Newton Running, an American brand of “natural running” shoes, has drawn an investment of between $10 million and $20 million from Fireman Capital Partners, the private equity firm of Paul Fireman, who built up the Reebok brand and sold it to Adidas five years ago for $3.8 billion. Dan Fireman, son of Paul and managing general partner of Fireman Capital, said that the firm would have a significant stake in Newton Running. Jerry Lee and Danny Abshire, who jointly founded the company in Colorado in 2005, would retain a majority stake. The company reportedly generated about $10 million in annual sales and has been doubling its turnover every year. Its shoes currently sell in the range of $135 to $175, but the range is to be expanded with lower-cost shoes in the $80 to $100 bracket. Dennis Baldwin and Steve Liggett, who headed product development, manufacturing and marketing for more than 15 years at Reebok, will represent Fireman Capital on Newton Running's board. Baldwin is a managing partner of Breakaway Parttners, a a marketing agency in Boston that will develop a comprehensive marketing campaign for the brand. Fireman's firm has already invested in Hudson Jeans, Evolution Fresh, Serena & Lily, IdeaPaint and Pilla.