Rubber compositions having a modified rubber component selected from a modified polybutadiene rubber, a modified styrene-butadiene rubber, or combinations thereof, the modification being with a functional group having a hydrogen bond acceptor atom. Such functional group may be selected from a pyridine, a pyrrolidone, an ether, a ketone or an epoxide, the rubber composition having a Tg of between −80° C. and −110° C.The rubber composition may include an efficient plasticizing resin, which when included in a mixture consisting of the modified rubber component and 67 phr of the efficient plasticizing resin, causes a Tg of the mixture to be at least 14° C. higher than the Tg of the modified rubber component. The rubber composition may described as having the hydrogen bond acceptor atom located at least two covalent bond lengths or alternatively three covalent bond lengths from a backbone of the modified rubber component.