Proteins with selected sequences fold into unique native conformation

Exact sequence analysis for three-dimensional hydrophobic-polar lattice proteins

“…For N → ∞ it is widely believed that in leading order the scaling law [36,37] C n = Aµ n C n γ−1 (4) holds, where n is the number of self-avoiding steps (i.e., n = N − 1). In this expression, µ C is the effective coordination number of the lattice, γ is a universal exponent, and A is a non-universal amplitude.…”

“…Although it is obvious that this model can describe the folding process very roughly only [4,5,6,7], much work has been done to find lowest-energy states and their degeneracy for given sequences, or in the inverse problem, to identify all sequences of given length whose native conformation matches a given target structure. As simple as this model seems to be, it has been proven to be an NP-complete problem in two and three dimensions [8].…”

Geometric and statistical properties of the mean-field hydrophobic-polar model, the large-small model, and real protein sequences

“…This model has been studied extensively by several groups in the last decade [3][4][5][6][7][8]. A mean-field version of the model that yields tremendous simplification was used to study the designability problem, and it was found that the designabilities of structures vary greatly (the terms structures and conformation classes will be used interchangeably in this paper), and that only a tiny portion of structures are highly designable.…”

“…Yet the folding of any particular protein is an extremely complex process; simulation of the folding of even a small protein remains an unsurmounted challenge to state-of-the-art computers [2]. Nevertheless, a good understanding of a number of general features of protein folding have been acquired in computational studies using simple lattice models [3][4][5][6][7][8]. One feature is the so-called funnel picture that leads to a two-state description of folding [5,9].…”

Pathway to copolymer collapse in dilute solution: Uniform versus random distribution of comonomers

“…12,13 The two-letter copolymer collapse problem also represents a simplified version of protein folding. 14,15 In proteins, amino acid sequences are not random, but are designed to ensure collapse and cooperative folding of the protein into its unique native state, [16][17][18][19] often via well-defined intermediate states. [20][21][22] Interestingly, simulations indicate that copolymers with specially designed proteinlike sequences created by "coloring" monomer units on the outside of a homopolymer globule 5,23,24 exhibit abrupt transitions relative to random copolymers, and form soluble globules rather than precipitating.…”