This paper presents an analytically tractable model
that captures the most elementary aspect of the protein
folding problem, namely that both the energy and the entropy
decrease as a protein folds. In this model, the system
diffuses within a sphere in the presence of an attractive
spherically symmetric potential. The native state is represented
by a small sphere in the center, and the remaining space
is identified with unfolded states. The folding temperature,
the time-dependence of the populations, and the relaxation
rate are calculated, and the folding dynamics is analyzed
for both golf-course and funnel-like energy landscapes.
This simple model allows us to illustrate a surprising
number of concepts including entropic barriers, transition
states, funnels, and the origin of single exponential relaxation
kinetics.