Substructures In Proteins Research Articles

A quantum chemical interaction energy dataset for accurately modeling protein-ligand interactions

Fast and accurate calculation of intermolecular interaction energies is desirable for understanding many chemical and biological processes, including the binding of small molecules to proteins. The Splinter [“Symmetry-adapted perturbation theory (SAPT0) protein-ligand interaction”] dataset has been created to facilitate the development and improvement of methods for performing such calculations. Molecular fragments representing commonly found substructures in proteins and small-molecule ligands were paired into >9000 unique dimers, assembled into numerous configurations using an approach designed to adequately cover the breadth of the dimers’ potential energy surfaces while enhancing sampling in favorable regions. ~1.5 million configurations of these dimers were randomly generated, and a structurally diverse subset of these were minimized to obtain an additional ~80 thousand local and global minima. For all >1.6 million configurations, SAPT0 calculations were performed with two basis sets to complete the dataset. It is expected that Splinter will be a useful benchmark dataset for training and testing various methods for the calculation of intermolecular interaction energies.

Modeling protein structure as a stable static equilibrium.

We present evidence that the protein structure can be modeled as a stable static equilibrium, determined mainly by compressive supports in the nonpolar interior. That is, protein structures derive their structural strength through the same mechanical principles as do conventional structures like bridges and buildings. This is based on the observation that the experimentally elucidated structural determinants, the interior nonpolar side chains, are engaged in strong compressions in static terms. At the same time, major substructures in proteins, helices and h-bonded strands, because of their geometry, inherently leave gaps in the space they occupy. Under the compressive force, nonpolar side chains from one substructure can protrude into the gaps of another neighboring substructure and block its motion. As a result, interlocking of substructures can form, which builds up the nonpolar core assembly. The native structure then is the one with the structurally most stable core assembly. While intuitively appealing, this is a radical departure from the prevailing thinking that protein native structure is determined by global energy minimum, which is founded on thermodynamic hypothesis. Furthermore, to develop an effective model for analyzing protein structure with conventional tools, a proper mechanical representation must be established. By proving that the stability of the equilibrium in compressive interactions is conditioned on a form of mechanical energy minimum, we show that our notion of native structure can be equally consistent with the thermodynamic hypothesis. By mathematically treating the blocking action, an interaction, as a bar, a physical object, we succeed in representing and analyzing the core assembly as truss, a conventional structure. In this paper we define and expound step-by-step increasingly integrated interlocking patterns. We then analyze the core assemblies of a large set of diverse protein database structures. A native structure can be distinguished from decoys by comparing the composition and strength of their core assemblies. We show the results for two sets of native structures vs decoys.

Stable Substructures in Proteins and How to Find Them Using Single-Molecule Force Spectroscopy.

Three-dimensional structures of proteins are a source of fascination for scientists, due to the beauty of their sequence-encoded architectures and their highly diverse range of functions. These functions include acting as powerful catalysts, signal receptors, and versatile molecular motors as well as being building blocks for macroscopic structures, thus defining the shape of multicellular organisms. How protein structure is organized and assembled at the sub-nanometer scale is of great current interest. Specifically, the discovery of stable substructures and supersecondary structures has inspired research into their potential use in rationally engineered proteins with tailor-made properties. Here, we show how the search for stable substructures in large proteins can benefit from recent advances in single-molecule force spectroscopy using highly sensitive dual-beam optical tweezers. Our chapter provides a step-by-step description of the experimental workflow for (1) preparing proteins for mechanical interrogation, (2) interpreting the data, and (3) avoiding the most commonly occurring mistakes.

Efficient SCOP-fold classification and retrieval using index-based protein substructure alignments

To investigate structure-function relationships, life sciences researchers usually retrieve and classify proteins with similar substructures into the same fold. A manually constructed database, SCOP, is believed to be highly accurate; however, it is labor intensive. Another known method, DALI, is also precise but computationally expensive. We have developed an efficient algorithm, namely, index-based protein substructure alignment (IPSA), for protein-fold classification. IPSA constructs a two-layer indexing tree to quickly retrieve similar substructures in proteins and suggests possible folds by aligning these substructures. Compared with known algorithms, such as DALI, CE, MultiProt and MAMMOTH, on a sample dataset of non-redundant proteins from SCOP v1.73, IPSA exhibits an efficiency improvement of 53.10, 16.87, 3.60 and 1.64 times speedup, respectively. Evaluated on three different datasets of non-redundant proteins from SCOP, average accuracy of IPSA is approximately equal to DALI and better than CE, MAMMOTH, MultiProt and SSM. With reliable accuracy and efficiency, this work will benefit the study of high-throughput protein structure-function relationships. IPSA is publicly accessible at http://ProteinDBS.rnet.missouri.edu/IPSA.php

FAMCS: Finding All Maximal Common Substructures in Proteins

Finding the common substructures shared by two proteins is considered as one of the central issues in computational biology because of its usefulness in understanding the structure-function relationship and application in drug and vaccine design. In this paper, we propose a novel algorithm called FAMCS (Finding All Maximal Common Substructures) for the common substructure identification problem. Our method works initially at the protein secondary structural element (SSE) level and starts with the identification of all structurally similar SSE pairs. These SSE pairs are then merged into sets using a modified Apriori algorithm, which will test the similarity of various sets of SSE pairs incrementally until all the maximal sets of SSE pairs that deemed to be similar are found. The maximal common substructures of the two proteins will be formed from these maximal sets. A refinement algorithm is also proposed to fine tune the alignment from the SSE level to the residue level. Comparison of FAMCS with other methods on various proteins shows that FAMCS can address all four requirements and infer interesting biological discoveries.

Protein structure comparison using bipartite graph matching and its application to protein structure classification.

A measure of protein structure similarity is calculated from the matching of pairs of secondary structure elements between two proteins. The interaction of each pair was estimated from their axial line segments and combined with other geometric features to produce an optimal discrimination between intrafamily and interfamily relationships. The matching used a fast bipartite graph-matching algorithm that avoids the computational complexity of searching for the full subgraph isomorphism between the two sets of interactions. The main algorithm used was the "stable marriage" algorithm, which works on the ranked "preferences" of one interaction for another. The method takes 1/10 of a second for a typical comparison making it suitable as a fast pre-filter for slower, more exhaustive approaches. An application to protein structure classification is described.

Stabilization of coiled-coil peptide domains by introduction of trifluoroleucine.

Substitution of leucine residues by 5,5,5-trifluoroleucine at the d-positions of the leucine zipper peptide GCN4-p1d increases the thermal stability of the coiled-coil structure. The midpoint thermal unfolding temperature of the fluorinated peptide is elevated by 13 degrees C at 30 microM peptide concentration. The modified peptide is more resistant to chaotropic denaturants, and the free energy of folding of the fluorinated peptide is 0.5-1.2 kcal/mol larger than that of the hydrogenated form. A similarly fluorinated form of the DNA-binding peptide GCN4-bZip binds to target DNA sequences with affinity and specificity identical to those of the hydrogenated form, while demonstrating enhanced thermal stability. Molecular dynamics simulation on the fluorinated GCN4-p1d peptide using the Surface Generalized Born implicit solvation model revealed that the coiled-coil binding energy is 55% more favorable upon fluorination. These results suggest that fluorination of hydrophobic substructures in peptides and proteins may provide new means of increasing protein stability, enhancing protein assembly, and strengthening receptor-ligand interactions.

Matching organic libraries with protein-substructures.

We present a general approach which allows automatic identification of sub-structures in proteins that resemble given three-dimensional templates. This paper documents its success with non-peptide templates such as beta-turn mimetics. We considered well-tested turn-mimetics such as the bicyclic turned dipeptide (BTD), spiro lactam (Spiro) and the 2,5-disubstituded tetrahydrofuran (THF), a new furan-derivative which was recently developed and characterized. The detected geometric similarity between the templates and the protein patches corresponds to r.m.s.-values of 0.3 A for more than 80% of the constituting atoms, which is typical for active site comparisons of homologous proteins. This fast automatic procedure might be of biomedical value for finding special mimicking leads for particular protein sub-structures as well as for template-assembled synthetic protein (TASP) design.

Protein structural alignments and functional genomics

Structural genomics-the systematic solution of structures of the proteins of an organism-will increasingly often produce molecules of unknown function with no close relative of known function. Prediction of protein function from structure has thereby become a challenging problem of computational molecular biology. The strong conservation of active site conformations in homologous proteins suggests a method for identifying them. This depends on the relationship between size and goodness-of-fit of aligned substructures in homologous proteins. For all pairs of proteins studied, the root-mean-square deviation (RMSD) as a function of the number of residues aligned varies exponentially for large common substructures and linearly for small common substructures. The exponent of the dependence at large common substructures is well correlated with the RMSD of the core as originally calculated by Chothia and Lesk (EMBO J 1986;5:823-826), affording the possibility of reconciling different structural alignment procedures. In the region of small common substructures, reduced aligned subsets define active sites and can be used to suggest the locations of active sites in homologous proteins.

Conservation of substructures in proteins: interfaces of secondary structural elements in proteasomal subunits

It is observed that during divergent evolution of two proteins with a common phylogenetic origin, the structural similarity of their backbones is often preserved even when the sequence similarity between them decreases to a virtually undetectable level. Here we analyzed, whether the conservation of structure along evolution involves also the local atomic structures in the interfaces between secondary structural elements. We have used as study case one protein family, the proteasomal subunits, for which 17 crystal structures are known. These include 14 different subunits of Saccharomyces cerevisiae, 2 subunits of Thermoplasma acidophilum and one subunit of Escherichia coli. The structural core of the 17 proteasomal subunits has 23 secondary structural elements. Any two adjacent secondary structural elements form a molecular interface consisting of two molecular patches. We found 61 interfaces that occurred in all 17 subunits. The 3D shape of equivalent molecular patches from different proteasomal subunits were compared by superposition. Our results demonstrate that pairs of equivalent molecular patches show an RMSD which is lower than that of randomly chosen patches from unrelated proteins. This is true even when patch comparisons with identical residues were excluded from the analysis. Furthermore it is known that the sequential dissimilarity is correlated to the RMSD between the backbones of the members of protein families. The question arises whether this is also true for local atomic structures. The results show that the correlation of individual patch RMSD values and local sequence dissimilarities is low and has a wide range from 0 to 0.41, however, it is surprising that there is a good correlation between the average RMSD of all corresponding patches and the global sequence dissimilarity. This average patch RMSD correlates slightly stronger than the Cα-trace RMSD to the global sequence dissimilarity.

Pairwise and multiple identification of three-dimensional common substructures in proteins.

In this paper, we present an algorithm to find three-dimensional substructures common to two or more molecules. The basic algorithm is devoted to pairwise structural comparison. Given two sets of atomic coordinates, it finds the largest subsets of atoms which are "similar" in the sense that all internal distances are approximately conserved. The basic idea of the algorithm is to recursively build subsets of increasing sizes, combining two sets of size k to build a set of size k + 1. The algorithm can be used "as is" for small molecules or local parts of proteins (about 30 atoms). When a high number of atoms is involved, we use a two step procedure. First we look for common "local" fragments by using the previous algorithm, and then we gather these fragments by using a Branch and Bound technique. We also extend the basic algorithm to perform multiple comparisons, by using one of the structures as a reference point (pivot) to which all other structures are compared. The solution is the largest subsets of atoms common to the pivot and at least q other structures. Although both algorithms are theoretically exponential in the number of atoms, experiments performed on biological data and using realistic parameters show that the solution is obtained within a few minutes. Finally, an application to the determination of the structural core of seven globins is presented.

A novel approach to molecular evolution study

Evolution of species is one of the major problems in biology and great effort has been devoted to its study along the years. The enormous number of macromolecular sequences now available has allowed the development of molecular evolution, since homologous molecules can be compared and phylogenetic trees are deduced from this analysis. Up to now, molecular evolution has been studied estimating the punctual mutations in the nucleic acid or amino acid sequences. Here we present a different scheme, analyzing changes in the secondary structure of a given protein along species. Since the principal features of a protein (function, adaptability, interactions with its medium and with other molecules, etc.) are determined by its spatial configuration, we can also think that changes in this conformation are correlated with the evolutionary pathway. Phylogenetic trees, then, will be principally based on physical processes, since conformation is essential for interactions and many changes of the sequence unrelated to variations in protein structure will not be considered in our scheme. We have first developed a method (Figureau et al., 1995) in order to discriminate definite substructures (~ helices, 13 sheets) in proteins from the primary sequence. These structures are correctly predicted, since the success rate for 3 states (~, [3, else) is about 80% (Soto et al, 1996). The algorithm is then sufficiently reliable to be applied to the evolution problem. As a first example, we have chosen the cytochrome c molecule, analyzing, in this case, changes in the location of c~ helices for 35 of these molecules corresponding to different species. The relevance of a given molecular conformation in the cytochrome c molecule is emphasized.

Efficient detection of three-dimensional structural motifs in biological macromolecules by computer vision techniques.

Macromolecules carrying biological information often consist of independent modules containing recurring structural motifs. Detection of a specific structural motif within a protein (or DNA) aids in elucidating the role played by the protein (DNA element) and the mechanism of its operation. The number of crystallographically known structures at high resolution is increasing very rapidly. Yet, comparison of three-dimensional structures is a laborious time-consuming procedure that typically requires a manual phase. To date, there is no fast automated procedure for structural comparisons. We present an efficient O(n3) worst case time complexity algorithm for achieving such a goal (where n is the number of atoms in the examined structure). The method is truly three-dimensional, sequence-order-independent, and thus insensitive to gaps, insertions, or deletions. This algorithm is based on the geometric hashing paradigm, which was originally developed for object recognition problems in computer vision. It introduces an indexing approach based on transformation invariant representations and is especially geared toward efficient recognition of partial structures in rigid objects belonging to large data bases. This algorithm is suitable for quick scanning of structural data bases and will detect a recurring structural motif that is a priori unknown. The algorithm uses protein (or DNA) structures, atomic labels, and their three-dimensional coordinates. Additional information pertaining to the structure speeds the comparisons. The algorithm is straightforwardly parallelizable, and several versions of it for computer vision applications have been implemented on the massively parallel connection machine. A prototype version of the algorithm has been implemented and applied to the detection of substructures in proteins.

Detection of common three-dimensional substructures in proteins.

We present a fully automatic algorithm for three-dimensional alignment of protein structures and for the detection of common substructures and structural repeats. Given two proteins, the algorithm first identifies all pairs of structurally similar fragments and subsequently clusters into larger units pairs of fragments that are compatible in three dimensions. The detection of similar substructures is independent of insertion/deletion penalties and can be chosen to be independent of the topology of loop connections and to allow for reversal of chain direction. Using distance geometry filters and other approximations, the algorithm, implemented in the WHAT IF program, is so fast that structural comparison of a single protein with the entire database of known protein structures can be performed routinely on a workstation. The method reproduces known non-trivial superpositions such as plastocyanin on azurin. In addition, we report surprising structural similarity between ubiquitin and a (2Fe-2S) ferredoxin.

The frequency of ion‐pair substructures in proteins is quantitatively related to electrostatic potential: A statistical model for nonbonded interactions

A statistical analysis of ion pairs in protein crystal structures shows that their abundance with respect to uncharged controls is accurately predicted by a Boltzmann-like function of electrostatic potential. It appears that the mechanisms of protein folding and/or evolution combine to produce a "thermal" distribution of local nonbonded interactions, as has been suggested by statistical-mechanical theories. Using this relationship, we develop a maximum likelihood methodology for estimation of apparent energetic parameters from the data base of known structures, and we derive electrostatic potential functions that lead to optimal agreement of observed and predicted ion-pair frequencies. These are similar to potentials of mean force derived from electrostatic theory, but departure from Coulombic behavior is less than has been suggested.

Identification of structural motifs from protein coordinate data: secondary structure and first-level supersecondary structure.

A computer program is described that produces a description of the secondary structure and supersecondary structure of a polypeptide chain using the list of alpha carbon coordinates as input. Restricting the term "secondary structure" to the conformation of contiguous segments of the chain, the program determines the initial and final residues in helices, extended strands, sharp turns, and omega loops. This is accomplished through the use of difference distance matrices. The distances in idealized models of the segments are compared with the actual structure, and the differences are evaluated for agreement within preset limits. The program assigns 90-95% of the residues in most proteins to at least one type of secondary element. In a second step the now-defined helices and strands are idealized as straight line segments, and the axial directions and locations are compiled from the input C alpha coordinate list. These data are used to check for moderate curvature in strands and helices, and the secondary structure list is corrected where necessary. The geometric relations between these line segments are then calculated and output as the first level of supersecondary structure. A maximum of six parameters are required for a complete description of the relations between each pair. Frequently a less complete description will suffice, for example just the interaxial separation and angle. Both the secondary structure and one aspect of the supersecondary structure can be displayed in a character matrix analogous to the distance matrix format. This allows a quite accurate two-dimensional display of the three-dimensional structure, and several examples are presented. A procedure for searching for arbitrary substructures in proteins using distance matrices is also described. A search for the DNA binding helix-turn-helix motif in the Protein Data Bank serves as an example. A further abstraction of the above data can be made in the form of a metamatrix where each diagonal element represents an entire secondary segment rather than a single atom, and the off-diagonal elements contain all the parameters describing their interrelations. Such matrices can be used in a straightforward search for higher levels of supersecondary structure or used in toto as a representation of the entire tertiary structure of the polypeptide chain.