The procedure of modifying the differential in a dg Lie algebra by a Maurer-Cartan element is called twisting. A similar operation can be defined for associative algebras, for A-infinity, L-infinity, Ger-infinity algebras and so on... In my talk, I will consider the category of dg operads which receive a map from the operad LIE_{\infty} governing L-infinity algebras. I will introduce a comonad Tw on this category and show that, if a dg operad O is a coalgebra over Tw, then O-algebras admit twisting which generalizes the above procedure for dg Lie algebras. I will apply this machinery to the Deligneconjecture and show that every solution of the Deligne conjecture is homotopy equivalent to one which is compatible with twisting. This talk is based on a joint work with Thomas Willwacher.