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.