How to guarantee optimal stability for most representative structures in the protein data bank

Abstract

We proposed recently an optimization method to derive energy parameters for simplified models of protein folding. The method is based on the maximization of the thermodynamic average of the overlap between protein native structures and a Boltzmann ensemble of alternative structures. Such a condition enforces protein models whose ground states are most similar to the corresponding native states. We present here an extensive testing of the method for a simple residue-residue contact energy function and for alternative structures generated by threading. The optimized energy function guarantees high stability and a well-correlated energy landscape to most representative structures in the PDB database. Failures in the recognition of the native structure can be attributed to the neglect of interactions between different chains in oligomeric proteins or with cofactors. When these are taken into account, only very few X-ray structures are not recognized. Most of them are short inhibitors or fragments and one is a structure that presents serious inconsistencies. Finally, we discuss the reasons that make NMR structures more difficult to recognizeCopyright 2001 Wiley-Liss, Inc.

Looking at structure, stability, and evolution of proteins through the principal eigenvector of contact matrices and hydrophobicity profiles

“…where U is a 20 × 20 symmetric matrix whose element U (a, b) represents the effective interaction, in units of k B T , of amino acids a and b; we use the interaction matrix derived by Bastolla et al (2001). For this interaction matrix the free energy function, Eq.…”

“…In the Structurally Constrained Neutral (SCN) model (Bastolla et al, 1999(Bastolla et al, , 2002(Bastolla et al, , 2003a(Bastolla et al, , 2003b, starting from the protein sequence in the PDB, amino acid mutations are randomly proposed and accepted according to a stability criterion based on an effective model of protein folding (Bastolla et al, 2000(Bastolla et al, , 2001. This "structural" approach has been pioneered by Schuster and co-workers, with a series of studies of neutral networks of RNA secondary structures (Schuster et al, 1994;Huynen et al, 1996;Fontana and Schuster, 1998) and it has been applied to proteins by several groups (Gutin et al, 1995;Bornberg-Bauer, 1997;Bornberg-Bauer and Chan, 1999;Babajide et al, 1997;Govindarajan and Goldstein, 1998;Bussemaker et al, 1997;Tiana et al, 1998;Mirny and Shakhnovich, 1998;Dokholyan and Shakhnovich, 2001;Parisi and Echave, 2001).…”

Knowledge-Based Energy Functions for Computational Studies of Proteins

“…This is the same functional form used in statistical potential, where the weight coefficients are derived from database statistics. The objectives of optimization are often maximization of energy gap between native protein and the average of decoys, or energy gap between native and decoys with lowest score, or the z-score of the native protein (Goldstein et al, 1992;Maiorov and Crippen, 1992;Thomas and Dill, 1996a;Koretke et al, 1996;Hao and Scheraga, 1996;Mirny and Shakhnovich, 1996;Vendruscolo and Domanyi, 1998;Koretke et al, 1998;Tobi et al, 2000a;Vendruscolo et al, 2000a;Dima et al, 2000;Micheletti et al, 2001;Bastolla et al, 2001).…”

“…A different class of knowledge-based potentials are based on optimization. In this case, the set of parameters for the potential functions are optimized by some criterion, e.g., by maximizing the energy gap between known native conformation and a set of alternative (or decoy) conformations (Goldstein et al, 1992;Maiorov and Crippen, 1992;Thomas and Dill, 1996a;Tobi et al, 2000a;Vendruscolo and Domanyi, 1998;Vendruscolo et al, 2000a;Bastolla et al, 2001;Dima et al, 2000;Micheletti et al, 2001;Dobbs et al, 2002;Hu et al, 2004).…”

“…The techniques that have been used for optimizing potential function include perceptron learning, linear programming, gradient descent, statistical analysis, and support vector machine (Tobi et al, 2000a;Vendruscolo et al, 2000a;Xia and Levitt, 2000;Bastolla et al, 2000Bastolla et al, , 2001Hu et al, 2004). These are standard techniques that can be found in optimization and machine learning literature.…”