Energy resolution and dynamical heterogeneity effects on elastic incoherent neutron scattering from molecular systems

Abstract

Incoherent neutron scattering is widely used to probe picosecond-nanosecond time scale dynamics of molecular systems. In systems of spatially confined atoms the relatively high intensity of elastic incoherent neutron scattering is often used to obtain a first estimate of the dynamics present. For many complex systems, however, experimental elastic scattering is difficult to interpret unambiguously using analytical dynamical models that go beyond the determination of an average mean-square displacement. To circumvent this problem a description of the scattering is derived here that encompasses a variety of analytical models in a common framework. The framework describes the time-converged part of the dynamic structure factor [the elastic incoherent scattering function (EISF)] and lends itself to practical use by explicitly incorporating effects due to the finite energy resolution of the instrument used. The dependence of the elastic scattering on wave vector is examined, and it is shown how heterogeneity in the distribution of mean-square displacements can be related to deviations of the scattering from Gaussian behavior. In this case, a correction to fourth order in the scattering vector can be used to extract the variance of the distribution of mean-square displacements. The formalism is used in a discussion of measurements on dynamics accompanying the glass transition in molecular systems. By fitting to experimental data obtained on a protein solution the present methodology is used to show how the existence of a temperature-dependent relaxation frequency can lead to a transition in the measured mean-square displacement in the absence of an EISF change.

A generalized mean-squared displacement from inelastic fixed window scans of incoherent neutron scattering as a model-free indicator of anomalous diffusion confinement

“…We remark that the neglection of higher order terms in the limit of zero q is the analogue to the wellknown Gaussian approximation that has been applied frequently to extract the apparent MSD. Using the series approximation, we introduce a very general account that can also easily be compared to earlier results on nonGaussian behavior, generally causing deviations in the q 4 term [11]. In experiments, the limit of zero q cannot be reached, and a polynomial fit in q 2 up to order q 4 should be used to obtain u 2 ω [18].…”

“…In the last decade, the physical meaning of the apparent MSD has been explored in several studies on the dependence on the instrumental resolution, from both theoretical [11][12][13][14][15][16] and experimental view points [17]. In a different approach to advance the analysis, the apparent MSD has been explicitly calculated using a dynamical model for the full quasi-elastic spectra, thereby allowing to separate internal from global dynamics during protein denaturation [18,19].…”

Long-time mean-square displacements in proteins

“…[33,38] The concept has also been incorporated into the formalism that describes the dynamics accompanying the glass transition in molecular systems. When the protein relaxation time decreases with temperature, as it usually does, it has been shown that measurement of r 2 R over a finite time window can introduce an apparent DT when there is no actual change in the elastic incoherent DSF, S(Q, ω = 0).…”

“…The heterogeneity introduces a correction to fourth order in Q that can be used to extract the variance of the distribution of mean-square displacements. [33,34] Similarly, the global MSD obtained from neutron scattering measurements depends on the energy resolution employed. The MSD is obtained from the elastic (ω = 0) component of the resolution broadened dynamic structure factor (DSF), S R (Q, ω = 0), as…”

“…When the protein relaxation time decreases with temperature, as it usually does, it has been shown that measurement of r 2 R over a finite time window can introduce an apparent DT when there is no actual change in the elastic incoherent DSF, S(Q, ω = 0). [33,38] To avoid this issue, identification and use of an intrinsic, long time MSD r 2 would be helpful. Several MD studies have been performed aimed at understanding the origin of elastic neutron scattering from proteins.…”