Features of Energy Landscape Topography in the Space of Torsion Angles for Macromolecules that Form Unique 3D Structures

Abstract

The topography of the potential energy surface (PES) for macromolecules in the configuration space of torsion angles was considered. The effects that interatomic repulsion exerts on the surface topography are discussed. Singularities in interatomic potentials were not found to critically affect the energy landscapes in the space of torsion angles because singularity points are inaccessible at thermal energies. Classically forbidden regions for motions in the vicinity of singularity points lead to an exponential decrease in the coefficients of the Fourier series expansion of the potential energy function as harmonic numbers increase. The minimal frustration principle, which underlies the current ideas that energy funnels exist to ensure the folding of biopolymers into unique 3D structures, was extended to include maxima of the energy landscape, yielding PESs whose topography is characterized not only by a global minimum, but also by a global maximum of the energy landscape (atomic spatial conflicts are excluded in this context). In this case with each of the angular variables, the coordinates of the extreme points differ strongly by π. The resulting surfaces are antisymmetric with respect to the reversal of the directions of the acting interatomic forces (namely, the regions of the global minimum and global maximum interchange when the sign of the interaction energy changes). The topography of such surfaces ideally provides the folding of a macromolecular chain into a unique 3D structure. Entropy effects that arise during the motion of a representative point along the PES form a smooth barrier around the entrance to the energy funnel at lower temperatures and destroy the energy funnel at higher temperatures. The effects agree with data on protein-folding kinetics.