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(h,c) = -Sigma N/i=1 c(i)h(i) = -(h.c) is the negative scalar product between two vectors in N-dimensional cartesian space: h = (h1,., hN), which represents monomer hydrophobicities and is sequence-dependent; and c = (c(1),., c(N)), 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 c, the best sequence is a vector h on the direction upon which the projection of c - c is maximal, where 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 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.

Thermodynamics of interactions between amino acid side chains: experimental differentiation of aromatic-aromatic, aromatic-aliphatic, and aliphatic-aliphatic side-chain interactions in water.

A stationary phase for high-pressure liquid chromatography has been prepared by derivatizing microparticulate silica gel with functionality mimicking the side chain of isoleucine. The chromatographic retentions of a series of hydrophobic and amphiphilic amino acid analytes on this stationary phase (Ile MSP) using an aqueous mobile phase were measured as a function of temperature from 273 K to 323 K. Observed temperature dependencies are consistent with a constant change in heat capacity, DeltaC degrees P, upon binding of the analyte to the stationary phase. The curvatures of plots of retention data versus temperature (related to the magnitude of DeltaC degrees P) are distinctly different for retention of aromatic and aliphatic analytes, with retention of aliphatic analytes Val, Ile, and Leu exhibiting the characteristic signature of the hydrophobic effect, i.e., a large negative DeltaC degrees P upon desolvation from water and a maximum of retention around room temperature. Retention of aromatic analytes (Trp, Phe, and Tyr) involves smaller heat capacity changes and pronounced negative enthalpies of interaction with the stationary phase. Estimates of DeltaC degrees P for the interactions of analyte side chains with the Ile side chain were obtained by fitting the temperature dependence of retention to an expression derived from thermodynamic considerations and chromatographic theory. Similar estimates were made for interactions with the Phe side chain, using previously published data for a phenylalanine mimic stationary phase (Phe MSP) (. Protein Sci. 1:786-795). As with the Ile MSP, the retentions of aliphatic analytes show temperature dependencies markedly different from those of aromatic analytes. Data from both phases indicate that a realistic differentiation can be made between the interactions of various types of amino acid side chains tested (i.e., aliphatic/aliphatic, aliphatic/aromatic, and aromatic/aromatic) by comparison of the corresponding thermodynamic functions for pairwise interactions. The retention of leucine on the Phe MSP and that of phenylalanine on the Ile MSP showed similar DeltaC degrees P values, suggesting that the aromatic-aliphatic interaction is reasonably independent of the residue attached to the stationary phase. This result is consistent with a one-to-one interaction and suggests a simple way to estimate the column-dependent phase factor, making it possible to compare entropies and free energies of interaction obtained using different MSPs. The possibilities for using MSP-derived interaction potentials in folding simulations are discussed.

Monte Carlo simulations of protein folding using inexact potentials: how accurate must parameters be in order to preserve the essential features of the energy landscape?

BACKGROUND: Monte Carlo simulations of the cubic lattice protein model with engineered sequences were performed in order to address the issue of potential accuracy required for folding. The potential used for sequence selection played the role of the 'real' potential and different levels of inaccuracy were introduced by addition of noise. RESULTS: The dependence of successful folding probability on potential noise was found to be sigmoidal and sequence-specific and can be described by an expression analytically derived from a simple theoretical model in which the density of states of the system contains a continuous region approximated by a Gaussian distribution separated from the unique native conformation by a large energy gap. CONCLUSIONS: The decrease in folding probability with potential inaccuracy results from an average decrease in the energy gap. Sequences with large energy gaps support larger inaccuracies while retaining the ability to fold properly. As the energy gap is known to correlate with thermal stability, we suggest a simple criterion for specific real sequence selection in order to maximize success probability in realistic folding simulations.