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Only a minority of patients with rare genetic diseases are presently diagnosed by exome sequencing, suggesting that additional unrecognized pathogenic variants may reside in noncoding sequence. In this work, we describe PromoterAI, a deep neural network that accurately identifies noncoding promoter variants that dysregulate gene expression. We show that promoter variants with predicted expression-altering consequences produce outlier expression at both the RNA and protein levels in thousands of individuals and that these variants experience strong negative selection in human populations. We observed that clinically relevant genes in patients with rare diseases are enriched for such variants and validated their functional impact through reporter assays. Our estimates suggest that promoter variation accounts for 6% of the genetic burden associated with rare diseases.