Principal components analysis dynamic

The important underlying components of protein motion during a simulation can be extracted by a Principal Component Analysis (PGA). It stands for a diagonalization of the variance-covariance matrix R of the mass-weighted internal displacements during a molecular dynamics simulation. 

Hayward et al. 1994] Hayward, S., Kitao, A., Go, N. Harmonic and anharmonic aspects in the dynamics of BPTI A normal mode analysis and principal component analysis. Prot. Sci. 3 (1994) 936-943 [Head-Gordon and Brooks 1991] Head-Gordon, T., Brooks, C.L. Virtual rigid body dynamics. Biopol. 31 (1991) 77-100... 

Steven Hayward, Akio Kitao, and Nobuhiro Go. Harmonic and anharmonic aspects in the dynamics of BPTI A normal mode analysis and principal component analysis. Physica Scripta, 3 936-943, 1994. 

M. A. Balsera, W. Wriggers, Y. Oono, and K. Schulten. Principal component analysis and long time protein dynamics. J. Phys. Chem., 100 2567-2572, 1996. 

One of the main attractions of normal mode analysis is that the results are easily visualized. One can sort the modes in tenns of their contributions to the total MSF and concentrate on only those with the largest contributions. Each individual mode can be visualized as a collective motion that is certainly easier to interpret than the welter of information generated by a molecular dynamics trajectory. Figure 4 shows the first two normal modes of human lysozyme analyzed for their dynamic domains and hinge axes, showing how clean the results can sometimes be. However, recent analytical tools for molecular dynamics trajectories, such as the principal component analysis or essential dynamics method [25,62-64], promise also to provide equally clean, and perhaps more realistic, visualizations. That said, molecular dynamics is also limited in that many of the functional motions in biological molecules occur in time scales well beyond what is currently possible to simulate. 

A more detailed decomposition of macromolecular dynamics that can be used not only for assessing convergence but also for other purposes is principal components analysis (PCA), sometimes also called essential dynamics (Wlodek et al. 1997). In PCA the positional covariance matrix C is calculated for a given trajectory after removal of rotational and translational motion, i.e., after best overlaying all structures. Given M snapshots of an N atom macromolecule, C is a 3N X 3A matrix with elements... 

Figure 6 (A) Scheme of the MUMO calculations used for calculating the dynamic conformation ensemble of SGCI. (B) Dynamic conformational ensemble of SGCI with the protease binding loop shown in dark grey. (C) Result of the principal component analysis on the inhibitor structures depicting that the dynamic conformational ensemble (blue circles) contains the conformers of corresponding to the enzyme-bound state (red boxes).

The principal component analysis of the dynamics revealed the hingebending motions of the protein. One end of the screw axis of the motions... 

Ku, W., Storer, R. H. and Georgakis, C., 1995, Disturbance Detection and Isolation by Dynamic Principal Component Analysis. Chemometrics and Intelligent Laboratory Systems, 30,... 

In both studies, nonmetric clustering outperformed the metric tests, although both principal components analysis and correspondence analysis yielded some additional insight into large-scaled patterns, which was not provided by the nonmetric clustering results. However, nonmetric clustering provided information without the use of inappropriate assumptions, data transformations, or other dataset manipulations that usually accompany the use of multivariate metric statistics. The success of these studies and techniques led to the examination of community dynamics in a series of two multispecies toxicity tests. 

R Srinivasan, C. Wang, WK Ho, and KW Lim. Dynamic principal component analysis based methodology for clustering process states in agile chemical plants. Ind. Engg. Chem. Research, 43 2123-2139, 2004. 

Modes of protein motion determined by harmonic dynamics or principal component analysis (PCA) serve to describe essential collective motions and they can be introduced directly into the docking procedure. Most conformational variations are captured approximately by a few essential modes. Included as additional variables in protein-ligand docking, they can be optimized and thus the collective protein motions and ligand conformations are simultaneously explored [91-93]. 

The objectives of this study were to quantify the trace metals in PM2 5 of Eastern and Western Canada, to analyze their annual and seasonal trends and identify their source origin, by evaluating a database of trace metal concentrations obtained over a 2-year period (May 2004-December 2006) from the NAPS network. Over 1000 PM2 5 samples collected at seven selected sites were analyzed by Inductively Coupled Plasma Mass Spectrometry (ICP-MS) after microwave assisted acid digestion. This technique offers low detection limits, wide linear dynamic range, multielement capability, ability to measure isotope ratios and high sample throughput. Principal Components Analysis (PCA) was used to identify sources of trace metals at each sampling site. 

Green s Function/Principal Component Analysis and Essential Dynamics... 

The idea of the Green s function/principal component analysis is closely related to the essential dynamics approach recently introduced into biomolecular simulations. Other similar works include those by Garcia, Ichiye and Karplus, Go and coworkers,and developers of the quasi-harmonic method. " The basic idea of the essential dynamics approach is to diagonalize a covariance matrix a whose elements are given by the formula... 

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