Intrinsic mean-square displacements in proteins

Abstract

The thermal mean square displacement (MSD) of hydrogen in proteins and its associated hydration water is measured by neutron scattering experiments and used an indicator of protein function. The observed MSD as currently determined depends on the energy resolution width of the neutron scattering instrument employed. We propose a method for obtaining the intrinsic MSD of H in the proteins, one that is independent of the instrument resolution width. The intrinsic MSD is defined as the infinite time value of r 2 that appears in the Debye-Waller factor. The method consists of fitting a model to the resolution broadened elastic incoherent structure factor or to the resolution dependent MSD. The model contains the intrinsic MSD, the instrument resolution width and a rate constant characterizing the motions of H in the protein. The method is illustrated by obtaining the intrinsic MSD r 2 of heparan sulphate (HS-0.4), Ribonuclease A and Staphysloccal Nuclase (SNase) from data in the literature.

Long-time mean-square displacements in proteins

“…The model I(Q, t) is the same as we used previously [36] to fit neutron data except that C(t) is a stretched exponential rather than a simple exponential used previously. In fits to neutron data we found [36] that the data was not sufficiently precise to distinguish between a stretched and simple exponential. In contrast, a simulation-derived I inc (Q, t) is more discriminating.…”

“…Thus correlations that persist to long times t = 10 λ −1 appears to be a feature of lysozyme. In an earlier study [36], we proposed a method to obtain the intrinsic MSD in proteins from fits to experiment, to observed resolution broadened S R (Q, ω = 0). The model I(Q, t) employed was the same as that used here in Eq.…”

“…Hence, the method proposed in Ref. (36) to obtain r 2 from experiment needs to be upgraded by replacing the exponential C(t) by a stretched exponential with β set at approximately 0.23.…”

“…Over this time range the extracted r 2 R is still increasing with decreasing W (increasing τ R ) indicating that the intrinsic, long time (τ R → ∞) value of r 2 has not been observed. [12,17,18,35] In an earlier paper [36], we proposed a method to extract the intrinsic, long time MSD r 2 from resolution dependent data. In the method, the intrinsic r 2 was defined in terms of the t = ∞ limit of the incoherent intermediate scattering function (ISF), I(Q, t), as…”

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

“…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].…”