Symmetry and native structure in lattice proteins

Theory of protein folding: the energy landscape perspective

The energy landscape theory of protein folding is a statistical description of a protein's potential surface. It assumes that folding occurs through organizing an ensemble of structures rather than through only a few uniquely defined structural intermediates. It suggests that the most realistic model of a protein is a minimally frustrated heteropolymer with a rugged funnel-like landscape biased toward the native structure. This statistical description has been developed using tools from the statistical mechanics of disordered systems, polymers, and phase transitions of finite systems. We review here its analytical background and contrast the phenomena in homopolymers, random heteropolymers, and protein-like heteropolymers that are kinetically and thermodynamically capable of folding. The connection between these statistical concepts and the results of minimalist models used in computer simulations is discussed. The review concludes with a brief discussion of how the theory helps in the interpretation of results from fast folding experiments and in the practical task of protein structure prediction.

Symmetry and the energy landscapes of biomolecules

The role of symmetry in the folding of proteins is discussed using energy landscape theory. An analytical argument shows it is much easier to find sequences with funneled energy landscape capable of fast folding if the structure is symmetric. The analogy with phase transitions of small clusters with magic numbers is discussed.

Symmetry in chemistry from the hydrogen atom to proteins

The last 2 decades have seen discoveries in highly excited states of atoms and molecules of phenomena that are qualitatively different from the "planetary" model of the atom, and the near-rigid model of molecules, characteristic of these systems in their low-energy states. A unified view is emerging in terms of approximate dynamical symmetry principles. Highly excited states of two-electron atoms display "molecular" behavior of a nonrigid linear structure undergoing collective rotation and vibration. Highly excited states of molecules described in the "standard molecular model" display normal mode couplings, which induce bifurcations on the route to molecular chaos. New approaches such as rigid-nonrigid correlation, vibrons, and quantum groups suggest a unified view of collective electronic motion in atoms and nuclear motion in molecules.