Another look at the conditions for the extraction of protein knowledge‐based potentials

Abstract

Protein knowledge-based potentials are effective free energies obtained from databases of known protein structures. They are used to parameterize coarse-grained protein models in many folding simulation and structure prediction methods. Two common approaches are used in the derivation of knowledge-based potentials. One assumes that the energy parameters optimize the native structure stability. The other assumes that interaction events are related to their energies according to the Boltzmann distribution, and that they are distributed independently of other events, that is, the quasi-chemical approximation. Here, these assumptions are systematically tested by extracting contact energies from artificial databases of lattice proteins with predefined pairwise contact energies. Databases of protein sequences are designed to either satisfy the Boltzmann distribution at high or low temperatures, or to simultaneously optimize the native stability and folding kinetics. It is found that the quasi-chemical approximation, with the ideal reference state, accurately reproduce the true energies for high temperature Boltzmann distributed sequences (weakly interacting residues), but less accurately at low temperatures, where the sequences correspond to energy minima and the residues are strongly interacting. To overcome this problem, an iterative procedure for Boltzmann distributed sequences is introduced, which accounts for interacting residue correlations and eliminates the need for the quasi-chemical approximation. In this case, the energies are accurately reproduced at any ensemble temperature. However, when the database of sequences designed for optimal stability and kinetics is used, the energy correlation is less than optimal using either method, exhibiting random and systematic deviations from linearity. Therefore, the assumption that native structures are maximally stable or that sequences are determined according to the Boltzmann distribution seems to be inadequate for obtaining accurate energies. The limited number of sequences in the database and the inhomogeneous concentration of amino acids from one structure to another do not seem to be major obstacles for improving the quality of the extracted pairwise energies, with the exception of repulsive interactions.

Multiscale Coarse-Graining of the Protein Energy Landscape

“…Folding-inspired approaches utilize known folding behavior to tune CG parameters that will result in a properly folded protein [18]–[22]. In a somewhat similar fashion, knowledge-based methods invoke statistical potentials derived from distributions of residue-residue interactions and secondary structure in all known protein structures [3], [13], [23]–[27].…”

Exhaustive Characterization of TCR–pMHC Binding Energy Estimated by the String Model and Miyazawa-Jernigan Matrix

“…This matrix was obtained from databases of known protein structures and has difference from the mean .... been used in some of the best known protein structure prediction and folding modeling algorithms [12][13][14]. In 1985, Miyazawa and Jernigan formalized the theory for contact interactions among 20 natural AAs based on the quasi-chemical approximation, which treats the chain connectivity effects and solvent effects with simple inter-residue parameters [37,38]. The M-J matrix was revised in 1996, in which there were 6 times more residue-residue contact pairs and used 1168 protein structures containing 1661 subunit sequences.…”

“…Because the M-J matrix used by Kosmrlj et al was the 1996 version, such higher order structure contributions were not considered. Moreover, because the quasi-chemical approximation breaks down at low temperature, we should be careful when applying the M-J matrix and similar models to temperature-dependent phenomena [38].…”

Recovering physical potentials from a model protein databank

“…We quantitatively recovered the original interaction potentials directly from structural correlations by solving the generalized-YBG equation (35) for this "extended" canonical ensemble (37). Several earlier studies have directly recovered contact potentials (64,65) or iteratively determined model potentials (32,(66)(67)(68). In contrast, we quantitatively recovered a complete molecular potential directly from a databank of off-lattice protein structures.…”

“…The two most common criticisms of knowledge-based approaches address (i) the approximate treatment of many-body correlations and, in particular, chain connectivity (26,27,(30)(31)(32)(33) and (ii) the treatment of structural statistics compiled from different proteins (27). It is well known that, for any condensed phase system, simple excluded volume (packing) effects generate nontrivial many-body correlations that complicate the relationship between interparticle interactions and structural correlations (34).…”