  Most single-molecule studies derive the kinetic rates of native,
intermediate, and unfolded states from equilibrium hopping experiments. Here,
we apply Kramers kinetic diffusive model to derive the force-dependent kinetic
rates of intermediate states from non-equilibrium pulling experiments. From the
kinetic rates, we also extract the force-dependent kinetic barriers and the
equilibrium folding energies. We apply our method to DNA hairpins with multiple
folding pathways and intermediates. The experimental results agree with
theoretical predictions. Furthermore, the proposed non-equilibrium
single-molecule approach permits us to characterize kinetic and thermodynamic
properties of native, unfolded, and intermediate states that cannot be derived
from equilibrium hopping experiments.
