Protein structure superposition

Given two sets of points A = ax, U2, -, and B = bi,b2,- bm) in three-dimensional (3-D) space, the protein superposition problem is to find the optimal subsets A P) and B Q) with IA(P)I = IB(Q)I, and the optimal rigid-body transformation Gopt between the two subsets A P) and B Q) that 

The two subsets A(P) and B(Q) define a correspondence, and p = IA(P)I = IB(Q)I is called the correspondence length. Once the optimal correspondence is defined, it is easy to find the optimal rotation and translation using the rigid-body transformation algorithm described earlier. The concept of optimal correspondence, however, requires more explanation. It is clear that p = l defines a trivial solution to the protein superposition problem Any point of A can be aligned with any point of B, with a cRMS of 0. In practice, we are interested in finding the largest possible value for p under the condition that A(P) and B Q) remain similar.  

Extension of the optimal path - Distance matrix alignment 

Structure-data-base comparison based on motif search Genetic algorithm (K2) or Simulated annealing (K2SA) 

Hierarchical protein strucmre superposition STRUCTAL-based program Markov transition model of evolution 

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Scoring Functions for Protein Structure Superposition Because the concept of optimal correspondence is ambiguous, the protein structure superposition problem is not uniquely defined. Instead, finding the best superposition of two proteins corresponds to a family of optimization problems, which are specified by the weight given to the similarity (preferably a small deviation between the two subsets), and the correspondence length (preferably large). 

Diederichs, K. Structural superposition of proteins with unknown alignment and detection of topological similarity using a six-dimensional search algorithm. Proteins Struc., Func., Genet. 1995, 23, 187-195. 

Finding a mapping between the atoms of the equivalent proteins is a preliminary step before the structural superposition. There are many ways of finding a mapping between a pair of macromolecu-lar targets. I will describe two of them in the following section. 

Fig. 5. Structural superposition of binding sites using Med-Sumo . The Surface Chemical Features (SCF) are used to superimpose the protein binding sites (toppanel).The SCF are represented in color code bar (bottom panel) and the SUMO score measure the quality of the 3D structural superimposition that is calculated using a bit-wise matching algorithm of the color code-bar fingerprint (bottom panel).

Fig. 8.10 Superposition ofTGT-1 (orange ligand, gray protein structure) and TGT-4 (cyan ligand, blue protein structure). Upon binding of 4, Aspl02 rotates towards the...

A model of the structure must be fit to the map. This used to be done with the "Richards box", a device containing a half-silvered mirror to give the illusion of superposition of a physical model and the electron density map (conventionally contoured in serial sections, traced onto transparent film, and stacked (17).) Recently, some protein structures have been determined using interactive computer graphics to fit a stick model of a structure to an electron density map (18, 19). 

Having defined the appropriate pharmacophore features, the expert must next derive the pharmacophore of interest. A prerequisite, in the absence of a protein structure, is a series of active molecules that are presumed to bind in the same way. The pharmacophore may then be derived from examining the disposition of pharmacophore features within the molecules to locate common distances and then generating a superposition of the molecules. The key elements of this process are pharmacophore feature perception, described above, conformational analysis to explore the conformational space of the ligands, and identification of the common features. 

Structure comparison methods are a way to compare three-dimensional structures. They are important for at least two reasons. First, they allow for inferring a similarity or distance measure to be used for the construction of structural classifications of proteins. Second, they can be used to assess the success of prediction procedures by measuring the deviation from a given standard-of-truth, usually given via the experimentally determined native protein structure. Formally, the problem of structure superposition is given as two sets of points in 3D space each connected as a linear chain. The objective is to provide a maximum number of point pairs, one from each of the two sets such that an optimal translation and rotation of one of the point sets (structural superposition) minimizes the rms (root mean square deviation) between the matched points. Obviously, there are two contrary criteria to be optimized the rms to be minimized and the number of matched residues to be maximized. Clearly, a smaller number of residue pairs can be superposed with a smaller rms and, clearly, a larger number of equivalent residues with a certain rms is more indicative of significant overall structural similarity. 

As mentioned above, several of these approaches have been employed to generate exhaustive clusterings of the protein structures into structural classes available via the resulting databases (DDD/FSSP/Dali [102], 3Dee [79], JOY/HOMSTRAD/DDBASE [112-114], structure cores LPFC [115]), These superposition-based classifications are complemented with classi-... 

Overview of the 3D-PSSM approach for protein structure prediction For any protein (superfamily) PSI-BLAST searches and profiles are computed and using the structural superposition of the (structurally related) family members. On the basis of... 

May, A. C. and M. S. Johnson, Improved genetic algorithm-based protein structure comparisons pairwise and multiple superpositions. Protein Eng, 1995. 8(9) p. 873-82. 

Figure 23 Structural superposition of lumazine protein (green, PDB entry code 3DDY ) and riboflavin synthase from Schizosaccharomycespombe (yellow, PDB entry code 1KZC ). The C-terminal segment of riboflavin synthase is marked by red color.

The basic problem with the fragment assembly method is the use of the least-squares superposition, which means that the proteins are being treated as rigid bodies. This may result in only a small number of equivalent positions being used to pinpoint a large part of the model, and information other than the Ca-positions in known structures is often neglected. Thus, another technique was developed to allow a more flexible representation of protein structure, both for comparison and modelling purposes. 

Fold recognition by determining which regions of a query protein of known sequence (but unknown structure) share a folding pattern of protein structure(s) in the library. Two approaches, structure superposition (overlap) and threading are generally employed. The results, if found, are a nomination of a known structure that has the same fold as the query protein. 

Rigid-body approaches are used for measuring the root-mean-sqnare deviation (RMSD) or average distance between two protein structures after superposition of... 

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