RMSD

A molecular fitting algorithm requires a numerical measure of the difference between two structures when they are positioned in space. The objective of the fitting procedure is to find the relative orientations of the molecules in which this function is minimised. The most common measure of the fit between two structures is the root mean square distance between pairs of atoms, or RMSD ... 

When fitting two structures, the aim is to find the relative orientations of the two molecules in which the RMSD is a minimum. Many methods have been devised to perform this seemingly irmocuous calculation. Some algorithms, such as that described by Ferro and Hermans [Ferro and Hermans 1977] use an iterative procedure in which the one molecule is moved relative to the other, gradually reducing the RMSD. Other methods locate the best fit directly, such as Kabsch s algorithm [Kabsch 1978]. 

A cluster analysis requires a measure of the similarity (or dissimilarity) between pairs of objects. When comparing conformations, the RMSD would be an obviou.s measure to use. 

A similarity measure is required for quantitative comparison of one strucmre with another, and as such it must be defined before the analysis can commence. Structural similarity is often measured by a root-mean-square distance (RMSD) between two conformations. In Cartesian coordinates the RMS distance dy between confonnation i and conformation j of a given molecule is defined as the minimum of the functional... 

Figure 1 The course of energy minimization of a DNA duplex with different choices of coordinates. The rate of convergence is monitored by the decrease of the RMSD from the final local minimum structure, which was very similar in all three cases, with the number of gradient calls. The RMSD was normalized by its initial value. CC, IC, and SG stand for Cartesian coordinates, 3N internal coordinates, and standard geometry, respectively.

In our last example we return to the issue of the possible damaging effects of the standard geometry constraints. Two long trajectories have been computed for a partially hydrated dodecamer DNA duplex of the previous example, first by using ICMD and second with Cartesian coordinate molecular dynamics without constraints [54]. Both trajectories started from the same initial conformation with RMSD of 2.6 A from the canonical B-DNA form. Figure 5 shows the time evolution of RMSD from the canonical A and B conformations. Each point in the figure corresponds to a 15 ps interval and shows an average RMSD value. We see that both trajectories approach the canonical B-DNA, while the RMSD... 

Figure 5 Time dependence of RMSD of atomic coordinates from canonical A- and B-DNA forms m two trajectories of a partially hydrated dodecamer duplex. The A and B (A and B coiTespond to A and B forms) trajectories started from the same state and were computed with internal and Cartesian coordinates as independent variables, respectively. (From Ref. 54.)...

A recent survey analyzed the accuracy of tliree different side chain prediction methods [134]. These methods were tested by predicting side chain conformations on nearnative protein backbones with <4 A RMSD to the native structures. The tliree methods included the packing of backbone-dependent rotamers [129], the self-consistent mean-field approach to positioning rotamers based on their van der Waals interactions [145],... 

Although comparative modeling is the most accurate modeling approach, it is limited by its absolute need for a related template structure. For more than half of the proteins and two-thirds of domains, a suitable template structure cannot be detected or is not yet known [9,11]. In those cases where no useful template is available, the ab initio methods are the only alternative. These methods are currently limited to small proteins and at best result only in coarse models with an RMSD error for the atoms that is greater than 4 A. However, one of the most impressive recent improvements in the field of protein structure modeling has occurred in ab initio prediction [155-157]. 

Number of Number of constraints RMSD (BB) Average target function (A) ... 

Fig. 8. Display of the backbone of the NMR structure of reduced E. halophila HiPIP (100) as a tube with variable radius, proportional to the backbone RMSD of each residue. The figure was generated with the program MOLMOL (143).

Theobald, D. L. Rapid calculation of RMSDs using a quaternion-based characteristic polynomial. Acta Crystallogr. 2005, A61, 478 80. 

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