Intermediate scattering function for macromolecules in solutions probed by neutron spin echo

The neutron-spin-echo method (NSE) is a powerful technique for studying internal dynamics of macromolecules in solutions because it can simultaneously probe length and time scales comparable to intramolecular density fluctuations of macromolecules. Recently, there has been increased, strong interest in studying protein internal motions using NSE. The coherent intermediate scattering function (ISF) measured by NSE depends on internal, rotational, and translational motions of macromolecules in solutions. It is thus critical, but highly nontrivial, to separate the internal motion from other motions in order to properly understand protein internal dynamics. Even though many experiments are performed at relatively high concentrations, current theories of calculating the ISF of concentrated protein solutions are either inaccurate or flawed by incorrect assumptions for realistic protein systems with anisotropic shapes. Here, a theoretical framework is developed to establish the quantitative relationship of different motions included in the ISF. This theory based on the dynamic decoupling approximation is applicable to a wide range of protein concentrations, including dilute cases. It is also, in general, useful for studying many other types of macromolecule systems studied by NSE.

Figure 1

(a) Calculated normalized form factor of a model system with polydisperse spheres, which has a Gaussian size distribution with 3-nm mean radius. The interparticle structure factor, $S\left(Q\right)$, shown in the figure is calculated based on a system interacting with only a hard sphere interaction. (b) Calculated effective diffusion coefficient using Eqs. (23) and (2). The calculated results are different at relatively high $Q$.