Root-mean-square deviation RMSD , measuring

For example, larger side chains could be represented by two united atoms [138]. Alternatively, an all-atom representation of the main chain could be employed with a reduced representation of the side chains [28]. Using this kind of representation and more elaborate statistical potentials, the structure of short peptides such as melittin, pancreatic polypeptide inhibitor, apamin [28], PPT, and PTHrP [138] have been predicted with an accuracy ranging from 1.7-A root-mean-square deviation, (RMSD) (measured for the a-carbon positions) for the small single helix of melittin to... 

The differences between ab initio and molecular mechanics generated dipole moments were discussed. The MM3(2000) force field is better able to reproduce experimental dipole moments for a set of forty-four molecules with a root mean squared deviation (rmsd) of 0.145 Debye compared with Hartree-Fock (rmsd 0.236 Debye), M0ller-Plesset 2 (rmsd 0.263 Debye) or MM3(96) force field (rmsd 0.164 Debye). The orientation of the dipole moment shows that all methods give comparable angle measurements with only small differences for the most part. This consistency within methods is important information and encouraging since the direction of the dipole moment cannot be measured experimentally. 

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... 

Another measure of the native state similarity is the root mean square deviation (RMSD) with respect to a reference (native) state given by... 

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... 

FIGURE 4.1 Example of different conformation accuracy levels, as measured by root mean squared deviation (RMSD). This example shows computationally generated conformations of axitinib (light gray) at various levels of dissimilarity to one particular crystallographic structure (dark gray). 

In addition to defining the correlation between predicted and experimental values, we need a means of measuring the magnitude of the error in the prediction. The most commonly used error measure in the cheminformatics literature is the root-mean-square deviation (RMSD), which is also known as the RMS error [33]. If we consider paired values X and F, RMSD can be calculated using the following equation... 

The root-mean-square deviation (rmsd) can be taken to be a measure of the precision of the correlations. The rmsd value was calculated from the difference between the experimental and calculated mole fractions according to the following equation. 

In order to verify the structural similarities of two conformations X = (xi, X2,..., x r) and X = (x l, Xj,..., X ), the most frequently used standard measure is the root mean square deviation (rmsd) of the respective stmctures,... 

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