“Engineers are more problem-solvers; cancer scientists tend to be more discoverers,” Dr. Jacks said in an interview. “And the combination is actually extremely powerful.”

“So we have engineers who are interested in nanotechnology, for delivering cancer drugs more effectively and more specifically to cancer cells  that’s an engineering problem,” he said. “We have other engineers who are interested in building new devices that can monitor the state of an individual’s health more sensitively and more continuously  imagine implantable sensors that would allow you to know whether your disease is in remission or undergoing relapse. Again, that’s an engineering problem.”

In his speech at the opening ceremony, Mr. Koch warned that government spending cuts could impede cancer research. And he urged donors to fill the gap.

“The National Institutes of Health, and the National Cancer Institute in particular, are facing serious cutbacks in their funding due to the massive deficits the federal government is incurring,” he said in his speech, in a tent outside the seven-story building. “If the cutbacks happen, it will significantly diminish the level of research that can be carried on at the Koch Institute. I earnestly ask you to do all you can to help maintain the superb research at the Koch Institute at its maximum level.”

Mr. Koch is tied with his brother Charles as the fifth wealthiest American in Forbes magazine’s most recent ranking, and came in 45th in the Chronicle of Philanthropy’s list of donors who gave the most in 2010. Stacy Palmer, the editor of the Chronicle, said that Mr. Koch was unusual in the wide range of his philanthropy, which supports cancer research, the arts and the public policy sphere.

His roles do not always fit neatly together.

His gift here means that one of the biggest donors to the Massachusetts Institute of Technology, home to some of the top climate scientists in the nation, is an owner of a company that Greenpeace called “a kingpin of climate change denial.”