Last April, President Obama assembled some of the nation’s most august scientific dignitaries in the East Room of the White House. Joking that his grades in physics made him a dubious candidate for “scientist in chief,” he spoke of using technological innovation “to grow our economy” and unveiled “the next great American project”: a $100 million initiative to probe the mysteries of the human brain.

Along the way, he invoked the government’s leading role in a history of scientific glories, from putting a man on the moon to creating the Internet. The Brain initiative, as he described it, would be a continuation of that grand tradition, an ambitious rebuttal to deep cuts in federal financing for scientific research.

“We can’t afford to miss these opportunities while the rest of the world races ahead,” Mr. Obama said. “We have to seize them. I don’t want the next job-creating discoveries to happen in China or India or Germany. I want them to happen right here.”

Absent from his narrative, though, was the back story, one that underscores a profound change taking place in the way science is paid for and practiced in America. In fact, the government initiative grew out of richly financed private research: A decade before, Paul G. Allen, a co-founder of Microsoft, had set up a brain science institute in Seattle, to which he donated $500 million, and Fred Kavli, a technology and real estate billionaire, had then established brain institutes at Yale, Columbia and the University of California. Scientists from those philanthropies, in turn, had helped devise the Obama administration’s plan.