SAN FRANCISCO — When Drew Houston played computer games like Starcraft in high school, he made some changes so the games ran more smoothly on his friends’ computers.

“He created this one little application, and it would basically display everybody’s shared files, and then if you clicked on a file, it would go ahead and ask everyone else on the network if they wanted to download it as well,” said Andrew Croswell, a friend of Mr. Houston’s from Acton-Boxborough Regional High School in Acton, Mass.

Mr. Houston, now 35, has since taken a version of that same concept and turned it into Dropbox, an online file storage and collaboration company that has grown rapidly since its founding in 2007.

Last month, Dropbox filed to go public, and when it does Mr. Houston will become the newest member of a small club of tech founders who steered a start-up all the way to Wall Street. (The company is expected to set a price range for its offering as soon as this coming week and trade on the stock market by the end of the month.)