Simplified models of protein folding exploiting the Lagrange radius of gyration of the hydrophobic component

Abstract

Studies are performed using an early proposed, but relatively little investigated, model that efficiently emulates a hydrophobic funneling effect in protein folding. Its simple form, introduced as a further interaction term going as the square of the separation distance, is suitable for initial searches of conformational space by parallel computation and special processors which use polynomial representation of pair-wise interactions. Use of such a term implies calculation of the square of the Lagrange radius of gyration, but weighted by hydrophobicity rather than the masses of the constituent particles. The unusual choice is justified by the observation that experimental protein structures have forms consistent with this Lagrange formalism for hydrophobic residues, and so compact model structures have appropriate density. However, since the long-range and square-power form strains open structures and leads to rapid generation of compact structures, such that for most of the simulation chain the movements result in intra-chain clashes, a rapid rejection algorithm is employed that prunes out similar but high energy structures. The studies also explore the choice of the simplest possible models which might be used to explore folding. Hence pancreatic trypsin inhibitor is modeled as a ‘string-of-beads’, where the beads represent residues of differing hydrophobicity. This model has only limited success, and because there are no identifiable common centers of interaction between the ‘string-of-beads’ model and all-atom protein representations, it encounters the difficulties: (a) of comparing such highly simplified models with observed structures, and (b) of using such models as a starting point for conversion to all-atom models. The conclusion is that this solvent treatment is best applied to all-atom simulations from the outset. Nonetheless, low energy predictions obtained in this simple study can be considered as having promising features, and provide interesting insight into protein folding and the funneling contribution.