Eigenvalues of the homogeneous finite linear one step master equation: applications to downhill folding.

Motivated by the observed time scales in protein systems said to fold "downhill," we have studied the finite, linear master equation, with uniform rates forward and backward as a model of the downhill process. By solving for the system eigenvalues, we prove the claim that in situations where there is no free energy barrier a transition between single- and multi-exponential kinetics occurs at sufficient bias (towards the native state). Consequences for protein folding, especially the downhill folding scenario, are briefly discussed.