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Brain structural volumes are highly heritable and are linked to multiple neuropsychological outcomes, including Alzheimer's disease (AD). Genome-wide association studies have successfully identified genetic variants associated with intracranial volume (ICV), total brain volume (TBV), hippocampal volume (HV), and lateral ventricular volume (LVV). However, these studies mostly focused on common genetic variants with minor allele frequencies (MAF) > 1%, and individuals included in most of these studies were of predominantly European ancestry. Here, we performed whole-genome sequence (WGS) association studies of MRI brain volumes in 7,674 individuals of diverse race and ethnicity from the Trans-Omics for Precision Medicine (TOPMed) program. We identified novel genetic loci on chromosomes 13 and 16 near and associated with HV and TBV, respectively (lead variants rs115674829, -value = 1.7×10 in pooled analysis and rs150440001, -value = 6.6×10 in black participants). Both lead variant minor A alleles are rarer in white participants (MAF = 0.14% and 0.03%) and in Hispanic participants (MAF = 1.5% and 0.17%) but more common in black participants (MAF = 13% and 1.5%). Rare variant aggregated analyses identified a gene encoding a kinase involved in neuroinflammation and promising target for AD treatment, suggestively associated with LVV (-value=5×10). This study provides new insights into the genetic correlates of brain structural volumes and illustrates the importance of leveraging WGS data and cohorts of diverse race and ethnicity to better characterize the genetic architecture of complex polygenic traits.