Folding protein models with a simple hydrophobic energy function: The fundamental importance of monomer inside/outside segregation

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(h⃗, c⃗) = −Σi=1N cihi = −(h⃗.c⃗) is the negative scalar product between two vectors in N-dimensional cartesian space: h⃗ = (h1, … , hN), which represents monomer hydrophobicities and is sequence-dependent; and c⃗ = (c1, … , cN), which represents the number of contacts made by each monomer and is conformation-dependent. A simple theoretical analysis shows that restrictions are imposed concomitantly on both sequences and native structures if the stability criterion for protein-like behavior is to be satisfied. Given a conformation with vector c⃗, the best sequence is a vector h⃗ on the direction upon which the projection of c⃗ − c̄⃗ is maximal, where c̄⃗ is the diagonal vector with components equal to c̄, 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 two-state 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.

A database and tools for 3-D protein structure comparison and alignment using the Combinatorial Extension (CE) algorithm

The database reported here is derived using the Combinatorial Extension (CE) algorithm which compares pairs of protein polypeptide chains and provides a list of structurally similar proteins along with their structure alignments. Using CE, structure–structure alignments can provide insights into biological function. When a protein of known function is shown to be structurally similar to a protein of unknown function, a relationship might be inferred; a relationship not necessarily detectable from sequence comparison alone. Establishing structure–structure relationships in this way is of great importance as we enter an era of structural genomics where there is a likelihood of an increasing number of structures with unknown functions being determined. Thus the CE database is an example of a useful tool in the annotation of protein structures of unknown function. Comparisons can be performed on the complete PDB or on a structurally representative subset of proteins. The source protein(s) can be from the PDB (updated monthly) or uploaded by the user. CE provides sequence alignments resulting from structural alignments and Cartesian coordinates for the aligned structures, which may be analyzed using the supplied Compare3D Java applet, or downloaded for further local analysis. Searches can be run from the CE web site, http://cl.sdsc.edu/ce.html, or the database and software downloaded from the site for local use.

A sampling problem in molecular dynamics simulations of macromolecules.

Correlations in low-frequency atomic displacements predicted by molecular dynamics simulations on the order of 1 ns are undersampled for the time scales currently accessible by the technique. This is shown with three different representations of the fluctuations in a macromolecule: the reciprocal space of crystallography using diffuse x-ray scattering data, real three-dimensional Cartesian space using covariance matrices of the atomic displacements, and the 3N-dimensional configuration space of the protein using dimensionally reduced projections to visualize the extent to which phase space is sampled.