Brownian Oscillator Analysis of Molecular Motions in Biomolecules

Dynamic analysis of biomolecules often works by the principle of difference spectroscopy: What is the qualitative difference in structural flexibility of a protein with and without ligand? This method, illustrated elsewhere in this book, is quite useful considering the complexity of biomolecules. Sometimes, however, differences between different samples are easier to obtain than reproducable identical results. This chapter is addressed to students of biophysics, who would like to proceed further. We present a modern statistical analysis of neutron scattering data applied to biomolecules. We start from the simple model of the harmonic oscillator, introduce the visco-elastic oscillator and conclude with a model-independent moment expansion of the density correlation function. To illustrate the method, a number of recent results on protein dynamics are presented. The power of neutron scattering is that it provides, both spectral and spatial, information from which one can reconstruct in principle the microscopic trajectory of labeled particles on a picosecond time scale. Such results can be used to test molecular dynamic simulations of biomolecules, and simulations can be used to interpret the neutron scattering spectra. Since protein–water interactions belong to the most interesting questions that can be approached with neutron scattering, we start with a brief outline on this topic.