Knowledge-based Potential Functions Research Articles

Monte Carlo sampling of near‐native structures of proteins with applications

Since a protein's dynamic fluctuation inside cells affects the protein's biological properties, we present a novel method to study the ensemble of near-native structures (NNS) of proteins, namely, the conformations that are very similar to the experimentally determined native structure. We show that this method enables us to (i) quantify the difficulty of predicting a protein's structure, (ii) choose appropriate simplified representations of protein structures, and (iii) assess the effectiveness of knowledge-based potential functions. We found that well-designed simple representations of protein structures are likely as accurate as those more complex ones for certain potential functions. We also found that the widely used contact potential functions stabilize NNS poorly, whereas potential functions incorporating local structure information significantly increase the stability of NNS.

Genetic algorithms for protein conformation sampling and optimization in a discrete backbone dihedral angle space

We have investigated protein conformation sampling and optimization based on the genetic algorithm and discrete main chain dihedral state model. An efficient approach combining the genetic algorithm with local minimization and with a niche technique based on the sharing function is proposed. Using two different types of potential energy functions, a Go-type potential function and a knowledge-based pairwise potential energy function, and a test set containing small proteins of varying sizes and secondary structure compositions, we demonstrated the importance of local minimization and population diversity in protein conformation optimization with genetic algorithms. Some general properties of the sampled conformations such as their native-likeness and the influences of including side-chains are discussed.

M-Score: A Knowledge-Based Potential Scoring Function Accounting for Protein Atom Mobility

A knowledge-based potential scoring function, named M-Score, has been developed based upon 2331 high-resolution crystal structures of protein-ligand complexes. M-Score considers the mobility of protein atoms, describing the location of each protein atom by a Gaussian distribution instead of a fixed position based upon the isotropic B-factors. This leads to an increase in the number of atom-pairs in the construction of knowledge-based potentials and a smoothing effect on the pairwise distribution functions. M-Score was validated using 896 complexes which were not included in the 2331 data set and whose experimentally determined binding affinities were available. The overall linear correlation coefficient (r) between the calculated scores and experimentally determined binding affinities (pKi or pKd) for these 896 complexes is -0.49. Evaluation of M-Score against 17 protein families showed that we obtained good to excellent correlations for six protein families, modest correlations for four protein families, and poor correlations for the remaining seven protein families.

Folding of Small Helical Proteins Assisted by Small-Angle X-Ray Scattering Profiles

This paper reports a computational method for folding small helical proteins. The goal was to determine the overall topology of proteins given secondary structure assignment on sequence. In doing so, a Monte Carlo protocol, which combines coarse-grained normal modes and a Hamiltonian at a different scale, was developed to enhance sampling. In addition to the knowledge-based potential functions, a small-angle X-ray scattering (SAXS) profile was also used as a weak constraint for guiding the folding. The algorithm can deliver structural models with overall correct topology, which makes them similar to those of 5 approximately 6 A cryo-EM density maps. The success could contribute to make the SAXS technique a fast and inexpensive solution-phase experimental method for determining the overall topology of small, soluble, but noncrystallizable, helical proteins.

Determining Protein Topology from Skeletons of Secondary Structures

We report a novel computational procedure for determining protein native topology, or fold, by defining loop connectivity based on skeletons of secondary structures that can usually be obtained from low to intermediate-resolution density maps. The procedure primarily involves a knowledge-based geometry filter followed by an energetics-based evaluation. It was tested on a large set of skeletons covering a wide range of protein architecture, including one modeled from an experimentally determined 7.6A cryo-electron microscopy (cryo-EM) density map. The results showed that the new procedure could effectively deduce protein folds without high-resolution structural data, a feature that could also be used to recognize native fold in structure prediction and to interpret data in fields like structure genomics. Most importantly, in the energetics-based evaluation, it was revealed that, despite the inevitable errors in the artificially constructed structures and limited accuracy of knowledge-based potential functions, the average energy of an ensemble of structures with slightly different configurations around the native skeleton is a much more robust parameter for marking native topology than the energy of individual structures in the ensemble. This result implies that, among all the possible topology candidates for a given skeleton, evolution has selected the native topology as the one that can accommodate the largest structural variations, not the one rigidly trapped in a deep, but narrow, conformational energy well.

Threading with environment-specific score by artificial neural networks

Protein threading programs align a probe amino acid sequence onto a library of representative folds of known protein structure to identify a structural homology. A scoring function is usually formulated in terms of the threading energy to evaluate the protein sequence-structure fitness. In this paper, a model named threading with environment-specific score (TES) is proposed to build a new threading score function with the use of artificial neural networks. Given a protein structure with a residue level environment description, the compatibility of residue in sequence with its structural environment is presented. A threading score is constructed by log-odds scores of predicted probabilities from the trained model to determine which residue best fits its environment. Two decoy sets are used to test the proposed TES method on discrimination of native and decoy protein three-dimensional structure. The results showed that the performance of the proposed method is comparable to those of knowledge-based potential energy function.

An in silico Exploration of the Neutral Network in Protein Sequence Space

Designating amino-acid sequences that fold into a common main-chain structure as “neutral sequences” for the structure, regardless of their function or stability, we investigated the distribution of neutral sequences in protein sequence space. For four distinct target structures (α, β,α/β and α+β types) with the same chain length of 108, we generated the respective neutral sequences by using the inverse folding technique with a knowledge-based potential function. We assumed that neutral sequences for a protein structure have Z scores higher than or equal to fixed thresholds, where thresholds are defined as the Z score for the corresponding native sequence (case 1) or much greater Z score (case 2). An exploring walk simulation suggested that the neutral sequences mapped into the sequence space were connected with each other through straight neutral paths and formed an inherent neutral network over the sequence space. Through another exploring walk simulation, we investigated contiguous regions between or among the neutral networks for the distinct protein structures and obtained the following results. The closest approach distance between the two neutral networks ranged from 5 to 29 on the Hamming distance scale, showing a linear increase against the threshold values. The sequences located at the “interchange” regions between the two neutral networks have intermediate sequence-profile-scores for both corresponding structures. Introducing a “ball” in the sequence space that contains at least one neutral sequence for each of the four structures, we found that the minimal radius of the ball that is centered at an arbitrary position ranged from 35 to 50, while the minimal radius of the ball that is centered at a certain special position ranged from 20 to 30, in the Hamming distance scale. The relatively small Hamming distances (5–30) may support an evolution mechanism by transferring from a network for a structure to another network for a more beneficial structure via the interchange regions.

A new hybrid Monte Carlo algorithm for protein potential function test and structure refinement

A new Hybrid Monte Carlo (HMC) algorithm has been developed to test protein potential functions and, ultimately, refine protein structures. The main principle of this algorithm is, in each cycle, a new trial conformation is generated by carrying out a short period of molecular dynamics (MD) iterations with a set of random parameters (including the MD time step, the number of MD steps, the MD temperature, and the seed for initial MD velocity assignment); then to accept or reject the new conformation on the basis of the Metropolis criterion. The novelty in this paper is that the potential in MD iterations is different from that in the MC step. In the former, it is a molecular mechanics potential, in the latter it is a knowledge-based potential (KBP). Directed by the KBP, the MD iteration is used to search conformational space for realistic conformations with low KBP energy. It circumvents the difficulty in using KBP functions directly in MD simulation, as KBP functions are typically incomplete, and do not always have continuous derivatives required for the calculation of the forces. The new algorithm has been tested in explorations of conformational space. In these test calculations the KBP energy was found to drop below the value for the native conformation, and the correlation between the root mean square deviation (RMSD) and the KBP energy was shown to be different from the test results in other references. At the present time, the algorithm is useful for testing new KBP functions. Furthermore, if a KBP function can be found for which the native conformation has the lowest energy and the energy/RMSD correlation is good, then this new algorithm also will be a tool for refinement of the theory-based structural models.

The Genetic Algorithm and the Conformational Search of Polypeptides and Proteins

Abstract The genetic algorithm is a technique of function optimization derived from the principles of evolutionary theory. We have adapted it to perform conformational search on polypeptides and proteins. The algorithm was first tested on several small polypeptides and the 46 amino acid protein crambin under the AMBER potential energy function. The probable global minimum conformations of the polypeptides were located 90% of the time and a non-native conformation of crambin was located that was 150kcal/mol lower in potential energy than the minimized crystal structure conformation. Next, we used a knowledge-based potential function to predict the structures of melittin, pancreatic polypeptide, and crambin. A 2.31 A ΔRMS conformation of melittin and a 5.33 A ΔRMS conformation of pancreatic polypeptide were located by genetic algorithm-based conformational search under the knowledge-based potential function. Although the ΔRMS of pancreatic polypeptide was somewhat high, most of the secondary structure was c...