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 anal ysis of the geometrical structure of this energy funnel. Principal coo rdinate analysis is used to project the high-dimensional conformation space onto a low-dimensional subspace of maximal variance, and to obta in 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 fea ture on the energy surface, and that the funnel has a non-trivial stru cture. It starts as a wide structure which narrows gradually until at some point it undergoes a sudden localization into small sub-basins. T hese characteristics agree with the expected role of funnels in protei n folding. At high energies (or unfolded state) an entropic factor bia ses the system's kinetic pathways to enter the funnel. After the syste m is well within the funnel region its structure changes and sudden lo calization allows rapid convergence to the folded conformation. (C) 19 97 Elsevier Science B.V.