Using the Unfolded State as the Reference State Improves the Performance of Statistical Potentials

Abstract

Distance-dependent statistical potentials are an important class of energy functions extensively used in modeling protein structures and energetics. These potentials are obtained by statistically analyzing the proximity of atoms in all combinatorial amino-acid pairs in proteins with known structures. In model evaluation, the statistical potential is usually subtracted by the value of a reference state for better selectivity. An ideal reference state should include the general chemical properties of polypeptide chains so that only the unique factors stabilizing the native structures are retained after calibrating on reference state. However, reference states available as of this writing rarely model specific chemical constraints of peptide bonds and therefore poorly reflect the behavior of polypeptide chains. In this work, we proposed a statistical potential based on unfolded state ensemble (SPOUSE), where the reference state is summarized from the unfolded state ensembles of proteins produced according to the statistical coil model. Due to its better representation of the features of polypeptides, SPOUSE outperforms three of the most widely used distance-dependent potentials not only in native conformation identification, but also in the selection of close-to-native models and correlation coefficients between energy and model error. Furthermore, SPOUSE shows promising possibility of further improvement by integration with the orientation-dependent side-chain potentials.

Improving the orientation-dependent statistical potential using a reference state

“…Presently available decoy sets were generated from three major sources: theoretical modeling, homology modeling, as well as real‐time simulation . The first class of decoy sets is not only less relevant to protein structural prediction procedure but also less discriminative in the evaluation of numerous prevalent statistical potentials . Therefore, these decoy sets were only used to optimize the weight for local interactions w .…”

“…According to the previous researches on the distance‐dependent statistical potentials, inclusion of a proper reference state to describe the general features of polypeptides can substantially enhance the power of these potentials, because the specific properties of the folded proteins are uniquely retained in the final energy after the exclusion of common features through subtracting the energy of the reference state . The earliest reference state was obtained from the average atomic distance distribution in known structures with permutated primary sequences .…”

“…The earliest reference state was obtained from the average atomic distance distribution in known structures with permutated primary sequences . Subsequently, the reference states were either derived from theoretical analysis on the distance distribution of random atom pairs or obtained from the unfolded state ensemble of polypeptides . All of these reference states were reported to improve the performance of distance‐dependent potentials.…”

An Atomistic Statistically Effective Energy Function for Computational Protein Design

“…A statistical coil model of the unfolded state with persistent native-like residual structure has been proposed as a useful reference state in the formulation of residue statistical potentials. 75 In the working model of the unfolded state used here, it is assumed that amino acid residues will interact in a sequence-dependent manner only with their immediate (local) neighbours in the protein chain, but that weak or incompletely formed (non-local) interactions with residues more distant in one dimensional sequence space will still contribute to solvent shielding. Statistical data obtained from structural analyses of partially and fully solvent-exposed three-residue fragments in regions of irregular structure in experimentally determined protein database structures have been used to derive an effective energy model of the unfolded protein state ensemble.…”

“…71 Efforts to improve SEEF accuracy, through iterative sculpting of protein folding energy landscapes, the definition of statistically and physically more robust reference states and better accounting of multi-body correlations, have further augmented their numbers. 46,50,61,72,[74][75][76] Many statistical functions described in the literature accomplish individual tasks required in CPD such as protein modelling and prediction 60,71,[75][76][77][78][79][80][81][82][83] , protein model error analysis 73,[84][85][86] , ligand docking and scoring 70,72,87-94 , residue network connectivity analysis 95 , prediction of protein mutant thermal stability 96,97 and evolution of artificial sequences 98 . However, few existing atomistic SEEFs treat the unfolded state explicitly, and the majority of functions are not well adapted to perform all of the different tasks required in CPD.…”