Distance root mean-squared deviation

An alternative measure of protein structure similarity is the distance root mean squared deviation (dRMS) that compares corresponding internal distances in the two sets of points ... 

Figure 13 Folding of poly-L-leucine during transfer across the water-hexane interface time evolution of the distance between the center of mass (COM) of the peptide backbone and the interface (solid line), and the distance root mean square deviation (RMSD) with respect to the ideal a-helix (dashed line)...

A much more satisfactory random network model has been discussed by Alben and Boutron 82h They used a model, proposed by Polk 78> for Ge(as), scaled to fit the observed nearest neighbor 00 distance of H20(as), and with H atoms added to the OO bonds according to the Pauling ice rule that guarantees the presence of only H20 molecules 65>. In the Polk model the bond length is everywhere the same and the 000 angles are distributed with root mean square deviation of 7° about 109°. For the case of Ge(as), the observed and model radial distribution functions are in excellent agreement. 

One of the simplest methods is the comparison of the initial structure of the macromolecule to that throughout the trajectory via a distance measure such as the root mean square deviation (RMSD). This method is most informative for a system like a folded protein under native conditions, where the molecule is expected to spend the vast majority of the time in conformations quite similar to the crystal structure. If one computes the RMSD time series against the crystal structure, one expects to see a rapid rise due to thermal fluctuations, followed by a long plateau or fluctuations about a mean at longer timescales. If the RMSD... 

Nj and Oj in equation (2.4) represent the number of atoms in the jth shell and root-mean-square deviation of the interatomic distances over Rj which results both from static and dynamic (thermal) disordering effects respectively. The scattering amplitude, Fj(k) is given by... 

Also in the staggered model approach the u-values for the halogen-halogen distances are composed of contribution both from framework vibration and torsional motion. The torsional motion part may be expressed by athe root-mean-square deviation from the minimum position. For the molecules so far described, the value of 00 is to a good approximation equal for the gauche and tram peaks. (This is of course not the case for molecules like 1,2-dihaloethanes). 

Tables Summary of the MD-simulated and optimized key distances (A) and the root-mean-square deviation (RMSD) of the simulated structures from the initial structure [115]...

Root-mean-square deviation of the coordinates of backbone atoms in the simulated structure from those in the initial structure Average distances from the stable trajectory of MD simulation... 

Table 1. Structural parameters for solvation shell of lithium ion in DMF as determined by XD measurements and least-squares fitting procedure average distances r, , root mean square deviations /y, and coordination numbers ny. Solution of LiQ (left) and of LiNCS (right).

Table 1. Maximum (Amax) and root mean square deviation (a) of bond distances (A) and bond angles and dihedral angles (°) compared to the NUMOL resnlts for different basis sets...

Table 1. Pairwise comparison of the topology and primary sequence of members of the short spacer family. The alpha carbon atoms defining the zinc protease fold (orange segment. Fig. 3) have been used in the topological superposition [56]. The distances refer to the root mean square deviations of this fold between pairs of structures. The corresponding pairwise primary sequence homology is also shown.

Abbreviations used in table MC - Monte Carlo aa - amino acid vdW - van der Waals potential Ig - immunoglobulin or antibody CDR - complementarity-determining regions in antibodies RMS -root-mean-square deviation r-dependent dielectric - distance-dependent dielectric constant e - dielectric constant MD - molecular dynamics simulation self-loops - prediction of loops performed by removing loops from template structure and predicting their conformation with template sequence bbdep - backbone-dependent rotamer library SCMF - self-consistent mean field PDB - Protein Data Bank Jones-Thirup distances - interatomic distances of 3 Ca atoms on either side of loop to be modeled. 

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. 

One more parameter must be specified for each inter-atomic distance. This is i7kj ) the root mean square deviation of the distance from its mean value Rkj" , he. the width of distribution of the distance which arises as a result of thermal vibrations and any possible structural disorder. These parameters are analogs of the thermal displacement of atoms in single-crystal X-ray analysis. Like the latter, o kj" are the most uncertain RDF fitting parameters. When these are varied, one should keep in mind both their typical values obtained in specific RDF studies of the various reference compounds, of known structure, and some physically reasonable limitations. ... 

Several techniques are available for similarity measures on three-dimensional stmctures. The most common technique is structure superposition or superimposition. In this technique, one stmcture is rotated or reoriented until it ean be superimposed onto the other stmcture (Wishart, 2005). The proeedure starts with identifying common reference points. As soon as these points are identified, one of the stmctures is rotated until these common reference points are almost matching with minimum differences, that is, minimal distance between equivalent positions on the protein stmcture. One of the most commonly used distance measures is root mean-square deviation (RMSD) (Xiong, 2006), determined as... 

Table II. Average values of radius of the 0(4) polygon (I), ) 0(4).. 0(4 ) distance between adjacent residues (II), 0(2)...0(3 ) distance between adjacent residues (III), root-mean-square deviation of 0(4) atoms from the least-squares plane (IV), and tilt-angle,b)...

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