Normal mode analysis of molecular

Sidebar 10.3 outlines the useful analogy to normal-mode analysis of molecular vibrations, where the null modes correspond to overall translations or rotations of the coordinate system that lead to spurious alterations of coordinate values, but no real internal changes of interatomic distances. For this reason, the internal metric M( of (10.29) is the starting point for analyzing intrinsic state-related (as opposed to size-related) aspects of a given physical system of interest. 

In view of the Hessian character (10.20) of the thermodynamic metric matrix M(c+2), the eigenvalue problem for M(c+2) [(10.23)] can be usefully analogized with normal-mode analysis of molecular vibrations [E. B. Wilson, Jr, J. C. Decius, and P. C. Cross. Molecular Vibrations (McGraw-Hill, New York, 1955)]. The latter theory starts from a similar Hessian-type matrix, based on second derivatives of the mechanical potential energy Vpot (cf. Sidebar 2.8) rather than the thermodynamic internal energy U. 

Hayward, S., Kitao, A., Berendsen, H.J.C. Model-free methods to analyze domain motions in proteins from simulation A comparison of normal mode analysis and molecular dynamics simulation of lysozyme. Proteins 27 (1997) 425-437. 

Various techniques exist that make possible a normal mode analysis of all but the largest molecules. These techniques include methods that are based on perturbation methods, reduced basis representations, and the application of group theory for symmetrical oligomeric molecular assemblies. Approximate methods that can reduce the computational load by an order of magnitude also hold the promise of producing reasonable approximations to the methods using conventional force fields. 

De Man and van Santen ° performed a normal mode analysis of both cluster and periodic models of zeolite lattices using the GVFF developed by Etchepare et al. In an attempt to find a relation between specific normal modes and the presence of particular substructures, de Man and van Santen compared spectra of zeolite lattices with those of lattice substructures, projected eigenvectors of a substructure in the framework onto the eigenvectors of the molecular model of the structure, and constructed the difference and sum spectra of frameworks with and without particular structural units. The study concluded that there is no general justification for correlating the presence of large structural elements with particular features in the vibrational spectra. 

Schuyler, A.D., Chirikjian, G.S. Normal mode analysis of proteins a comparison of rigid cluster modes with Cq. coarse graining. Journal of Molecular Graphics and Modelling 2004, 22,183. 

To decompose the vibrational energy of a flexible molecule into single-mode contributions, it is useful to perform an instantaneous normal-mode analysis - of the vibrational dynamics. In this approach, we choose a structure at the instantaneous position r(t) and consider the normal mode vibrations around this reference structure. We expand the molecular potential energy up to second order... 

Conformation and the Collective Motions of Protein Normal Mode Analysis and Molecular Dynamics Simulations of Melittin in Water and in Vacuum. 

Ryu, S., Stratt, R.M. (2004). A case study in the molecular interpretation of the optical Kerr efifeet speetra Instantaneous-normal-mode analysis of the OKE speetrum of liquid benzene. J. Phys. Chem. B 108 6782-6795. 

Ryu, S. Stratt, R. M. (2004). A case study in the molecular interpretation of optical Kerr effect spectra Instantaneous-normal-mode analysis of the OKE spectrum of liquid benzene. Journal cf Physical Chemistry B, 108,6782-6795 Seki, S. Hayamizu, K. Tsuzuki, S. Fujii, K Umebayashi, Y. Mitsugi, T. Kobayashi, T. Ohno, Y. Kobayashi, Y. Mita, Y. Miyashiro, H. Ishiguro, S. (2009). Relationships between center atom species (N, P) and ionic conductivity, viscosity, density, selfdiffusion coefficient of quaternary cation room-temperature ionic liquids. Physical Chemistry Chemical Physics, 11,3509-3514... 

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. 

D. M. Ferguson, G. L. Seibel, and P. A. Kollman, AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules, Comp. Phys. Comm. 91 1 (1995). 

Siihre, K. and Sanejouand, Y. H. (2004a) On the potential of normaL-mode analysis for solving difficult molecular-replacement problems. Acta Crystallogr. D 60, 796-799. 

Some important systems, which certainly do not fulfill the assumptions of harmonic transition state theory are gas phase reactions. In the gas phase, there are zero-modes such as translation and rotation, and these lead to totally different configuration integrals than those obtained from a normal mode analysis. For these species one can in a simple manner modify the terms going into the HTST rate by incorporating the molecular partition functions [3,119]. 

Wipff, G., Wurtz, J. M. (1988) Dynamics Views of Macrocyclic Receptors Molecular Dynamics Simulations and Normal Modes Analysis, in Pullman, R. (eds.), Transport through Membranes, Carriers, Channels and Pumps, Reidel, Dorbrecht, pp 1-26. 

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