Recognition of native structure from complete enumeration of low-resolution models with constraints

From Extraction of Local Structures of Protein Energy Landscapes to Improved Decoy Selection in Template-Free Protein Structure Prediction

Due to the essential role that the three-dimensional conformation of a protein plays in regulating interactions with molecular partners, wet and dry laboratories seek biologically-active conformations of a protein to decode its function. Computational approaches are gaining prominence due to the labor and cost demands of wet laboratory investigations. Template-free methods can now compute thousands of conformations known as decoys, but selecting native conformations from the generated decoys remains challenging. Repeatedly, research has shown that the protein energy functions whose minima are sought in the generation of decoys are unreliable indicators of nativeness. The prevalent approach ignores energy altogether and clusters decoys by conformational similarity. Complementary recent efforts design protein-specific scoring functions or train machine learning models on labeled decoys. In this paper, we show that an informative consideration of energy can be carried out under the energy landscape view. Specifically, we leverage local structures known as basins in the energy landscape probed by a template-free method. We propose and compare various strategies of basin-based decoy selection that we demonstrate are superior to clustering-based strategies. The presented results point to further directions of research for improving decoy selection, including the ability to properly consider the multiplicity of native conformations of proteins.

A computational pathway for bracketing native-like structures fo small alpha helical globular proteins

Impressive advances in the applications of bioinformatics for protein structure prediction coupled with growing structural databases on one hand and the insurmountable time-scale problem with ab initio computational methods on the other continue to raise doubts whether a computational solution to the protein folding problem--categorized as an NP-hard problem--is within reach in the near future. Combining some specially designed biophysical filters and vector algebra tools with ab initio methods, we present here a promising computational pathway for bracketing native-like structures of small alpha helical globular proteins departing from secondary structural information. The automated protocol is initiated by generating multiple structures around the loops between secondary structural elements. A set of knowledge-based biophysical filters namely persistence length and radius of gyration, developed and calibrated on approximately 1000 globular proteins, is introduced to screen the trial structures to filter out improbable candidates for the native and reduce the size of the library of probable structures. The ensemble so generated encompasses a few structures with native-like topology. Monte Carlo optimizations of the loop dihedrals are then carried out to remove steric clashes. The resultant structures are energy minimized and ranked according to a scoring function tested previously on a series of decoy sets vis-a-vis their corresponding natives. We find that the 100 lowest energy structures culled from the ensemble of energy optimized trial structures comprise at least a few to within 3-5 angstroms of the native. Thus the formidable "needle in a haystack" problem is narrowed down to finding an optimal solution amongst a computationally tractable number of alternatives. Encouraging results obtained on twelve small alpha helical globular proteins with the above outlined pathway are presented and discussed.

Protein decoy sets for evaluating energy functions

Energy functions are crucial ingredients of protein tertiary structure prediction methods. Assessing the quality of energy functions is therefore of prime importance. It requires the elaboration of a standard evaluation scheme, whose key elements are: i). sets that contain the native and several non-native structures of proteins (decoys) in order to test whether the energy functions display the expected quality features and ii). measures to evaluate the reliability of energy functions. We present here a survey of the recent advances in these two related fields. In a first part, we analyze and review the large number of decoy sets that are available on the web, and we summarize the characteristics of a challenging decoy set. We then discuss how to define the quality of energy functions and review the measures related to it.

A novel approach to decoy set generation: designing a physical energy function having local minima with native structure characteristics

We suggest a new approach to the generation of candidate structures (decoys) for ab initio prediction of protein structures. Our method is based on random sampling of conformation space and subsequent local energy minimization. At the core of this approach lies the design of a novel type of energy function. This energy function has local minima with native structure characteristics and wide basins of attraction. The current work presents our motivation for deriving such an energy function and also tests the derived energy function. Our approach is novel in that it takes advantage of the inherently rough energy landscape of proteins, which is generally considered a major obstacle for protein structure prediction. When local minima have wide basins of attraction, the protein's conformation space can be greatly reduced by the convergence of large regions of the space into single points, namely the local minima corresponding to these funnels. We have implemented this concept by an iterative process. The potential is first used to generate decoy sets and then we study these sets of decoys to guide further development of the potential. A key feature of our potential is the use of cooperative multi-body interactions that mimic the role of the entropic and solvent contributions to the free energy. The validity and value of our approach is demonstrated by applying it to 14 diverse, small proteins. We show that, for these proteins, the size of conformation space is considerably reduced by the new energy function. In fact, the reduction is so substantial as to allow efficient conformational sampling. As a result we are able to find a significant number of near-native conformations in random searches performed with limited computational resources.

Natural coordinate representation for the protein backbone structure

A new model for describing the geometry of the C(alpha) backbone atoms in protein molecules is derived. This model uses one continuous variable per amino acid. This is half the number of degrees-of-freedom used in traditional backbone models. The new model was tested on 721 PDB structures and its average accuracy was determined to be 1.14 A cRMSD. This model can be used as a description of local structure that provides higher resolution than the traditional secondary structure categories. Also, because this structure description is one-dimensional, it can be used to align structures with the same efficiency and convergence properties available in the popular sequence alignment tools. Furthermore, the 1:1 correspondence with the amino acid sequence has implications for combined sequence/structure alignment. Conventional secondary structure prediction was used to further reduce the number of degrees-of-freedom in 16 test proteins. In those cases, the average cRMSD degraded from 0.96 to 2.33 A while the number of degrees-of-freedom improved (reduced) by more than 30%.

Distinguishing native conformations of proteins from decoys with an effective free energy estimator based on the OPLS all-atom force field and the Surface Generalized Born solvent model

Protein decoy data sets provide a benchmark for testing scoring functions designed for fold recognition and protein homology modeling problems. It is commonly believed that statistical potentials based on reduced atomic models are better able to discriminate native-like from misfolded decoys than scoring functions based on more detailed molecular mechanics models. Recent benchmark tests on small data sets, however, suggest otherwise. In this work, we report the results of extensive decoy detection tests using an effective free energy function based on the OPLS all-atom (OPLS-AA) force field and the Surface Generalized Born (SGB) model for the solvent electrostatic effects. The OPLS-AA/SGB effective free energy is used as a scoring function to detect native protein folds among a total of 48,832 decoys for 32 different proteins from Park and Levitt's 4-state-reduced, Levitt's local-minima, Baker's ROSETTA all-atom, and Skolnick's decoy sets. Solvent electrostatic effects are included through the Surface Generalized Born (SGB) model. All structures are locally minimized without restraints. From an analysis of the individual energy components of the OPLS-AA/SGB energy function for the native and the best-ranked decoy, it is determined that a balance of the terms of the potential is responsible for the minimized energies that most successfully distinguish the native from the misfolded conformations. Different combinations of individual energy terms provide less discrimination than the total energy. The results are consistent with observations that all-atom molecular potentials coupled with intermediate level solvent dielectric models are competitive with knowledge-based potentials for decoy detection and protein modeling problems such as fold recognition and homology modeling.