Normal mode analysis refinement

In the following, the method itself is introduced, as are the various techniques used to perform normal mode analysis on large molecules. The method of normal mode refinement is described, as is the place of normal mode analysis in efforts to characterize the namre of a protein s conformational energy surface. 

Normal Mode Analysis of Biological Molecules A. Normal Mode X-Ray Refinement... 

Figure 2 Internal RMSF of residues (average over heavy atoms) determined for human lysozyme by the X-ray normal mode refinement method applied to real X-ray data (heavy curve), m comparison with results from a normal mode analysis on a single isolated lysozyme molecule (lightweight curve). (From Ref. 33.)...

Evidence exists that some of the softest normal modes can be associated with experimentally determined functional motions, and most studies apply normal mode analysis to this purpose. Owing to the veracity of the concept of the normal mode important subspace, normal mode analysis can be used in structural refinement methods to gain dynamic information that is beyond the capability of conventional refinement techniques. 

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. 

Glucagon is one of the few small proteins on which a normal-mode analysis has been done (Tasumi et al., 1982). It contains 29 amino acid residues, and its structure has been determined to 3 A resolution (Bernstein et al., 1977). The force field used in the calculation was that refined for a side-chain point-mass approximation (Dwivedi and Krimm, 1984b). The computer program was one specifically designed to handle such large molecules (Tasumi et al., 1982). At the time it could not include hydrogen bonds, but more recent versions are able to do so (Ataka and Tasumi, 1986). The present results must, therefore, be taken as mainly illustrative. 

Ma, J., New advances in normal mode analysis of supermolecular complexes and applications to structural refinement. Cum Protein Pept. Sci., 5, 119 (2004). 

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 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. 

This model has the advantage that the atomic polar tensor elements can be determined at the equilibrium geometry from a single molecular orbital calculation. Coupled with a set of trajectories (3R /3G)o obtained from a normal coordinate analysis, the IR and VCD intensities of all the normal modes of a molecule can be obtained in one calculation. In contrast, the other MO models require a separate MO calculation for each normal mode, since the (3p,/3G)o contributions for each unit are determined by finite displacement of the molecule along each normal coordinate. Both the APT and FPC models are useful in readily assessing how changes in geometry or refinements in the vibrational force field affect the frequencies and intensities of all the vibrational modes of a molecule. 

Modern vibrational spectroscopy of polypeptides and proteins, as outlined in the previous pages, has made a significant initial contribution as a tool for the detailed analysis of conformation in such molecules. Yet much more remains to be done, both with respect to further refinements in the inputs to the normal-mode calculations as well as in applications to the many general and specific structures that need to be studied. We consider below only briefly some aspects of such future developments. 

Since the structure of PAIB has not been determined in detail by diffraction methods, the normal-mode studies [110] were based on a 3io structure obtained from conformational analysis [111] (Figure 5-7). The vibrational studies compared experimental data with predictions for two helices, and the results clearly favored the 3io- over the a-helix. The threefold screw symmetry of this structure results in El and Ez species modes reducing to doubly degenerate E species modes. The main chain force field was the same as that for aj-PLA, with additional force constants refined for the (CH3)2 group. Some modes from the full analysis [110] are compared with those of ai-PLA in Table 5-11. 

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