Fast hinge detection algorithms for flexible protein structures

ART-RRT: As-Rigid-As-Possible search for protein conformational transition paths

The possible functions of a protein are strongly related to its structural rearrangements in the presence of other molecules or environmental changes. Hence, the evaluation of transition paths of proteins, which encodes conformational changes between stable states, is important since it may reveal the underlying mechanisms of the biochemical processes related to these motions. During the last few decades, different geometry-based methods have been proposed to predict such transition paths. However, in the cases where the solution requires complex motions, these methods, which typically constrain only locally the molecular structures, could produce physically irrelevant solutions involving self-intersection. Recently, we have proposed ART-RRT, an efficient method for finding ligand-unbinding pathways. It relies on the exploration of energy valleys in low-dimensional spaces, taking advantage of some mechanisms inspired from computer graphics to ensure the consistency of molecular structures. This article extends ART-RRT to the problem of finding probable conformational transition between two stable states for proteins. It relies on a bidirectional exploration rooted on the two end states and introduces an original strategy to attempt connections between the explored regions. The resulting method is able to produce at low computational cost biologically realistic paths free from self-intersection. These paths can serve as valuable input to other advanced methods for the study of proteins. A better understanding of conformational changes of proteins is important since it may reveal the underlying mechanisms of the biochemical processes related to such motions. Recently, the ART-RRT method has been introduced for finding ligand-unbinding pathways. This article presents an adaptation of the method for finding probable conformational transition between two stable states of a protein. The method is not only computationally cost-effective but also able to produce biologically realistic paths which are free from self-intersection.

NAHAL-Flex: A Numerical and Alphabetical Hinge Detection Algorithm for Flexible Protein Structure Alignment

Flexible proteins are proteins that have conformational changes in their structures. Protein flexibility analysis is critical for classifying and understanding protein functionality. For that analysis, the hinge areas where proteins show flexibility must be detected. To detect the location of the hinges, previous methods have utilized the three-dimensional (3D) structure of proteins, which is highly computational. To reduce the computational complexity, this study proposes a novel text-based method using structural alphabets (SAs) for detecting the hinge position, called NAHAL-Flex. Protein structures were encoded to a particular type of SA called the protein folding shape code (PFSC), which remains unaffected by location, scale, and rotation. The flexible regions of the proteins are the only places in which letter sequences can be distorted. With this knowledge, it is possible to find the longest alignment path of two letter sequences using a dynamic programming (DP) algorithm. Then, the proposed method looks for regions where the alphabet sequence is distorted to find the most probable hinge positions. In order to reduce the number of hinge positions, a genetic algorithm (GA) was utilized to find the best candidate hinge points. To evaluate the method's effectiveness, four different flexible and rigid protein databases, including two small datasets and two large datasets, were utilized. For the small dataset, the NAHAL-Flex method was comparable to state-of-the-art structural flexible alignment methods. The result for the large datasets show that NAHAL-Flex outperforms some well-known alignment methods, e.g., DaliLite, Matt, DeepAlign, and TM-align; the speed of NAHAL-Flex was faster and its result was more accurate than the other methods.

Finding semirigid domains in biomolecules by clustering pair-distance variations

Dynamic variations in the distances between pairs of atoms are used for clustering subdomains of biomolecules. We draw on a well-known target function for clustering and first show mathematically that the assignment of atoms to clusters has to be crisp, not fuzzy, as hitherto assumed. This reduces the computational load of clustering drastically, and we demonstrate results for several biomolecules relevant in immunoinformatics. Results are evaluated regarding the number of clusters, cluster size, cluster stability, and the evolution of clusters over time. Crisp clustering lends itself as an efficient tool to locate semirigid domains in the simulation of biomolecules. Such domains seem crucial for an optimum performance of subsequent statistical analyses, aiming at detecting minute motional patterns related to antigen recognition and signal transduction.

A spectral approach to protein structure alignment

A new intrinsic geometry based on a spectral analysis is used to motivate methods for aligning protein folds. The geometry is induced by the fact that a distance matrix can be scaled so that its eigenvalues are positive. We provide a mathematically rigorous development of the intrinsic geometry underlying our spectral approach and use it to motivate two alignment algorithms. The first uses eigenvalues alone and dynamic programming to quickly compute a fold alignment. Family identification results are reported for the Skolnick40 and Proteus300 data sets. The second algorithm extends our spectral method by iterating between our intrinsic geometry and the 3D geometry of a fold to make high-quality alignments. Results and comparisons are reported for several difficult fold alignments. The second algorithm's ability to correctly identify fold families in the Skolnick40 and Proteus300 data sets is also established.

Optimal identification of semi-rigid domains in macromolecules from molecular dynamics simulation

Biological function relies on the fact that biomolecules can switch between different conformations and aggregation states. Such transitions involve a rearrangement of parts of the biomolecules involved that act as dynamic domains. The reliable identification of such domains is thus a key problem in biophysics. In this work we present a method to identify semi-rigid domains based on dynamical data that can be obtained from molecular dynamics simulations or experiments. To this end the average inter-atomic distance-deviations are computed. The resulting matrix is then clustered by a constrained quadratic optimization problem. The reliability and performance of the method are demonstrated for two artificial peptides. Furthermore we correlate the mechanical properties with biological malfunction in three variants of amyloidogenic transthyretin protein, where the method reveals that a pathological mutation destabilizes the natural dimer structure of the protein. Finally the method is used to identify functional domains of the GroEL-GroES chaperone, thus illustrating the efficiency of the method for large biomolecular machines.