Narrow Results

The sequence and structure of a large body of proteins are becoming increasingly available. It is desirable to explore mathematical tools for efficient extraction of information from such sources. The principles of graph theory, which was earlier applied in fields such as electrical engineering and computer networks are now being adopted to investigate protein structure, folding, stability, function and dynamics. This review deals with a brief account of relevant graphs and graph theoretic concepts. The concepts of protein graph construction are discussed. The manner in which graphs are analyzed and parameters relevant to protein structure are extracted, are explained. The structural and biological information derived from protein structures using these methods is presented.

We consider two types of Go models of a protein (crambin) and study their kinetics through molecular dynamics simulations. In the first model, the residue–residue contact interactions are selected based on a cutoff distance, R_c. The folding times strongly depend on the value of R_c and nonmonotonically. This indicates a need for a physically determined set of native contacts. One may accomplish it by considering the van der Waals radii of the residual atoms and checking if the atoms overlap. In the second model, non-native attractive contacts are added to the system. This leads to bad foldability. However, for a small number of such extra contacts there is a slight acceleration in the kinetics of folding.

We have investigated the folding of two helix-bundle proteins, 36-residue Villin headpiece and 56-residue E-domain of Staphylococcal protein A, by combining molecular dynamics (MD) simulations with Coarse-Grained United-Residue (UNRES) Force Field and all-atom force field. Starting from extended structures, each of the proteins was folded to a stable structure within a short time frame using the UNRES model. However, the secondary structures of helices were not well formed. Further refinement using MD simulations with the all-atom force field was able to fold the protein structure into the native-like state with the smallest main-chain root-mean-square deviation of around 3 Å. Detailed analysis of the folding trajectories was presented and the performance of GPU-based MD simulations was also discussed.

Predicting protein folding rate from amino acid sequence is an important challenge in computational and molecular biology. Over the past few years, many methods have been developed to reflect the correlation between the folding rates and protein structures and sequences. In this paper, we present an effective method, a combined neural network — genetic algorithm approach, to predict protein folding rates only from amino acid sequences, without any explicit structural information. The originality of this paper is that, for the first time, it tackles the effect of sequence order. The proposed method provides a good correlation between the predicted and experimental folding rates. The correlation coefficient is 0.80 and the standard error is 2.65 for 93 proteins, the largest such databases of proteins yet studied, when evaluated with leave-one-out jackknife test. The comparative results demonstrate that this correlation is better than most of other methods, and suggest the important contribution of sequence order information to the determination of protein folding rates.

This paper deals both prediction of stable (native) protein structures and the analysis of the dynamic behavior of protein structures. An improved micro genetic algorithm with intergenerational projection technique is introduced to inversely predict the stable structure of native folded proteins. Discussions are provided on how an optimization technique, such as the genetic algorithms can be used to solve the protein structure prediction (or folding) problem. A lattice model for protein structures is used in the construction of the grand structure of proteins. Examples of predicted native protein structure are presented. Cubic structures are obtained for proteins with 27 monomers, which agree well with the reported prediction using the Monte Carlo (MC) method. For larger systems, 64 and 125 unit long proteins, structures found using the present method are not cubic but they are near-cubic and fairly compact. Methods of molecular dynamics are then used to analyze the dynamic behavior of the predicted protein structures.

We compare the efficiency of two prominent techniques for simulation of complex systems: parallel tempering and Wang–Landau sampling. We show that both methods are of comparable efficiency but are optimized for different platforms. Parallel tempering should be chosen on multi-processor system while Wang–Landau sampling is easier to implement on a single-processor computer.

A crucial event in protein folding is the formation of a folding nucleus, which is a structured part of the protein chain in the transition state. We demonstrate a correlation between locations of residues involved in the folding nuclei and locations of predicted amyloidogenic regions. The average Φ-values are significantly greater inside amyloidogenic regions than outside them. We have found that fibril formation and normal folding involve many of the same key residues, giving an opportunity to outline the folding initiation site in protein chains. The search for folding initiation sites for apomyoglobin and ribonuclease. A coincides with the predictions made by other approaches.

Self-avoiding walks (SAWs) are the source of very difficult problems in probability and enumerative combinatorics. They are of great interest as, for example, they are the basis of protein structure prediction (PSP) in bioinformatics. The authors of this paper have previously shown that, depending on the prediction algorithm, the sets of obtained walk conformations differ: For example, all the SAWs can be generated using stretching-based algorithms whereas only the unfoldable SAWs can be obtained with methods that iteratively fold the straight line. A deeper study of (non-)unfoldable SAWs is presented in this paper. The contribution is first a survey of what is currently known about these sets. In particular, we provide clear definitions of various subsets of SAWs related to pivot moves (unfoldable and non-unfoldable SAWs, etc.) and the first results that we have obtained, theoretically or computationally, on these sets. Then a new theorem on the number of non-unfoldable SAWs is demonstrated. Finally, a list of open questions is provided and the consequences on the PSP problem is proposed.

Understanding how proteins fold is essential to our quest in discovering how life works at the molecular level. Current computation power enables researchers to produce a huge amount of folding simulation data. Hence there is a pressing need to be able to interpret and identify novel folding features from them. In this paper, we model each folding trajectory as a multi-dimensional curve. We then develop an effective multiple curve comparison (MCC) algorithm, called the enhanced partial order (EPO) algorithm, to extract features from a set of diverse folding trajectories, including both successful and unsuccessful simulation runs. Our EPO algorithm addresses several new challenges presented by comparing high dimensional curves coming from folding trajectories. A detailed case study of applying our algorithm to a miniprotein Trp-cage²⁴ demonstrates that our algorithm can detect similarities at rather low level, and extract biologically meaningful folding events.

We have proposed a parallel simulated annealing using genetic crossover as one of powerful conformational search methods, in order to find the global minimum energy structures for protein systems. The simulated annealing using genetic crossover method, which incorporates the attractive features of the simulated annealing and the genetic algorithm, is useful for finding a minimum potential energy conformation of protein systems. However, when we perform simulations by using this method, we often find obviously unnatural stable conformations, which have "knots" of a string of an amino-acid sequence. Therefore, we combined knot theory with our simulated annealing using genetic crossover method in order to avoid the knot conformations from the conformational search space. We applied this improved method to protein G, which has 56 amino acids. As the result, we could perform the simulations, which avoid knot conformations.