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  2. A topological approach for protein classification : Computational and Mathematical Biophysics
  3. Mariel Vazquez

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The directions of the arrows that symbolize each segment show the direction from N- to C-termini.

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Unless explicitly indicated with black arrows, the segments in the top structure are aligned to segments directly below. All these programs were run using default parameters, and no effort was made to adjust the parameters for specific cases. To estimate the statistical significance of the comparisons described above, the non-parametric Wilcoxon signed rank test was used CLICK and the other methods were tested for alignment accuracy on a data set of structures of pairs of homologous proteins.

In all, this data set comprised of structures. This second data set is used to quantitatively assess the performance of CLICK when structure similarity is low, as in the case of distant homologues. Structural similarities between proteins in this data set could be indicative of evolutionary relationships between the proteins despite pronounced structural differences in fold topology The structural alignments of alternative conformations produce a useful comparison of structures that exhibit domain motion or rigid body shifts.

A characterization of such motions may lead to an improved understanding of the relationship between structure and function. The structure comparisons of alterative conformations were carried out for 22 proteins. This included 20 proteins from the Hinge Atlas 51 , DNA Polymerase Beta proteins 2bpf, 2fmq and maltodextrin binding proteins 1omp, 1anf. A subset of pair-wise alignments was benchmarked by the SARA server The program run time increases with increase in i sizes of input structures and ii number of best matched cliques. The exact dependence on these two factors is difficult to compute as they may be independent of one another.

All atomic, cartoon, ribbon and surface representation of proteins and RNA shown in this study were rendered using Chimera In this section, we begin by describing our efforts at optimizing parameters and extensive benchmarking. We establish that our method performs better than, or at the least, at par with popular existing methods. At each step, the structure overlap SO value was computed. While matching cliques, residue equivalences are decided upon after a least squares fit [ Equation 5 ].

These data show that the larger the clique size, the better is the SO value. Running time also increases with clique size. Another grid search was performed with n in the range [3, 9] and RMSD cut-off threshold in the interval 0. Again, SO was computed at each step. The optimal value of RMSD cut-off for a particular clique size was chosen as that value above which there was no change in the SO value Table 3. In general, the RMSD cut-off value increases monotonically with clique size.

To evaluate the contribution of secondary structure and solvent accessibility to the accuracy of the structure alignments, CLICK runs with and without these features were compared Supplementary Figure S1 in Supplementary Data. Clearly, the inclusion of secondary structure and solvent accessibility features improved alignment accuracy. The best matching fragments according to SO of the aligned pair are first matched. The subsequent matches are between fragments that were not previously aligned. CLICK is used to detect such conformational changes at the level of domains or even sub-domains.

Twenty-two pairs of the same protein in different conformations were chosen from the Hinge Atlas database 51 , DNA Polymerase Beta proteins, and maltodextrin binding proteins. In each case, CLICK produced multiple alignments for each pair of conformers, corresponding to the number of domains that exhibited conformational change with respect to one another Supplementary Table S2 in Supplementary Data.

A topological approach for protein classification : Computational and Mathematical Biophysics

One example of such flexible alignments is between the conformers of rat DNA polymerase beta 55 and human DNA polymerase beta 56 pdb codes 2bpf and 2fmq Figure 7 a and b. While such large domain motions are easy to detect, smaller conformational changes are harder to spot. Consider the alignment between two metallothioneins-2 of human 57 and rat liver 58 PDB codes 2mhu and 2mrt, respectively.

The hinge regions of the conformational changes captured by these alignments is at the C- and N-termini of the complementary alignments. Because of a conformational change domain motion about a hinge , the pink and bright green domains do not align structurally. The corresponding sequence alignments are shown below the ribbon diagrams. CLICK fragments the alignment between the two metallothioneins, PDB codes 2mhu red , and 2mrt green into two, to account for a small conformational change.

The sequence alignment implied by the structural alignment is displayed under the ribbon diagram. In our effort to unearth cases of convergent structural evolution, we have detected several instances of ATP binding sites that look geometrically similar between proteins belonging to different fold families data not shown. The base and sugar of the bound ATPs superimpose to within 0. No knowledge of the bound ATPs or their binding sites was used in the computation of equivalent residues.

The sequence alignment resulting from the 3D superimposition of the two structures shows that three of the 15 residues constituting the binding site are identical, while seven others are similar in the two structures Figure 10 b. The binding of ATP to the active site results in 12 hydrogen bonds, of which in eight cases the same or similar atoms are involved as hydrogen bond donors and acceptors. The regions that superimpose are shown in ribbon representation while the unmatched regions are shown in trace representation. The location of the ATP molecules bound to both structures is shown in stick representation.

The sequence alignment between the two proteins as inferred from the structural alignment is show below. Residue side chains and the bound ATP molecules are represented as stick and color coded by atom type. Hydrogen bonds are shown as blue dotted lines.

Another application of CLICK was to again detect similar ligand binding sites in topologically distinct proteins, only in this case the binding site comprised of a well-studied sequence motif, the Walker motif 61 , Using the structure of the multidrug ABC transporter Sav from Staphylococcus aureus 63 pdb 2onj:A as query, which had the conserved Walker A and Walker B motifs, we searched the PDB for topologically different regions of proteins that matched these motifs structurally.

In all of the 19 hits the Aspartic acid was always conserved and within 8. In all of these 18 cases, the Aspartic acid from the reverse walker motif interacts indirectly with the nucleotide though a metal ion or via water-mediated hydrogen bonds. It appears that the Aspartic acid plays the same role both the Walker B motif and its reverse.


The Aspartic acid is absolutely conserved among all homologues in both the regular and reverse Walker B motifs. The residues that precede the Aspartic acid in the Walker B motif are hydrophobic, on average, times out of ; while the residues that follow the conserved Aspartic acid in the reverse motif were hydrophobic, on average, only six times out of In the Walker B motif, the hydrophobic residues that precede the Aspartic acid have no direct role in interacting with the nucleotide ligand. Their high degree of conservation is probably not directly related to nucleotide binding.

The presence of non-hydrophobic equivalents in the reverse Walker B motif also probably has no direct effect on nucleotide binding.

Nucleic Acids - Biological Molecules Simplified #3

These findings suggest that it is possible for non-sequential versions of motifs to perform the same role as their sequential counterparts. The reverse Walker B motif qualifies as yet another example of convergent evolution in a ligand-binding site. Topologically different Walker B motifs. The walker motif of multi-drug ABC transporter from S.

The bound nucleotides and the side chains of the residues in the Walker A and B motifs are represented as sticks.

Mariel Vazquez

In this study we formalize the protein superimposition problem as one of comparing two sets of points in 3D space. Each of the points is given attributes, such as its Cartesian coordinates, secondary structure, the accessible area of the amino acid it represents, etc. In principle, every point can be bestowed with many different attributes, as long as we lay down the rules for matching such points. For instance, Cartesian coordinates are matched by a many-body least squares fit and are only considered if the over all RMSD is within a certain threshold and transitions are only possible between certain secondary structure and solvent accessible classes.

The resulting protein structure alignments detect structural similarity by matching local residue packing and are independent of protein topology. We have shown that our method, CLICK, performs at par or slightly better than other methods over three sets of benchmarks. The benchmarks include pair-wise alignments implied by multiple structural alignments of HOMSTRAD families, 64 of which form another set of so called difficult cases where the structural relationships are distant.

Also included in the benchmarks is a set of pair-wise alignments between proteins that are structurally similar but topologically distinct. The superior performance of CLICK over the other data sets was not an exercise to show the superiority of one method over another. We merely wanted to test CLICK over conventional data sets of alignments, to ensure fidelity of alignments. We have showcased the utility of CLICK at obtaining biological insights with three different examples. First, we showed that CLICK aligns pairs of protein structures, even when conformational changes alter the positioning of domains or sub-domain with respect to one another.

CLICK alignments are sensitive enough to recognize conformational changes even in sub-domains which as small as 30 residues in length. We propose that CLICK could be an integral part of molecular dynamics trajectory analysis tools to detect conformational changes corresponding to low-frequency modes during the course of protein dynamics. Second, we have shown that our method is ideally suited to look for similarities in binding site sub-structures. We demonstrated this by aligning two ATP bound proteins with one another.

The alignment perfectly matched the binding site residues, and the bound ATP. We have since used this approach to construct a library of ATP binding site geometries, as defined by the atoms of the binding site residues. Such ligand-binding site geometry libraries could prove very useful in constructing models of proteins that are known to, or suspected to bind ligands.

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The conformation of residues identified as part of the binding site can be refined according to this library when transitioning from apo to holo structural forms. We believe that such examples when sytematized would significantly change our perception of evolutionary relationships between proteins. Lastly, we have identified variants of sequence motifs that mediate ligand binding.

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