The protein-folding problem was first posed about one half-century ago. The term refers
to three broad questions: (i) What is the physical code by which an amino acid sequence
dictates a protein's native structure? (ii) How can proteins fold so fast? (iii) Can
we devise a computer algorithm to predict protein structures from their sequences?
We review progress on these problems. In a few cases, computer simulations of the
physical forces in chemically detailed models have now achieved the accurate folding
of small proteins. We have learned that proteins fold rapidly because random thermal
motions cause conformational changes leading energetically downhill toward the native
structure, a principle that is captured in funnel-shaped energy landscapes. And thanks
in part to the large Protein Data Bank of known structures, predicting protein structures
is now far more successful than was thought possible in the early days. What began
as three questions of basic science one half-century ago has now grown into the full-fledged
research field of protein physical science.