Deviation root-mean-square difference

Statistical methods are the most popular techniques for EN analysis. The potential difference and coupling current signals are monitored with time. The signals are then treated as statistical fluctuations about a mean level. Amplitudes are calculated as the standard deviations root-mean-square (rms) of the variance according to (for the potential noise)... 

Several ways may be used to characterize the spread or dispersion in the originai data. The range is the difference between the iargest vaiue and the smaiiest vaiue in a set of observations. However, aimost aiways the most efficient quantity for characterizing variabiiity is the standard deviation (aiso caiied the root mean square). 

In order to examine whether this sequence gave a fold similar to the template, the corresponding peptide was synthesized and its structure experimentally determined by NMR methods. The result is shown in Figure 17.15 and compared to the design target whose main chain conformation is identical to that of the Zif 268 template. The folds are remarkably similar even though there are some differences in the loop region between the two p strands. The core of the molecule, which comprises seven hydrophobic side chains, is well-ordered whereas the termini are disordered. The root mean square deviation of the main chain atoms are 2.0 A for residues 3 to 26 and 1.0 A for residues 8 to 26. 

In analytical chemistry one of the most common statistical terms employed is the standard deviation of a population of observations. This is also called the root mean square deviation as it is the square root of the mean of the sum of the squares of the differences between the values and the mean of those values (this is expressed mathematically below) and is of particular value in connection with the normal distribution. 

Figure 3. A comparison of the aC backbone of PelC with PelE. The aCs which superimpose within a root-mean-square deviation of 1.5 A are shown in black and those, within 3.0 A are shown in dark gray. The remaining backbone regions are shown in light The largest structural differences occur in the loops capping one end of the parallel p as well as in those comprising the putative substrate binding groove.

Statishcal criteria of Eq. (24) are too good the standard deviation, which was created on the basis of different measurements by various authors, is much less than even the experimental error of determinahon. This could be due to mutual intercorrelation of descriptors leading to over-ophmistic statistics [18]. Another reason may be the lack of diversity in the training set. The applicahon of the solvation equation to data extracted from the MEDchem97 database gave much more modest results n = 8844, = 0.83, root mean square error = 0.674, F = 8416... 

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. 

Moreover, the objective function obtained by minimizing the square of the difference between the mole fractions calculated by UNIQUAC model and the experimental data. Furthermore, he UNIQUAC structural parameters r and q were carried out from group contribution data that has been previously reported [14-15], The values of r and q used in the UNIQUAC equation are presented in table 4. The goodness of fit, between the observed and calculated mole fractions, was calculated in terms RMSD [1], The RMSD values were calculated according to the equation of percentage root mean square deviations (RMSD%) ... 

Structural biology provides a final way to define an E2 enzyme. As expected from the strong sequence conservation, the E2 core domain adopts a conserved fold. At the time this article was being prepared, twelve different E2 structures had been deposited in the Protein Data Bank. The average root-mean-square deviation of... 

The sequence conservation is reflected in a highly conserved secondary and tertiary structure that is most clearly illustrated in the three-dimensional superposition of C atoms. Ignoring the C-terminal domains of PVC and HPII, the deviation of C atoms in a superposition of HPII with PVC, BLC, PMC, and MLC results in root mean square deviations of 1.1,1.5,1.6, and 1.5 A for 525, 477, 471, and 465 eqiuvalent centers, respectively (83). In other words, there is very little difference in the tertiary structure of the subunits over almost the complete length of the protein. The large and small subunits are shown in Fig. 8 for comparison. 

As an illustration of the load balancing achieved in a typical 32 processor calculation, we present the CPU usage for each of the 31 slave processes in Fig. 4. The difference between maximum and minimum CPU times is here 0.41 sec., and the overall root mean square deviation is 0.45%. This is very satisfactory, and it would seem unlikely that load balancing will present serious problems in future applications unless a significantly larger number of processors is employed. 

It is a straightforward matter to fit various model profiles to realistic, exact computed profiles, selecting a greater or lesser portion near the line center of the exact profile for a least mean squares fit. In this way, the parameters and the root mean square errors of the fit may be obtained as functions of the peak-to-wing intensity ratio, x = G(0)/G(comax)- As an example, Fig. 5.8 presents the root mean square deviations thus obtained, in units of relative difference in percent, for two standard models, the desymmetrized Lorentzian and the BC shape, Eqs. 3.15 and 5.105, respectively. 

Table 8.2 Root mean square deviation (RMSD) of the backbone of the aligned models of the h AR. The main difference among the models is due to the loops, which represent the most variable region of the templates and consequently of the models. Particular attention has to be given to EL2 because it is part of the binding pocket and it can directly interact with ligands...

We used p instead of = in Equation 5.37 because the exact numerical value depends on the definition of the uncertainties—you will see different values in different books. If we define At in Figure 5.13 as the full width at half maximum or the root-mean-squared deviation from the mean, the numerical value in Equation 5.37 changes. It also changes a little if the distribution of frequencies is not Gaussian. Equation 5.37 represents the best possible case more generally we write... 

The crystal structures of the E. coli DHFR-methotrexate binary complex (Bolin et al., 1982), of the Lactobacillus casei (DHFR-NADPH-methotrexate ternary complex (Filman et al., 1982), of the human DHFR-folate binary complex (Oefner et al., 1988), and of the mouse (DHFR-NADPH-trimethoprim tertiary complex (Stammers et al., 1987) have been resolved at a resolution of 2 A or better. The crystal structures of the mouse DHFR-NADPH-methotrexate (Stammers et al., 1987) and the avian DHFR—phenyltriazine (Volz et al., 1982) complexes were determined at resolutions of 2.5 and 2.9 A, respectively. Recently, the crystal structure of the E. coli DHFR—NADP + binary and DHFR-NADP+-folate tertiary complexes were resolved at resolutions of 2.4 and 2.5 A, respectively (Bystroff et al., 1990). DHFR is therefore the first dehydrogenase system for which so many structures of different complexes have been resolved. Despite less than 30% homology between the amino acid sequences of the E. coli and the L. casei enzymes, the two backbone structures are similar. When the coordinates of 142 a-carbon atoms (out of 159) of E. coli DHFR are matched to equivalent carbons of the L. casei enzyme, the root-mean-square deviation is only 1.07 A (Bolin et al., 1982). Not only are the three-dimensional structures of DHFRs from different sources similar, but, as we shall see later, the overall kinetic schemes for E. coli (Fierke et al., 1987), L. casei (Andrews et al., 1989), and mouse (Thillet et al., 1990) DHFRs have been determined and are also similar. That the structural properties of DHFRs from different sources are very similar, in spite of the considerable differences in their sequences, suggests that in the absence, so far, of structural information for ADHFR it is possible to assume, at least as a first approximation, that the a-carbon chain of the halophilic enzyme will not deviate considerably from those of the nonhalophilic ones. 

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