  The protein folding is regarded as a quantum transition between torsion
states on polypeptide chain. The deduction of the folding rate formula in our
previous studies is reviewed. The rate formula is generalized to the case of
frequency variation in folding. Then the following problems about the
application of the rate theory are discussed: 1) The unified theory on the
two-state and multi-state protein folding is given based on the concept of
quantum transition. 2) The relationship of folding and unfolding rates vs
denaturant concentration is studied. 3) The temperature dependence of folding
rate is deduced and the non-Arrhenius behaviors of temperature dependence are
interpreted in a natural way. 4) The inertial moment dependence of folding rate
is calculated based on the model of dynamical contact order and consistent
results are obtained by comparison with one-hundred-protein experimental
dataset. 5) The exergonic and endergonic foldings are distinguished through the
comparison between theoretical and experimental rates for each protein. The
ultrafast folding problem is viewed from the point of quantum folding theory
and a new folding speed limit is deduced from quantum uncertainty relation. And
finally, 6) since only the torsion-accessible states are manageable in the
present formulation of quantum transition how the set of torsion-accessible
states can be expanded by using statistical energy landscape approach is
discussed. All above discussions support the view that the protein folding is
essentially a quantum transition between conformational states.
