Eigenvalues of the Homogeneous Finite Linear One Step Master Equation: Applications to Downhill Folding

Motivated by claims about the nature of the observed timescales in protein systems said to fold downhill, we have studied the finite, linear master equation which is a model of the downhill process. By solving for the system eigenvalues, we prove the often stated 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.