Normal Mode Theory and Harmonic Potential Approximations

Abstract

CONTENTS 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Potential Wells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Normal Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.1 Vibrational Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.2 Langevin and Brownian Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4 Interpretation and Analysis of Normal Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Normal mode analysis (NMA) has become one of the standard techniques in the study of the dynamics of biological macromolecules. It is primarily used for identifying and characterizing the slowest motions in a macromolecular system, which is inaccessible by other methods. This chapter explains what normal mode analysis is and what one can do with it without going beyond its limit of validity. The focus of this chapter is on proteins, although normal mode analysis can equally well be applied to other macromolecules (e.g., DNA) and tomacromolecular assemblies ranging in size fromprotein-ligand complexes to a whole ribosome. By definition, normal mode analysis is the study of harmonic potentialwells by analytic means. Section 1.2 of this chapter will therefore deal with potential wells and harmonic approximations. Section 1.3 is about normal mode approaches to different physical situations, and Section 1.4 discusses how useful information can be extracted from normal modes.