Non-Mendelian inheritance during inbreeding of Cav3.2 and Cav2.3 deficient mice

The mating of 77 heterozygous pairs (Cav3.2[+|−] x Cav3.2[+|−]) revealed a significant deviation of genotype distribution from Mendelian inheritance in weaned pups. The mating of 14 pairs (Cav3.2[−|−] female x Cav3.2[+|−] male) and 8 pairs (Cav3.2[+|−] female x Cav3.2[−|−] male) confirmed the significant reduction of deficient homozygous Cav3.2[−|−] pups, leading to the conclusion that prenatal lethality may occur, when one or both alleles, encoding the Cav3.2T-type Ca2+ channel, are missing. Also, the mating of 63 heterozygous pairs (Cav2.3[+|−] x Cav2.3[+|−]) revealed a significant deviation of genotype distribution from Mendelian inheritance in weaned pups, but only for heterozygous male mice, leading to the conclusion that compensation may only occur for Cav2.3[−|−] male mice lacking both alleles of the R-type Ca2+ channel. During the mating of heterozygous parents, the number of female mice within the weaned population does not deviate from the expected Mendelian inheritance. During prenatal development, both, T- and R-type Ca2+ currents are higher expressed in some tissues than postnatally. It will be discussed that the function of voltage-gated Ca2+ channels during prenatal development must be investigated in more detail, not least to understand devastative diseases like developmental epileptic encephalopathies (DEE).

Genotyping of mice. Tail biopsies from 21 day old mice were used for the extraction of genomic DNA.
Contaminating protein and RNA were enzymatically digested by protease and RNAse, respectively.
For the PCR amplification of indicative Ca v 3.2 DNA-fragments, about 1 µg DNA was introduced and amplified with the WT-forward primer 5′-ATT CAA GGG CTT CCA CAG GGT A-3′ and the WT-reverse / KOforward primers 5′-CAT CTC AGG GCC TCT GGA CCA C-3′ and KO-reverse primer 5′-GCT AAA GCG CAT GCT CCA GAC TG-3′ 17  PCRs for both genotypings were performed using a DNAEngine Peltier thermal cycler (BioRad, Germany) or a PTC-200 Peltier thermal cycler (MJ Research, Biozym Diagnostik, Germany) with the initial denaturation (94 °C for 10 min) followed by 34 cycles (denaturation at 94 °C for 60 s, annealing at 60 °C for 90 s, extension at 72 °C 4 min) and final extension at 72 °C for 10 min. The PCR products were separated by agarose gel electrophoresis and fluorescent bands were detected on a Herolab UVT-28 M transilluminator by UV irradiation (312 nm excitation wavelength) (Fig. 1).

Data analysis and statistics.
The assumption of normal distribution of data was tested by the Kolmogorov-Smirnov test. The Student's t-test was used for the comparison of two experimental groups. Data were analyzed by one-way ANOVA for multiple comparisons. Statistical analysis was performed with the GraphPad Prism software (version 8). The Mendelian genotype distributions were tested by a chi-square test for Mendelian ratios by the use of the algorithm on the web page https ://www.ihh.kvl.dk/htm/kc/popge n/genet ik/apple ts/ki.htm. The calculated chi-square values were evaluated and converted into a probability (p-)value by using tables 4-1 19 .
Ethical approval. All applicable international, national and institutional guidelines for the care and use of animals were followed.

Results
During the routine breeding for Ca v 3.2-deficient mice over a time period of 12 years, the number of genotyped knockout mice (Fig. 1) was severely under represented (the distribution for the genotypes within each group of born mice is summarized in Supplement-table S1 to S3). The consecutive systematic evaluation of wild type, heterozygous and Ca v 3.2-deficient pups from 99 breeding pairs (Table 1) revealed a highly significant reduction of heterozygous and even more significant reduction of homozygous Ca v 3.2-deficient mice. For comparison, the breeding history was also analyzed for the Ca v 2.3-deficient mouse lines.  17 , suggesting a compensatory upregulation of these channels.

Analysis of the genotypes for
PCR-genotyping results. The genotyping of the litter was performed postnatally by PCR on total DNA isolated from tail biopsies (Fig. 1C,D). The amplified DNA fragments were clearly separated from each other by agarose gel electrophoresis to ensure exact genotype identification (Fig. 1A). The oligonucleotide primers were designed to detect easily and precisely DNA fragments from wild type and Ca v 3.2 deficient mice. The intensities of DNA fragments were strong enough to identify wild type (3 mice plus 1 reference DNA), heterozygous (11 mice plus 1 reference DNA) and Ca v 3.2-deficient candidates (3 candidates plus 1 reference DNA) (Fig. 1A). The negative control (no tail DNA included) did not contain DNA fragments of the references sizes (480 bp for wt or 330 bp for KO). . Consecutively, the observed genotype distribution differed from the expected Mendelian ratio and the deviation was significant as deduced from the Chi-squared derived (CHSQ) p-values for both, males (p < 0.001) and females (p < 0.01) ( Table 1). For another statistical comparison, the mean values of pups per breeding for each sex and genotype were calculated ( Fig. 2A). Heterozygous mice from both sexes were still superior in number (1.3-fold for males and 1.6-fold for females), but did not reach the two-fold majority predicted from theory. When comparing the expected two-fold number with the real number of heterozygous pups, it was significantly reduced for both sexes (p = 0.0002 for males and p = 0.0023 for females) (see red stars in Fig. 2A).

Distribution of individual genotypes in
When comparing the homozygous Ca v 3.2-deficient mice from both sexes with the homozygous Ca v 3.2-competent mice, they were significantly reduced as well (p < 0.001 for males and p = 0.009 for females) ( Fig. 2A).
During 22 breeding events, one parent was heterozygote and the other homozygote. According to Gregor Mendel, half of the pups should be heterozygotes and the other half homozygote for Ca v 3.2-deficiency. However, in both sexes, the number of Ca v 3.2 deficient mice was reduced. While 36 heterozygous male pups were born, only 17 homozygous Cav3.2 null mice were born (for females 24 heterozygous pups and only 13 null mice). Thus, the ratio was significant reduced for the male Ca v 3.2-deficient mice (p = 0.007 for males and p = 0.063 for females) (Fig. 2B), leading to the conclusion that the null hypothesis has to be rejected and that as an alternative hypothesis, the inactivation of the Ca v 3.2 gene in mice may cause prenatal lethality, which does not penetrate to all but to many of the individuals.
Analysis of the genotypes for Ca v 2.3/R-type mice. Next, we were interested in the breeding results for Ca v 2.3-deficient mice, which are known to exhibit a deficit in the flagellar speed of moving sperms as well as in the acrosome reaction 21,22 . The Ca v 2.3 channels mediating R-type Ca 2+ currents have been inactivated in mice by homologous recombination and by successive breeding with cre-deleter mice 23 . The deletion of exon 2 of the murine cacna1e gene was designed to delete the IS1 region in the channel protein and to impair the synthesis of a functional full length channel transcript. It caused the complete loss of Ca v 2.3 channel protein as proven  23 . After inbreeding of heterozygous parents, the genotyping of the litter was performed postnatally by PCR on total DNA isolated from tail biopsies (Fig. 1B,C). The oligonucleotide primers were designed to detect reliably DNA fragments from all genotypes. The intensities of DNA fragments were sufficiently strong to identify wild type (6 mice plus 1 reference DNA), heterozygous (3 mice plus 1 reference DNA) and Ca v 2.3-deficient candidates (7 www.nature.com/scientificreports/ candidates plus 1 reference DNA) (Fig. 1B). The negative control (no tail DNA included) did not contain DNA fragments of the references sizes (1056 bp for wt or 86 bp for KO).

Distribution of individual genotypes in the mouse lines for the Ca v 2.3 gene inactivation.
During 63 breeding events from heterozygous parents, the mean litter size did not differ between male (3.6 ± 0.2) and female pups (3.3 ± 0.2) (  Fig. 3), leading to the conclusion that in male mice the null hypothesis has to be rejected and that as an alternative hypothesis the inactivation of one allele of Ca v 2.3 must cause developmental problems, leading to a clear reduction of heterozygous male pups, which may only be compensated when both Ca v 2.3 alleles are missing.

Discussion
Our most important findings are related to deviations of genotype distributions from the expected normal Mendelian inheritance among weaned pups. For both Ca 2+ channel types, the genotypes of the weaned offspring were significantly different from the expected Mendelian ratios.
To demonstrate that one may exclude a false genotyping, examples for the determination by PCR were included showing that indicative DNA-fragments could reliably be amplified. Further, an erroneous determination of sex can be excluded, because the sex determination was performed by an experienced coworker. If a continuous miss-determination of male heterozygous pups would have occurred, the number of heterozygote female pups must have been significantly elevated from the expected Mendelian ratio, which is not the case.
Another mistake, which could explain the "non-Mendelian ratios", would be if unintentionally the breeding pairs would not have been all heterozygous. We can exclude it, as all parents were re-genotyped when the breeding was started. Further, we checked the data for the Ca v 3. So far, only for the ion conducting Ca v α1 subunit of the cardiac L-type Ca 2+ channel a prenatal lethality is known 25 . No viable Ca v 1.2(−|−) mice were born, but the number of heterozygous pups was normal, corresponding to the expected Mendelian ratio. The developing Ca v 1.2-deficient pups died before day 14.5 postcoitum (p.c.) but up to day 12.5 p.c., the embryonic hearts contracted with identical frequency in wild type, heterozygous and homozygous Ca v 1.2 deficient mice. So far, it has remained unclear, which unidentified L-type like Ca 2+ current may enable the normal prenatal beating between day 12.5 and 14.5 p.c. in Ca v 1.2-deficient mice 25,26 . www.nature.com/scientificreports/ For the Ca v 3.2-deficient matings, a continuous reduction in the offspring number was observed for both sexes, when one or both alleles were inactivated in the pups. It is currently unknown and would be interesting to investigate, why the lack of the Ca v 3.2 allele causes prenatal lethality in some but not in all cases.
Ca v 3.2 belongs to the subfamily of low-voltage activated T-type Ca 2+ channels. They are expressed in many developing tissues and involved in regulating cell proliferation, differentiation, growth and death 27 . Both, the development of T-type channel isotypes and the development of electrophysiologically defined T-type currents reveals higher levels during embryonic states compared to the postnatal development (see Fig. 1 in 27 . There is sufficient evidence for a high expression of T-type Ca 2+ channels in embryonic tissues at the molecular level 28 , which appears to be especially important for cardiac 29,30 and neuronal development 31,32 . Using information from the gnomAD data base, which quantifies the functional constraints for human genes, CACNA1H is not under significant functional constraint in the human population, though no individuals with homozygous loss of function alleles have been observed. Its o/e number with 0.38 (CI 0.28-0.5) is high, illustrating that the number of observed per expected (o/e) nucleotide variants found indicates a much higher functional constraint for CACNA1E, which is among the most constrained genes in the human genome with an o/e value of only 0.07 (CI 0.04-0.12).
While for the inherited mutations in humans, the functional constraints for the CACNA1E are much higher than for the CACNA1H gene, it does not seem to be the case for the investigated mouse models in the present study. The investigation of the role of the cacna1e gene in a neurotoxin Parkinson's mouse model revealed that the Cav2.3 knockout even reduced activity-associated nigral somatic Ca 2+ signals and Ca 2+ -dependent afterhyperpolarizations, leading to full protection from degeneration in vivo [2a].
On the other side, the o/e evaluation for the CACNA1E gene in the gnomAD data base fits well with the observation that de novo mutations in CACNA1E are critical. Recently, for Ca v 2.3 in 30 children de novo gainof-function mutations were identified, which cause developmental and epileptic encephalopathy with contractures, macrocephaly and dyskinesias 33 ). These disturbances in addition cause early death in the young patients.
The ion conducting subunit Ca v 2.3 forms the central pore of the pharmacoresistant R-type Ca 2+ channels, which also exhibit higher expression levels during prenatal development than postnatally 34,35 . The sex specific effect of one allele loss in heterozygotes may relate to the function of Ca v 2.3 during acrosome formation 21,22 . Sperms lacking Ca v 2.3 show altered Ca 2+ responses, a reduced acrosome reaction and a strong subfertility phenotype 36 . If the loss of one Ca v 2.3 allele affects the acrosome reaction substantially, the loss of both alleles in homozygous KOs could have triggered a corresponding compensation reaction, e.g. by upregulation of another voltage-gated Ca 2+ channel.
Probably the sex-selective deviation from the Mendelian ratio may include sex-specific hormonal effects, similar as it was reported for effects of Zn 2+ ions on glucose homeostasis 37 .
In the literature, paradoxical inheritance with heterozygosity has been listed as one out of ten different non-Mendelian inheritance patterns 38 . Such rare cases of unusual segregation patterns are found in some specific diseases, as for example for glaucoma involving the K423E allele of TIGR (trabecular meshwork-inducible glucocorticoid response) gene, which is only seen in heterozygotes 39  www.nature.com/scientificreports/ are reported in the same review, which are related to a defect in the ephrin-B1 gene and to the craniofrontonasal syndrome, for which even heterozygous females are more severely affected than hemizygous mutant males 40,41 .

Conclusion and future perspectives
Our findings show that in depth investigations are needed to understand the prenatal developmental role of voltage-gated Ca 2+ channels. For mutations of the human Ca v 2.3 R-type Ca 2+ channel several gain-of-function mutations have been reported and they severely change the juvenile development during the mentioned developmental and epileptic encephalopathy 33 . A better understanding of this complex disease would help to find a better therapy for treating the children, which have a low life time expectancy.