Root-mean-square-deviation prediction

The ternary diagrams shown in Figure 22 and the selectivi-ties and distribution coefficients shown in Figure 23 indicate very good correlation of the ternary data with the UNIQUAC equation. More important, however, Table 5 shows calculated and experimental quarternary tie-line compositions for five of Henty s twenty measurements. The root-mean-squared deviations for all twenty measurements show excellent agreement between calculated and predicted quarternary equilibria. 

It is known that ab initio methods are not accurate in reproducing or predicting molecular dipole moments. For example, a typical basis set minimization with no additional keywords was carried out, and the results show that the computed magnitude of the dipole moment is not particularly accurate when compared with experimental values. For alcohols, MP2 has a root mean squared deviation of 0.146 Debye, while HF had a deviation of 0.0734 Debye when measured against the experimental values. 

It is quite instructive to compare these new measurements (which lie outside the data bases available at the time the various mass models were formulated) with predictions from the models. For such comparisons it is convenient to define A = Predicted Mass - Measured Mass. A > 0 thus denotes cases where the binding energy has been predicted to be too low and conversely, A < 0 corresponds to a prediction of too much nuclear binding. Table 1 summarizes average and root-mean-square deviations for twelve models. 

At the end of the equilibration protocol, a 3D-QSAR equation with a good correlation (r = 0.81) and a low root mean square deviation (rmsd 0.85) on the estimated interaction energies were derived. The predictive power of the model was evaluated with a test set of 11 taxanes and epothilones, obtaining a prediction coefficient of 0.78. 

Root mean square error in prediction (RMSEP) (or root mean square deviation in prediction, RMSDP). Also known as standard error in prediction (SEP) or standard deviation error in prediction SDEP), is a function of the prediction residual sum of squares PRESS, defined as... 

When the square variable is a difference between values predicted by a model or an estimator and the values actually observed, this quantity take the name of root mean square deviation RMSD or root mean square error, RMSE) and is among the regression parameters. 

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. 

Predictions for Ternary Mixtures. Excess volumes were calculated from the equations of state for the nearly equimolar ternary mixtures of N2 - Ar —J— CH4 and Ar -f- CH4 -f- C2H6 for which data are given in Appendix B of Reference 11. The root mean square deviations between the experimental and calculated VE values are given in Table V. Only component and binary parameters from Tables I, II, and III were used in these calculations. 

Table V. Root Mean Square Deviations (cm3 mol 1) between Model Predictions and the Experimental VE Data for Nearly Equimolar Ternary Mixtures from Rerefence 11, pp. 183—184...

In this work component critical volumes were taken from Reid et al. (23). They are given in Table VI, along with root mean square deviations between the correlation predictions and the isothermal compressibilities tabulated in Appendix A of Reference 11 (pressures up to 50 MPa). For Ar, CH4, and C2HG the correlation is quite accurate, giving isothermal compressibilities with average deviations within 5%. Deviations for N2 are on this order for 91 and 100 K, but they become... 

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 elaborated force field and the above described MCRE technique proved to predict the 3-D structure of many globular proteins to a very good accuracy (e.g., of the order of 2 A of the root mean square deviation, rms). Having in hand such a tool, one may consider questions that are related to the prion disease propagation. 

The stability of proteins refers to the maintenance of a defined three-dimensional structure with specific thermodynamic and functional properties. High-resolution structures in the crystalline state and in solution have reached a stage at which the atomic coordinates of proteins can be compared with an accuracy down to root mean square deviation (r.m.s.d.) values less than 1 A. However, even this precision does not allow the fi ee energy of stabilization to be calculated from the coordinates, nor does it allow predictions with respect to the dynamics of functionally relevant local interactions in active or regulatory sites of homologous proteins. The fluctuations between preferred conformations of native proteins involved in such functionally important motions may very well show amplitudes and angles of up to 50 A and 20°, respectively. ... 

---