In what circumstances will an attorney be disqualified from representing a client in a separate federal action?

In Cinema 5, Ltd v. Cinerama, Inc., supra, 528 F.2d 1384, an attorney was a partner in two firms, one in Buffalo, the other in New York City. While the Buffalo firm was representing client A as a defendant in an antitrust action in the Western District of New York, the New York City firm had filed suit against the same client A in the Southern District of New York alleging a conspiracy involving the client in an unlawful takeover attempt. When the defendants in the New York City action moved to have the firm disqualified from representing the plaintiffs in that proceeding, the firm defended on the ground that there was no substantial relationship between the two cases and thus no grounds for its disqualification.