Difference Distance Matrix Research Articles

The Bio3D packages for structural bioinformatics.

Bio3D is a family of R packages for the analysis of biomolecular sequence, structure, and dynamics. Major functionality includes biomolecular database searching and retrieval, sequence and structure conservation analysis, ensemble normal mode analysis, protein structure and correlation network analysis, principal component, and related multivariate analysis methods. Here, we review recent package developments, including a new underlying segregation into separate packages for distinct analysis, and introduce a new method for structure analysis named ensemble difference distance matrix analysis (eDDM). The eDDM approach calculates and compares atomic distance matrices across large sets of homologous atomic structures to help identify the residue wise determinants underlying specific functional processes. An eDDM workflow is detailed along with an example application to a large protein family. As a new member of the Bio3D family, the Bio3D-eddm package supports both experimental and theoretical simulation-generated structures, is integrated with other methods for dissecting sequence-structure-function relationships, and can be used in a highly automated and reproducible manner. Bio3D is distributed as an integrated set of platform independent open source R packages available from: http://thegrantlab.org/bio3d/.

Non-cryogenic structure of a chloride pump provides crucial clues to temperature-dependent channel transport efficiency

Non-cryogenic protein structures determined at ambient temperature may disclose significant information about protein activity. Chloride-pumping rhodopsin (ClR) exhibits a trend to hyperactivity induced by a change in the photoreaction rate because of a gradual decrease in temperature. Here, to track the structural changes that explain the differences in CIR activity resulting from these temperature changes, we used serial femtosecond crystallography (SFX) with an X-ray free electron laser (XFEL) to determine the non-cryogenic structure of ClR at a resolution of 1.85 Å, and compared this structure with a cryogenic ClR structure obtained with synchrotron X-ray crystallography. The XFEL-derived ClR structure revealed that the all-trans retinal (ATR) region and positions of two coordinated chloride ions slightly differed from those of the synchrotron-derived structure. Moreover, the XFEL structure enabled identification of one additional water molecule forming a hydrogen bond network with a chloride ion. Analysis of the channel cavity and a difference distance matrix plot (DDMP) clearly revealed additional structural differences. B-factor information obtained from the non-cryogenic structure supported a motility change on the residual main and side chains as well as of chloride and water molecules because of temperature effects. Our results indicate that non-cryogenic structures and time-resolved XFEL experiments could contribute to a better understanding of the chloride-pumping mechanism of ClR and other ion pumps.

SCEDS: protein fragments for molecular replacement in Phaser.

A method is described for generating protein fragments suitable for use as molecular-replacement (MR) template models. The template model for a protein suspected to undergo a conformational change is perturbed along combinations of low-frequency normal modes of the elastic network model. The unperturbed structure is then compared with each perturbed structure in turn and the structurally invariant regions are identified by analysing the difference distance matrix. These fragments are scored with SCEDS, which is a combined measure of the sphericity of the fragments, the continuity of the fragments with respect to the polypeptide chain, the equality in number of atoms in the fragments and the density of C(α) atoms in the triaxial ellipsoid of the fragment extents. The fragment divisions with the highest SCEDS are then used as separate template models for MR. Test cases show that where the protein contains fragments that undergo a change in juxtaposition between template model and target, SCEDS can identify fragments that lead to a lower R factor after ten cycles of all-atom refinement with REFMAC5 than the original template structure. The method has been implemented in the software Phaser.

Solution Structures of Ca2+-CIB1 and Mg2+-CIB1 and Their Interactions with the Platelet Integrin αIIb Cytoplasmic Domain

The calcium- and integrin-binding protein 1 (CIB1) is a ubiquitous Ca(2+)-binding protein and a specific binding partner for the platelet integrin αIIb cytoplasmic domain, which confers the key role of CIB1 in hemostasis. CIB1 is also known to be involved in apoptosis, embryogenesis, and the DNA damage response. In this study, the solution structures of both Ca(2+)-CIB1 and Mg(2+)-CIB1 were determined using solution-state NMR spectroscopy. The methyl groups of Ile, Leu, and Val were selectively protonated to compensate for the loss of protons due to deuteration. The solution structure of Ca(2+)-CIB1 possesses smaller opened EF-hands in its C-domain compared with available crystal structures. Ca(2+)-CIB1 and Mg(2+)-CIB1 have similar structures, but the N-lobe of Mg(2+)-CIB1 is slightly more opened than that of Ca(2+)-CIB1. Additional NMR experiments, such as chemical shift perturbation and methyl group solvent accessibility as measured by a nitroxide surface probe, were carried out to further characterize the structures of Ca(2+)-CIB1 and Mg(2+)-CIB1 as well as their interactions with the integrin αIIb cytoplasmic domain. NMR measurements of backbone amide proton slow motion (microsecond to millisecond) dynamics confirmed that the C-terminal helix of Ca(2+)-CIB1 is displaced upon αIIb binding. The EF-hand III of both Ca(2+)-CIB1 and Mg(2+)-CIB1 was identified to be directly involved in the interaction of CIB1 with αIIb. Together, these data illustrate that CIB1 behaves quite differently from related EF-hand regulatory calcium-binding proteins, such as calmodulin or neuronal calcium sensor proteins.

Ligand-Induced Structural Transitions, Mutational Analysis, and ‘Open’ Quaternary Structure of the M. tuberculosis Feast/Famine Regulatory Protein (Rv3291c)

Rv3291c is a member of the feast/famine regulatory protein family that is known to form stable protein–DNA complexes. We report a specific oligomeric transition between hexadecameric and octameric/lower-order oligomers in the presence of Phe that supports an effector-mediated model for the disassembly of a nucleosome-like particle. We had generated two mutants, Gly102Thr and Glu104Ala, which are part of the essential 100–106 effector-binding loop. The Gly102Thr mutant adopts an unusual ‘open’ quaternary structure and offers interesting functional insights co-related to the binding of an effector. This is similar to the previously reported Escherichia coli Lrp co-crystallized in the presence of DNA where the interactions of the substrate with the N-terminal DNA binding domain presumably lead to symmetry deviations to the oligomeric association. The present structure represents a direct evidence to support that changes made to the effector-binding domain at the C-terminus also result in a functionally relevant quaternary structural change. Conversely, the Glu104Ala mutant retains the closed quaternary association observed in the native protein and reveals nonsymmetrical interaction effects in the two subunits of the dimer. We also report that the native protein unexpectedly binds Lys but does not recognize Arg and offer a structural explanation for it. Error-scaled difference distance matrix analysis suggests that the protein has a relatively flexible core that is presumably needed to mediate the structural changes necessary for the protein's regulatory functions.

Product cost estimation model in early design phase based on cost cluster

A cost estimation model based on cost cluster is presented with big samples in early product design phase be-cause precise cost estimation in early adptive or derivative product design phase is very difficult. Euclidean distance be-tween samples and estimating product are calculated to express their similarity. Difference matrix, distance matrix and similar-ity matrix are built base on euclidean distance sets between samples and indeterminate estimation product, then most corre-lated sample sets are selected to get interval of estimated cost based on cost cluster analysis. An example of brake disc shows invalidity of the cost cluster model. The result of experiment proved that cost cluster model was able to separate relative order of qulity of the samples.

A new methodology for the simulation of flexible protein–ligand interactions

A methodology has been developed for the simulation of induced fit between a ligand and its target protein. It utilizes constrained molecular dynamics where atoms determined to be immobile from difference distance matrix studies are fixed. Application of this methodology to HIV-1 reverse transcriptase (RT) as the example target protein has demonstrated its robustness. Short simulation times are sufficient to achieve good refinement of docking poses resulting from exchange of structurally dissimilar inhibitors between crystal structures.

Enthalpy measurement using calorimetry shows a significant difference in potential energy between the active and latent conformations of PAI-1

A central feature of the serpin inhibition mechanism is insertion of the reactive center loop into the central beta-sheet (beta-sheet A). This insertion also occurs when the reactive center loop is cleaved without protease inhibition. Using this effect, we have measured the enthalpy (DeltaH) of loop cleavage and insertion for plasminogen activator inhibitor 1 (PAI-1) as -38 kcal/mol. Because loop insertion can be blocked by incorporating a peptide into the central beta-sheet, it was possible to assign -7 kcal/mol to loop cleavage and -31 kcal/mol to loop insertion. These values are lower than values reported for the serpins alpha 1 -proteinase inhibitor and antithrombin of -53 to -63 kcal/mol, respectively, for loop insertion with negligible enthalpy for loop cleavage. A free energy difference of -9 kcal/mol has been reported between the active and spontaneously loop inserted "latent forms" of PAI-1, which is significantly smaller in magnitude than the -31 kcal/mol of enthalpy we measured for loop insertion. Because the enthalpy should relate closely to those regions of PAI-1 that have moved to lower potential energy, a difference distance matrix is presented that identifies regions of PAI-1 that move during loop insertion.

Extraction of geometrically similar substructures: Least-squares and Chebyshev fitting and the difference distance matrix

In analysis, comparison and classification of conformations of proteins, a common computational task involves extractions of similar substructures. Structural comparisons are usually based on either of two measures of similarity: the root-mean-square (r.m.s.) deviation upon optimal superposition, or the maximal element of the difference distance matrix. The analysis presented here clarifies the relationships between different measures of structural similarity, and can provide a basis for developing algorithms and software to extract all maximal common well-fitting substructures from proteins. Given atomic coordinates of two proteins, many methods have been described for extracting some substantial (if not provably maximal) common substructure with low r.m.s. deviation. This is a relatively easy task compared with the problem addressed here, i.e., that of finding all common substructures with r.m.s. deviation less than a prespecified threshold. The combinatorial problems associated with similar subset extraction are more tractable if expressed in terms of the maximal element of the difference distance matrix than in terms of the r.m.s. deviation. However, it has been difficult to correlate these alternative measures of structural similarity. The purpose of this article is to make this connection. We first introduce a third measure of structural similarity: the maximum distance between corresponding pairs of points after superposition to minimize this value. This corresponds to fitting in the Chebyshev norm. Properties of Chebyshev superposition are derived. We describe relationships between the r.m.s. and minimax (Chebyshev) deviations upon optimal superposition, and between the Chebyshev deviation and the maximal element of the difference distance matrix. Combining these produces a relationship between the r.m.s. deviation upon optimal superposition and the maximal element of the difference distance matrix. Based on these results, we can apply algorithms and software for finding subsets of the difference distance matrix for which all elements are less than a specified bound, either to select only subsets for which the r.m.s.deviation is less than or equal to a specified threshold, or to select subsets that include all subsets for which the r.m.s. deviation is less than or equal to a threshold.

Extraction of geometrically similar substructures: Least‐squares and Chebyshev fitting and the difference distance matrix

In analysis, comparison and classification of conformations of proteins, a common computational task involves extractions of similar substructures. Structural comparisons are usually based on either of two measures of similarity: the root-mean-square (r.m.s.) deviation upon optimal superposition, or the maximal element of the difference distance matrix. The analysis presented here clarifies the relationships between different measures of structural similarity, and can provide a basis for developing algorithms and software to extract all maximal common well-fitting substructures from proteins. Given atomic coordinates of two proteins, many methods have been described for extracting some substantial (if not provably maximal) common substructure with low r.m.s. deviation. This is a relatively easy task compared with the problem addressed here, i.e., that of finding all common substructures with r.m.s. deviation less than a prespecified threshold. The combinatorial problems associated with similar subset extraction are more tractable if expressed in terms of the maximal element of the difference distance matrix than in terms of the r.m.s. deviation. However, it has been difficult to correlate these alternative measures of structural similarity. The purpose of this article is to make this connection. We first introduce a third measure of structural similarity: the maximum distance between corresponding pairs of points after superposition to minimize this value. This corresponds to fitting in the Chebyshev norm. Properties of Chebyshev superposition are derived. We describe relationships between the r.m.s. and minimax (Chebyshev) deviations upon optimal superposition, and between the Chebyshev deviation and the maximal element of the difference distance matrix. Combining these produces a relationship between the r.m.s. deviation upon optimal superposition and the maximal element of the difference distance matrix. Based on these results, we can apply algorithms and software for finding subsets of the difference distance matrix for which all elements are less than a specified bound, either to select only subsets for which the r.m.s.deviation is less than or equal to a specified threshold, or to select subsets that include all subsets for which the r.m.s. deviation is less than or equal to a threshold. Proteins 33:320–328, 1998. © 1998 Wiley-Liss, Inc.

Rigid domains in proteins: an algorithmic approach to their identification.

A rigid domain, defined here as a tertiary structure common to two or more different protein conformations, can be identified numerically from atomic coordinates by finding sets of residues, one in each conformation, such that the distance between any two residues within the set belonging to one conformation is the same as the distance between the two structurally equivalent residues within the set belonging to any other conformation. The distance between two residues is taken to be the distance between their respective alpha carbon atoms. With the methods of this paper we have found in the deoxy and oxy conformations of the human hemoglobin alpha 1 beta 1 dimer a rigid domain closely related to that previously identified by Baldwin and Chothia (J. Mol. Biol. 129: 175-220, 1979). We provide two algorithms, both using the difference-distance matrix, with which to search for rigid domains directly from atomic coordinates. The first finds all rigid domains in a protein but has storage and processing demands that become prohibitively large with increasing protein size. The second, although not necessarily finding every rigid domain, is computationally tractable for proteins of any size. Because of its efficiency we are able to search protein conformations recursively for groups of non-intersecting domains. Different protein conformations, when aligned by superimposing their respective domain structures, can be examined for structural differences in regions complementing a rigid domain.

Molecular structure matching by simulated annealing. III. The incorporation of null correspondences into the matching problem

This paper extends an application of the method of simulated annealing for molecular matching so that the best common subsets of atom positions can be identified. Null correspondences are introduced into the difference distance matrix to enable poorly matched positions to be ignored in minimizing the objective function. The efficiency of the algorithm in finding correct subsets is rigorously tested.

Molecular structure matching by simulated annealing. I. A comparison between different cooling schedules

This paper outlines an application of the theory of simulated annealing to molecular matching problems. Three cooling schedules are examined: linear, exponential and dynamic cooling. The objective function is the sum of the elements of the difference distance matrix between the two molecules generated by continual reordering of one molecule. Extensive tests of the algorithms have been performed on random coordinate data together with two related protein structures. Combinatorial problems, inherent in the assignment of atom correspondences, are effectively overcome by simulated annealing. The algorithms outlined here can readily optimize molecular matching problems with 150 atoms.

Plastic adaptation toward mutations in proteins: Structural comparison of thymidylate synthases

The structure of thymidylate synthase (TS) from Escherichia coli was solved from cubic crystals with a = 133 A grown under reducing conditions at pH 7.0, and refined to R = 22% at 2.1 A resolution. The structure is compared with that from Lactobacillus casei solved to R = 21% at 2.3 A resolution. The structures are compared using a difference distance matrix, which identifies a common core of residues that retains the same relationship to one another in both species. After subtraction of the effects of a 50 amino acid insert present in Lactobacillus casei, differences in position of atoms correlate with temperature factors and with distance from the nearest substituted residue. The dependence of structural difference on thermal factor is parameterized and reflects both errors in coordinates that correlate with thermal factor, and the increased width of the energy well in which atoms of high thermal factor lie. The dependence of structural difference on distance from the nearest substitution also depends on thermal factors and shows an exponential dependence with half maximal effect at 3.0 A from the substitution. This represents the plastic accommodation of the protein which is parameterized in terms of thermal B factor and distance from a mutational change.