The BCKDHA, BCKDHB, and DBT genes are critical components in the metabolic pathway responsible for breaking down the branched-chain amino acids: leucine, isoleucine, and valine. These genes encode for different subunits of the branched-chain alpha-keto acid dehydrogenase complex (BCKD). This complex is crucial for proper metabolic function, and mutations in these genes can lead to metabolic disorders.