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Epileptic encephalopathies are a devastating group of severe childhood epilepsy disorders for which the cause is often unknown. Here we report a screen for de novo mutations in patients with two classical epileptic encephalopathies: infantile spasms (n = 149) and Lennox–Gastaut syndrome (n = 115). We sequenced the exomes of 264 probands, and their parents, and confirmed 329 de novo mutations. A likelihood analysis showed a significant excess of de novo mutations in the ∼4,000 genes that are the most intolerant to functional genetic variation in the human population (P = 2.9 × 10⁻³). Among these are GABRB3, with de novo mutations in four patients, and ALG13, with the same de novo mutation in two patients; both genes show clear statistical evidence of association with epileptic encephalopathy. Given the relevant site-specific mutation rates, the probabilities of these outcomes occurring by chance …