The Silicon Valley investors who thought the nascent tech start-up Google was a good idea back in 1999 are now putting their money behind another zany scheme: accountable care organizations, the networks of doctors and hospitals that experts hope will save the health system millions of dollars.

Kleiner Perkins Caufield & Byers, the venture capital firm that also provided early funding for Genentech, Amazon.com and AOL, and other investment companies are pouring $61 million into Essence Group Holdings Corp., a St. Louis-based company that helps doctors build the networks.

The money will help Essence’s technology arm, Lumeris, market software that enables collaboration among doctors, hospitals and insurers in accountable care groups. Essence believes the market for related products and services could reach $80 billion, and that as much as $1 trillion in revenue could pass through the accountable care organizations that use them within 10 years.

Essence began in 2006 when a group of investors came together to try to “prove that we could bend the cost curve in the health system,” said chief executive Mike Long in an interview. The investors group, led by John Doerr, a partner at Kleiner Perkins and legend in Silicon Valley, launched a small St. Louis health plan as its laboratory and put a $150 million into the experiment (Doerr’s initial investment in Essence was made as an individual). Four years later, Essence concluded that the plan was able to provide better health care at a lower price than competitors and Essence is now moving to sell the ideas far and wide.

While the federal health law envisions a version of ACOs that would care for Medicare patients and allow doctors and hospitals to share any money they save, the rules for the program received a chilly reception in the industry.

But the interest of major venture capitalists — and of existing players like OptumHealth, a unit of UnitedHealth Group — shows how seriously the private sector is taking the concept.

Making health care cheaper is catching on with investors, said Long, who also ran WebMD. Essence’s investors “recognized that the increasing health care spending was going to bankrupt the country,” he said. “If there’s a big problem in the country, and if you solve it, there are rewards.”