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Abstract
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.