Nanostructured　materials　can　direct　stem　cell　lineage　commitment　solely　by　their　various,　but　controllable,　geometric　cues,　which　would　be　very　important　for　their　future　application　in　bone　tissue　engineering　and　bone　regeneration.　However,　the　mechanisms　by　which　nano-geometric　cues　dictate　the　osteogenic　differentiation　of　stem　cells　remain　unclear.　Epigenetics　is　central　to　cellular　differentiation,　a　process　that　regulates　heritable　and　long-lasting　alterations　in　gene　expression　without　changing　the　DNA　sequence.　Here,　we　explored　the　varied　osteogenic　behaviors　of　human　adipose-derived　stem　cells　(hASCs)　on　titanium　dioxide　(TiO2)　nanotube　arrays　of　different　diameters.　Both　in　vitro　and　in　vivo　studies　demonstrated　that　the　nanoscale　geometry　influenced　cellular　differentiation　and　TiO2　nanotubes　with　a　diameter　of　70　nm　was　the　optimal　dimension　for　the　osteogenic　differentiation　of　hASCs.　Moreover,　we　observed　that　TiO2　nanotubes　promoted　the　osteogenic　differentiation　of　hASCs　by　upregulating　methylation　level　of　histone　H3　at　lysine　4　(H3K4)　in　the　promoter　regions　of　osteogenic　genes　Runx2　and　osteocalcin,　by　inhibiting　demethylase　retinoblastoma　binding　protein　2　(RBP2).　These　results　revealed,　for　the　first　time,　the　epigenetic　mechanism　by　which　nanotopography　directs　stem　cell　fate.　(C)　2014　Elsevier　Ltd.　All　rights　reserved.