The supinator. (Deep branch of radial nerve labeled at upper right and lower right. Dorsal interosseous is this nerve after passing the supinator, at lower right.)
It descends along the interosseous membrane, anterior to the extensor pollicis longus muscle, to the back of the carpus, where it presents a gangliform enlargement from which filaments are distributed to the ligaments and articulations of the carpus.
Posterior interosseous neuropathy is purely a motor syndrome resulting in finger drop due to no extension of IP joints and radial wrist deviation on extension.