ABSTRACT
CONTENTS 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 12.2 Collective-Mode Description of Protein Dynamics . . . . . . . . . . . . . . . . . . 234 12.3 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 12.4 Langevin Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 12.5 Conservation and Convergence of Collective Variables . . . . . . . . . . . . 239 12.6 Anharmonicity of Energy Landscape and JAMModel . . . . . . . . . . . . . 241 12.7 Application of JAM Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 12.8 Application of the Normal Mode Concept to the Dynamics
Crystallographic Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 12.9 Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 12.10 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
The nature of the protein dynamics is often stated complex and anharmonic. However, the framework of the normal mode analysis (NMA), in which protein dynamics is described as a linear combination of collective variables and harmonic multidimensional energy surface is assumed, is of great use to elucidate complex dynamics of proteins. The reason of this statement will be threefold. First, collective description of protein dynamics, a key concept of the NMA, has been applied successfully to a number of protein systems
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(see, reviews [1-5]). Small number of large-amplitude modes dominantly determines atomic fluctuation of proteins. Since protein dynamics takes place extremely anisotropic, it can be efficiently described by an appropriate set of collective variables. Furthermore, the concepts of “important subspace” [6] and “essential subspace” [7] propose the possibility that “important” or “essential” protein motions take place in a dimensionally small subspace spannedby a subset of collective variables. Second, NMAis useful as an idealized reference to investigate real complex systems. Although anharmonic aspects of protein dynamics draw attention, a large number of degrees of freedom can be approximated to be harmonic [7-14]. Anharmonic degrees of freedoms in protein dynamics were discussed by examining the deviation from purely harmonic systems. Third, very low-frequency normal modes are relevant to protein function. This has been believed for years, and the conceptof “dynamicdomain” recently succeeded infindingevident examples [15-19]. This has been achieved by comparing conformational variations observed in crystal structures to conformational fluctuations calculated by NMA, molecular dynamics (MD), and principal component analysis (PCA). In this chapter, some extensions of NMA and applications of NMA con-
cepts to investigate protein dynamics in the native state are introduced. For this purpose, we describe PCA [7, 9, 10, 20]. Langevin mode analysis (LMA) [21, 22] and Jumping-among-minima model (JAM) [3, 14], and discuss the anharmonic nature of protein energy landscape. Also, some applications of NMA concept to the analysis experimental data, the applications in nuclear magnetic resonance (NMR) [23], x-ray crystallography [24, 25], and neutron scattering [10, 26, 27], are focused.
