An Analytical Approach to the Protein Designability Problem

We present an analytical method for determining the designability of protein structures. We apply our method to the case of two-dimensional lattice structures, and give a systematic solution for the spectrum of any structure. Using this spectrum, the designability of a structure can be estimated. We outline a heirarchy of structures, from most to least designable, and show that this heirarchy depends on the potential that is used.Comment: 16 pages 4 figure

A New Algorithm for Protein Design

We apply a new approach to the reverse protein folding problem. Our method uses a minimization function in the design process which is different from the energy function used for folding. For a lattice model, we show that this new approach produces sequences that are likely to fold into desired structures. Our method is a significant improvement over previous attempts which used the energy function for designing sequences.Comment: 10 pages latex 2.09 no figures. Use uufiles to decod

Hiking in the energy landscape in sequence space: a bumpy road to good folders

With the help of a simple 20 letters, lattice model of heteropolymers, we investigate the energy landscape in the space of designed good-folder sequences. Low-energy sequences form clusters, interconnected via neutral networks, in the space of sequences. Residues which play a key role in the foldability of the chain and in the stability of the native state are highly conserved, even among the chains belonging to different clusters. If, according to the interaction matrix, some strong attractive interactions are almost degenerate (i.e. they can be realized by more than one type of aminoacid contacts) sequence clusters group into a few super-clusters. Sequences belonging to different super-clusters are dissimilar, displaying very small ($\approx 10$) similarity, and residues in key-sites are, as a rule, not conserved. Similar behavior is observed in the analysis of real protein sequences.Comment: 17 pages 5 figures Corrected typos added auxiliary informatio

Folding and Misfolding of Designed Heteropolymer Chains with Mutations

We study the impact of mutations (changes in amino acid sequence) on the thermodynamics of simple protein-like heteropolymers consisting of N monomers, representing the amino acid sequence. The sequence is designed to fold into its native conformation on a cubic lattice. It is found that quite a large fraction, between one half and one third of the substitutions, which we call 'cold errors', make important contributions to the dynamics of the folding process, increasing folding times typically by a factor of two, the altered chain still folding into the native structure. Few mutations ('hot errors'), have quite dramatic effects, leading to protein misfolding. Our analysis reveals that mutations affect primarily the energetics of the native conformation and to a much lesser extent the ensemble of unfolded conformations, corroborating the utility of the ``energy gap'' concept for the analysis of folding properties of protein-like heteropolymers.Comment: 12 pages, Latex (Revtex