A Criterion That Determines Fast Folding of Proteins: A Model Study
Abstract
We consider the statistical mechanics of a full set of two-dimensional protein-like heteropolymers, whose thermodynamics is characterized by the coil-to-globular (
T
θ
) and the folding (
T
f
) transition temperatures. For our model, the typical time scale for reaching the unique native conformation is shown to scale as
τ
f
∼F(M)exp(σ/
σ
0
)
, where
σ=1−
T
f
/
T
θ
,
M
is the number of residues, and
F(M)
scales algebraically with
M
. We argue that
T
f
scales linearly with the inverse of entropy of low energy non-native states, whereas
T
θ
is almost independent of it. As
σ→0
, non-productive intermediates decrease, and the initial rapid collapse of the protein leads to structures resembling the native state. Based solely on {\it accessible} information,
σ
can be used to predict sequences that fold rapidly.