Nucleic acids normal mode analysis

Lindahl, E., Azuara, C., Koehl, P. and Delarue, M. (2006) NOMAD-Ref visuahzation, deformation and refinement of macromolecular structures based on all-atom normal mode analysis. Nucleic Acid Res. 34, W52-56. 

More traditional applications of internal coordinates, notably normal mode analysis and MC calculations, are considered elsewhere in this book. In the recent literature there are excellent discussions of specific applications of internal coordinates, notably in studies of protein folding [4] and energy minimization of nucleic acids [5]. 

Normal mode analysis is a versatile technique which is capable of providing a compact description of the vibrational dynamics of both small molecules and proteins and nucleic acids. For small molecules in particular, the technique is closely coupled to both the interpretation of vibrational spectroscopic data and the development of molecular mechanical force fields. When normal modes are determined using a force field model, vibrations of specific frequencies can be assigned to particular correlated atomic displacements. Force field parameters can be tested and refined by comparing... 

The application of normal mode analysis to macromolecules such as proteins and nucleic acids has only recently become more common. Normal modes can be calculated either using harmonic analysis, where the second derivative matrix of the potential energy is calculated for a minimized structure, or using quasi-harmonic analysis, where the matrix of correlations of atomic displacements is calculated from a molecular dynamics (MD) trajectory. At temperatures below about 200 K, protein dynamics are primarily harmonic. Above this temperature there is appreciable non-harmonic motion which can be studied using quasi-elastic scattering techniques. There is evidence that such anharmonic motions are also important for protein function and quasi-harmonic analysis allows them to be incorporated implicitly to some extent within a harmonic model. 

The technique of normal mode analysis has been described as a relatively simple procedure for obtaining an exact solution to the approximate equations of motion for a chemical system. Despite its severe approximation (that the dynamics of a system can be represented by the sum of harmonic terms that are only strictly valid for small displacements), the normal mode technique has proven to perform well at predicting many experimentally observed properties. The preceding applications have illustrated the variety of ways in which normal modes can serve to define the dynamic structure and eneiget-ics of small molecules, proteins, and nucleic acids and to aid in the interpretation and refinement of experimental data. This technique is likely to see increased use in the future. 

Suhre, K. and Sanejouand, Y. H. (2004b) ElNemo a normal mode web server for protein movement analysis and the generation of templates for molecular replacement. Nucleic Acids Res. 32, W610-614. 

The most complete picture of conformational flexibility of pyrimidine rings in nucleic acid bases has been provided by molecular dynamics study of isolated molecules using ab initio Carr-Parinello method [45]. According to these studies, the population of planar conformation of heterocycle does not exceed 20% for thymine, cytosine, and guanine and amounts to about 30% for adenine (Table 21.4). These values are considerably smaller as compared to estimations based on vibrational frequencies mentioned above. Such difference is quite natural because in the case of vibrational analysis, only the lowest ring out-of-plane normal mode is considered. However, there are also smaller contributions of the other ring out-of-plane vibrations not included in this analysis. Therefore, such estimation should be considered as an upper limit for assessment of population of planar conformation of ring. 

A critical pre-requisite to using Raman and resonance Raman spectroscopy to examine the excited-state structural dynamics of nucleic acids and their components, is the determination of the normal modes of vibration for the molecule of interest. The most definitive method for determining the normal modes is exhaustive isotopic substitution, subsequent measurement of the IR and Raman spectra, and computational analysis with the FG method of Wilson, Decius, and Cross [77], Such an analysis is rarely performed presently because of the improvements in accuracy of ab initio and semi-empirical calculations. Ab initio computations have been applied to most of the nucleobases, which will be described in more detail below, resulting in relatively consistent descriptions of the normal modes for the nucleobases. 

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