Folding Protein Models with a Simple Hydrophobic Energy Function: The Fundamental Importance of Monomer Inside/Outside Segregation
Abstract
The present study explores a "hydrophobic" energy function for folding simulations of the protein lattice model. The contribution of each monomer to conformational energy is the product of its "hydrophobicity" and the number of contacts it makes, i.e., E( > to{h}, > to{c}) =Σ _{i=1}^{N}c_{i}h_{i} =( > to{h}. > to{c}) is the negative scalar product between two vectors in Ndimensional cartesian space: > to{h} =(h_{1},...,h_{N}) which represents monomer hydrophobicities and is sequencedependent; and > to{c} =(c_{1},...,c_{N}), which represents the number of contacts made by each monomer and is conformationdependent. A simple theoretical analysis shows that restrictions are imposed concomitantly on both sequences and native structures if the stability criterion for proteinlike behavior is to be satisfied. Given a conformation with vector > to{c}, the best sequence is a vector > to{h} on the direction upon which the projection of > to{c}  > to{{c}} is maximal, where > to{{c}} is the diagonal vector with components equal to {c}, the average number of contacts per monomer in the unfolded state. Best native conformations are suggested to be not maximally compact, as assumed in many studies, but the ones with largest variance of contacts among its monomers, i.e., with monomers tending to occupy completely buried or completely exposed positions. This inside/outside segregation is reflected on an apolar/polar distribution on the corresponding sequence. Monte Carlo simulations in two dimensions corroborate this general scheme. Sequences targeted to conformations with large contact variances folded cooperatively with thermodynamics of a twostate transition. Sequences targeted to maximally compact conformations, which have lower contact variance, were either found to have degenerate ground state or to fold with much lower cooperativity.
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 October 1999
 DOI:
 10.1073/pnas.96.22.12482
 Bibcode:
 1999PNAS...9612482P