Rms deviations

Usually, two conformations are regarded as geometrically different if their minimized RMS deviation is equal to or larger than 0.3 A in Cartesian space RMSx z)> or 30 " in torsion angle space (RMSja). respectively. 

As the number of conformations increases exponentially with the number of rotatable bonds, for most molecules it is not feasible to take all possible conformations into account. However, a balanced sampling of the conformational space should be ensured if only subsets arc being considered. In order to restrict the number of geometries output, while retaining a maximum of conformational diversity, ROTATE offers the possibility of classifying the remaining conformations, i.c., similar conformations can be combined into classes. The classification is based on the RMS deviation between the conformations, either in Cartesian (RMS y 7if [A]) or torsion space in [ ], The RMS threshold, which decides whether two... 

They compared the PME method with equivalent simulations based on a 9 A residue-based cutoflF and found that for PME the averaged RMS deviations of the nonhydrogen atoms from the X-ray structure were considerably smaller than in the non-PME case. Also, the atomic fluctuations calculated from the PME dynamics simulation were in close agreement with those derived from the crystallographic temperature factors. In the case of DNA, which is highly charged, the application of PME electrostatics leads to more stable dynamics trajectories with geometries closer to experimental data [30]. A theoretical and numerical comparison of various particle mesh routines has been published by Desemo and Holm [31]. 

In deciding the convergence of these averages, the RMS deviation of a value from its average (i.e, Dxi may be a very useful indicator. 

In addition to bein g able to plot sim pie in stan tan eous values of a quantity x along a trajectory and reporting the average, , HyperChem can also report information about the deviation of x from its average value. Ihese RMS deviations may have particular sign ifican ce in statistical tn ech an ics or just represen t lh e process of convergence of the trajectory values. 

For purposes of exploring fluctuations and determining the convergence of these statistical averages the root mean square (RMS) deviation in x is also computed ... 

As many as four plots are possible with colors red, green, blue and black. Each plot is scaled independent of the others and the colored labels identify the minimum and maximum of the plot and the name of the quantity being plotted. In addition to the values of X, the RMS deviation in x (Dx) can be plotted. The plot of Dx converges to the RMS deviation of x at the end of the run and represents the current value of the RMS deviation at any point in the plot. 

Note that has the significance of being the mean value of the square of the deviations of individual Mi values from the mean M. Accordingly, a is sometimes called the root mean square (rms) deviation. 

FIG. 8-38 Histogram plotting frequency of occurrence, c = mean, <3 = rms deviation. Also shown is fit by normal probability distribution. 

The scope of the early papers was to use the SK approach to accurately interpolate the results of first principles calculations of the energy bands and densities of states. An important characteristic of these calculations is that the first, second, and third nearest neighbor interactions are treated as independent parameters, which is advantageous for minimizing the rms deviation from the first principles bands. 

ISF). However, in the P6s crystal form ( intermediate state ), the cluster binding subdomain appears to be detached from the base fold fi sheets 1 and 2) in an open conformation 42). If the functional domains of the two crystal forms are superposed using the base fold residues, the rms deviation of the Ca positions of the cluster binding... 

The RMS displacement as a function of time for the shifted potential simulations are shown in Figure 3. As expected for this functional form, the longer cutoff distances result in a smaller RMS deviation from X-ray. The results for the 100 picosecond analysis section of all of the simulations are summarized in Table IV. For Table IV, the term "rdie" indicates that a distant dependant dielectric was used, cdie indicates that a constant dielectric was used, and eps2 indicates that the electrostatic forces have been scaled by 0.5. 

Table 8-7. Frequency scaling factors, rms deviation, proportion outside a 10 % error range and listings of problematic cases [cm-1] for several methods employing the 6-31G(d) basis set. Taken from Scott and Radom, 1996.

Non-uniform prior prejudice. The dynamic range of the exp( ) map is reduced from 966 to a value of 3.3 when a NUP of spherical valence monopoles is used as a consequence, the size of the Lagrange multipliers is reduced by between one and two orders of magnitudes, and the error due to series truncation in the -map is less than 0.213 e A 3 in absolute value everywhere in the cell, the rms deviation from the model being as low as 0.212 e A 3 (Figure 2(b)).3... 

Both the determination of the effective number of scatterers and the associated rescaling of variances are still in progress within BUSTER. The value of n at the moment is fixed by the user at input preparation time for charge density studies, variances are also kept fixed and set equal to the observational c2. An approximate optimal n can be determined empirically by means of several test runs on synthetic data, monitoring the rms deviation of the final density from the reference model density (see below). This is of course only feasible when using synthetic data, for which the perfect answer is known. We plan to overcome this limitation in the future by means of cross-validation methods. 

As mentioned in Section 4.1.1, the number of random scatterers n has to be chosen in input. Five BUSTER runs used values of n in the series n = nvafcnce x N N = 60, 70, 80, 90, 100. The rms deviation from the reference map varied between 0.0317 and 0.0293 e A 3, the latter value pertaining to the run with N = 90 this value of n was then used in the calculation described below. 

The average map and the rms deviation from the average were computed ... 

Sections of the density from one of these fits, which we will refer to as calculation B, are shown in Figure 7 the MaxEnt deformation density in the COO- plane is shown in Figure 7(a) Figure 7(b) is the difference between the MaxEnt valence density and the reference density in the same plane. The lower noise content of the data is clearly visible, when the map is compared with the one for calculation A in particular, the lone pairs on the oxygen atoms are better defined. The rms deviation from the reference is as low as 0.023 e A 3. 

Comparisons between optimized and X-ray structures were once again made by calculating root-mean-square (RMS) deviations. When comparing all heavy atoms in the protein, the total RMS deviation is approximately 1.7 A, irrespective of method for the model system or the ONIOM implementation (mechanical, ONIOM-ME, or electronic embedding, ONIOM-EE). The largest deviations occur for residues in the vicinity of the second monomer. Therefore, adding the second monomer to the model should improve the calculated geometries. 

One reason for the relatively large RMS deviations, compared to the active sites of MMO and RNR, is that the active-site residues are not coordinated to the selenium (see Figure 2-8). The lack of a structural anchor leads to a relatively unstable active-site geometry. An alternative formulation is that the presence of a metal center with strong ligand interactions is one reason the active-site model works comparatively well for many metal enzymes. 

Another important reason for the significant deviation between calculated and X-ray structures can be the low resolution (2.9 A) of the X-ray structure. It is well known that X-ray structures may miss disordered water molecules inside the enzyme. The X-ray structure of the bovine erythrocyte GPx has a significantly higher resolution (2.0 A) and that structure contains two water molecules in the active site [63], Unfortunately that X-ray structure is not complete. In order to test for the presence of water molecules at the active site of the mammalian GPx, calculations were performed with two additional water molecules at the active site. This reduced the RMS deviation to from 0.97 to 0.19k for ONIOM(B3LYP/6-31G(d) Amber)-ME and suggests the presence of water molecules also in the active site of mammalian GPx. In our investigation of the reaction mechanism, these water molecules turns out to be critical. 

Figure 2-13. RMS deviations between X-ray structure and optimized geometries for active-site and ONIOM (B3LYP Amber) models...

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