## Introduction

The human genetic study of infertility has historically classified male infertility and female infertility as distinct diseases, leading to the assembly of many separate cohorts for the study of sex-specific reproductive processes1,2,3,4. However, numerous molecular and physiological mechanisms of fertility regulation are shared between male and female mammals5. For instance, programmed germ cell degeneration is a pervasive part of gonadal biology in both sexes6,7. In human males, roughly 80% of the meiotic descendants of spermatogonial stem cells undergo apoptosis prior to ever becoming mature spermatozoa8. Likewise, human females are born with ~500,000 oocytes and ovulate roughly 400 times after menarche. However, only roughly 1000 oocytes survive the sojourn to menopause, representing colossal germ cell loss not attributable to ovulation9. This ratio of surviving:apoptotic germ cells differs between species, but is narrowly maintained within species8,10. The principles that govern the loss versus survival of given germ cells are poorly understood.

Defects in germ cell development intrinsic to the gonad are defined as primary gonadal dysfunction. Primary gonadal dysfunction — which manifests as early idiopathic menopause in women and oligo-/azoo-spermia in men — is a subset of the infertility phenotype that is tractable for human genetic analysis and has a prevalence of at least 1% in adult males and females11,12. We previously identified a reproducible association between rare copy number variant (CNV) burden and oligo-spermia and azoo-spermia in men13,14. One of several candidate loci from this study included the complement regulatory CUB and Sushi multiple domains 1 (CSMD1) gene.

The primary protein sequence of CSMD1 shares homology with complement-interacting proteins15. Complement acts as an inflammatory/phagocytic signal in the innate immune system16, and previous work has shown that classical complement components C1q and C3 are also responsible for microglia-mediated phagocytosis of excess neuronal cells in a normal post-natal developmental process known as synaptic pruning17. Common variants in CSMD1 (refs. 18,19) and complement C4 (ref. 20) have also been associated with schizophrenia in independent, well-powered human association studies. Furthermore, some of the most significantly associated variants previously associated with azoospermia include the greater MHC locus, which encompasses complement C2, C4, and factor B21,22. CSMD1 is also known to inhibit the classical complement pathway in vitro15,23.

In this study, we incorporate array and exome sequencing data from a large cohort of early idiopathic menopause from the Women’s Health Initiative24 to search for novel, shared factors required for normal gonadal function in both sexes, identifying an association with the gene CSMD1 in male and female gonadal dysfunction, and replicate our findings with samples from the UK Biobank25. We characterize the expression patterns of CSMD1 in female and male gonads and measure morphological and reproductive traits in Csmd1-knockout mice, thereby adding a level of functional support to our genetic findings. Finally, to consolidate the putative roles of complement with Csmd1-mediated pathology, we investigate the in situ abundance of macrophages and complement component C3 in Csmd1-wildtype versus Csmd1-null tissues. Our findings highlight the value of human genetic analysis as an entry point into surprising and previously unappreciated pathways in disease processes — in this case, a novel connection between of complement-related processes and gonadal function.

## Results

### CSMD1 is associated with gonadal failure in both sexes

Due to the strong purifying selection against infertility mutations, we hypothesized that male and female gonadal dysfunction are driven largely by rare mutation events. To test this hypothesis, we obtained SNP array and phenotype data from 12,002 women (515 cases of early idiopathic menopause vs. 11,487 normal menopause controls) and 2,072 men (321 cases of oligo-spermia or azoo-spermia vs. 1,751 normospermic controls) with documented reproductive health history. Due to reduced linkage disequilibrium between common SNPs and rare variants, we instead leveraged the SNP log R ratios and B-allele frequencies to perform ab initio discovery of CNVs that occupy the entire allele frequency spectrum (Supplementary Data 1). We performed rigorous call and sample QC with emphasis on high confidence calls based on established methods (see Methods section13,14,26, Supplementary Fig. 1). We then applied filters to enrich for rare, deleterious CNVs. We used these CNVs to perform a gene-based, case-control rare variant association separately in males and females. This approach allows for interrogation across the genome with a substantially lower multiple hypothesis burden than is required for traditional common-variant GWAS.

Our rare variant association study identified a significant association between early idiopathic menopause and deletions overlapping the CSMD1 gene located on chromosome 8p23.2 (OR = 16; PLINK nominal p-value = 4.0 × 10−4; PLINK genome-wide p-value = 0.015; Fig. 1, Supplementary Tables 1, 2, Supplementary Data 2). This association signal replicated in GEMINI13, our smaller cohort of male oligo-/azoo-spermia cases (OR = 3.3; PLINK nominal p-value = 6.5 × 10−3). This CNV association is driven by an enrichment of rare deletions in cases, all of which are clustered at the 5′ end of the gene within introns 1–3 (5′-deletions; Fig. 1a).

To further replicate the association between deletions in CSMD1 and risk for gonadal dysfunction, we assembled an independent female early idiopathic menopause case-control cohort using the UK Biobank (see Methods section). After CNV QC and rigorous case/control selection, we obtained a cohort of 63,064 women with both reliable phenotype data and CNV calls (1,873 cases versus 59,947 controls). We again observed a significant association between early menopause and rare 5′-deletions of CSMD1 (OR = 3.03, logistic regression p-value < 5 × 10−4, Fig. 1a, b). To summarize the overall risk conferred by rare CSMD1 5′-deletions of all sizes, we performed a meta-analysis across all three cohorts (OR = 3.6 95% CI [2.14−6.01]; meta-analysis logistic regression p-value = 1.2 × 10−6; Fig. 1c; Supplementary Table 1).

We further tested our association using genotypes ascertained by an orthogonal genotyping modality, by analyzing rare (MAF < 0.01) CSMD1 single nucleotide variants (SNVs) from exome sequencing performed on a subset of the WHI cohort (n = 1526). We performed a single-locus quantitative trait analysis and found a statistically significant association between rare, deleterious CSMD1 SNVs and age at menopause (SKAT single-locus p-value < 5 × 10−3; Fig. 1, see Methods section). The CSMD1 protein product consists almost entirely of alternating/repeating CUB (complement C1r/C1s, Uegf, Bmp1) and Sushi/CCP (complement control protein) domains (Fig. 2a). Thus, in order to assess the relative contribution of in CUB versus Sushi domain SNVs to age at menopause, we fit linear models to partition the association signal among these two domains. The CSMD1 SNV association was driven almost exclusively by mutations in the CUB (βCUB = −0.86), but not Sushi (βSUSHI = 0.046) domains (Wilcoxon rank-sum test p-value = 0.043; Fig. 1d, see Methods section). Our regression model estimates that each CUB domain SNV accelerates the onset of menopause by ~10 months. Finally, a well-powered common variant GWAS in a female cohort of 182,416 individuals identified 3 common SNPs within CSMD1 to be significantly and independently associated with age at menarche and subsequently replicated in >300,000 individuals27,28 (Fig. 1). Subsequent work in the same cohort showed age of menarche and menopause to be positively correlated. Furthermore, the common CSMD1 SNPs associated with age of menarche also correctly predicted age of menopause in the expected direction (βrs2688325= 0.014; βrs7828501= 0.021; βrs7463166= 0.031)29.

The phenotype of idiopathic early menopause indicates problems in ovarian function. Predictable consequences of such ovarian dysfunction are irregular or absent menses and reduced fecundity. To further clarify the role of CSMD1 deletions in female reproductive traits, we tested for association with 4 additional reproductive phenotypes available from the UKBB (see Methods section). Of these traits, we identified a significant association with age at last live birth (n = 76,686, linear regression p-value = 4.1 × 10−3, Fig. 1e). Individuals with CSMD1 deletions show a reduced reproductive lifespan across all quartiles of the cumulative distribution, corresponding to an average reduction of 1 year. To compare relative effect sizes, our fitted model predicts that obesity status reduces reproductive lifespan by 0.6 years, and smoking status reduces reproductive lifespan by 1 year (see Methods section). The maximum age at last birth among our controls is 51 years, versus 40 years for CSMD1 deletion carriers. However, we note that 99.6% of control individuals have completed childbearing by age 36, indicating that traditional measures of fertility (e.g. fecundity) would not necessarily capture ovarian dysfunction related to CSMD1 deletions.

In summary, we detected associations between rare variants in CSMD1 and gonadal dysfunction (i) across multiple classes of genetic variation; (ii) ascertained by orthogonal genotyping platforms; (iii) occupying multiple points along the allele frequency spectrum; and (iv) in multiple populations and cohorts.

### Detailed CSMD1 expression patterns in male and female gonads

CSMD1 encodes for an extremely large (>3,000 amino acid) transmembrane protein with a large extracellular portion consisting of alternating CUB and Sushi complement-interacting domains15. The protein encoded by CSMD1 is conserved between human and mouse, with 93% amino acid sequence identity and 100% domain synteny (Fig. 2a). In humans, CSMD1 is expressed in both male and female gonads (Supplementary Fig. 2), but extremely little is known of its molecular function, particularly in the context of fertility. Thus, we first performed RNA-seq on mouse gonads and confirmed that Csmd1 mRNA is expressed in both whole ovaries and whole testes (Fig. 2b, Supplementary Fig. 3), consistent with previous work30,31. Next, we detailed patterns of in situ CSMD1 protein expression through the different stages of ovulation using a validated CSMD1 antibody (Supplementary Fig. 4). Throughout oogenesis, CSMD1 shows lower expression in oocytes of early follicles (i.e. primordial and primary follicles) and higher expression in oocytes of late follicles (i.e. secondary, tertiary, and pre-ovulatory follicles; Fig. 2c). Supporting theca cells, which circumscribe the mature follicles, are also CSMD1-positive (Fig. 2c, asterisk). The post-ovulatory corpus luteum shows no specific CSMD1 expression (Fig. 2d). Female oocytes require substantial physical interaction with surrounding somatic cells32. At high magnification, CSMD1 is expressed along transzonal projections which connect the somatic granulosa cells to the oocyte membrane (Fig. 2d).

In the testes, Csmd1 mRNA is minimally expressed at 20 days and more robustly expressed at 40 days of age which coincides with the onset of sexual maturity. Mammalian testes demonstrate exceptional transcriptional complexity, owing to the highly coordinated spatial and temporal synchronization required for successful spermatogenesis throughout male adult life30. Therefore, to capture a more detailed transcriptional portrait of Csmd1 in testes, we purified germ cell subpopulations using established FACS protocols (see Methods section; Supplementary Fig. 3a). Subsequent RNA-seq of purified germ cells reveals low levels of Csmd1 expression in spermatogonia and primary spermatocytes and peak expression in secondary spermatocytes and spermatids (Fig. 2b; Supplementary Fig. 3).

We also performed immunofluorescence on seminiferous tubule cross-sections which show that CSMD1 protein is expressed at the germ cell membrane across multiple aspects of spermatogenesis, including at the interface of elongated spermatids and somatic Sertoli cells, but is absent from spermatozoa, recapitulating mRNA expression patterns (Fig. 2e; Supplementary Fig. 3). While tubule cross-sections effectively capture information from the lumenal stages of spermatogenesis, much of the spatial variance of basal germ cells, Sertoli cells, and interstitial cells (e.g. macrophages) occurs along the longitudinal axis33. Therefore, we also performed immunofluorescence on whole-mount longitudinal preparations of individual seminiferous tubules. CSMD1 is expressed in a hatched pattern which is reminiscent of the actin bundles found at the Sertoli–Sertoli blood–testis barrier and the Sertoli-spermatid interface34 (Fig. 2f).

### Csmd1 KO causes fertility phenotypes across multiple tissues

Association studies in humans are effective in identifying candidates for disease risk. However, owing to the extensive linkage disequilibrium structure in the human genome, even statistically robust and reproducible associations may implicate linked but biologically non-causal loci (sometimes up to megabase scales)35. In order to confirm a role for CSMD1 in mammalian reproduction, we obtained a previously described mouse strain with a knockout of the first exon of Csmd1 (refs. 31,36) (Supplementary Fig. 4). RNA-seq of knockout females demonstrated robust loss of Csmd1 expression in the ovaries. In testes, we observe a more complex perturbation of expression, with absent or highly reduced expression of exons 1–57, but upregulation of exons 58–70. Finally, we cross-referenced multiple expression modalities (RNA-seq, CSMD1 immunofluorescence, β-Gal immunofluorescence, and X-gal staining; Fig. 2; Supplementary Fig. 4) and found multiple lines of evidence corroborating expected CSMD1 spatial patterns in wildtype tissues. We also identified nonspecific signal in KO tissues, in particular in our CSMD1 immunofluorescence assay (Supplementary Fig. 4c).

We generated a colony of Csmd1 wildtype, heterozygous, and knockout mice and observed the effect of genotype on fertility, gonadal morphology and function in male and female mice. In males, Csmd1 knockout leads to variable, but statistically significant, defects across multiple dimensions of gonad function and fertility. First, we observed an increase in infertility rate among knockout males (30%) compared to wildtype (4.5%) (linear regression p-value = 4 × 10−4, Fig. 3a). Second, knockout males show on average a 25% reduction in the daily sperm production compared to controls (Wald test p-value = 0.029, Fig. 3b). Third, a subset of Csmd1 knockout males suffer from profound anatomic and histopathologic derangement of the testes (Fig. 3c–e; Supplementary Fig. 5). Remarkably, the most severe examples of germ cell elimination (Sertoli cell-only syndrome), could be observed as early as 34 days of age (Fig. 3c; Supplementary Fig. 5). This time point corresponds to the approximate onset of male sexual maturity and the emergence of the spermatid germ cells, where Csmd1 is maximally expressed. Neither knockout nor wildtype testes showed evidence of derangement prior to sexual maturity (Supplementary Fig. 5c). Both histologic severity (none, mild, and severe) and age of onset (postnatal day 34 through day 300) were highly variable between individuals. In fact, different foci within the same testis of Csmd1 knockout mice often simultaneously present different degrees of seminiferous tubule degeneration (Fig. 3d). Finally, significantly fewer germ cells express the male germ cell antigen TRA98 (Poisson regression p-value < 2 × 10−16; Supplementary Fig. 5d), in both atrophic and normal tubules, suggesting that knockout testes suffer from expression perturbations in addition to, or perhaps presaging, loss of germ cells and frank degeneration. Together, these observations indicate that the Csmd1 knockout mutation is not fully penetrant and may be influenced by environmental and/or stochastic events. However, even after accounting for age covariates, testes derangement status segregates significantly with Csmd1 genotype (multivariate ANOVA p-value = 7.69 × 10−3; see Methods section; Fig. 3e). Lastly, we performed serial backcrossing for 9 generations on a subset of mice to validate the effect of the Csmd1 null allele on an approximately constant genetic background (see Methods section). We recapitulated the degeneration phenotype in these backcrossed male knockouts (Supplementary Fig. 5e), indicating that Csmd1 genotype status — not genetic background — drives this signal of degeneration.

Detailed histological analysis of 50 knockout testes revealed heterogenous and distinct classes of degeneration in Csmd1−/− testes (Fig. 3d). Spermatogenesis begins to become disorganized, especially at the late steps of spermiogenesis, with failure of spermiation, fewer numbers of elongating spermatids in the lumen, and ectopic mixing of spermatid steps in stages IX–XII. This is followed by the sloughing of all types of germ cells into the lumen; remaining germ cells can be observed in abnormal tubules that appear to be missing one or more waves of spermatogenesis, and these eventually resolve as Sertoli cell-only tubules. Sloughed germ cells can be seen downstream in the epididymis, and, occasionally they obstruct the downstream rete testis leading to dilation of the upstream tubules.

Three non-exclusive scenarios may account for the net loss of germ cells in Csmd1 knockouts: (i) increased germ cell death; (ii) failure of germ cell proliferation/maturation; and (iii) increased phagocytic clearance of germ cells. We did not observe obvious differences in the abundance of apoptotic germ cells apparent by H&E staining. We excluded systemic endocrine defects that would be observed in the case of failure of the hypothalamus or pituitary (Supplementary Fig. 6). We also did not observe any developmental stage-specific accumulation or depletion of germ cells as characterized in maturation arrest/failure of meiosis37,38. Finally, we did not observe significant differences in the proliferation marker PCNA levels between Csmd1 wildtype (9.4%) and knockout (7.0%) testes.

### Complement C3 deposition is increased on Csmd1 KO testes

FACS-purification and RNA-seq of wildtype male germ cells show that C3 and Csmd1 mRNA expression are negatively correlated throughout spermatogenesis (Fig. 4a); in contrast to Csmd1, C3 mRNA is most highly expressed in spermatogonia and decreases precipitously in subsequent stages. In wildtype testes, we observed abundant signal of both C3 protein and macrophage marker F4/80 in the interstitial space between seminiferous tubules, but never across the blood–testis barrier (Fig. 4b). Next, we estimated macrophage abundance and C3 protein deposition in Csmd1 wildtype vs. knockout testes (Fig. 4c; Supplementary Fig. 7). The percentage of C3-positive deposition is significantly higher in Csmd1 knockout testes than in wildtype (x̅wt = 1.7%; x̅ko = 6.6%; ANOVA p-value = 7.7 × 10−4). C3 is a secreted, circulating protein whose mRNA is expressed by multiple cell types — including the germ cells themselves. Therefore, we also measured C3 mRNA expression in Csmd1 wildtype versus knockout purified male germ cells (Fig. 4d). C3 mRNA expression does not differ between wildtype and knockout germ cells of any type, indicating that the germ cells are not necessarily the source of the increased C3 protein deposition.

### Csmd1 KO ovaries are reduced in quality

The observed rate of infertility in knockout females (3/37, 8.1%) was not significantly higher compared to controls (5/115, 4.3%, Fig. 5a). The female infertility phenotype we ascertained in human does not likely represent congenital infertility, but instead adult-onset early menopause, which is difficult to model in mice39. Thus, we searched for more subtle gonadal defects associated with Csmd1 genotype. We estimated female time to pregnancy based on retrospective husbandry records. From these records, we generated a well-calibrated null distribution of time to conception in females of all genotypes which demonstrates distinct periodicity lasting 4–5 days, recapitulating the periodicity of the mouse female estrous cycle (Fig. 5b). Next, we stratified our population by maternal genotype. For wildtype mothers, the bulk of conceptions occurred within the first estrous cycle as expected40, whereas most Csmd1 knockout mothers required a time equivalent to two or more cycles to achieve pregnancy (βGT = 10.4; linear regression p-value = 0.012). A small minority of knockout females required many cycles to achieve pregnancy (>60 days). Circulating gonadotropin levels did not differ between wildtype and knockouts after controlling for estrous stage, suggesting that this reduction in mating success was not secondary to impaired hormonal input (Supplementary Fig. 6). Csmd1 knockout females had significantly smaller ovaries by mass when controlling for age, (quadratic regression p-value = 8.1 × 10−3; Fig. 5c; Table 1), and knockout females showed significantly more atretic follicles and fewer normal pre-ovulatory follicles at necropsy (Hotelling t-test p-value = 3.5 × 10−3; Fig. 5d). In a subset of female knockout ovaries, we observed inflammatory changes associated with infiltration of lipid-engorged macrophages (foam cells) and occasional ovarian cysts (Fig. 5e, f). Altogether, we find that Csmd1 knockout females display ovarian defects that are normally associated with progressive wildtype aging (i.e. smaller ovary size41, increase in atretic follicles42, and enrichment of foam cell macrophages43), but at significantly accelerated rates and higher proportions in knockouts.

### C3 is abundant in follicles and colocalizes with CSMD1

In wildtype ovaries, C3 is localized to the oocyte surface in normal developing follicles, colocalized with CSMD1, and then observed to be diffused in large amounts throughout the corpus luteum (Fig. 6), which does not express CSMD1. Macrophages are a prominent cell type in the ovarian stroma but are excluded from early stage follicles; they later invade corpora lutea and degrading follicles44. Furthermore, C3 colocalizes with macrophages in the corpus luteum, atretic follicles, and among developing follicles to variable degrees. C3 is also abundant within the early follicular antrum, suggesting that C3 may be important for remodeling the connections between granulosa cells during antrum formation (Fig. 6b). Previous work has shown that activated C3 is present in human antral follicular fluid at levels comparable to sera45.

### Csmd1 KO mothers have impaired mammary branching

Interestingly, while knockout females achieved fewer pregnancies per estrous cycle, the average number of offspring born per successful pregnancy did not differ significantly between wildtype and knockout mothers (x̅wt = 6.6 (95% CI [5.4−7.8]); x̅ko = 6.9 (95% CI [5.7−8.1]); Table 1). However, pups borne of Csmd1 knockout mothers suffered from significantly higher mortality rates during the neonatal period (1–10 days) when compared to wildtype/heterozygous mothers (% mortalityWT+het = 10.5% (95% CI [3.6−17.5%]); % mortalityKO = 50.0% (95% CI [30.0−70.0%]); Poisson regression p-value = 7.93 × 10−7; Fig. 7a). We performed necropsy on expired offspring which revealed an absence of milk spots, suggesting death by starvation. Because neonatal mortality segregated with maternal genotype but not offspring genotype or paternal genotype, we hypothesized that this increase in mortality was caused by nursing defects in Csmd1-deficient mothers. CSMD1 is expressed in the normal mammary gland through the adult life cycle of wildtype females on both lumenal epithelial cells and myoepithelial cells of the mammary ducts, and on numerous stromal cells (Fig. 7b, c). Mammary glands from knockout females showed reduced density of the epithelial branching network during mid-pregnancy and post-nursing (Fig. 7d). Quantification of duct morphology in nulliparous wild type and knockout animals shows a significant reduction of lateral branching prior to pregnancy (Fig. 7e, f). Finally, we measured C3 and CSMD1 expression patterns in wildtype mammary glands (Fig. 7g). As early as puberty, C3 can be seen in high levels within the mammary duct lumen of virgin animals. C3 is also expressed within vesicles of specific subsets of CSMD1-positive stromal cells (Fig. 7g).

### Csmd1−/−C3−/− double KO males and females are infertile

Based on previous findings that CSMD1 is a negative regulator of C3, we predicted that removal of C3 would partially or completely alleviate the morphological degeneration and fertility defects observed in Csmd1 knockout mice. To test this prediction, we generated colonies of C3−/− single KO mice and C3/ Csmd1/ double KO mice. We did not observe any severely deranged C3−/− testes or ovaries (Supplementary Fig. 8). Surprisingly, we found no evidence of rescue of the Csmd1−/− single KO phenotype in double KO males or females (Supplementary Fig. 9). Instead, we observed an unmasked phenotype of more severe histological degeneration in all DKO females, characterized by far more extensive invasion of foam cell macrophages, extensive pyknosis, and deformed follicles. We also observed loss of cellularity in the mucosal layer of the oviduct (Supplementary Fig. 9b). We monitored the fertility of 19 DKOs (10 males and 9 females) and, of these, only 4 (21%) produced progeny after at least 3–7 months of mating (3 males and 1 female; Supplementary Fig. 9, Supplementary Table 3). These extreme phenotypes are not observed in Csmd1 or C3 single KOs46, suggesting that the combined effect of Csmd1 and C3 on fertility is synergistic.

## Discussion

We used a rare variant association approach to search for genes that modulate both male and female gonadal function, and identified the complement regulator CSMD1 to be reproducibly associated across multiple patient cohorts and different classes of genetic variation. Our study was powered to capture rare variants of mild to moderate effect — that is, mutations that significantly increase risk of developing infertility, but still potentially segregating in the population. Conversely, our study was poorly powered to identify extremely rare/de novo, highly penetrant infertility mutations (e.g. TEX11 (ref. 38), SYCE1 (refs. 38,47), SPIDR48). We found that multiple types of genetic perturbations of CSMD1 associate with infertility traits in humans, most notably deletions within introns 1–3 of the gene. Intronic deletions can affect gene function by altering splicing, RNA stability, and transcriptional regulation, and recent work has shown that such deletions tend to reduce transcript levels when they perturb expression of their host gene, although upregulation is also possible49. All infertility-associated deletions found in this study fall within 500 kb of 3 independent GWAS peaks for age at menarche. In the GTEx atlas, we found that only two tissues show significant CSMD1 expression-associated quantitative trait loci (eQTL): thyroid and testis50 (Supplementary Fig. 10). Although the CSMD1 gene body spans over 2 Mb of the genome, all of these eQTL are clustered within a 390 kb window spanning introns 1 and 2. The 3 noncoding GWAS SNPs from Day et al.28 are not in appreciable LD with the GTEx eQTL. We also screened ENCODE51 for functional annotations in this region. Functional summaries (e.g. chromHMM output) are not yet available for testis, ovary or mammary gland; instead we used functional summaries derived from 6 human cell lines and identified 4 consensus CTCF sites within the region (Supplementary Fig. 10). We conclude that CSMD1 introns 1 and 2 likely harbor functional elements that can influence gene expression in testis, but additional functional data are needed to map these elements, as well as potential elements in ovary and mammary gland.

Furthermore, we found that rare protein-coding SNVs within the CUB domains of CSMD1 are significantly associated with age at menopause. According to the Residual Variation Intolerance Score (RVIS) only 0.169% of genes in the genome are more intolerant to protein coding changes than CSMD1 (ref. 52). Likewise, CSMD1 is massively depleted for rare loss-of-function (LoF) variation in the gnomAD reference database53, with a pLI score of 1.0. This depletion of LoF variation is especially striking given the local increase in CSMD1 de novo SNV mutation rate54,55, which is also corroborated by the substantial enrichment of rare synonymous variation in CSMD1 (ref. 53). Altogether we favor a LoF effect of CSMD1 mutations in human primary gonadal dysfunction.

How do our mouse studies relate to the human genetic findings and what are their limitations? We characterized a Csmd1 genetic knockout construct that was not strictly identical to any of the rare patient mutations found in our study. Further complicating our interpretation of the mouse data is our finding that Csmd1 KO gonads display nonspecific and/or residual expression signal; a phenomenon previously observed in Csmd1 KO brain36. Given the exceptional intolerance of CSMD1 to LoF variation in humans, we hypothesize that incomplete Csmd1 loss-of-function is buffered by functional redundancy56 (e.g. from Csmd2 and Csmd3)57, and that complete loss-of-function of Csmd1 would lead to much more severe and/or systemic phenotypes in both humans and mice. A complete tissue-specific and/or inducible loss-of-function knockout of Csmd1 could help to better disentangle these potential effects but would be technically prohibitive due to the size of the gene.

Despite these practical limitations, the mouse mutants provided an invaluable and previously undescribed functional link between CSMD1 and reproductive function. Our human samples were ascertained based on pathologic loss of germ cells, and/or reduced reproductive lifespan. We observed heterogeneous gonadal defects corresponding to reduced reproductive lifespan and premature germ cell loss in both male and female Csmd1 KO mice, and these phenotypes were unexpectedly exacerbated in Csmd1/, C3/ double KO mice. While we have neither explicitly nor implicitly defined the mechanism of CSMD1 mutations on gonadal function here, we have constructed a framework that implicates overzealous activation of the complement pathway as a potential contributor to the pathophysiology of the disease, due to the known molecular function of CSMD1 as a complement inhibitor15, the spatiotemporal patterns of complement-related proteins and cell types in the gonads, and the excess complement deposition on Csmd1 KO testes.

While complement has a long-appreciated role in innate immunity, it also plays a prominent role in the regulation of self cells during normal postnatal development. A classic example of this phenomenon is complement-mediated synaptic pruning in the developing brain, a process that is under genetic influence and can confer risk for disease when dysregulated20,58. Here, we have reported abnormal post-natal development in Csmd1 knockout animals for three additional tissues; we have observed complement and CSMD1 protein expression in all three tissues, and previous work has shown that macrophages are essential for proper development in all three tissues. A parsimonious model to describe the set of defects we observe here is that macrophages (and potentially other phagocytes such as Sertoli cells) regulate and refine developing cells in testis, ovaries, and mammary by controlled deposition of complement onto their cell surface, accompanied by subsequent phagocytosis.

Specifically, in the testis, increased C3 deposition in Csmd1 knockout taken in context of the known complement-inhibitory function of CSMD1 (ref. 23) suggests that overzealous complement-mediated phagocytosis of developing germ cells by macrophages and/or Sertoli cells underlies at least part of the testicular defects. C3 mRNA and protein are much more highly expressed in the interstitial spermatogonial layer, which is physically sequestered from the lumenal aspect of the tubules by the blood–testis barrier;59 Conversely, CSMD1 is largely expressed in the adlumenal compartment (Fig. 2e, f). Spermatogonial fate is closely tied to interstitial macrophages33, which are abundant in the testis, express factors essential for spermatogonial differentiation, and enter the tubules and phagocytose germ cells during aging and disease60,61. Concerted apoptosis of differentiating spermatogonial stem cells is a prominent and quantitatively reproducible feature of normal spermatogenesis62. If complement marks some targets of phagocytosis in the testis in an analogous manner to that shown in the brain63, ectopic complement activation across the blood–testis barrier may inappropriately activate the apoptotic and phagocytic apparatus in Csmd1 KO testes. Remarkably, TEP1 (a distant ortholog of C3) has been shown to clear apoptotic germ cells in the mosquito testis by this very process64

Macrophage activity in the ovary is very carefully regulated in time and space during the estrous cycle. Prior to ovulation, macrophages are excluded from the granulosa layer of follicles of all types — except the atretic follicles, which are invaded by macrophages and do not ovulate65,66,67. After ovulation, macrophages invade the ruptured follicle which undergoes apoptosis/phagocytic luteolysis, forming the corpus luteum68. We showed that CSMD1 is also highly expressed on oocytes of the developing follicle, but not in the corpus luteum (Fig. 2d). CSMD1 loss of function may allow for premature macrophage invasion of the developing follicle, leading to excessive oocyte atresia, fewer ovulations, and reduced probability of pregnancy (Fig. 5).

In addition to the gonads, CSMD1 may also participate in post-natal developmental processes across other tissue systems. We have demonstrated a robust association between neonatal mortality rate and maternal Csmd1 genotype status, with corresponding reduction in the epithelial network of the maternal mammary gland (Fig. 7). The mammary gland is a highly motile network of branching epithelial tissue that advances and recedes during different stages of post-natal development (i.e. puberty, pregnancy, nursing, etc69.). The characteristic directionality of mammary branching is conferred by polarized cell proliferation and phagocytosis mediated by macrophage remodeling, especially in anticipation of nursing70. Furthermore, multiple complement and complement-regulatory components are robustly upregulated during periods of apoptosis and phagocytosis in the mammary tissue of multiple species including humans71,72, though the functional significance of this regulatory program is unknown. Breast milk itself also suppresses complement activation73. Finally, CSMD1 is expressed on the lumenal aspect of mammary ducts and terminal end buds, where much of the pregnancy-associated breast remodeling occurs15,74 (Fig. 7b). We observed a reduction in mammary epithelial density, due to reduction in secondary or tertiary branch points, whose normal geneses are governed by multiple upregulatory and downregulatory chemotactic signals in concert with physical interaction with phagocytic cells (i.e. macrophages)75.

The unmasking of a more severe phenotype in C3/Csmd1 DKO mice is an unexpected but previously documented signature of complement-mediated disease. For example, double knockout of complement factor H (CFH) and factor P (CFP) unexpectedly converts mild C3 glomerulonephritis to lethal C3 glomerulonephritis in mice76. Similarly, CFH/C3 DKO unexpectedly unmasks a more severe form of age-related macular degeneration in mice77. Multiple explanations for this phenomenon have been set forth, including a dual role of C3, differences between fluid-phase and local C3 activation, and context-specific C3 gain-of-function. Finally, we cannot exclude the possibility of primary defects outside of the gonads causing pathology in our double knockouts (e.g. altered hemostasis, central defects, etc.). More extensive mutation constructs including conditional knockouts and allelic series may help to distinguish among these scenarios.

Altogether, our human genetic and model organism findings lend support to a role of CSMD1 across multiple tissue types, and unveil a potential role for the complement system in postnatal developmental processes across multiple tissues in the body. When interpreted in context of existing observations from mammalian brain and other model organisms, we predict that macrophage mediated complement activity on self cells is a normal and highly controlled process in many developmental systems in metazoans. Furthermore, a wealth of literature shows that genetic dysregulation of complement and complement-regulating factors is a core feature of several heritable diseases beyond infertility;20,58,78,79,80,81,82,83,84,85,86,87; we therefore consider CSMD1 to also be a reasonable candidate for many of these diseases. Our work highlights the need for deeper investigation into the role of immune system components in reproductive tissues, and the opportunities that such work can have to illuminate and connect common biological processes that produce disease in more complex contexts across the body.

## Methods

### Human patient populations

All human genetic studies were reviewed and approved by the Institutional Review Board of Washington University in St. Louis, under protocol numbers #201107177 and #201109261 and all participants provided informed consent. Male idiopathic infertility cases were clinically ascertained and pre-screened for chromosome Y deletions and compared against normospermic controls13,14. WHI-SHARe. To create an analogous case-control cohort of female gonadal dysfunction, we turned to the SNP Health Association Resource (SHARe)88. We constructed early idiopathic case and control definitions from the dense reproductive phenotype data collected on each subject. A self-reported age of menopause before 40 years was used as the only case inclusion criterion. Case exclusion criteria were oophorectomy prior to age 40, a diagnosis of lupus or rheumatoid disease, and a “yes” answer to the question “Did a doctor ever say that you had cancer, a malignant growth, or tumor?”. Smoking history, which is a known factor influencing ovarian reserve, was controlled for during the analysis of genetic data.

UK Biobank. This research has been conducted using the UK Biobank Resource under Application Number ‘17085’. We generated a table of phenotype data for constructing early idiopathic menopause case and control labels using controlled-access data from the UK Biobank. Exclusion criteria for the study were: withdrawn consent, poor heterozygosity or missingness as defined by the UK Biobank; >10 relatives in the UK Biobank cohort; not used in autosome phasing, apparent sex chromosome aneuploidy; mismatch between genetic and self-reported sex; ever smoker; any self-reported non-Caucasian ancestry; oophorectomy prior to age 40; prior diagnosis of rheumatoid arthritis, lupus, or pelvic cancer; mismatch between self-reported ethnicity or age at menopause among three assessments; SNP array call rate <98%. In the case of pairs of 2nd degree relatives or closer, the one individual with the lower SNP-call rate was dropped. The inclusion criteria for POI case status were self-reported age of menopause <40 years old, and all remaining individuals in the cohort (after exclusions mentioned above) were used as controls.

### Mouse colony breeding

We acquired a constitutive Csmd1 knockout mouse (Mus musculus) on a mixed 129SvEvBrd:C57BL/6 background from the UC Davis KOMP Repository (Project ID CSD118901)89. A 1.086 kb deletion encompassing Csmd1 exon 1 and part of intron 1 were replaced with a lacZ/neomycin cassette. Deletion of this segment was confirmed with Southern blot and PCR. Due to the extreme size of Csmd1 (1.6 Mb), we also analyzed RNA seq data across all 70 exons in knockout testes and ovaries. In ovaries, knockout read counts relative to wildtype are suppressed across all 70 exons. In testes, knockout read counts relative to wildtype are broadly suppressed across exons 1-57 and upregulated from exons 58-70. The amino acid coding portion of these upregulated exons range in size from 45 bp to 180 bp. The translational viability of these fragments is unknown. All littermate tissue comparisons in this study (described below) were generated from damheterozygous × sireheterzygous crossings from this original colony. Next, to eliminate variance in phenotype explained by variance in background genotype (if any), we serially backcrossed the Csmd1 mutation onto a constant C57BL/6 background for 5 generations. From this F5 backcross generation we performed a damheterozygous × sireheterozygous cross from this to create wildtype and knockout littermates, and performed analogous histology and immunofluorescence experiments as with the original colony (described below; Supplementary Fig. 5e). We performed microsatellite genotyping of these littermates to estimate the C57BL/6 background after backcrossing (Washington University Rheumatic Disease Core). We estimated the F5 proportion of C57BL/6 ancestry of 0.91 (95% CI [0.89−0.93]). For DKO experiments, we introgressed a C3 mutant line90 until we achieved Csmd1/C3 DKO mice. All animal experiments were performed in compliance with the regulations of the Animal Studies Committee at Washington University in St. Louis under protocols #20120244 and #20160089.

### CNV and SNV discovery

Array data for the Women’s Health Initiative SHARe cohort were downloaded from the NCBI Database of Genotypes and Phenotypes (dbGAP accession number phg0000g1.v2). SHARe samples were genotyped on the Affymetrix 6.0 platform. We created a high-quality set of CNV calls for all cohorts using our own internal pipelines. SHARe samples were processed with Affy6CNV (a wrapper that we wrote for the Birdsuite package91) for data processing and QC. We obtained raw SNP array data from the UK Biobank and performed single sample CNV discovery using PennCNV92. Individuals with >200 CNV calls were dropped. CNV calls with PennCNV quality score >30 were retained, and adjacent CNVs in the same sample were merged. All qPCR validation of CSMD1 CNV calls were performed on Applied Biosystems TaqMan assay # Hs0367742_cn (catalog #4400291). We used Human RNase P for the reference assay (catalog #4403326). We used standard Applied Biosystems TaqMan protocols in 10 µL reaction volumes. We generated 4 to 8 technical replicates for each sample in a 384 well plate. PCR conditions were as follows: 50 °C for 2 min, 95 °C for 10 min, then 40 cycles of 95 °C for 15 s and 60 °C for 1 min. TaqMan copy number was estimated using the CopyCaller software and compared to PennCNV copy number estimates.

Exome sequencing was performed on a subset of the WHI subjects as part of the Women’s Health Initiative Sequencing Project (WHISP); all available WHISP BAM files were downloaded from the NCBI Database of Genotypes and Phenotypes (dbGaP accession phs000200.v10.p3.c1 and phs000200.v10.p3.c2)93. Genotypes were recalled, jointly, from 1668 WHI BAM files using Haplotype Caller, recalibrated and cleaned according to GATK best practices using GATK-3.2.2.

### Association testing

CNVs. Rare CNVs were associated with case-control status using generalized linear models. For the SHARe association analysis, we included the top 10 ancestry eigenvectors (calculated from the full SHARe genotype matrix) and smoking history as covariates. For the UK BioBank association analyses, and we included as covariates BMI, smoking history (or individuals with any history of smoking were excluded, where noted) and the top 10 ancestry eigenvectors calculated from the full UK Biobank SNP genotype matrix.

In addition to idiopathic early menopause (defined above in Human patient populations), we performed association testing for the following 4 traits for UKBB subjects (Unique Data Identifier codes in parentheses): Length of menstrual cycle (3710), Number of live births (2734), Age at last live birth (2764), all-cause female infertility IC10 code (N97).

SNVs. We tested for an association between rare SNVs in CSMD1 and age at menopause in the WHI samples using the Sequence Kernel Association Test (SKAT)94, weighting each variant with the Combined Annotation Dependent Depletion (CADD) value95. Five ancestry eigenvectors and smoking history were included as covariates; significance was evaluated using bootstrapping with 5000 samples.

### Testes dissociation and cell sorting and RNA extraction

We adapted existing methods for dissociation and germ cell purification96 which we describe below. Sexually mature (40 ± 1 days old), male mice were sacrificed, and their testes were decapsulated and homogenized in a 1× MEM solution (Gibco 11430-030) containing 120 U/mL Type I Collagenase (Worthington Biochemical LS004194) and 1 mg/mL DNAse I (Roche 10104159001), and agitated for 15 min. 1× MEM was replaced and added with 50 mg/mL Trypsin (Worthington Biochemical 54J15037) and 1 mg/mL DNAse I and agitated for 15 minutes, then mechanically homogenized for 3 min. 50 mg/mL Trypsin and 1 mg/mL DNAse I were added and agitated again for 15 min. We added 0.4 mL heat inactivated Fetal Bovine Serum (Sigma F1051), 5 μL Hoescht 33342 (Life Technologies H3570), and 1 mg/mL DNAse I, and agitated for 15 minutes. Individual cells were dissociated by pipetting sequentially through two 40 μm cell strainers (Falcon 352340). For each individual mouse, one dissociated testis was used for whole tissue RNA extraction and sequencing, and the other testis was used for germ cell purification, RNA extraction, and sequencing. All dissociation steps were performed at 33 °C. Dissociated testes were sorted on a modified MoFlo cytometer (Beckman Coulter) at the Washington University Siteman Flow Cytometry Core using a krypton-ion laser97. Cells that are stained with Hoechst can be clustered in two wavelengths: (i) blue fluorescence, which is informative of DNA content, and (ii) red fluorescence, which is informative about chromatin state and Hoechst efflux from the cell. Our gating strategy is graphically summarized in Supplementary Fig. 3. Based on these parameters, we separated homogenized testes suspensions into four purified populations: (i) spermatogonia, (ii) primary spermatocytes, (iii) secondary spermatocytes, and (iv) spermatids. These separated populations were collected and RNA extraction performed on them. RNA from whole testes was extracted with the RNeasy Plus Mini Kit (Qiagen 74134), and RNA from FACS-purified germ cell populations was extracted with the RNeasy Plus Micro Kit (Qiagen 74034).

### RNA-seq

Whole testis, whole ovaries, and purified male germ cell subpopulations were obtained from wildtype and Csmd1 null siblings (summarized in Supplementary Data 3). We extracted polyadenylated mRNAs from each tissue/cell type and converted these into RNA-seq libraries. Three biological replicates of each tissue or cell type were sequenced with a 2 × 101 bp paired-end protocol. Reads were mapped to Ensembl Mus musculus reference R72 and transcript expression levels were summarized as reads-per-kb of exon per million-mapped reads (RPKM) using the TopHat2 package98. RPKMs were adjusted for batch effects and cryptic covariates using PEER99, quantile normalized, and then the R package poissonSeq was used for differential expression analyses100.

### Immunostaining and imaging

Testes and ovaries were dissected, fixed in 4% paraformaldehyde (Electron Microscopy Sciences), and embedded in paraffin. We baked 5 μm sections at 60 °C for 1 h, deparaffinized in Xylenes, and rehydrated into PBS (Corning). Antigen retrieval was done in boiling citrate buffer (10 mM sodium citrate, 0.05% Tween-20, pH 6.0) for 20 min. Sections were blocked in PBS containing 0.2% Triton X-100 and 5% normal donkey serum (Jackson Laboratories) for 1 h at room temperature and then incubated with primary antibodies diluted in blocking solution over night at 4 °C. After washing with PBS-Tx (PBS containing 0.2% Triton X-100), they were incubated with fluorescent secondary antibodies in blocking solution for 1 h at room temperature, washed with PBS-Tx, and treated with 0.2% Sudan Black in 70% EtOH for 10 min, followed by PBS washes. The sections were then counterstained with Hoechst dye 33342 diluted 1:500 in PBS for 5 min, washed once with PBS-Tx for 2 min and then with PBS, and mounted in ProLong Diamond anti-fade mounting medium (Molecular Probes). Imaging was done on an Olympus LSM700 confocal microscope using Zen software, and images were processed using Photoshop CS5 (Adobe). Antibodies used were gt α-CSMD1 N20 (Santa Cruz Biotechnology sc-68280 1:100), rb α-mouse vasa homolog (MVH) (Abcam 13840, 1:1,000), donkey α-gt CF594 (Biotium #20116 1:300), and donkey α-rb Alexa488 (Life Technologies #A-21206 1:300), rb α-β-gal (Cappel #55976 1:333), rat F4/80 BM8 (Santa Cruz Biotechnology sc-52664 1:50), donkey α-rat Alexa488 (Life Technologies #A-21208 1:300), rb α-C3 (Abcam 200999, 1:2000), and gt α-rb Alexa568 (Life Technologies #A-11011, 1:300). Testes were decapsulated in 1x PBS and the tubules were gently teased apart and fixed in 4% paraformaldehyde in 1× PBS for 2 h at 4 °C. After washing with PBS and blocking in PBS containing 0.2% Triton X-100 and 5% normal donkey serum for 1.5 h at room temperature, they were incubated in primary antibodies overnight at 4 °C in blocking solution and processed as the cross-sectional IF experiments were described above33. For immunohistochemistry, 5 μm paraffin sections were treated as above, except the secondary antibody was biotin-coupled horse α-goat (Vector Laboratories, BA-9500, 1:200), and detection was done using the Vectastain Elite ABC kit (Vector Laboratories, PK-6100) and DAB Peroxidase Substrate kit (Vector Laboratories SK-4100) per the manufacturer’s instructions. Sections were counterstained with hematoxylin, mounted in Cytoseal Xyl (Thermo Scientific), and imaged on a Zeiss Axioplan 2 microscope equipped with an Olympus DP71 camera and DP software. For X-gal staining, whole tissues were fixed in 4% PFA in PBS for 2 h, washed with PBS, and stained in X-gal (GoldBio #X4281C1) overnight101. Tissues were embedded in paraffin, sectioned at 5 μm, and counterstained with hematoxylin.

### Histology

Freshly-dissected gonads were fixed under agitation in Modified Davidson’s fixative (Electron Microscopy Sciences 64133-50) for 24 h and Bouin’s fixative (Electron Microscopy Sciences 26367-01) for 24 h. Fixed tissues were embedded in paraffin and sectioned at 5 μm. Sectioned tissues were stained with hematoxylin and counter-stained with either Periodic acid-Schiff reagent102 or eosin. Stained testes from 65 individual mice of known age and genotype (12 wildtype, 53 knockout) were provided to a single mouse pathologist in a blinded fashion. All samples received a score of 0 (no damage), 1 (mild damage), or 2 (severe damage) (see Supplementary Fig. 5a for exemplars). In order to estimate the effect of genotype on score, we fit a linear analysis of variance model:

$$y_{ijk} = \mu + \alpha _i + \beta _j + \varepsilon _{ijk}$$
(1)

where yijk is the damage score for individual k, μ average damage score across all animals, αi is the effect of genotype i, βj is the effect of age j, and εijk is the random error associated with the kth observation.

### Germ cell quantification

We performed immunofluorescence as described above on a pair of 34 day old male littermates (the same individuals as seen in Supplementary Fig. 5c) using TRA98 antibody (Abcam ab82527 1:200). We generated count data for total cells (filtering based on size and shape), and for TRA98-positive cells (filtering based on green fluorescence) using the ImageJ software package. In order to estimate the effect of genotype on TRA98 cell count, we fit the following model:

$${\mathrm{ln}}\left( {y_i} \right) = \beta _{\it{0}} + \beta _{\it{1}}X_{{\it{1}}i} + \beta _{\it{2}}X_{{\it{2}}i} + \varepsilon _i$$
(2)

Where yi is the TRA98-positive count in image i, and X1 is the genotype (Csmd1 wildtype versus knockout), and X2 is the total cell count. εi is the nuisance variable for image i.

We sacrificed 229 adult mice (106 males and 123 females), and measured body weights and bilateral gonad weights at necropsy. For males, mean body weight was 37.1 g, mean testes weight was 273 mg, and mean age was 201 days. For females, mean body weight was 31.3 g, mean ovary weight was 32 mg, and mean age was 234 days. In order to estimate the effect of genotype on gonad weight, we fit the following linear model:

$$y_i = \beta _0 + \beta _{\it{1}}X_{{\it{1}}i} + \beta _{\it{2}}X_{{\it{2}}i} + \beta _{\it{3}}X_{{\it{3}}i} + \varepsilon _i$$
(3)

Where yi is the gonad weight in individual i, and X1i, X2i, and X3i are the genotype, age, and body weight of individual i, respectively. εi is the nuisance variable for individual i.

### Quantifying daily sperm production

Daily sperm production (DSP) was estimated using the Triton-X 100 nuclear solubilization method103. Frozen testes were quickly thawed at room temperature and approximately half was used to estimate DSP. Sample weight was registered for full testis and tissue fragment used for the assay. To burst all cells, except for spermatid heads, the tissue was sonicated in DSP buffer (0.9% NaCl, 0.01% sodium azide (SAZ), 0.05% Trition-X-100) using short pulses (3 × 10 s at 30% amplitude). Sperm heads were then collected by centrifugation (10 min at 500×g) and used in 1:1 dilutions with 0.4% Trypan Blue for estimation of cell density per homogenate in a hemacytometer. These values were then used to estimate the total number of spermatids per testis [number spermatids in homogenate divided by sample weight (g) and multiplied by the full testis weight (g)]. In mouse spermiogenesis, steps 14–16 take 4.84 days (developing spermatids), therefore, DSP was calculated by dividing the total number of spermatids in one testis per 4.84 days.

### Follicle count analysis

We sacrificed 15 sexually mature female mice, of which 10 were wildtype and 5 were knockout genotypes. Bilateral ovaries were fixed, sectioned to 5 μm, and stained with H&E. We identified primordial follicles, primary follicles, secondary follicles, early antral follicles, antral follicles, preovulatory follicles, atretic follicles, and corpora lutea across each section based on histologic appearance104. In order to estimate the effect of genotype on gonad weight, we fit the following model:

$${\mathrm{ln}}\left( {y_i} \right) = \beta _{\it{0}} + \beta _{\it{1}}X_{{\it{1}}i} + \beta _{\it{2}}X_{{\it{2}}i} + \varepsilon _i$$
(4)

Where yi is the number of total oocytes in bilateral ovaries of individual i, and X1i and X2i are genotype and age, respectively. εi is the nuisance variable for individual i.

### Breeding time analysis

We compiled comprehensive husbandry information over a period of greater than 1 year corresponding to 151 litters born representing all possible Csmd1 wildtype, heterozygote, and knockout sire/dam breeding combinations. We calculated the number of days between first sire/dam co-habitation and birth of each litter. Next we subtracted an estimated C57BL/6 gestation time of 19 days105 to estimate time to conception. We also calculated parental ages at conception. All density plots depicted in Fig. 5b reflect estimated time to conception for all 151 litters. In order to estimate the effect of maternal genotype on mating success, we controlled for paternal genotype by including wildtype sires only. We then fit the following linear model:

$$y_i = \beta _{\it{0}} + \beta _{\it{1}}X_{{\it{1}}i} + \beta _{\it{2}}X_{{\it{2}}i} + \beta _{\it{3}}X_{{\it{3}}i} + \varepsilon _i$$
(5)

Where yi is the estimated time to conception for mating pair i, X1i is maternal genotype (wildtype, heterozygote, or knockout), X2i is maternal age at conception, and X3i is paternal age at conception. εi is the nuisance variable.

### Litter size analysis

We bred 44 females (8 wildtype, 27 heterozygote, and 9 homozygote) with 41 males (4 wildtype, 26 heterozygote, and 11 homozygote) over a period of 10 months to produce 99 litters, totaling 688 live births. All 9 parental genotype permutations [wtdam × wtsire, wtdam × hetsire … homdam × homsire] were represented multiple times (excepting hetdam × wtsire). We counted deaths in during the neonatal period (defined as 1–10 days by convention, although the vast majority of deaths occurred within 24–48 h) and subtracted from the live birth total to obtain the final number of surviving pups (550 total). Next, we stratified each litter by maternal and paternal genotype status (Csmd1 wildtype or heterozygous versus knockout) and fit the following model:

$${\mathrm{ln}}\left( {y_i} \right) = \beta _{\it{0}} + \beta _{\it{1}}X_{{\it{1}}i} + \beta _{\it{2}}X_{{\it{2}}i} + \varepsilon _i$$
(6)

Where yi is the number of surviving pups in litter i, and X1i and X2i are the maternal and paternal genotypes, respectively. εi is the nuisance variable for litter i.

### Mammary gland whole-mount analysis

Female littermates were collected at four developmental time points: (i) pre-pubescent (<30 days of age); (ii) adult virgins; (iii) mid-pregnancy (estimated 14 days after copulation); (iv) post-weaning (7 days after weaning pups from mother’s nursing). Freshly-dissected whole inguinal mammary glands were fixed overnight in Carnoy’s solution (60% ethanol, 30% chloroform, 10% glacial acetic acid). Fixed tissues were washed and rehydrated in ethanol and water and stained in Carmine alum histological stain (0.5% Aluminum potassium sulfate, 0.2% Carmine) for 48 h. Stained tissues were dehydrated with increasing concentrations of ethanol and stored in xylene to clear lipids for 48 h. Finally, tissues were flattened mechanically and suspended in pure methyl salicylate prior to imaging. Due to the large size of whole mammary tissues, overlapping fields of view were captured and stitched together using the “Photomerge” function in Adobe Photoshop. Gaps in the backdrop of the merged images were filled using the “Content aware fill” function in Adobe Photoshop — if and only if the gaps did not overlap any portion of the tissue proper. All original images are available on the Conrad Lab website. To perform statistical comparison of duct morphology between genotypes, measurements of mammary gland ducts were derived from images using AngioTool64 v0.6a106. First, a skeleton representation of the branched duct structure is generated from the input image, which is then used to compute a variety of morphological and spatial parameters for branching characterization. Since this software detects the branches by contrast on a black background, the images of whole mount mammary glands of adult mice were transformed into a compatible input using ImageJ 1.51n.

### Hormone measurements

We collected serum from 9 males (4 wildtype versus 5 knockout; mean age = 103 days) and 16 females in the proestrous stage (7 wildtype versus 9 knockout; mean age = 96 days) via submandibular collection. Each wildtype individual was matched with ≥1 knockout littermate. Female estrous cycle was determined first by external inspection of the vaginal opening, then by vaginal cytology107. Vaginal swabs were collected, transferred to a glass slide, and inspected under light microscopy. Proestrus, estrus, metestrus, and diestrus staging was then classified based on the relative counts of leukocytes, nucleated epithelial cells, and cornified epithelial cells. Only confirmed proestrous females were selected for blood draws and hormone measurements. All blood was drawn at approximately the same time of day, clotted for 90 min at room temperature, and centrifuged at 2000×g for 15 min. Samples were stored at −20 °C prior to hormone measurements. Male samples were quantified for LH/FSH (EMD Millipore) and testosterone (Immuno-Biological Laboratories Inc), and female samples were quantified for LH/FSH and estradiol (CALBIOTECH) by the University of Virginia Ligand Assay and Analysis Core.

### C3 deposition assay

Testes obtained post-dissection from Csmd1 knockout and wild-type mice were decapsulated and washed in 1× PBS before mincing. Minced tissue was subjected to enzymatic dissociation as described above. The crude cell preparation thus obtained was treated with ACK buffer (Life Technologies) for 5 min at room temperature to lyse erythrocytes present if any in the cell preparation. The isolated cells were incubated in α-C3 (B9) primary antibody (Santa Cruz Biotechnology sc-28294, 1:100) diluted in FACS buffer (1× PBS, 5%FBS, 0.1% Sodium azide) along with 10% Fc block (to minimize non-specific binding and background fluorescence) for 45 min at room temperature, followed by gt α-mouse Alexa488 (Abcam #A11029 1:250) incubation of 90 mins at RT in the dark with 3 washes of ice cold FACS buffer after each antibody incubation. Flow cytometry was performed with an Accuri C6 cytometer (BD Biosciences).

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.