Quantitative visualization of a macromolecular potential energy ''funnel''

Potential energy ''funnels'' have become a conceptual cornerstone for understanding protein folding. Recently it was demonstrated that such an energy funnel exists in a full atomistic model of the tetrapeptide isobutyryl-(ala)(3)-NH-methyl, which is the smallest polypeptide that can have ''secondary'' structure (O.M. Becker and M. Karplus, J. Chem. Phys., 106 (1997) 1495). In this paper we present a quantitative analysis of the geometrical structure of this energy funnel. Principal coordinate analysis is used to project the high-dimensional conformation space onto a low-dimensional subspace of maximal variance, and to obtain a unique quantitative visualization of a multidimensional funnel in a polypeptide system. The present analysis shows that, in this system, the ''entrance horizon'' of the funnel is the largest structural feature on the energy surface, and that the funnel has a non-trivial structure. It starts as a wide structure which narrows gradually until at some point it undergoes a sudden localization into small sub-basins. These characteristics agree with the expected role of funnels in protein folding. At high energies (or unfolded state) an entropic factor biases the system's kinetic pathways to enter the funnel. After the system is well within the funnel region its structure changes and sudden localization allows rapid convergence to the folded conformation. (C) 1997 Elsevier Science B.V.