Of proteins normal modes

Brooks B and M Karplus 1983. Harmonic Dynamics of Proteins Normal Modes and Fluctuations in Bovine Pancreatic Trypsin Inhibitor. Proceedings of the National Academy of Sciences USA 80 6571-6575. 

B. Brooks and M. Karplus, Harmoiuc dynamics of proteins normal modes and fluctuations in bovine pancreatic tiypsin inhibitor, Proc. Natl. Acad. Sci. USA, 80(21), 6571-6575(1983). 

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

One of the most common applications of protein normal mode analysis is to the study of hinge-bending in certain multi-domain proteins. Because functional sites are often found in the clefts between domains in such proteins, hinge-bending motions have been postulated to be integral to their function. An understanding of the dynamics of such systems is then critical to understanding their mechanism of action. 

Nonnal mode analysis was first applied to proteins in the early 1980s [1-3]. Much of the literature on normal mode analysis of biological molecules concerns the prediction of functionally relevant motions. In these studies it is always assumed that the soft normal modes, i.e., those with the lowest frequencies and largest fluctuations, are the ones that are functionally relevant. The ultimate justification for this assumption must come from comparisons to experimental data. Several studies have been made in which the predictions of a normal mode analysis have been compared to functional transitions derived from two X-ray conformers [4-7]. These smdies do indeed suggest that the low frequency normal modes are functionally relevant, but in no case has it been found that the lowest frequency normal mode corresponds exactly to a functional mode. Indeed, one would not expect this to be the case. 

We now address the repulsion of localized normal modes of proteins. As illustrated by cytochrome c above, the large majority of normal modes of globular proteins are spatially localized. As such, the vibrations of proteins have much in common with those of ID disordered systems. One important consequence of strong localization of normal modes in ID disordered systems is that frequencies of normal modes whose localization centers overlap in space are generally very different [145-147]. This trend gives the appearance of repulsion of mode frequencies between pairs of nearby localized modes. Such mode repulsion has important consequences on the temperature dependence of the anharmonic decay rates of normal modes of proteins [111,148,149], as seen above. 

Detailed analyses of the vibrational spectra of raacromolecules, however, have provided a deeper understanding of structure and interactions in these systems (Krimm, 1960). An important advance in this direction for proteins came with the determination of the normal modes of vibration of the peptide group in A -methylacetamide (Miyazawa et al., 1958), and the characterization of several specific amide vibrations in polypeptide systems (Miyazawa, 1962, 1967). Extensive use has been made of spectra-structure correlations based on some of these amide modes, including attempts to determine secondary structure composition in proteins (see, for example, Pezolet et al., 1976 Lippert et al., 1976 Williams and Dunker, 1981 Williams, 1983). 

From the results of the normal-mode dynamics it is evident that different residues contribute in varying degrees to the different modes of BPTI. This suggests that mutations can affect the internal motions of proteins in specific ways. Thus site-directed mutagenesis may alter not only the structure but also the dynamics of a protein molecule. 

Since the electron spin relaxation rate in Eq. 114 is dominated by the low-frequency modes, an understanding of the origin of the unusual temperature dependence for proteins is of particular interest as a probe of the motional properties. Use of the normal-mode calculation for BPTI136 yields an exponent 7 = 0.35 for the density of states in the frequency range of interest (0 to 50 cm-1).493 This is in accord with the experimental estimates, although BPTI is not one of the proteins studied experimentally. However, the inelastic neutron data,29 as well as normal-mode calculations,36a suggest that the frequency dependence of g( ) is similar for different proteins in the low-frequency range. 

The infrared spectra of proteins exhibit absorption bands associated with their characteristic amide group, the structural unit common to ail molecules of this type (shown in Figure 6.2a). An isolated planar amide group gives rise to five in-plane modes and one out-of-plane normal mode. The in-plane modes are due to C=0 stretching, C— N... 

Rai BK, Durbin SM et al (2003) Direct determination of the complete set of iron normal modes in a Porphyrin-Imidazole model for carbonmonoxy-heme proteins (Fe(TPP)(CO) (1-MeIm)]. J Am Chem Soc 125 6927-6936... 

Quasi-harmonic analysis is the computation of the normal modes of a molecule from atomic displacements generated by a molecular dynamics simulation. In this case, the atomic coordinate fluctuations are inversely related to the force constants, which are the second derivatives of the potential function. This formulation allows anharmonic motions, arising either from continuous diffusive motion or from transitions between wells, to be included implicitly within a harmonic representation, Brooks and co-workers " have carried out a comparison of different approaches to calculating the harmonic and quasiharmonic normal modes for the protein bovine pancreatic trypsin inhibitor (BPTI) with different force field and simulation models, Yet another approach, called essential dynamics, differs from quasi-harmonic analysis in that the atomic masses are not considered and motion is not reduced to a harmonic form, ... 

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. 

The influence of solvent can be incorporated in an implicit fashion to yield so-called langevin modes. Although NMA has been applied to allosteric proteins previously, the predictive power of normal mode analysis is intrinsically limited to the regime of fast structural fluctuations. Slow conformational transitions are dominantly found in the regime of anharmonic protein motion. 

The essential slow modes of a protein during a simulation accounting for most of its conformational variability can often be described by only a few principal components. Comparison of PGA with NMA for a 200 ps simulation of bovine pancreatic trypsic inhibitor showed that the variation in the first principal components was twice as high as expected from normal mode analy-si.s ([Hayward et al. 1994]). The so-called essential dynamics analysis method ([Amadei et al. 1993]) is a related method and will not be discussed here. 

An interesting approach has recently been chosen in the MBO(N)D program ([Moldyn 1997]). Structural elements of different size varying from individual peptide planes up to protein domains can be defined to be rigid. During an atomistic molecular dynamics simulation, all fast motion orthogonal to the lowest normal modes is removed. This allows use of ca. 20 times longer time steps than in standard simulations. 

Amadei et al. 1993] Amadei, A., Linssen, A.B.M., Berendsen, H.J.C. Essential Dynamics of Proteins. Proteins 17 (1993) 412-425 [Balsera et al. 1997] Balsera, M., Stepaniants, S., Izrailev, S., Oono, Y., Schiilten, K. Reconstructing Potential Energy Functions from Simulated Force-Induced Unbinding Processes. Biophys. J. 73 (1997) 1281-1287 [Case 1996] Case, D.A. Normal mode analysis of protein dynamics. Curr. Op. Struct. Biol. 4 (1994) 285-290... 

D. A. Case. Normal mode analysis of protein dynamics. Curr. Opin. Struc. Biol., 4 385-290, 1994. 

Among the main theoretical methods of investigation of the dynamic properties of macromolecules are molecular dynamics (MD) simulations and harmonic analysis. MD simulation is a technique in which the classical equation of motion for all atoms of a molecule is integrated over a finite period of time. Harmonic analysis is a direct way of analyzing vibrational motions. Harmonicity of the potential function is a basic assumption in the normal mode approximation used in harmonic analysis. This is known to be inadequate in the case of biological macromolecules, such as proteins, because anharmonic effects, which MD has shown to be important in protein motion, are neglected [1, 2, 3]. 

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