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Spotting the difference in molecular dynamics simulations of biomolecules
M. Stone and R. J. Brooks, J. R. Stat. Soc., Ser. B: Methodol. 52, 237 (1990).
It should be noted that the term is not included in the original definition of LDA-ITER. We added this term as this is more reasonable when the input size differs.
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Technically, if the probability distribution can be written as a product of the Gaussian distribution and an other distribution, we can employ a similar approximation by integrating the other distribution. However, determining whether the condition holds is beyond the scope of current research.
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We note that even if the terminal residues are removed from the dataset, the overall distribution of the intensity for PLS-DA is unchanged except for the termini being cut off and the scaling. Thus the residue 96 remains almost undetected in the first PLS-DA mode.
In Fig. 4(d) of Ref. 39, the authors presented the structure and NMR chemical shifts of PDZ2 of human PTP1E (hPTP1E), which is possibly reconstructed from Fig. 3(a) of Ref. 42. However, the original data in the cited reference are taken from the NMR spectroscopy of the mouse PTP-BL protein titrated with the human Fas ligand. Furthermore, in transplanting data from PTP-BL (mouse) to hPTP1E (human), they seem to have misassigned residue 13, which corresponds to residue 6 in human PDZ2 with proper alignment to residue 5. Thus, the structure of PDZ2-PTP-BL in Fig. 8 should look slightly different from the corresponding hPTP1E structure in Ref. 39.
Theoretically, the similarity between two sets of d random orthogonal vectors is , giving 0.04 and 0.07 for T4L and PDZ2, respectively, when d = 20.
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Comparing two trajectories from molecular simulations conducted under different conditions is not a trivial task. In this study, we apply a method called Linear Discriminant Analysis with ITERative procedure (LDA-ITER) to compare two molecular simulation results by finding the appropriate projection vectors. Because LDA-ITER attempts to determine a projection such that the projections of the two trajectories do not overlap, the comparison does not suffer from a strong anisotropy, which is an issue in protein dynamics. LDA-ITER is applied to two test cases: the T4 lysozyme protein simulation with or without a point mutation and the allosteric protein PDZ2 domain of hPTP1E with or without a ligand. The projection determined by the method agrees with the experimental data and previous simulations. The proposed procedure, which complements existing methods, is a versatile analytical method that is specialized to find the “difference” between two trajectories.
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