Case study: APH1B xQTL and AD GWAS¶

This notebook documents the analysis of xQTL case study on a targeted gene, APH1B.

  • Section 0: Sanity check
  • Section 1: Fine-mapping for xQTL and GWAS
  • Section 2: Multi-context colocalization with Bellenguez 2022
  • Section 3: Refinement of colocalized loci with other AD GWAS
  • Section 4: Assessment of multi-context xQTL effect sizes
  • Section 5: Multi-context causal TWAS (including conventional TWAS and MR)
  • Section 6: Context specific multi-gene fine-mapping
  • Section 7: Epigenomic QTL and their target regions
  • Section 8: Context focused validation in other xQTL data
  • Section 9: Non-linear effects of xQTL
  • Section 10: in silico functional studies in iPSC model
  • Section 11: Functional annotations of selected loci
  • Section 12: Candidate loci as trans-xQTL

Overview¶

FunGen-xQTL resource contains 67 xQTL contexts as well as 9 AD GWAS fine-mapped genome-wide. The overarching goal for case studies is to use these resource to raise questions and learn more about gene targets of interest.

Overall, a case study consists of the following aspects:

  • Check the basic information of the gene
  • Check the existing xQTL and integrative analysis results, roughly including
    • Summary table for univariate fine-mapping
    • Marginal association results
    • Multi-gene and multi-context fine-mapping
    • Multi-context colocalization with AD GWAS
    • TWAS, MR and causal TWAS
    • Integration with epigenetic QTL
    • Quantile QTL
    • Interaction QTL
    • Validation:
      • Additional xQTL data in FunGen-xQTL
      • Additional AD GWAS data-set already generated by FunGen-xQTL
    • In silico functional studies
      • Additional iPSC data-sets
    • Functional annotations of variants, particularly in relevant cellular contexts
  • Creative thinking: generate hypothesis, search in literature, raise questions to discuss

Computing environment setup¶

In [109]:
region_p
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In [121]:
pip_p
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Section 0: Sanity check¶

Check the basic information of the gene¶

  • To gain a preliminary understanding of this gene’s expression—specifically, whether it is cell-specific—can help us quickly determine if our results are consistent with expectations.

Useful websites:

  1. check gene function, (immune) cell type specificity, tissue specifity, protein location: https://www.proteinatlas.org
  2. check gene position and structure: https://www.ncbi.nlm.nih.gov/gene/
  3. other collective information: https://www.genecards.org

Check the existing results which are inputs to this analysis¶

In [1]:
source('/data/interactive_analysis/rf2872/codes/cb_plot.R')
source('/data/interactive_analysis/rf2872/codes/utilis.R')
for(file in list.files("/data/colocalization/colocboost/R", pattern = ".R", full.names = T)){
          source(file)
        }
gene_name = 'APH1B'

dir.create(paste0('plots/', gene_name), recursive = T)

get basic target gene information

In [2]:
target_gene_info <- get_gene_info(gene_name = gene_name)
target_gene_info
$gene_info
A data.table: 1 x 14
region_id#chrstartendTSSLD_matrix_idLD_sumstats_idLD_sumstats_id_oldTADB_indexTADB_idgene_startgene_endsliding_windowsgene_name
<chr><chr><dbl><dbl><int><chr><chr><chr><chr><chr><int><int><chr><chr>
ENSG00000138613chr15622760176548000063276017chr15:61125463-63051119,chr15:63051119-6668053715_61125463-63051119,15_63051119-6668053715_61125463-63051119,15_63051119_66680537TADB_1132,TADB_1133,TADB_1134chr15_58574103_63343138,chr15_60834681_64158021,chr15_61390525_665177046327601863309126chr15:54171378-63343138,chr15:56375966-64158021,chr15:58574103-66517704,chr15:60834681-67685794,chr15:61390525-69257131,chr15:64234460-70062762,chr15:65293216-73640125APH1B
$target_LD_ids
A matrix: 1 x 2 of type chr
chr15:61125463-63051119chr15:63051119-66680537
$target_sums_ids
A matrix: 1 x 2 of type chr
15_61125463-6305111915_63051119-66680537
$gene_region
'chr15:62276017-65480000'
$target_TAD_ids
A matrix: 1 x 3 of type chr
chr15_58574103_63343138chr15_60834681_64158021chr15_61390525_66517704
In [3]:
gene_id = target_gene_info$gene_info$region_id
chrom = target_gene_info$gene_info$`#chr`

Take a quick look for the expression of target gene in ROSMAP bulk data, we don't want them to be too low

In [4]:
source('/data/interactive_analysis/rf2872/codes/utilis.R')
expression_in_rosmap_bulk(target_gene_info)
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Section 1: Fine-mapping for xQTL and GWAS¶

see notebook

In [5]:
region_p

Bellenguez et al GWAS signals has many overlap with CS from other xQTL sources. This motivates us to look further. The figure above shows the ranges of CS to give us a loci level idea. Below, we show the variants in those CS, color-coding the variants that are shared between them in the same color. In particular, AD GWAS signals are also captured by a few xQTL data, although at this point we don't have formal statistical (colocalization) evidences for these observations yet.

In [6]:
pip_p

Section 2: Multi-context colocalization with Bellenguez 2022¶

This is done using ColocBoost. The most updated version of ColocBoost results are under path s3://statfungen/ftp_fgc_xqtl/analysis_result/ColocBoost/2024_9/

In [7]:
cb_res <- readRDS(paste0("/data/analysis_result/ColocBoost/2024_9/",gene_id,"_res.rds") )
In [8]:
#save colocboost results
cb_res_table <- get_cb_summary(cb_res) 

saveRDS(cb_res_table, paste0(gene_name, "_colocboost_res.rds"))
In [9]:
cb <- plot_cb(cb_res = cb_res, cex.pheno = 1.5, x.phen = -0.2)
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In [ ]:
options(repr.plot.width=6, repr.plot.height=6)

ggplot(APH1B_int_res, aes(x = variant_id, y = qvalue_interaction)) +
  geom_point(alpha = 0.7, size = 6) +
  labs(title = "qvalue for APH1B csets in interaction association nalysis",
       x = "Gene Name",
       y = "qvalue_interaction",
       size = "qvalue_interaction") +
  theme_minimal(base_size = 14) +
  theme(panel.background = element_blank(),
        panel.grid.major = element_line(color = "grey80"),
        legend.position = NULL,
        axis.text.x = element_text(angle = 45, hjust = 1))  + ylim(0,1)
  # scale_color_manual(values = colorRampPalette(brewer.pal(8, "Set1"))(length(unique(flat_var$gene_name))))
ggsave('plots/APH1B/sec11.interaction_association_APH1B_lessPIP25.pdf', height = 5, width = 8) 
In [11]:
# colocalized variants
cb_res_table
A data.frame: 1 x 8
colocalized phenotypespurity# variantshighest VCPcolocalized indexcolocalized variantsmax_abs_z_variantcset_id
<chr><dbl><dbl><dbl><chr><chr><chr><chr>
Ast; Oli; Exc; DLPFC; AC; PCC; Monocyte; AD_Bellenguez_2022120.80863064999; 5009chr15:63277703:C:T; chr15:63279621:C:Tchr15:63279621:C:Tcoloc_sets:Y2_Y3_Y5_Y7_Y8_Y9_Y10_Y16:CS1
In [12]:
# effect sign for each coloc sets
get_effect_sign_csets(cb_res)
$`coloc_sets:Y2_Y3_Y5_Y7_Y8_Y9_Y10_Y16:CS1` =
A data.frame: 2 x 9
variantsAstOliExcDLPFCACPCCMonocyteAD_Bellenguez_2022
<chr><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl>
chr15:63277703:C:Tchr15:63277703:C:T4.5487675.8604386.841697.8176476.8376884.8950185.0489559.495798
chr15:63279621:C:Tchr15:63279621:C:T4.5487675.8604386.841697.8337406.5943494.6499045.0489559.100000
In [13]:
# LD between coloc sets
get_between_purity_simple(cb_res, gene.name = gene_id, path = '/data/colocalization/QTL_data/eQTL/')

Here, different colors refer to different 95% Colocalization Sets (CoS, a metric developed in ColocBoost indicating that there is 95% probabilty that this CoS captures a colocalization event). We only included ROSMAP data for this particular ColocBoost analysis. In this case, we observe cell specific eQTL, bulk sQTL colocalization on ROSMAP data with AD as two separate CoS, suggesting two putative causal signals. We did not detect colocalization with pQTL of statistical significance although from Section 1 there are some overlap with pQTL signals in fine-mapping CS, the overlapped variants in CS have small PIP.

Section 3: Refinement of colocalized loci with other AD GWAS¶

Here we refine the colocalization with other AD GWAS to iron out any heterogeniety between studies (heterogeniety can come from many sources), to get additional candidate loci from these more heterogenous sources as candidates to study.

In [14]:
AD_cohorts <- c('AD_Jansen_2021', 'AD_Bellenguez_EADB_2022', 'AD_Bellenguez_EADI_2022',
             'AD_Kunkle_Stage1_2019', 'AD_Wightman_Excluding23andMe_2021',
             'AD_Wightman_ExcludingUKBand23andME_2021', 'AD_Wightman_Full_2021')
cb_ad <- plot_cb(cb_res = cb_res, cex.pheno = 1.5, x.phen = -0.2, add_gwas = TRUE, gene_id = gene_id, cohorts = AD_cohorts)
No pvalue cutoff. Extract all variants names.No pvalue cutoff. Extract all variants names.No pvalue cutoff. Extract all variants names.No pvalue cutoff. Extract all variants names.No pvalue cutoff. Extract all variants names.No pvalue cutoff. Extract all variants names.No pvalue cutoff. Extract all variants names.
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In [15]:
pdf('plots/APH1B/sec3.colocboost_res_allad.pdf', width = 10, height = 5)
replayPlot(cb_ad$p)
dev.off()
pdf: 2

Section 4: Assessment of multi-context xQTL effect sizes¶

Option 1: ColocBoost + MASH¶

Use colocboost variants and check for mash posterior contrast to see if the effect size are shared or specific or even opposite. Advantage is that colocboost result is AD GWAS informed; issue is that marginal posterior effects is not always the joint

In [16]:
mash_p <- mash_plot(gene_name = 'APH1B')
for (plot in mash_p) {
    print(plot)
}
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Option 2: mvSuSiE¶

Use mvSuSiE multicontext fine-mapping results --- the bubble plot to check posterior effects. Issue is that we don't have this results yet, and this is limited to one cohort at a time, without information from AD.

We should go for option 1 by default and if we want to make claim about opposite effect size we double-check with mvSuSiE multicontext analysis.

Section 5: Multi-context causal TWAS (including conventional TWAS and MR)¶

The most updated version of cTWAS analysis are under path s3://statfungen/ftp_fgc_xqtl/analysis_result/cTWAS/

TWAS results¶

We report TWAS from all contexts and methods from the pipeline. Here we will filter it down to the best performing methods and only keep contexts that are significant.

In [17]:
plot_TWAS_res(gene_id = gene_id, gene_name = gene_name)
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MR results¶

This is only available for genes that are deemed significant in TWAS and have summary statistics available for effect size and standard errors in GWAS, in addition to z-scores --- current version does not support z-scores although we will soon also support z-scores in MR using MAF from reference panel.

cTWAS results¶

To be updated soon.

Section 6: Context specific multi-gene fine-mapping¶

A quick analysis: using the xQTL-AD summary table (flatten table)¶

We extract from xQTL-AD summary table the variants to get other genes also have CS with the variants shared by target gene and AD.

In [18]:
multigene_flat <- get_multigene_multicontext_flatten('Fungen_xQTL_allQTL.overlapped.gwas.export.APH1B.rds', sQTL = 'no_MSBB')
multigene_flat
A data.frame: 29 x 6
gene_id#chrstartendgene_namecontexts
<chr><chr><int><int><chr><chr>
ENSG00000035664chr156407203264072033DAPK2 BM_36_MSBB_eQTL,BM_44_MSBB_eQTL
ENSG00000074410chr156338184563381846CA12 Knight_eQTL,BM_10_MSBB_eQTL,BM_44_MSBB_eQTL,Ast_DeJager_eQTL,DLPFC_DeJager_eQTL,PCC_DeJager_eQTL,Ast_Kellis_eQTL,Ast_mega_eQTL,ROSMAP_PCC_sQTL,STARNET_eQTL
ENSG00000074621chr156561137765611378SLC24A1 MiGA_SVZ_eQTL
ENSG00000090470chr156513380765133808PDCD7 MiGA_SVZ_eQTL
ENSG00000103642chr156312183263121833LACTB MiGA_SVZ_eQTL,Exc_DeJager_eQTL
ENSG00000103657chr156383394763833948HERC1 MiGA_THA_eQTL,ROSMAP_AC_sQTL,ROSMAP_DLPFC_sQTL
ENSG00000103710chr156507668965076690RASL12 BM_22_MSBB_eQTL,ROSMAP_AC_sQTL,ROSMAP_PCC_sQTL
ENSG00000103742chr156542294665422947IGDCC4 BM_22_MSBB_eQTL,Ast_DeJager_eQTL,Inh_DeJager_eQTL,DLPFC_DeJager_eQTL,PCC_DeJager_eQTL,AC_DeJager_eQTL,Inh_Kellis_eQTL,Ast_mega_eQTL,ROSMAP_AC_sQTL,ROSMAP_DLPFC_sQTL
ENSG00000129003chr156206047262060473VPS13C ROSMAP_PCC_sQTL
ENSG00000138614chr156561128865611289INTS14 MiGA_THA_eQTL
ENSG00000140416chr156304263163042632TPM1 ROSMAP_DLPFC_sQTL
ENSG00000140455chr156350451063504511USP3 Mic_DeJager_eQTL,Mic_mega_eQTL,OPC_mega_eQTL
ENSG00000166128chr156318955963189560RAB8B OPC_Kellis_eQTL,Ast_mega_eQTL,DLPFC_Bennett_pQTL,ROSMAP_AC_sQTL,ROSMAP_PCC_sQTL,ROSMAP_DLPFC_sQTL,STARNET_eQTL
ENSG00000166794chr156416313364163134PPIB MiGA_GTS_eQTL,Inh_Kellis_eQTL
ENSG00000166803chr156438768664387687PCLAF MiGA_GTS_eQTL
ENSG00000166839chr156491190164911902ANKDD1A Ast_Kellis_eQTL
ENSG00000169118chr156435617264356173CSNK1G1 ROSMAP_AC_sQTL,ROSMAP_DLPFC_sQTL
ENSG00000171914chr156239052562390526TLN2 MiGA_GTS_eQTL,AC_DeJager_eQTL,ROSMAP_AC_sQTL,ROSMAP_PCC_sQTL
ENSG00000174446chr156649777966497780SNAPC5 MiGA_SVZ_eQTL
ENSG00000174498chr156537800165378002IGDCC3 MiGA_GTS_eQTL
ENSG00000180304chr156470328064703281OAZ2 MiGA_SVZ_eQTL
ENSG00000180357chr156446074164460742ZNF609 ROSMAP_PCC_sQTL
ENSG00000185088chr156315802063158021RPS27L MiGA_THA_eQTL,ROSMAP_PCC_sQTL
ENSG00000186198chr156504538665045387SLC51B BM_44_MSBB_eQTL
ENSG00000205502chr156216528462165285C2CD4B MiGA_THA_eQTL
ENSG00000241839chr156484188264841883PLEKHO2 MiGA_SVZ_eQTL
ENSG00000246922chr156511519965115200UBAP1L Inh_Kellis_eQTL
ENSG00000249240chr156484194764841948AC069368.1ROSMAP_AC_sQTL
ENSG00000259316chr156438143964381440AC087632.2ROSMAP_AC_sQTL,ROSMAP_DLPFC_sQTL

Other genes implicated are PROC and HS6ST1 in MiGA cohort which may share causal eQTL with APH1B. Further look into the data-set --- using these genes as targets and repeating what we did above for APH1B --- might be needed to establish a more certain conclusion.

Alternatively, we may be able to apply a multi-gene statistical fine-mapping test on APH1B region to find these genes, as you will see in the section below.

A statistically solid approach: mvSuSiE multi-gene analysis¶

This multi-gene fine-mapping analysis was done for each xQTL context separately. We will need to check the results for all contexts where this gene has an xQTL, in order to identify if there are other genes also sharing the same xQTL with this target gene. We included other genes in the same TAD window along with this gene, and extended it into a sliding window approach to include multiple TADs just in case. You need to check the sliding windows belongs to that gene (TSS) on analysis repo.

In [19]:
sliding_windows <- target_gene_info$gene_info$sliding_windows %>% strsplit(., ',') %>% unlist %>% as.character
sliding_windows
  1. 'chr15:54171378-63343138'
  2. 'chr15:56375966-64158021'
  3. 'chr15:58574103-66517704'
  4. 'chr15:60834681-67685794'
  5. 'chr15:61390525-69257131'
  6. 'chr15:64234460-70062762'
  7. 'chr15:65293216-73640125'

The most updated version of mvSuSiE multi-gene results are under path s3://statfungen/ftp_fgc_xqtl/analysis_result/mvsusie_multi_gene_test/multi_gene/ Currently it is still WIP. You can revisit this later when we prompt you to. Here is an example for APH1B:

In [20]:
mnm_gene <- list()
for (window in sliding_windows) {
    mnm_gene_tmp <- NULL
    mnm_gene_tmp <- tryCatch(
        readRDS(paste0('/data/analysis_result/mvsusie_multi_gene/multi_gene/ROSMAP_multi_gene.', window, '.mnm.rds')),
        error = function(e) NULL
    )
    
    if (!is.null(mnm_gene_tmp)) {
        if(target_gene_info$gene_info$region_id %in% mnm_gene_tmp$mvsusie_fitted$condition_names){
        tryCatch({
            p <- mvsusieR::mvsusie_plot(mnm_gene_tmp$mvsusie_fitted, sentinel_only = F, add_cs = T)
            print(p)  # This ensures the plot is displayed in JupyterLab
        }, error = function(e) NULL)
        } else {
            message('There is mnm result for sliding window ',window,', but not include target gene ', gene_name, ' in CS')
        }
        mnm_gene <- append(mnm_gene, list(mnm_gene_tmp))
    }
}

In this case, there is no statistical evidence for APH1B sharing any of its xQTL with other genes in ROSMAP Microglia data we looked into; although we have not analyzed MiGA this way yet (which showed some potential signals from the quick analysis above).

Section 7: Epigenomic QTL and their target regions¶

fsusie, see notebook

Generate a crude plot to determined whether the story is interesting¶

This is a crude version of the case study plot which shows the fsusie Effect (colored line), the gene body (black arrow), the epi-QTL (large dots with the same color as the effects) and ADGWAS cs position (small red dots).

Only produce the refine plot if we can see either:

  1. There are sharing snp between epi-QTL and AD CS
  2. There are the AD CS located within one of the effect range
  3. The crude plot suggest something interesting
In [21]:
options(repr.plot.width = 40, repr.plot.height = 40)

 ggplot() + theme_bw() +  facet_grid(cs_coverage_0.95+study + region ~ ., labeller = labeller(.rows = function(x) gsub("([_:,-])", "\n", x)), scale = "free_y") +

      theme(text = element_text(size = 20), strip.text.y = element_text(size = 25, angle = 0.5)) +
     # xlim(view_win) +
      ylab("Estimated effect") +
   #   geom_line(data = haQTL_df %>% mutate(study = "haQTL effect") %>% filter(CS == 5),
    #            aes_string(y = "fun_plot", x = "x", col = "CS"), size = 4, col = "#00AEEF") +
  geom_line(data = effect_of_interest ,
                aes_string(y = "fun_plot", x = "x", col = "cs_coverage_0.95"), size = 4) +  
    geom_point(data = effect_of_interest ,
                aes_string(y = "pip", x = "pos", col = "cs_coverage_0.95"), size = 4) +
    theme(text = element_text(size = 40), strip.text.y = element_text(size = 15, angle = 0.5), 
            axis.text.x = element_text(size = 40), axis.title.x = element_text(size = 40)) +
      xlab("Position") +
      ylab("Estimated\neffect") +
      geom_segment(arrow = arrow(length = unit(1, "cm")), aes(x = gene_start, xend = gene_end, y = 1, yend = 1), size = 6,
                  data = tar_gene_info$gene_info, alpha = 0.3) +
      geom_text(aes(x = (gene_start + gene_end) / 2, y = 1 , label = gene_name), size = 10, 
              data = tar_gene_info$gene_info)+
        geom_point(aes(x = pos, y = pip  ) ,color = "red", data = flatten_table%>%filter( str_detect(study,"AD_") , cs_coverage_0.95 != 0  )%>%mutate(AD_study = study%>%str_replace_all("_","\n" ))%>%select(-study,-region,-cs_coverage_0.95) ) 

Section 8: Context focused validation in other xQTL data¶

see notebook

add fake version for now, so you don't have to refer to above link

Background: our "discovery set" is ROSMAP but we have additional "validation" sets including:

  • STARNET
  • MiGA
  • KnightADRC
  • MSBB
  • metaBrain
  • UKB pQTL

TODO:

  • Get from Carlos WashU CSF based resource (pQTL and metabolomic QTL)

This section shows verification of findings from these data-sets. In principle we should check them through sections 1-6 more formally. In practice we will start with colocalization via colocboost --- since our study is genetics (variant and loci level) focused. We can selectively follow them up for potentially intereting validations. We therefore only demonstrate validation via colocboost as a starting point.

In [22]:
finempping_contexts <- readRDS(paste0(gene_name, '_finemapping_contexts.rds')) # from sec1
In [23]:
finempping_contexts <- get_norosmap_contexts(finempping_contexts)
In [24]:
cb_ad <- plot_cb(cb_res = cb_res, cex.pheno = 1.5, x.phen = -0.2, add_QTL = TRUE, cohorts = finempping_contexts, gene_id = gene_id)
No pvalue cutoff. Extract all variants names.No pvalue cutoff. Extract all variants names.No pvalue cutoff. Extract all variants names.No pvalue cutoff. Extract all variants names.No pvalue cutoff. Extract all variants names.

In conclusion from what's shown above, when we check the association signals in STARNET and MiGA on colocalization established from ROSMAP and AD GWAS, we see additional evidences.

Section 9: Non-linear effects of xQTL¶

see notebook

APOE interaction¶

In [25]:
options(repr.plot.width=6, repr.plot.height=6)

ggplot(APH1B_int_res, aes(x = variant_id, y = qvalue_interaction)) +
  geom_point(alpha = 0.7, size = 6) +
  labs(title = "qvalue for APH1B csets in interaction association nalysis",
       x = "Gene Name",
       y = "qvalue_interaction",
       size = "qvalue_interaction") +
  theme_minimal(base_size = 14) +
  theme(panel.background = element_blank(),
        panel.grid.major = element_line(color = "grey80"),
        legend.position = NULL,
        axis.text.x = element_text(angle = 45, hjust = 1))  + ylim(0,1)
  # scale_color_manual(values = colorRampPalette(brewer.pal(8, "Set1"))(length(unique(flat_var$gene_name))))
ggsave('plots/APH1B/sec11.interaction_association_APH1B_lessPIP25.pdf', height = 5, width = 8) 

In conclusion, there is no interaction QTL with APOE identified.

Section 10: in silico functional studies in iPSC model¶

see notebook

In [26]:
vars_p
In [27]:
apoe_p

Section 11: Functional annotations of selected loci¶

see notebook

TODO

  • Touch base with Ryan on the snATAC annotations
  • Run this by Pavel to see if there are additional comments on how we do this
In [28]:
func_p

Section 12: Candidate loci as trans-xQTL¶

see notebook

In [29]:
options(repr.plot.width=12, repr.plot.height=6)
if(!is.null(flat_var)){
    ggplot(flat_var, aes(x = gene_name, y = pip, size = pip)) +
      geom_point(alpha = 0.7) +
      labs(title = paste0("PIP values for trans fine mapped Genes in ", gene_name ," csets with AD"),
           x = "Gene Name",
           y = "PIP",
           size = "PIP",
           color = "CS Coverage 0.95 Min Corr") +
      theme_minimal(base_size = 14) +
      theme(panel.background = element_blank(),
            panel.grid.major = element_line(color = "grey80"),
            legend.position = NULL,
            axis.text.x = element_text(angle = 45, hjust = 1))  
      # scale_color_manual(values = colorRampPalette(brewer.pal(8, "Set1"))(length(unique(flat_var$gene_name))))
    ggsave(paste0('plots/APH1B/sec12.trans_fine_mapping_',gene_name,'.pdf'), height = 5, width = 8)
} else{
    message('There are no detectable trans signals for ', gene_name)
}

Creative thinking: generate hypothesis, search in literature, raise questions to discuss¶

You can now generate some preliminary hypotheses based on the above results. Next, you should search for evidence in the literature to support or refine these hypotheses and identify additional analyses needed to confirm them.