ABSTRACT
Simulations of protein structure were originally based on a hard-sphere potential coupled with the requirement to avoid steric interactions [Ramachandran, Ramakrishnan, and Sasiekharan 1963; Némethy and Scheraga 1965]. This approach evolved into the use of physically more realistic pairwise interatomic potentials, initially to compute structure [De Santis et al. 1963; Brant and Flory 1965; Levitt and Lifson 1969; Momany et al. 1975] and, subsequently, to compute folding pathways with molecular dynamics (MD) [McCammon, Gelin, and Karplus 1977]. The underlying assumption in these simulations was the thermodynamic hypothesis proposed by An nsen (1973), viz., that the native structure of a protein is the one for which the free energy of the protein, and its surroundings, is a minimum. Regardless of whether internal (torsional angle) or external (Cartesian) coordinates are used to describe protein structure, the number of such degrees of freedom and of pairwise interactions for even a moderate-size protein are too large for simulations with available computer software and hardware. To compound the dif culty, MD with an all-atom description of a polypeptide chain cannot achieve the millisecond-to-second time scale of folding of all but the very fast-folding proteins with currently available algorithms and computers. Therefore, coarse-grained models are resorted to, in which the number of degrees of freedom and the number of interaction centers are considerably smaller than those involved in all-atom simulations.
