds at E9.5. Embryos were fixed with 4% paraformaldehyde for 30min at 4°C, then washed three times for 20 min in 0.1 m PBS at 4°C before incubation in X-gal wash buffer (0.02% Igepal, 0.01% Na-deoxycholate, 2 mm MgCl2, 100 mm Na–phosphate) for 5 min at room temperature, transfered to X-gal staining solution [1 mg/ml X-Gal, 5 mm K3Fe(CN)6, 5 mm K4Fe(CN)6 in X-Gal wash buffer] and incubated at 37°C. After 30 min, embryos were rinsed in 0.1 m PBS, 3 × 5 min then 2 × 1 h and post-fixed with 4% paraformaldehyde overnight at 4°C. Images were collected with Leica Applications Suite software running a Leica DFC310 FX camera fitted to a Leica M165 FC stereomicroscope.
Tissue collection and microarray
For expression studies in adult tissues, approximately 0.5 cm3 of liver was excised from each of the experimental female mice and placed in RNA-Later (Ambion) solution at 4°C overnight to prevent RNA degradation. Embryonic tissues for comparative expression studies were collected from pregnant dams at E9.5, so that cranial tissues from the otic vesicle rostrally were placed in RNA-later solution and frozen at −80°C. Remaining tissues were genotyped and RNA was extracted from female Lrp6+/+ and Lrp6+/− littermates. The RNeasy Mini Kit (Qiagen) was used to isolate total RNA from liver and embryo tissues. This method included a DNAse treatment to digest genomic DNA followed by column purification. The RNA samples were used to make cRNA probes that were hybridized to the Affymetrix Mouse 430 2.0 expression array, which includes over 39 000 transcripts. Procedures were carried out according to Affymetrix protocols for single-round amplifications.
The design consisted of two groups; the first included four of each of the Lrp6 wild-type and heterozygous animals on control 2 ppm FA, while the other group was fed a 10 ppm FA diet. This design was treated as a two-way factorial arrangement. In this design, main effects as well as the interaction effect could be evaluated. However, the interaction effect was of primary interest here as this evaluates the differential impact of FA supplementation in Lrp6 wild-type and heterozygous animals.
Background correction, normalization and summarization of probe-level data
The ‘robust multichip analysis' method was used for background adjustment of perfect match (PM) probe intensities (36). With this method, model-based background-corrected PM signals were computed assuming a normal–exponential convolution model for the distribution of probe intensities. Probe intensities were corrected for global standardization, variance-stabilization and normality. The sample intensities were all brought on the same scale through standardization (scaling and centering) of each feature. To ensure that the assumptions of normality and homoscedasticity across the samples between experimental groups were met in our statistical model (e.g. when detecting differential expression), the data were transformed using the generalized log (also known as arcsinh(x)) (37,38). After transformation, the data were returned on an approximate base-2 log scale, where variances were approximately independent of the mean intensities. We applied a probe-specific probe set summarization algorithm to convert the previous normalized probe level signals into expression values. We used the ‘PM only’ probe-specific method, along with the ‘Medianpolish' summarization method (36).
Statistics on genotype–diet interaction effects
Bayesian hierarchical model selection
The interaction effect of FA supplementation with Lrp6 variants was evaluated with a specialized Bayesian hierarchical model known as ‘spike and slab’ regression, which was introduced by Lempers (39) and Mitchell and Beauchamp (40) as a Bayesian approach to model selection in linear regression models. The expression ‘spike and slab' refers to the prior for the regression coefficients used in their Bayesian hierarchy which assumed the regression coefficients were mutually independent with a two-point mixture distribution composed of a uniform flat distribution (the slab) and a degenerate distribution at zero (the spike). George and McCulloch (41) used a scale (variance) mixture of two normal distributions, which was highly advantageous and led to an efficient Gibbs sampling algorithm that heavily popularized the spike and slab approach. These were extended to the class of rescaled spike and slab models by Ishwaran and Rao (42). Rescaling the response by the square root of the sample size divided by the root mean square error led to a non-vanishing penalization effect, which, when used in tandem with a continuous bimodal prior, ensures many useful model selection properties for the posterior mean of the regression coefficients (42,43).
Recently, Ishwaran and Rao (43) looked in depth at the geometry of generalized ridge regression (GRR), a method introduced by Hoerl and Kennard (44) as a way to overcome correlated and ill-conditioned regression settings. This analysis showed that GRR possesses unique advantages in high dimensional correlated settings, i.e. the P bigger than n problem, but more interestingly, that weighted GRR (WGRR) regression could potentially be even more effective. Noting that the posterior mean from a rescaled spike and slab model is a type of WGRR estimator, they showed that these estimators, when coupled with dimension reduction, could be highly effective for prediction in high dimensional large P, small n problems.
Actual variable selection is achieved with a three-step process that includes: (i) pre-filtering of variables to a manageable dimension size (because P ? n), followed by (ii) spike and slab regression estimation, which is in turn followed by (iii) a non-negative least squares step. The spike and slab estimates have a selective shrinkage property so that only variables whose effects are truly null are estimated in a way that they are shrunk towards zero, i.e. the null, and away from true signal, which is not shrunken. Here true signal is estimated with a specialized (non-shrunk) generalized ridge estimator known as the minimum least squares estimator (43). The application of non-negative least squares shrinks spike and slab-regression GRR estimates to those that correspond to noise down to zero (43). This step simply allows one to make a formal decision about which GRR effects are truly noise versus signal, without the need to set an a priori significance level. The selective shrinkage property of spike and slab regression GRR estimates allows this last step to be particularly effective. As shown by Ishwaran and Rao (43), this three-step process also has optimal variable selection properties including variable selection consistency, i.e. with probability going to 1, only true signal is identified—i.e. no false positives or negatives. Although this is an asymptotic result, it also translates into good finite sample properties.
Interaction effect
An interaction effect was deemed important not only if it survived the above thresholding procedure, but also if at least one of its corresponding main effects were also found to be significant. Analysis of genotype–diet interactions identified genes that were differentially expressed between the wild-type and heterozygous states of Lrp6 and that differed between the 2 and the 10 ppm FA diets. All calculations were performed using a new R library called ‘SpikeSlab’ available from the R CRAN repository (www.cran.r-project.com).
Building consensus lists of genes
In our Bayesian hierarchical model selection approach, our interest is in generating a posterior distribution of the regression coefficients, from which we focus on the posterior mean, in order to determine which genes enter the model. Because the joint posterior distributions that are generated do not have closed form solutions, the coefficient estimation process requires approximating (sampling from) these joint posterior distributions by means of the Gibbs sampler and Markov chain Monte Carlo (MCMC) algorithm. Due to the stochastic nature of the algorithm used, we obtain slightly different lists of genes for each run of the MCMC algorithm. One way around this is to build a consensus list of all the genes that appear at a certain frequency over several outputted models. In this way, we generated a consensus list of 2195 genes for the embryo data in which all were found to co-vary 100% reproducibly (20 times out of 20 MCMC runs). Similarly, we built a consensus list of 1112 genes for the liver.
Curation
All interaction plots and functional pathway analyses were done with default IPA filters and after curation of the consensus lists. For the curation KIAA, RIKEN, UNKNOWN, PSEUDOGENES, PREDICTED and duplicated probes from the same gene with opposite coefficient signs were removed. Otherwise the median coefficient was taken for consistent duplicated probes. Final curated consensus lists consisted of 1650 genes for the embryo and 960 for the liver.
Pathway and network analysis
IPA software (Ingenuity Systems®, www.ingenuity.com) was used to identify biological pathways and networks defined by the interaction-significant genes. Affymetrix identifiers for these genes were uploaded into the software. Each gene identifier was mapped to its corresponding gene object in the IPA knowledge base. Differentially expressed genes were then mapped to the global molecular network that is developed from information in the Ingenuity Knowledge Base.
Many of the genes that mapped to the global molecular network were associated with a canonical pathway in the Ingenuity Knowledge Base and were thus eligible for canonical pathway analysis. Significance of the association between the data set and the canonical pathway was measured in two ways: (i) a ratio of the number of differentially expressed genes from the data set that map to the pathway divided by the total number of all the genes that exist in the canonical pathway, and (ii) Fischer's exact test was used to calculate a P-value for the probability that the association between the genes in the data set and the canonical pathway is explained by chance alone. Pathways passing the P-value threshold of 0.05 were considered significantly associated with our data set. IPA also associated many differentially expressed genes with networks in the Ingenuity Knowledge Base. Networks for these genes were then algorithmically generated based on their connectivity. A score that was the negative log of the P-value of the right-tailed Fisher's exact test was assigned for each network. This score takes into account the number of eligible genes in our data set and the size of the network to calculate the fit between each network and the genes in the data set.
SUPPLEMENTARY MATERIAL
Conflict of Interest statement. None declared.
FUNDING
This work was supported by the NIH (NS058979), The WCMC-TMHRI initiative to M.E.R., NIH (NRSA NS059562) to J.D.G. and NIH (HD037485) to J.H.N.
Supplementary Material
Supplementary Data
1. Harris M.J., Juriloff D.M. Mouse mutants with neural tube closure defects and their role in understanding human neural tube defects. Birth Defects Res. A Clin. Mol. Teratol. 2007;79:187–210. [PubMed]
2. Harris M.J., Juriloff D.M. An update to the list of mouse mutants with neural tube closure defects and advances toward a complete genetic perspective of neural tube closure. Birth Defects Res. A Clin. Mol. Teratol. 2010;88:653–669. [PubMed]
3. Gray J.D., Ross M.E. Mechanistic insights into folate supplementation from Crooked tail and other NTD-prone mutant mice. Birth Defects Res. A Clin. Mol. Teratol. 2009;85:314–321. [PMC free article] [PubMed]
4. Carter M., Ulrich S., Oofuji Y., Williams D.A., Ross M.E. Crooked tail (Cd) models human folate-responsive neural tube defects. Hum. Mol. Genet. 1999;8:2199–2204. [PubMed]
5. Carter M., Chen X., Slowinska B., Minnerath S., Glickstein S., Shi L., Campagne F., Weinstein H., Ross M.E. Crooked tail (Cd) model of human folate-responsive neural tube defects is mutated in Wnt coreceptor lipoprotein receptor-related protein 6. Proc. Natl Acad. Sci. USA. 2005;102:12843–12848. [PubMed]
6. Schweizer L., Varmus H. Wnt/Wingless signaling through beta-catenin requires the function of both LRP/Arrow and frizzled classes of receptors. BMC Cell Biol. 2003;4:4. [PMC free article] [PubMed]
7. Pinson K.I., Brennan J., Monkley S., Avery B.J., Skarnes W.C. An LDL-receptor-related protein mediates Wnt signalling in mice. Nature. 2000;407:535–538. [PubMed]
8. Kokubu C., Heinzmann U., Kokubu T., Sakai N., Kubota T., Kawai M., Wahl M.B., Galceran J., Grosschedl R., Ozono K., et al. Skeletal defects in ringelschwanz mutant mice reveal that Lrp6 is required for proper somitogenesis and osteogenesis. Development. 2004;131:5469–5480. [PubMed]
9. Ernest S., Carter M., Shao H., Hosack A., Lerner N., Colmenares C., Rosenblatt D.S., Pao Y.H., Ross M.E., Nadeau J.H. Parallel changes in metabolite and expression profiles in crooked-tail mutant and folate-reduced wild-type mice. Hum. Mol. Genet. 2006;15:3387–3393. [PubMed]
10. Copp A.J., Greene N.D., Murdoch J.N. The genetic basis of mammalian neurulation. Nat. Rev. Genet. 2003;4:784–793. [PubMed]
11. Beaudin A.E., Stover P.J. Folate-mediated one-carbon metabolism and neural tube defects: balancing genome synthesis and gene expression. Birth Defects Res. C Embryo Today. 2007;81:183–203. [PubMed]
12. Logan C.Y., Nusse R. The Wnt signaling pathway in development and disease. Annu. Rev. Cell Dev. Biol. 2004;20:781–810. [PubMed]
13. Yang Y. Growth and patterning in the limb: signaling gradients make the decision. Sci. Signal. 2009;2:pe3. [PubMed]
14. Zerlin M., Julius M.A., Kitajewski J. Wnt/Frizzled signaling in angiogenesis. Angiogenesis. 2008;11:63–69. [PubMed]
15. Kubota T., Michigami T., Ozono K. Wnt signaling in bone metabolism. J. Bone Miner. Metab. 2009;27:265–271. [PubMed]
16. Hackam A.S. The Wnt signaling pathway in retinal degenerations. IUBMB Life. 2005;57:381–388. [PubMed]
17. Finkelstein J.E., Hauser E.R., Leonard C.O., Brusilow S.W. Late-onset ornithine transcarbamylase deficiency in male patients. J. Pediatr. 1990;117:897–902. [PubMed]
18. Nijhout H.F., Reed M.C., Lam S.L., Shane B., Gregory J.F., 3rd, Ulrich C.M. In silico experimentation with a model of hepatic mitochondrial folate metabolism. Theor. Biol. Med. Model. 2006;3:40. [PMC free article] [PubMed]
19. MacFarlane A.J., Perry C.A., Girnary H.H., Gao D., Allen R.H., Stabler S.P., Shane B., Stover P.J. Mthfd1 is an essential gene in mice and alters biomarkers of impaired one-carbon metabolism. J. Biol. Chem. 2009;284:1533–1539. [PubMed]
20. Detrait E.R., George T.M., Etchevers H.C., Gilbert J.R., Vekemans M., Speer M.C. Human neural tube defects: developmental biology, epidemiology, and genetics. Neurotoxicol. Teratol. 2005;27:515–524. [PMC free article] [PubMed]
21. Hague W.M. Homocysteine and pregnancy. Best Pract. Res. Clin. Obstet. Gynaecol. 2003;17:459–469. [PubMed]
22. van Guldener C., Stehouwer C.D. Homocysteine-lowering treatment: an overview. Expert Opin. Pharmacother. 2001;2:1449–1460. [PubMed]
23. Ernest S., Christensen B., Gilfix B.M., Mamer O.A., Hosack A., Rodier M., Colmenares C., McGrath J., Bale A., Balling R., et al. Genetic and molecular control of folate-homocysteine metabolism in mutant mice. Mamm. Genome. 2002;13:259–267. [PubMed]
24. Greene N.D., Copp A.J. Inositol prevents folate-resistant neural tube defects in the mouse. Nat. Med. 1997;3:60–66. [PubMed]
25. Ross M.E. Wiley Interdiscip. Rev. Syst. Biol. Med. in press: 2010. Gene-environment interactions: folate metabolism and the embryonic nervous system. [PMC free article] [PubMed]
26. Dulbecco R., Freeman G. Plaque production by the polyoma virus. Virology. 1959;8:396–397. [PubMed]
27. Pike S.T., Rajendra R., Artzt K., Appling D.R. Mitochondrial C1-tetrahydrofolate synthase (MTHFD1L) supports the flow of mitochondrial one-carbon units into the methyl cycle in embryos. J. Biol. Chem. 2010;285:4612–4620. [PubMed]
28. Mato J.M., Corrales F.J., Lu S.C., Avila M.A. S-Adenosylmethionine: a control switch that regulates liver function. FASEB J. 2002;16:15–26. [PubMed]
29. Thompson M.D., Monga S.P. WNT/beta-catenin signaling in liver health and disease. Hepatology. 2007;45:1298–1305. [PubMed]
30. Nejak-Bowen K., Monga S.P. Wnt/beta-catenin signaling in hepatic organogenesis. Organogenesis. 2008;4:92–99. [PMC free article] [PubMed]
31. Loenen W.A. S-adenosylmethionine: jack of all trades and master of everything. Biochem. Soc. Trans. 2006;34:330–333. [PubMed]
32. Wallace H.M., Fraser A.V., Hughes A. A perspective of polyamine metabolism. Biochem. J. 2003;376:1–14. [PubMed]
33. Bistulfi G., Diegelman P., Foster B.A., Kramer D.L., Porter C.W., Smiraglia D.J. Polyamine biosynthesis impacts cellular folate requirements necessary to maintain S-adenosylmethionine and nucleotide pools. FASEB J. 2009;23:2888–2897. [PubMed]
34. Giarre M., Semenov M.V., Brown A.M. Wnt signaling stabilizes the dual-function protein beta-catenin in diverse cell types. Ann. N. Y. Acad. Sci. 1998;857:43–55. [PubMed]
35. Mohamed O.A., Clarke H.J., Dufort D. Beta-catenin signaling marks the prospective site of primitive streak formation in the mouse embryo. Dev. Dyn. 2004;231:416–424. [PubMed]
36. Irizarry R.A., Bolstad B.M., Collin F., Cope L.M., Hobbs B., Speed T.P. Summaries of Affymetrix GeneChip probe level data. Nucleic Acids Res. 2003;31:e15. [PMC free article] [PubMed]
37. Huber W., von Heydebreck A., Sultmann H., Poustka A., Vingron M. Variance stabilization applied to microarray data calibration and to the quantification of differential expression. Bioinformatics. 2002;18(Suppl. 1):S96–S104. [PubMed]
38. Durbin B.P., Hardin J.S., Hawkins D.M., Rocke D.M. A variance-stabilizing transformation for gene-expression microarray data. Bioinformatics. 2002;18(Suppl. 1):S105–S110. [PubMed]
39. Lempers F.B. Posterior Probabilities of Alternative Linear Models. Rotterdam: Rotterdam University Press; 1971.
40. Mitchell T.J., Beauchamp J.J. Bayesian variable selection in linear regression. J. Am. Stat. Assoc. 1988;83:1023–1036.
41. George E.I., McCullouch R.E. Variable selection via Gibbs sampling. J. Am. Stat. Assoc. 1993;88:881–889.
42. Ishwaran H., Rao J.S. Spike and slab gene selection for multigroup microarray data. J. Am. Stat. Assoc. 2005;100:764–780.
43. Ishwaran H., Rao J.S. Generalized ridge regression: geometry and computational solutions when p is larger than n. Roy. Stat. Soc. Ser. B Theor. Method. (under review.
44. Hoerl A.E., Kennard R.W. Ridge regression: Biased estimation for non-orthogonal problems. Technometrics. 1970;12:55–67.
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