Proteins fold reliably into a unique 3-dimensionalstructure essential to their biological function.
My thesis work aims to theoretically understand the
mechanism of protein folding kinetics. I use a
cooperative variational model and focus on two-state fast
folding proteins. Specifically, I extend a variational
model to include specific nonnative interactions, which
is a convenient way to increase structural cooperativity.
The free energy surface of the protein is approximated
with the help of a reference Hamiltonian that describes
a polymer chain inhomogeneously constrained to the native
structure. Folding routes are found by connecting the
globule and native minima through a series of connected
local minima and saddle-points. The folding rates are
determined by the barrier crossing dynamics at
the top of free energy barrier.
The calculated folding rates are
directly compared with experimental measured rates.
Predicted rates for 28 two-state fast folding
proteins not only well correlated with experimental
folding rates, but also the range of predicted
folding rates is same as the wide range of measured
folding rates (typically six to nine orders of
magnitude). Most models fail to predict such a
wide-ranged folding rates since they have too low
cooperativity to mimic real proteins. Moreover,
the structure of transition state ensembles is
predicted for each protein. Compared to the
noncooperative case, cooperativity sharpens the
interface region between folded and unfolded region.
Another major part of this thesis focuses on
characterizing the spatial properties of folding
nucleus. The detailed calculations confirm the
general picture of folding as the capillarity-like
growth of a diffuse folding nucleus. Through the
evolution of packing fraction in folded core and
interface region, the 27 two-state fast folding
proteins can be classified into three classes.
The packing fraction at transition state ensembles
can give the description about the compactness of
transition state ensembles which experimentally
are characterized by the spatial distribution of
Phi-values. My predictions are consistent
with experimental measurements for most proteins.
My work elucidates that how Phi-value analysis can
be understood by the spatial structure of the
critical nucleus.
Finally, I study the effect of stability on folding mechanism.
I observe the Hammond shift of position of transition state
ensembles, signatures of downhill folding and unfolding, and
catastrophes (singular critical points in the free energy
surface). The mechanism behind these observations are still in
investigation.
The cooperative variational model studied in this thesis is
successful in predicting folding rates and structure of
transition state ensembles for two-state fast folding
proteins. Moreover, the studies of spatial properties of
folding nucleus directly give a reasonable explaination
for experimental Phi-value analysis for the first time.