Kari Schroeder at the University of California in Davis, US, and colleagues sampled the genes from various populations around the globe, including two at the eastern edge of Siberia, 53 elsewhere in Asia and 18 Native American populations. The study examined samples from roughly 1500 people in total, including 445 Native Americans.
The team looked for a series of nine repeating chunks of DNA, known as 9RA, which falls in a non-coding region of chromosome 9.
They found the 9RA sequence in at least one member of all the Native American populations tested, such as the Cherokee and Apache people. The two populations in eastern Siberia, where the Bering land bridge once connected Asia to North America, also tested positive for the 9RA sequence.
If memory serves, the basic model is of three major migrations represented by the major linguistic groups of Amerind, Na-Dene, and Aleut-Eskimo. Ruhlen has posited that these occurred at 11,000, 7,000 and 3,000 BP, which seems about what I had been taught, too.
Also came across this paper by Bonatto and Salzano that came up with something similar: "These results support a model for the peopling of the Americas in which Beringia played a central role, where the population that originated the Native Americans settled and expanded." That paper appears to be freely available.