Buffed energy landscapes: another solution to the kinetic paradoxes of protein folding

The energy landscapes of proteins have evolved to be different from most random heteropolymers. Many studies have concluded that evolutionary selection for rapid and reliable folding to a given structure that is stable at biological temperatures leads to energy landscapes having a single dominant basin and an overall funnel topography. We show here that, although such a landscape topography is indeed a sufficient condition for folding, another possibility also exists, giving a previously undescribed class of foldable sequences. These sequences have landscapes that are only weakly funneled in the conventional thermodynamic sense but have unusually low kinetic barriers for reconfigurational motion. Traps have been specifically removed by selection. Here we examine the possibility of folding on these "buffed" landscapes by mapping the determination of statistics of pathways for the heterogeneous nucleation processes involved in escaping from traps to the solution of an imaginary time Schroedinger equation. This equation is solved analytically in adiabatic and "soft-wall" approximations, and numerical results are shown for the general case. The fraction of funneled vs. buffed proteins in sequence space is estimated, suggesting the statistical dominance of the funneling mechanism for achieving foldability.