Molecular Human Reproduction, Vol. 8, No. 5, 434-440,
May 2002
© 2002 European Society of Human Reproduction and Embryology
Embryology |
Proacrosin-deficient mice and zona pellucida modifications in an experimental model of multifactorial infertility
Institute of Human Genetics, University of Göttingen, Heinrich Düker Weg 12, D-37073 Göttingen, Germany
Abstract
In humans, male and female partners contribute more or less equally to the infertility problem. In 
20% of infertile couples, the concurrence of male and female factors is suggested to be responsible for infertility. Neither of these factors are known nor is there a model system to prove this assumption. We present such a model system in the mouse, in which the lack of acrosin in the male and modifications of the zona pellucida (ZP) in the female result in a significant reduction of the fertilization rate in vitro. We generated mice carrying a deletion in the proline-rich region (PRR) of the proacrosin gene, resulting in the absence of proacrosin in the homozygous PRR–/– male mouse. Under normal conditions, sperm from the proacrosin-deficient mice are still capable of ZP penetration and fertilization. In this study, modifications of the ZP of oocytes after superovulation were achieved by treatment with dimethylsulphoxide or aroclor-1254 or by in-vitro ageing. It is known that under these conditions, a time-dependent hardening of the ZP occurs. The rates of fertilization in vitro of treated and aged oocytes using sperm from PRR–/– mice were found to be significantly reduced when compared with those reached with wild-type sperm. The relevance of the acrosin status and ZP condition for fertilization success were further substantiated by the finding that the fertilization rate with PRR–/– sperm is affected by the thickness of the ZP. Our results demonstrate that the lack of acrosin in sperm in combination with modifications to the ZP can affect fertility and can be an experimental model for the study of unexplained infertility in human couples in which both male- and female-derived factors are suggested to be the underlying causes.
fertilization/infertility/sperm acrosin/zona pellucida
Introduction
It is suggested that in 20% of infertile couples, the combination of factors derived from both partners are responsible for their reproductive failure. Until now these factors have been unknown and it would be difficult to analyse them in the human. Therefore, establishment of mouse models in which both sexes contribute to the fertility problem could offer useful information for the subsequent management of infertile couples. In this study, we have established a mouse model in which factors derived from both sexes, namely acrosin-deficient sperm as a male factor and modifications of the zona pellucida (ZP) as a female factor, are involved in fertility disturbances.
Acrosin, an endoprotease with a trypsin-like substrate specificity, is localized in the acrosomal matrix as an enzymatically inactive zymogen, proacrosin, that is converted into the active form as a consequence of the acrosome reaction. The physiological role of acrosin in the fertilization process has long been believed to be the limited proteolysis of the ZP. Using homologous recombination, we and others (Baba et al., 1994
; Adham et al., 1997) have successfully produced male mice lacking acrosin in their sperm. However, these sperm can penetrate the ZP and fertilize oocytes. We have also shown that acrosin-deficient sperm have a selective disadvantage with respect to wild-type sperm. The acrosin-deficient sperm have a delay in ZP penetration when compared with wild-type sperm and IVF experiments with mixtures of wild-type and acrosin-deficient sperm resulted only in wild-type offspring. Furthermore, a reduced acrosin activity has been found in sperm of some infertile patients when compared with sperm from fertile volunteers (Schill and Henkel, 1999; Cui et al., 2000).
The ZP consists of three major proteins called ZP1, ZP2 and ZP3 (Eberspaecher et al., 2001). The functions of these proteins have been analysed in detail by homologous recombination (Rankin et al., 1999, 2001; Wassarman, 1999). The deletion of any of these genes results in severe disturbances of the ZP structure and infertility. In addition, modifications of the ZP by chemicals like dimethylsulphoxide (DMSO) or aroclor-1254 or ageing of the oocytes in vitro have been found to result in fertility disturbances due to ZP hardening (Vincent et al., 1990; Fukuda et al., 1992; Greenfeld et al., 1998). DMSO is widely used as a cryoprotectant and has been found to cause proteolytic modifications of the ZP glycoprotein ZP2 and inhibition of sperm binding (Vincent et al., 1990). These effects of DMSO are caused by premature exocytosis of the cortical granules, a process that is usually initiated on fertilization (Vincent et al., 1991). The hardening effect of DMSO on the mouse ZP requires the presence of an oocyte and is associated with a reduction in the number of cortical granules present.
Aroclor-1254 belongs to the polychlorinated biphenyls (PCBs) group. PCBs have been reported to adversely affect reproduction in laboratory and wild animals. Aroclor-1254 has been found to significantly reduce the number of fertilized oocytes due to ZP hardening. ZP hardening has also been observed in oocytes aged in vivo and in vitro (Nogues et al., 1988), and zona hardening appears to be an indicator of oocyte ageing. In rabbits and mice, the fertilization rate has been found to be reduced in ageing oocytes in a time-dependent manner (Fukuda et al., 1992; Adenot et al., 1997). In humans, zona hardening, although not readily quantifiable, may also be induced by in-vitro culture and by in-vivo ageing (De Vos and Steirteghem, 2000).
Here, we report results of reduced fertilization rates of oocytes with a modified ZP by proacrosin-deficient sperm as compared with wild-type sperm. It is clearly shown that female and male factors interact together, resulting in reduced fertility, while each factor alone is compensated by a normal counterpart.
Materials and methods
Construction of the proline-rich region (PRR) targeting vector
We have previously cloned and determined the restriction map of the genomic fragment containing the mouse proacrosin gene (Adham et al., 1997). To assemble the targeting vector, the 4 kb SalI/KpnI fragment containing exon 5 and the 3' flanking region of the gene (Figure 1A) was subcloned into SalI/KpnI restricted Bluescript vector (clone PRR1). The clone PRR1 was digested with BstXI to delete the 224 bp fragment coding the proline-rich domain. The XhoI/XbaI PGK–Neo cassette was isolated from the pPNT vector (Tybulewicz et al., 1991) and ligated with the BstXI-digested clone PRR1 after filling the end with Klenow enzyme (clone PRR2). The 5.5 kb EcoRI/SalI genomic fragment containing exons 1–4 was isolated from the cosmid clone and inserted in the EcoRI/SalI-digested clone PRR2 to yield the clone PRR3. Finally, the EcoRI/HindIII PGK–TK cassette was isolated from the pPNT vector and inserted in the SmaI-digested clone PRR3 by blunt end ligation to give the final targeting vector (Figure 1A). The targeting construct was linearized at the unique NotI site located in the Bluescript polylinker before electroporation.
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Embryonic stem cell culture and generation of chimeric mice
Embryonic stem (ES) cell line R1 (provided by Dr A.Nagy, Toronto, Canada) was cultured as previously described (Joyner, 1993
). Confluent plates were washed in phosphate-buffered saline (PBS) and trypsinized and the cells were suspended in the same buffer. Aliquots of this cell suspension were mixed with 50 µg linearized targeted vector and electroporated at 250 V and 500 µF using a Bio-Rad gene pulser apparatus (Bio-Rad, Munich, Germany). Cells were plated onto non-selective medium in the presence of G418-resistant embryonic mouse fibroblasts. Selection was applied using medium containing G418 at 350 µg/ml and gancyclovir (2 µmol/l). After 10 days of selection, individual drug-resistant clones were picked into 24-well trays. Three days later, individual recombinant ES clones were replicated into 24-well trays for freezing, isolation of genomic DNA and subsequent genotyping by Southern blot analysis. Chimeric mice from ES cells carrying the disrupted allele were generated by aggregating 10–15 compact ES cells between two 2.5-day-old embryos of the CD1 mouse strain as described (Joyner, 1993). The chimeric male mice were mated with 129/Sv and CD1 females to produce offspring on these backgrounds. Male and female heterozygous mice were genotyped by Southern blot and PCR analysis. PCR was performed according to standard protocols to discriminate wild-type and mutant alleles in the DNA from mouse tails. Primer sequences were as follows: F1 (PRR sense), 5'-TGGACTGGATTCCTTCCAAGA-3'; R1 (PRR antisense), 5'-TCTCAGCAAGAATGGAGGAGGGGC-3' (Klemm et al., 1990); R2 (pgk antisense), 5'-TCTCAGCCCAGAAAGCGAAGG-3' (Adham et al., 2001). Thermal cycling was carried out for 35 cycles of denaturation at 94°C for 1 min, annealing at 62°C for 30 s and elongation at 72°C for 30 s.
Southern blot analysis
For Southern blot analysis, genomic DNA was extracted from ES cells and mouse tails, digested with EcoRI, electrophoresed and blotted onto Hybond N membranes (Amersham, Freiburg, Germany). The blots were hybridized with a 32P-labelled 1.5 kb XbaI/EcoRI fragment (Figure 1A,B
). Hybridization was carried out at 65°C overnight in hybridization solution: 6xSSC, 5xDenhardts, 0.1% sodium dodecyl sulphate (SDS), 100 µg/ml denatured salmon sperm DNA. Filters were washed twice at 65°C to final stringency at 0.2xSSC/0.1% SDS (Adham et al., 2001).
RNA analysis
For Northern blot analysis, total RNA was extracted from testis using the RNA Now Kit (ITC Biotechnologies, Heidelberg, Germany) according to the manufacturer's recommendation. The RNA was size-fractionated by electrophoresis on a 1% agarose gel containing formaldehyde and blotted onto a nylon membrane (Amersham) (Sambrook et al., 1989). The membrane was hybridized with a random-primed proacrosin cDNA fragment (Klemm et al., 1990) under the same conditions used for Southern blot analysis. Rehybridization was carried out using a human elongation factor 2 cDNA probe (Rapp et al., 1987).
To verify the results of the Northern blot analysis, total RNA (10 µg) was reverse transcribed using the R1 primer. Synthesis of cDNA was performed using 200 IU of Superscript reverse transcriptase (Gibco BRL, Karlsruhe, Germany) and 40 IU of RNasin (Boehringer, Mannheim, Germany) according to the manufacturer's recommendation in a final volume of 20 µl. PCR was carried out with 2 µl of synthesized cDNA, 10 pmol each of reverse primer R1 and forward primer F1 and 3 IU of Taq polymerase. Cycling conditions were 30 s at 94° C, 30 s at 58° C and 30 s at 68° C, for 35 cycles.
Treatment of oocytes
Oocytes were recovered from adult CD1 mice by induction of superovulation with i.p. injection of 5 IU pregnant mare serum gonadotrophin (Intergonan 5 IU; Intervet, Tönisvorst, Germany) followed 48 h later by 5 IU HCG (Predalon; Organon, Oberschleißheim, Germany) i.p. (Hogan et al., 1986). For treatment of oocytes with DMSO or aroclor-1254, animals were killed 12.5 h after HCG injection. The oviducts were transferred immediately to 37°C prewarmed M2 medium (Sigma, Taufkirchen, Germany). For DMSO treatment, the cumulus mass was exposed to hyaluronidase (150 IU/ml; Sigma) for 2–5 min, and freed oocytes were transferred to M16 medium (Sigma) pre-equilibrated at 37°C and 5% CO2. Oocytes were pooled, counted and distributed among control and experimental groups as indicated in the `Results' section. The procedures were adopted to minimize temperature fluctuations and stress to oocytes. For experimental treatments, oocytes were transferred at time 0 to M16 medium with different concentrations of DMSO or aroclor-1254 (both Sigma) according to schedules described in the `Results' section. After exposure of oocytes to DMSO or aroclor-1254, the oocytes were washed three times in M16 medium. After treatment, the oocytes which showed spontaneous activation (8–10%) were removed to rule out the parthenogenetic activation of oocytes during treatment.
For ageing experiments, adult CD1 females were killed 12.5 h after HCG injection. Cumulus mass was released and oocytes were transferred to M16 medium pre-equilibrated at 37°C and 5% CO2 and incubated for different times according to schedules described in the `Results' section.
Measurement of ZP thickness
Different mouse strains were used for the determination of ZP thickness (129/Sv, C57/Bl, CD1, FVB, NMRI, Balb/C, DBA, SWR, Aj, NZW and Akr). Three 5-week-old females of each strain were superovulated as described above. At 12–14 h after HCG injection the oocytes were isolated by dissection of the oviduct in M2 medium (Sigma) and treatment with M2 containing hyaluronidase (150 IU/ml; Sigma) to remove the cumulus, washed in M2 and then maintained in M16 (Sigma). Measurements of ZP thickness were performed under an inverted Olympus BX60 light microscope (Olympus, Hamburg, Germany) at 400x magnification using the AnalySIS 3.0 soft imaging system. Fifteen oocytes per female were used for the measurements according to a previously described procedure for micromorphometric analysis (Michelmann et al., 1995).
Fertilization assay
Five wild-type and five mutant males on both genetic backgrounds were mated with CD1 females and the number of offspring was counted. For IVF, sexually mature male mice (wild-type and mutant mice on the hybrid CD1x129/Sv background) were used. Sperm were isolated from the cauda epididymis of each male group and capacitated in IVF medium (Medicult, Jyllinge, Denmark) at 37°C for 1.5 h. Female CD1 mice were superovulated. Oocytes and sperm (n = 105–106) were incubated for 1–6 h at 37°C under 5% CO2 in air in IVF medium (Hogan et al., 1986). At the end of incubation, the oocytes were washed three times in M16 medium and the oocytes which showed spontaneous activation were removed to rule out parthenogenetic activation during incubation with sperm. The oocytes were tested for the presence of male and female pronuclei after 5 h and the day after for development to the 2-cell stage with a Zeiss microscope.
Results
Targeted disruption of the proline-rich domain of the proacrosin gene
A replacement targeting vector was designed to delete the 224 bp BstXI fragment coding the proline-rich domain of the proacrosin gene. The fragment was replaced with the neomycin phosphotransferase II (Neo) gene under the control of the phosphoglycerate kinase promoter. Introduction of a negative selection marker, the herpex simplex virus thymidine kinase (TK) gene, at the end of the construct (Figure 1A) enabled us to use positive/negative selection (Joyner, 1993). The targeting vector was electroporated into the R1 ES cell line. Targeted integration to the proacrosin gene was verified by Southern blot analysis using an external hybridization probe located 3' to the targeting construct (Figure 1A). As expected for a homologous recombination event, the wild-type locus showed a 13.5 kb EcoRI fragment and the targeted locus a 15.2 kb EcoRI fragment (Figure 1B). Three clones which had undergone correct homologous recombination were obtained. These clones were aggregated independently between two CD1 embryos 2.5 days old to generate chimeric mice. Two male chimeras were obtained and both transmitted the targeted gene through their germ line to produce heterozygous male and female animals. In both backgrounds, mixed CD1x129/Sv and 129/Sv, heterozygous mice were viable and fertile and showed no abnormalities. Heterozygous animals were mated and 25% of the offspring were homozygous for the mutant allele.
Expression analysis of the proacrosin gene
Northern blot with total RNA prepared from testes of mice with the three genotypes (+/+, +/–, –/–) showed that the full-length proacrosin cDNA sequences produced a 1.6 kb transcript in testicular RNA of PRR+/+ and PRR+/– but not in RNA of PRR–/– mice (Figure 1C). Rehybridization of the Northern blots with the 224 bp BstXI cDNA fragment revealed the same results. The Northern blot was rehybridized with human elongation factor 2 cDNA to demonstrate the integrity of RNA. To verify Northern blot results, RT–PCR with testicular RNA of mice with the three genotypes was performed and no PCR product could be amplified from RNA of PRR–/– mice (data not shown). From these results, it can be concluded that the insertion of the neomycin sequence in exon 5 leads to instability of the proacrosin mRNA.
Analysis of fertility of PRR–/– mice
To investigate the consequences of proacrosin gene disruption on male fertility, we intercrossed 10 PRR–/– males on the CD1x129/Sv mixed and 129/Sv background with five wild-type females for 3 months. All matings of PRR–/– males on both backgrounds were productive and the average litter size (12.1 for CD1x129/Sv and 6.7 for 129/Sv) was not significantly altered as compared with the breeding of wild-type littermates with wild-type females. Consistent with previous results (Adham et al., 1997), a significant delay (P < 0.05) in the penetration of ZP was observed in IVF assays using sperm from PRR–/– mice compared with that from wild-type mice (Figure 2A).
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Fertilization of oocytes with modified ZP by proacrosin-deficient sperm
To examine the ability of PRR–/– mouse sperm to interact with oocytes with a modified ZP, the oocytes were treated with DMSO or aroclor-1254 before IVF. Furthermore, the ability of sperm lacking proacrosin to fertilize aged oocytes was examined.
A total of 985 oocytes (from three separate experiments) were placed into 0.6, 0.8, 1.0 or 1.2 mol/l DMSO in M16 at 37°C for 30 min. Oocytes were then rinsed thoroughly through three washes of medium before IVF. The treated oocytes were divided into two groups. One group was incubated with wild-type sperm, while the other was incubated with sperm lacking proacrosin for 6 h. As compared with wild-type sperm (fertilization rates of 89.6% for 0.6 mol/l DMSO and 84% for 0.8 mol/l DMSO), significant reductions (P < 0.05) in fertilization rates were observed for IVF using sperm lacking proacrosin with oocytes treated with 0.6 and 0.8 mol/l DMSO (60% for 0.6 mol/l and 52% for 0.8 mol/l; Figure 2B).
A total of 877 oocytes with cumulus mass (from three separate experiments) were exposed to 0.1, 1.0 or 10 µg/ml aroclor-1254 for 6 h. Thereafter, oocytes were washed and incubated with wild-type or mutant sperm lacking proacrosin. For wild-type sperm, fertilization rates of 28 and 25% for 1.0 and 10 µg/ml aroclor-1254 respectively were obtained. As compared with wild-type sperm, a significant reduction (P < 0.05) in fertilization rates was found in IVF assays with sperm lacking proacrosin and oocytes treated with aroclor-1254 (16% for 1.0 µg/ml and 12% for 10 µg/ml; Figure 2C).
To examine the effect of ZP hardening due to ageing of oocytes in vitro, 843 oocytes were prepared 12 h after HCG injection. Oocytes were cultured for 0, 2, 6 or 8 h and then divided into two groups and incubated with either wild-type sperm or sperm from PRR–/– mice. The results are shown in figure 2D. The sperm from PRR–/– mice showed a decreased fertilization rate of oocytes cultured in vitro (33% for 6h and 21% for 8 h) as compared with wild-type sperm (68% for 6 h and 47% for 8 h; P < 0.05).
Fertilization of oocytes differing in ZP thickness
For different mouse strains, ZP thickness was determined (Figure 3) and compared using Student's t-test (Statistica software program; StatSoft Inc, Tusla, USA). A significant difference between the ZP thickness of oocytes from CD1 and DBA strains was found, although the diameter of the oocytes from these two strains showed no significant differences (data not shown). These two strains were therefore used for the IVF assays. Oocytes from CD1 and DBA strains were incubated with wild-type and proacrosin-deficient sperm for 1.5 and 3 h respectively. After incubation, the oocytes were washed intensively in M16 and incubated in 5% CO2 at 37°C. Fertilization rate was calculated as the percentage of oocytes which developed to the 2-cell stage. A significant difference was found between the fertilization rates of CD1 and DBA oocytes incubated for 1.5 h with wild-type and proacrosin-deficient sperm respectively (A versus B as compared with C versus D; Figure 4). These results indicate that the delay in fertilization by proacrosin-deficient sperm is more pronounced with CD1 oocytes which have a thicker ZP.
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Discussion
Acrosin is a typical serine protease and as with other members of the serine protease superfamily, the coding sequence of the proacrosin gene is spread over five exons (Klemm et al., 1990). Exons 2, 3 and 5 code for the three active sites (His, Asp and Ser) forming the charge relay system responsible for the hydrolytic capacity of the enzyme. Similar to other serine proteases like prothrombin or tissue plasminogen activator, proacrosin has acquired an additional functional domain, the proline-rich domain at the carboxy-terminal. Klemm et al. have calculated that in evolution, gene duplication generating the ancestral proacrosin gene took place 1 billion years ago and in mammals the proacrosin structure at the genomic and protein levels is highly conserved (Klemm et al., 1991). Since the discovery of proacrosin, different functions of its enzymatically active forms 
- and ß-acrosin have been postulated. It was assumed that acrosin is involved in sperm–oocyte recognition and binding, ZP penetration and even very early embryogenesis (Klemm et al., 1991; McLeskey et al., 1998; Jansen et al., 2001). However, in 1994 it was shown that proacrosin-deficient male mice are fertile (Baba et al., 1994). These results were confirmed by our own data obtained with proacrosin knock-out mice. Although the knock-out mice produced by both groups were found to not exhibit proacrosin protease activity in sperm, at the transcriptional level 1.6 and 3.2 kb fusion transcripts were obtained with testicular RNA in Northern blot analysis using a 1.4 kb proacrosin full length cDNA (Adham et al., 1997). The knock-out mouse reported here lacks the proacrosin transcript and is therefore a real knock-out for the proacrosin gene. Similar results to those of others (Baba et al., 1994, Adham et al., 1997) were obtained.
Adham et al. have shown that proacrosin-deficient sperm have a selective disadvantage in fertilization as compared with wild-type sperm (Adham et al., 1997). Proacrosin-deficient sperm show delayed penetration of ZP, and in competition with wild-type sperm in IVF experiments they have no chance to fertilize oocytes. The delay in fertilization with proacrosin-deficient sperm was confirmed with our knock-out mice, which were generated on two different genetic backgrounds, namely CD1x129/Sv mixed and 129/Sv. To examine the effect of ZP thickness on this fertilization delay, IVF assays were performed using oocytes with different thicknesses of ZP and sperm from wild-type and proacrosin-deficient mice. We measured ZP thickness of oocytes from different strains of mice. The ZP of oocytes from strain CD1 was found to be significantly thicker than that from strain DBA. Incubation of CD1 and DBA oocytes with wild-type sperm did not result in fertilization differences, but incubation with acrosin-deficient sperm resulted in significantly reduced fertilization with CD1 oocytes as compared with DBA oocytes. This result indicates that there is reduced fertilization with proacrosin-deficient sperm for oocytes with thicker ZP.
Taking into consideration the observation of Adham et al. that the proacrosin-deficient sperm have a selective disadvantage in ZP penetration as compared with wild-type sperm (Adham et al., 1997), it can be suggested that proacrosin might play a role in sperm competition. In polygamous species, sperm of different males could differ in fertilization success depending on their acrosin activity. These differences could be due to mutations in the proacrosin gene. In the human, reduced acrosin activity has been found in sperm of infertile men, although mutations in the proacrosin gene of infertile men have not yet been described. While some groups have suggested that acrosin activity is an important index for the evaluation of human male fertility (Shimizu et al., 1997; Schill and Henkel, 1999; Cui et al., 2000), other groups have demonstrated that acrosin activity of human sperm does not correlate with fertilization rates in vitro (Sharma et al., 1994; Yang et al., 1994; Yie et al., 1996). It is possible that reduced acrosin activity in the male in combination with female factors, such as thickness of the ZP, could play a role in human fertility. It has been shown that in IVF trials with normal semen, the ZP of fertilizable oocytes is significantly thinner than that of oocytes which cannot be fertilized (Check et al., 1998).
Two hypotheses for delayed fertilization by proacrosin-deficient sperm have been discussed. The first hypothesis considered a role for proacrosin in the acrosome reaction (Yamagata et al., 1998). It was shown that the delayed sperm penetration of the ZP in proacrosin-deficient mice results from the altered role of protein dispersal from the acrosome. Thus, proacrosin likely accelerates the dispersal of proteins from the sperm acrosome. The second hypothesis discussed the role of proacrosin in the binding of sperm to the ZP (Moreno et al., 1999; Furlong et al., 2000; Howes et al., 2001). Howes et al. observed that interactions between the ZP2 glycoprotein and proacrosin occurs during secondary binding of sperm to the ZP in the fertilization process (Howes et al., 2001). It was demonstrated that ZP2 binds to proacrosin-deficient sperm considerably less effectively than to wild-type sperm.
It has been believed that modifications of ZP concerning structure, elasticity and thickness could reduce the chance of sperm to interact with the ZP and fertilize the oocytes (Rankin and Dean, 1996; Check et al., 1998; Magerkurth et al., 1999). Together, delayed fertilization due to proacrosin deficiency and improper sperm–oocyte interaction due to ZP modification could result in the significant reduction of fertilization rate seen in our model system.
Our results support the hypothesis that modifications of the ZP of the oocyte, leading to hardening or thickness, in combination with proacrosin-deficiency of sperm, reduce fertilization success in mice. With respect to the human, it might be possible that sperm with reduced acrosin activity in combination with oocytes with a modified ZP could result in so-called unexplained infertility. Therefore, proacrosin-deficient mice provide an useful experimental model for the study of male and female factors in couples affected by unexplained infertility.
Acknowledgements
We thank H.W.Michelmann for his help with ZP measurement, S.Wolf for technical assistance and Angelika Winkler for secretarial assistance. This work was supported by a grant of the Deutsche Forschungsgesellschaft to W.E. (SFB 271).
Notes
1 To whom correspondence should be addressed. E-mail: wengel{at}gwdg.de 
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Submitted on October 25, 2001; accepted on February 11, 2002.
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