Shared genetic loci between Alzheimer's disease and multiple sclerosis: Crossroads between neurodegeneration and immune system

BACKGROUND
Neuroinflammation is involved in the pathophysiology of Alzheimer's disease (AD), including immune-linked genetic variants and molecular pathways, microglia and astrocytes. Multiple Sclerosis (MS) is a chronic, immune-mediated disease with genetic and environmental risk factors and neuropathological features. There are clinical and pathobiological similarities between AD and MS. Here, we investigated shared genetic susceptibility between AD and MS to identify putative pathological mechanisms shared between neurodegeneration and the immune system.


METHODS
We analysed GWAS data for late-onset AD (N cases = 64,549, N controls = 634,442) and MS (N cases = 14,802, N controls = 26,703). Gaussian causal mixture modelling (MiXeR) was applied to characterise the genetic architecture and overlap between AD and MS. Local genetic correlation was investigated with Local Analysis of [co]Variant Association (LAVA). The conjunctional false discovery rate (conjFDR) framework was used to identify the specific shared genetic loci, for which functional annotation was conducted with FUMA and Open Targets.


RESULTS
MiXeR analysis showed comparable polygenicities for AD and MS (approximately 1800 trait-influencing variants) and genetic overlap with 20% of shared trait-influencing variants despite negligible genetic correlation (rg = 0.03), suggesting mixed directions of genetic effects across shared variants. conjFDR analysis identified 16 shared genetic loci, with 8 having concordant direction of effects in AD and MS. Annotated genes in shared loci were enriched in molecular signalling pathways involved in inflammation and the structural organisation of neurons.


CONCLUSIONS
Despite low global genetic correlation, the current results provide evidence for polygenic overlap between AD and MS. The shared loci between AD and MS were enriched in pathways involved in inflammation and neurodegeneration, highlighting new opportunities for future investigation.


Introduction
Alzheimer's disease (AD) is the most common forms of dementia, characterised by progressive neurodegeneration and specific neuropathological features (Jack Jr et al., 2016). AD is a major health problem in most countries, with high costs for health services and society . Usually, the clinical features of AD include specific memory decline, apathy, anxiety, and depression in earlier stages, with conversion to impaired communication, psychotic symptoms, confusion, and disorientation at the late stages (Jack Jr et al., 2016). The pathophysiology of AD is characterised by the accumulation of amyloid-beta (Aβ) and hyperphosphorylated tau protein, which lead to the production of amyloid plaques and neurofibrillary tangles (Golde, 2022). After the TREM2 gene discovery (Jonsson et al., 2013;Sherva et al., 2022), research in immunological mechanisms implicated in AD has increased (Piller, 2022). Chronic activation of the immune cells in the brain and immune cell trafficking from the periphery via the bloodbrain barrier contributes to the neuroinflammatory response, which is involved in the neurodegenerative processes in AD (Leng and Edison, 2021). Further, immune-based drugs preventing Aβ accumulation have shown promising effects in early AD (Van Dyck et al., 2023;Thambisetty and Howard, 2023).
Most AD cases emerge after 65 years of age (late-onset AD) and have complex genetic inheritance without a clear family history. Estimated heritability for AD from twin studies is 58-79% (Gatz et al., 2006), and estimated SNP heritability from genome-wide association studies (GWAS) is 3.1-6.9% (Lambert et al., 2013;Wightman et al., 2021;Bellenguez et al., 2022). A small number (<1%) of AD cases are familial, with mainly early onset (Tanzi, 2012), and associated with rare, genetic mutations in amyloid-pathway genes (Campion et al., 1999). Other early-onset cases are mostly associated with the same rare/common variants as late-onset AD (eg, TREM2, SORL1, RUFY1, PSD2, RIN3, and others, Kunkle et al., 2017). For late-onset AD, the genetics is more complex. The most well-known genetic risk factor is apolipoprotein E (APOE), yet there is also a strong polygenic component. Moreover, rare mutations, for example, the mutation in microtubule-associated protein tau gene (MAPT, Strang et al., 2019) and common variants (Wightman et al., 2021), contributed to late-onset AD. The most recent late-onset AD GWAS identified 75 AD risk loci (Bellenguez et al., 2022). Functional annotation of these loci revealed the involvement of microglia, immune cells, and protein catabolism, which can be relevant for developing new treatment regimens. Several implicated genes, such as TNIP1, LILRA5, TREM1, HLA-DRB1, CR1, GLU, play an essential role in the function of the immune system. Furthermore, proteomic studies in AD showed the involvement of molecular pathways linked to neuroinflammation, such as proinflammatory interleukins and cytokines molecules (Wingo et al., 2021).
Multiple sclerosis (MS) is a chronic, immune-mediated, and neurodegenerative disease of the central nervous system (Waubant et al., 2019). MS has a strong genetic influence, and large GWAS have identified 200 non-major histocompatibility complex (MHC) and 32 MHCloci associated with MS, with a SNP heritability (h2) around 48% (Patsopoulos et al., 2019). Immune-mediated myelin damage is important in disease activity and progression, and neuroinflammation is the key component of the pathogenesis of MS. Further, anti-inflammatory and immunomodulatory treatments are effective in relapsing-remitting MS and work at the earlier stages of the disease . However, these medications have a small impact in progressive MS and late stage of the disease due to the activation of neurodegenerative processes, which start at early stages of MS (Kaufmann et al., 2022) and suggest partly overlapping disease mechanisms with neurodegenerative diseases such as AD (Amezcua, 2022). Further, shared peripheral immunity mechanism was shown between AD and MS (Rossi et al., 2021). Moreover, there is a higher frequency of AD-related dementia (Mahmoudi et al., 2022), and neuropathologically confirmed neurodegenerative pathology in MS (Londoño et al., 2022).
Despite different clinical manifestations of AD and MS, shared genetic risk factors have been previously reported. For example, APOE4, the most important genetic risk factor for AD, has been reported to be a predictor of MS velocity, severity, and cognitive decline (Naseri et al., 2022), although there are contradictory results (Masterman et al., 2002). Further, the MHC region and immune-associated genes have been implicated in both diseases. MS is twice as common in women as in men, probably caused by hormonal and genetic factors . AD is also more prevalent in women, and this sex difference is related to higher life expectancy in women (Mielke et al., 2014;Beam et al., 2018), genetic architecture, and neurobiological vulnerability in postmenopausal females (Podcasy and Epperson, 2016). There are few cases of comorbid AD and MS (Luczynski et al., 2019) but MS show signs of amyloid pathology in the brain and impaired Aβ metabolism in cerebro-spinal fluid (Petitfour et al., 2022;Johansson et al., 2022;Pietroboni et al., 2017), suggesting overlapping pathobiology.
There is an enormous interest in drug development in AD (Cacabelos, 2022). Many pharmacological companies have focused on developing disease-modifying therapies using different monoclonal antibodies to prevent plaque formation (aducanumab, gantenerumab, lecanemab) and anti-tau therapy with designed tau-neutralised antibodies (Ossenkoppele et al., 2022). While the FDA has approved aducanumab, and lecanemab, the progress in AD drug development is limited due to the small effect of the medication on clinical progression and relation to amyloid build-up (Cummingd et al., 2022). Evidence suggests that drugs are twice as likely to be approved for clinical use if they are supported by GWAS evidence (Nelson et al., 2015). As such, GWAS can be a costefficient approach to prioritise new drug targets. Moreover, integrating overlapping genetic associations between AD and MS with multiomics and clinical data may guide the design of immune-related drugs for AD.
Previous reports show shared genetics risk factors between neurodegenerative disorders (AD, Parkinson's disease, and multiple system atrophy) and different somatic immune-mediated disorders Witoelar et al., 2017). Additionally, positive associations with both maternal and clinical AD have been reported to be a liability to MS using a multivariable Mendelian randomization study (Yeung et al., 2022). There are few cross-trait GWAS results for MS due to low power in previous GWAS (Andreassen et al., 2014;Elvsåshagen et al., 2020). However, the recent large GWAS from the IMSGC is more powerful (Patsopoulos et al., 2019).
Traditional methods for investigating genetic overlap between diseases include genetic correlation and polygenic risk score, which build on the assumption that genetic effect directions between two traits are predominantly concordant across the genome. This seems not to be the case with brain-related traits where there is a mixture of concordant and discordant directions of genetic effects across overlapping variants Frei et al., 2019). In contrast, MiXeR  estimates the total number of trait-specific and shared genetic variants influencing two traits regardless of effect direction, which seems more relevant for investigating molecular pathways of brainrelated diseases. Further, conditional-conjunctional false discovery rate (cFDR) method can be used to identify shared genetic loci between traits  and Local Analysis of [co]Variant Association (LAVA) for local genetic correlation (Werme et al., 2022).
The present study aims to reveal molecular mechanisms involving the immune system in AD, by investigating shared genetic architecture and overlapping genetic loci between AD and MS. This can pave the way for precision therapeutic strategies targeting neuroinflammation in neurodegenerative processes involved in AD.

Samples
GWAS summary statistics for AD from the Psychiatric Genomics Consortium (PGC) were used in this study (Wightman et al., 2021), excluding the 23andMe sample and data from the IGAP consortium due to overlap with control cohorts in the MS GWAS. The summary statistics for AD were partly based on the UKB cohort which included both cases and proxy-cases, and controls (Wightman et al., 2021). The final sample size was 64,549 cases and 634,442 controls. The MS GWAS summary statistics were obtained from the International Multiple Sclerosis Genetics Consortium (IMSGC; discovery phase, 14,802 cases and 26,703 controls, Patsopoulos et al., 2019). Participants in both GWAS were predominantly of European ancestry. Detailed descriptions of cohorts and samples are available in original publications (Wightman et al., 2021, Patsopoulos et al., 2019. For the validation of findings in AD we used summary statistics from an independent dataset with 2784 AD cases and 5222 controls recruited from several case-control and familybased studies of African Americans (Kunkle et al., 2021). A detailed description of the cohorts included in this analysis are provided in the Supplementary Material (Kunkle et al., 2021, Supplementary Note;Supplementary Tables 1-3). A study flowchart is presented in Fig. 1.

Gaussian causal mixture modelling method (MiXeR)
For investigation of the genetic architecture of AD and MS we used MiXeR software , https://github.com/precimed/mixer, Shadrin et al., 2020. Due to the high impact of the APOE region in AD we followed the analysis setup used in Holland et al. (2020) treating chromosome 19 separately from the other chromosomes. Additionally, we excluded the MHC region , due to the intricate linkage disequilibrium (LD) structure. Results are presented as Venn diagrams displaying the proportion of trait-specific and shared traitinfluencing SNPs followed by the standard deviation across 20 independent runs, log-likelihood plots and tables with parameters estimated by the MiXeR model, explaining 100% of the heritability.

Linkage disequilibrium score regression (LDSC) and local analysis of [co]variant association (LAVA)
For establishing genome-wide genetic correlation (rg) we used LDSC (Bulik-Sullivan et al., 2015) and for local rg analysis we used LAVA (Werme et al., 2022). For LAVA analysis we followed the protocol described in original article using the LD reference panel based on 1000 Genomes phase 3 genotype data for European samples (Werme et al., 2022;1000Genomes Project Consortium et al., 2015, and the partition of the genome into 2495 regions with average size of 1 Mb. Only regions revealing significant estimated SNP heritability (p < 0.05/2495) in both AD and MS were used to estimate local genetic correlations between the traits.

Quantile-quantile (QQ) plots and conditional false discovery rate (cFDR) analyses
We used conditional quantile-quantile (QQ) plots to visualise polygenic enrichment. Each conditional QQ plot shows the distribution of P values in the GWAS of the primary phenotype for a subset of variants selected based on the significance of their association with the conditional phenotype at three levels: P_secondary < 0.1, P_secondary < 0.01, and P_secondary < 0.001. For QQ plots production, we excluded variants within 3 regions: with complex LD patterns (MHC region: chr6:25119106-33,854,733) and regions linked to dementia phenotype (MAPT region: chr17:40000000-47,000,000; APOE region: chr19:42000000 47,000,000). Conditional QQ plots were produced in both directions: conditioning AD on MS, and conditioning MS on AD. Successive leftward deflection of the variant strata with increasing significance in the conditional phenotype in both directions suggests genetic overlap between traits. We used cFDR method including conditional FDR (condFDR) and conjunctional FDR (conjFDR) analyses (https://github.com/precimed/pleiofdr, Frei et al., 2019. We applied condFDR as the first part of the analysis (Supplementary1) and conjFDR analysis to identify shared genetic loci. According to standard protocols, the FDR significance cut-offs were 0.01 for condFDR and 0.05 for conjFDR (Cheng et al., 2021;Smeland et al., 2020).

Validation phase
We examined the significance of the identified lead variants shared between AD and MS in the independent cohort of AD (Kunkle et al., 2021). The sign-concordance test was not performed due to the absence of information about the direction of effect in the validation summary statistics.
We applied two SNP-to-gene mapping strategies, including (1) positional mapping according to FUMA with 10 kb window size and (2) Open Targets modelling for the annotation, which combined positional mapping as a distance between the variant and each gene's canonical transcription start site, eQTL, pQTL, splicingQTL and epigenomic data, and functional prediction , database version from October 2022). After excluding mapped genes in the MHC region, we applied genes to function analysis as implemented in FUMA. We used the Molecular Signatures Database to evaluate enrichment in immunological gene sets. We also applied MAGMA to summary statistics on AD and MS to test for enrichment of GWAS signals in 54 tissues (de Leeuw et al., 2015). The 54 gene-sets were defined by gene-expression levels from 54 GTEx tissues (GTEx Consortium, 2015).
We used Cytoscape (version 3.9.1, Shannon et al., 2003) with STRING database for pathway analysis.

Univariate and bivariate MiXeR show similar polygenicity between AD and MS and large genetic overlap despite negligible global genetic correlation
Our LDSC analysis of current GWAS data shows weak non-significant genetic correlation between AD and MS (rg = 0.03, standard error (SE) = 0.07, P = 0.67). AD heritability estimated by LDSC was 0.0421, SE = 0.007. MS heritability estimated by LDSC was 0.3059, SE = 0.0256. Univariate MiXeR estimated the SNP heritability (h2) = to 0.088 for AD (h2 for chromosome 19 + h2 for all other autosomes) and 0.249 for MS (h2 for chromosome 19 + h2 for all other autosomes).
Using univariate MiXeR we show that AD and MS show similar polygenicity. The number of trait-influencing variants was estimated to 1763 variants for AD and 1802 for MS. Bivariate MiXeR analysis revealed polygenic overlap on autosomes excluding chromosome 19 ( Fig. 2A, and Fig. 1, Supplementary) and for chromosome 19 (Fig. 2B, and Fig, 1, Supplementary) with adequate quality of model fit suggested by log-likelihood plots and Akaike information criteria. For all chromosomes the predicted number of shared loci between MS and AD was around 400, for chromosome 19 specifically it was 15 variants (Fig. 2C). The observed substantial genetic overlap with minor genetic correlation suggests a balanced mixture of concordant and discordant genetic effects across shared loci.

ConjFDR analysis identify shared genomic loci between AD and MS
Conditional Q-Q plots for AD and MS revealed strong enrichment in both directions (Fig. 4). Observed significant leftward shift for the group of SNPs with higher significance indicated genetic enrichment and possible shared genetic background between AD and MS. After the application of condFDR for both traits we showed comparable power to unconditional FDR analysis (Manhattan plot, Supplementary 1, Figs. 2 and 3).
ConjFDR analysis identified 16 loci jointly associated with AD and MS (see Manhattan plot at Fig. 5, Table 1). Six of them were novel for AD and three for MS according to GWAS catalog and novelty checking protocol. Furthermore, 50% of lead SNPs (8/16) had the same effect direction on MS and AD. These results are consistent with the observation of data low global genetic correlation between two diseases because SNPs have mixed directions of effects, which was also supported by the LAVA results.
To replicate our genetic findings, we used summary statistics from an independent Afro-American cohort with AD. One locus was nominally significant in the independent cohort but did not survive the multiple testing correction (rs35866622, p_replication = 0.0037). Other loci identified in our conjFDR analysis were non-significant in the independent Afro-American cohort at both nominal and multiple testing correction levels.

Functional annotation of identified loci
Positional mapping with FUMA showed that most of the identified lead variants were intronic (68.8%, 11/16) ( Table 1, Fig. 6, Supplementary, A). One of the lead SNPs (rs35866622 in MAMSTR gene) has CADD score above 12.37, suggesting high deleteriousness. This lead SNP was nominally significant in the Afro-American population. The Locus zoom plot for this variant and circos plot for chromosome 19 are presented at Figs. 4 and 5, A (Supplementary).
According to Regulome Database classification, the rs10400902 (CTSH gene) variant can affect binding. Two other SNPs (rs 1,846,190 and rs10806425) in HLA-DQA1 and BACH2 have classification 3a and are less likely to affect binding.
Then we performed analysis using Open Targets platform to aggregate evidence linking variants to genes and revealed that in 8 cases other genes than in FUMA were mapped according to Open Targets algorithm (presented at Table 1 as the second gene in column "Gene" and in Table 2 in Supplementary for results from weighted models and pQTL, eQTL, sQTL). We used the gene-to-function analysis in FUMA for all genes highlighted by either FUMA or Open Targets (24 genes) to understand which pathways and tissues might be involved. Five identified genes were highly expressed in brain tissue -ALDOA, COPA, however these genes also revealed high expression rates in other tissues. BACH2, FAM117B genes had elevated expression during early prenatal period and for ETS2 in adulthood ( Supplementary Fig. 5., B). Evaluated genes were up-regulated in the spleen using GTEx 30 general tissue types database ( Supplementary Fig. 6, B). Additionally, we performed MAGMA analysis for MS and AD summary statistics and revealed two common tissues (spleen and whole blood) using GTEx 54 general tissue types database ( Supplementary Fig. 7, for spleen p = 2.1949e-05 and p = 1.0743e-17, for whole blood p = 0.00010933 and p = 7.7985e-13 for Using pathway analysis, only molecular signatures database revealed several significant changes: according to positional gene sets (MsigDB c1) which reflect the gene architecture and chromosomal changes there are structural changes at chromosome 1 (Chr1q23) for genes FCRL2, FCRL1, COPA, NHLH1 (see Supplementary Fig. 6.C).

Discussion
Here we applied state-of-the-art statistical tools to improve our knowledge of the genetic underpinnings of the relationship between AD and MS. According to our results, the polygenicity of AD and MS was similar, but less than for other psychiatric disorders Hindley et al., 2022). Substantial genetic overlap between AD and MS was revealed using MiXeR, estimated to 400 trait-influencing variants, using an AD-specific setup of the MiXeR previously published by Holland D (Holland et al., 2020). In this setup, chromosome 19 is analysed separately, to mitigate potential violations of the MiXeR model assumptions due to the extreme significance of the APOE region in AD. As demonstrated previously, this setup improves model fitness and provides higher sensitivity to polygenic components.
A total of 16 shared genetic loci were revealed by the cFDR approach using current GWAS data. Annotated genes in shared loci were enriched in molecular signalling pathways involved in inflammation and the structural organisation of neurons. Taken together, these findings support a shared genetic architecture between AD and MS, and implicate novel molecular pathways. Despite the observed substantial genetic overlap, the genetic correlation between AD and MS was negligible and insignificant, suggesting a mixed direction of effects in the shared loci. This is supported by the LAVA analysis revealing a balanced mixture of concordant and discordant shared loci scattered throughout the genome. These findings indicate that common variants that influence the genetic risk for diverse neurological phenotypes may have risk-enhancing and risk-reducing effects on different disorders or be involved in the same processes with different effect directions on disease. We hypothesise that immunological pathways are influenced in different ways: in MS immunological activation can lead to relapse (Wei et al., 2021), while in AD it can be connected to protective health-related immune perturbation and maintain proper metabolic clearance (Piehl et al., 2022;Cisbani and Rivest, 2021). Additionally, it can be linked to the idea that microglia can play both neuroprotective and deleterious roles in neurological disease pathogenesis: Aβ and damaged myelin can prompt a transcriptional shift in microglia to promote the upregulation of microglial phagocytic machinery to clear the pathology (Ennerfelt and Lukens, 2023). Immunological involvement might confirm the effectiveness of humanised monoclonal antibodies in AD therapies, such as lecanemab (https://www.fda.gov/news-events/press-announcements/f da-grants-accelerated-approval-alzheimers-disease-treatment). Moreover, unearthing the mechanism by which the immunological system can modify pathology in neurodegenerative diseases can be important for future directions of drug development.
The immune system's involvement in the pathogenesis of late-onset AD was suggested by the recent AD GWASs (Wightman et al., 2021;Jansen et al., 2019;Bellenguez et al., 2022). In our study FUMA gene to function analysis revealed an essential component of immunological function according to Molecular Signatures Database, and FUMA tissue specificity analysis for shared loci revealed the involvement of spleen in both disorders. These results were confirmed by MAGMA which displayed significant enrichment in spleen and blood tissue for both conditions supporting previous studies Wightman et al., 2021). Furthermore, it pointed to the immune system's involvement in both diseases. Additionally, the present study showed the involvement of shared immune-related gene loci between AD and MS and identified several novel loci. FCRL1 and FCRL2 genes were previously described as involved in AD pathophysiology (Cohen et al., 2020) and have an essential role in immunological pathways. These genes encode a member of the immunoglobulin receptor superfamily and are one of several Fc receptor-like glycoproteins clustered on the long arm of chromosome 1. This locus on chromosome 1 was previously described in MS (International Multiple Sclerosis Genetics Consortium (IMSGC) et al., 2013) but it is novel for AD.
COPA was reported to be an essential gene in developing of systemic immune disorders such as psoriasis, lung immune disorders, and others (Watkin et al., 2015), and it can be linked to immune pathology in MS and AD. Other genes potentially involved in immune system pathogenesis include BACH2, which is associated with NF-kappa b signalling (Boche and Gordon, 2022), BLNK, which is a B-cell linker protein and is associated with B-cell signalling (Turkoglu et al., 2021), and CR1, a complement C3b/C4b receptor 1 involved in different complement associated processes. Decreased expression of CR1 protein was shown to occur in systemic lupus erythematosus, sarcoidosis, and AD (Crehan et al., 2012). PVR, or CD155, belongs to a large family of immunoglobulin (Ig)-like molecules called nectins and nectin-like proteins, which mediate cell-cell adhesion, cell migration, and cell polarisation by interacting with other nectins, and has also been established as an

Table 1
Genomic loci are jointly associated with Alzheimer's disease (AD) and multiple sclerosis (MS) at conjunctional FDR (conjFDR) < 0.05. For each identified locus the table presents the rs number of the lead SNP, its chromosomal position and alleles, the nearest gene and its functional category, and the number of base pairs (distance) between the lead SNP to the gene according to FUMA, as well as p-values and effect sizes (odds ratios for MS, z-scores for AD) from the original summary statistics on AD and MS. The effect sizes are given with reference to allele 1 (A1). CADD score was used for predicting the deleteriousness of variants. Regulome database (RDB) score was used for functional annotation. Columns "Novel_in_" means novelty for SNP in the disease. Column p in "Kunkle_et_al" presented p value in replication dataset. Significant value marked in bold.

Locus
Lead immunomodulatory receptor, which is able to activate and inhibit natural killer cells (Lupo and Matosevic, 2020). Additionally, HLA involvement links to the importance of inflammatory pathways in the pathogenesis of both diseases as previously described (Lindbohm et al., 2022). Using Cytoscape and the STRING protein database (Szklarczyk et al., 2017), we revealed interactions between HLA, CTSH and BATCH2 proteins which are strongly linked to the immune system and protein metabolism pathways (Fig. 9., Supplementary). In both diseases, it was linked with the same effect direction in cFDR and LAVA. However, it should be treated with caution due to intricate LD structure in this region. The knowledge of the new immune genes potentially involved in AD pathology can be linked to new drug development. After the discovery of TREM2 mutations the study of a new target drug has been started (A Phase 2 Study to Evaluate Efficacy and Safety of AL002 in Participants With Early Alzheimer's Disease -Full Text View -ClinicalTrials.gov, NCT04592874). Moreover, many monoclonal antibodies to different targets entered phase 1 and 2 of clinical trials during the last years (Cummingd et al., 2022). Once more confirmatory studies on the role of neuroinflammation in AD are conducted, the development of new AD medications in this area could accelerate (Olloquequi et al., 2022).
In addition to the immune system, other processes are shared between the two disorders. MAPK3 is involved in the phosphorylation of tau proteins microtubule-associated protein 2 and 4, which link to microtubules system and neurodegeneration (Lund et al., 2014). PLXNC1 encodes a member of the plexin family, which is involved in the regulation of axon guidance, cell motility and migration, and the immune response. CTSH encoded a cathepsin H protein which can be involved in lysosomal pathology and neurodegeneration (Drobny et al., 2022). Functional annotation highlighted a SNP on chromosome 19 with a highly deleterious CADD score, which contains MAMSTR and is replicated in an independent study. The mutation has different directions in AD and MS, and the involvement of this SNP was described previously.
A gap between the number of shared trait-influencing variants predicted by MiXeR and the number of shared loci identified by the cFDR approach can be attributed to undiscoverable "missing" heritability due to current insufficient GWAS power (Wightman et al., 2021), rare and structural variants (Matthews and Turkheimer, 2022;Andrews et al., 2023). Furthermore, a substantial increase in current sample sizes is required for both disorders to detect most of the common risk variation at the genome-wide significance level. The heritability for AD was lower than for MS. The small difference between AD heritability estimates obtained with MiXeR and LDSC methods might be attributed to the different mathematical models underlying these methods Bulik-Sullivan et al., 2015). LDSC is based on the infinitesimal model which assume that each variant has an effect on the phenotype (Bulik-Sullivan et al., 2015), which might be suboptimal for late-onset neurological disorders with complex genetic architecture (Baker et al., 2023). On the other hand, MiXeR assumes that only a fraction of variants influences the phenotype while remaining genomic variants have zero effect.
This study has some limitations. Due to the inclusion of the most recent GWAS data for both AD and MS in our discovery analysis, our replication analysis was limited to a small AD GWAS based on a sample with different ancestry, which can explain the low replication level. Although genetics plays a substantial role in the etiology of AD and MS, and there is genetic overlap between the disorders, the part of environmental influences should not be omitted as well as differences in neuropathological processes due to gene-environment interplay, epistatic effects and other pathological pathways involved in the pathogenesis of AD and MS.
In summary, the main findings of our study were comparable polygenicities for AD and MS with 20% of trait-influencing variants being shared between the disease despite negligible global genetic correlation. ConjFDR analysis identified 16 shared genetic loci between AD and MS, with 8 having concordant direction of effects. Annotated genes in shared loci were enriched in molecular signalling pathways involved in inflammation and the structural organisation of neurons. These findings provide molecular genetic insights into the immune mechanisms involved in AD.

Declaration of Competing Interest
O.A.A. has received speaker's honorarium from Janssen, Sunovion and Lundbeck and is a consultant for cortechs.ai, Milken and Biogen. Dr. Dale is a Founder of and holds equity in CorTechs Labs, Inc., and serves on its Scientific Advisory Board. He is a member of the Scientific Advisory Board of Human Longevity, Inc. and receives funding through research agreements with General Electric Healthcare and Medtronic, Inc. The terms of these arrangements have been reviewed and approved by UCSD in accordance with its conflict of interest policies. Geir Selbaek has received honoraria as a participant at advisory board meetings for Roche and Biogen. Remaining authors have no conflicts of interest to declare.

Data availability
GWAS data without IGAP and 23andme from PGC-ALZ were downloaded: https://www.med.unc.edu/pgc/download-results/ and additionally modified by request. GWAS data for IMSGC can be obtained after request to IMSGC data access committee: https://imsgc.net. Publicly available summary statistics for Afro-American with p-value were received from NG00100 -Alzheimer's disease in African Americans(NIAGADS). Statistical analyses were performed in MATLAB and Python, using existing tools available on GitHub, including conditional/conjunctional false discovery rate (https://github.com/precimed/pleiofdr).

Acknowledgements
All GWAS investigated in the present study were approved by the local ethics committees, and informed consent was obtained from all participants. The authors thank the researchers of the IMSGC, PGC and ADGC consortia for access to data, and for all participants who provided samples. We gratefully acknowledge support from the American National Institutes of Health (NS057198, EB00790), the Research Council of Norway (#229129, 213837, 324252, 326813, 300309, 273291, 223273, 248980, 296030), the South-East Norway Regional Health Authority (2022-073), KG Jebsen Stiftelsen (SKGJ-MED-021), Norwegian Health Association ("Nasjonalforeningen for folkehelsen", #22731). This project has received funding from the European Union's