(Reuters) -Groups representing Columbia University professors on Tuesday sued the Trump administration over its effort to force the university to tighten rules on campus protests and put a Middle Eastern studies department under outside oversight, among other measures, by canceling $400 million in federal funding and threatening to withhold billions more in the future. "This action challenges the Trump administration’s unlawful and unprecedented effort to overpower a university’s academic autonomy and control the thought, association, scholarship, and expression of its faculty and students," the American Association of University Professors and the American Federation of Teachers said in their lawsuit in Manhattan Federal Court. "The Trump administration is coercing Columbia University to do its bidding and regulate speech and expression on campus by holding hostage billions of dollars in congressionally authorized federal funding - funding that is responsible for positioning the American university system as a global leader in scientific, medical, and technological research and is crucial to ensuring it remains so," they said.