Long-time mean-square displacements in proteins

Determination of Dynamical Heterogeneity from Dynamic Neutron Scattering of Proteins

Motional displacements of hydrogen (H) in proteins can be measured using incoherent neutron-scattering methods. These displacements can also be calculated numerically using data from molecular dynamics simulations. An enormous amount of data on the average mean-square motional displacement (MSD) of H as a function of protein temperature, hydration, and other conditions has been collected. H resides in a wide spectrum of sites in a protein. Some H are tightly bound to molecular chains, and the H motion is dictated by that of the chain. Other H are quite independent. As a result, there is a distribution of motions and MSDs of H within a protein that is denoted dynamical heterogeneity. The goal of this paper is to incorporate a distribution of MSDs into models of the H incoherent intermediate scattering function, I(Q,t), that is calculated and observed. The aim is to contribute information on the distribution as well as on the average MSD from comparison of the models with simulations and experiment. For example, we find that simulations of I(Q,t) in lysozyme are well reproduced if the distribution of MSDs is bimodal with two broad peaks rather than a single broad peak.

Dynamic Neutron Scattering by Biological Systems

Dynamic neutron scattering directly probes motions in biological systems on femtosecond to microsecond timescales. When combined with molecular dynamics simulation and normal mode analysis, detailed descriptions of the forms and frequencies of motions can be derived. We examine vibrations in proteins, the temperature dependence of protein motions, and concepts describing the rich variety of motions detectable using neutrons in biological systems at physiological temperatures. New techniques for deriving information on collective motions using coherent scattering are also reviewed.

Influence of cosolvents, self-crowding, temperature and pressure on the sub-nanosecond dynamics and folding stability of lysozyme

We studied the effects of temperature and hydrostatic pressure on the dynamical properties and folding stability of highly concentrated lysozyme solutions in the absence and presence of the osmolytes trimethylamine-N-oxide (TMAO) and urea. Elastic incoherent neutron scattering (EINS) was applied to determine the mean-squared displacement (MSD) of the protein's hydrogen atoms to yield insights into the effects of these cosolvents on the averaged sub-nanosecond dynamics in the pressure range from ambient up to 4000 bar. To evaluate the additional effect of self-crowding, two protein concentrations (80 and 160 mg mL^-1) were used. We observed a distinct effect of TMAO on the internal hydrogen dynamics, namely a reduced mobility. Urea, on the other hand, revealed no marked effect and consequently, no counteracting effect in an urea-TMAO mixture was observed. Different from the less concentrated protein solution, no significant effect of pressure on the MSD was observed for 160 mg mL^-1 lysozyme. The EINS experiments were complemented by Fourier-transform infrared (FTIR) spectroscopy measurements, which led to additional insights into the folding stability of lysozyme under the various environmental conditions. We observed a stabilization of the protein in the presence of the compatible osmolyte TMAO and a destabilization in the presence of urea against temperature and pressure for both protein concentrations. Additionally, we noticed a slight destabilizing effect upon self-crowding at very high protein concentration (160 mg mL^-1), which is attributable to transient destabilizing intermolecular interactions. Furthermore, a pressure-temperature diagram could be obtained for lysozyme at these high protein concentrations that mimics densely packed intracellular conditions.

The Photosystem II Subunit S under Stress

Nonphotochemical quenching is the protective mechanism against overexcitation of photosystem II, triggered by excess ΔpH in photosynthetic membranes. The light-harvesting complexes (LHCs), the de-epoxidation of violaxanthin to zeaxanthin, and the photosystem II subunit S (PsbS) work in synergy for an optimized multilevel response. Understanding the fine details of this synergy has proven challenging to scientific research. Here, we employ large-scale, all-atom molecular simulations and beyond experimental insight, we proceed a step further in identifying the PsbS dynamics that could possibly be associated with this synergy. For the first time, to our knowledge, we probe the distinct behavior of PsbS under ΔpH that probes the details of the potential dimer-to-monomer transition, and in a violaxanthin/zeaxanthin-rich membrane, at an all-atom resolution. We propose that the lumen-exposed residues, threonine 162 and glutamic acid 173, form stabilizing hydrogen bonds between the PsbS monomers only at high lumen pH, whereas at low pH (excess ΔpH) this interaction is lost, and leads to higher flexibility of the protein and potentially to the dimer-to-monomer transition. Lastly, we discuss how conformational changes under the presence of ΔpH/zeaxanthin are related to the PsbS role in the current nonphotochemical quenching model in the literature. For the latter, we probe a PsbS-monomeric LHCII association. The association is proposed to potentially alter the monomeric LHCII sensitivity to ΔpH by changing the pKa values of interacting LHCII residues. This serves as an example where protonation-ligation events enhance protein-protein interactions fundamental to many life processes.

Homogeneous and heterogeneous dynamics in native and denatured bovine serum albumin

Quasielastic incoherent neutron spectroscopy experiments reveal that chemical denaturation significantly modifies the internal dynamics of bovine serum albumin.

Self-consistent molecular dynamics calculation of diffusion in higher n-alkanes

Diffusion is one of the key subjects of molecular modeling and simulation studies. However, there is an unresolved lack of consistency between Einstein-Smoluchowski (E-S) and Green-Kubo (G-K) methods for diffusion coefficient calculations in systems of complex molecules. In this paper, we analyze this problem for the case of liquid n-triacontane. The non-conventional long-time tails of the velocity autocorrelation function (VACF) are found for this system. Temperature dependence of the VACF tail decay exponent is defined. The proper inclusion of the long-time tail contributions to the diffusion coefficient calculation results in the consistency between G-K and E-S methods. Having considered the major factors influencing the precision of the diffusion rate calculations in comparison with experimental data (system size effects and force field parameters), we point to hydrogen nuclear quantum effects as, presumably, the last obstacle to fully consistent n-alkane description.

Quasielastic neutron scattering in biology: Theory and applications

Neutrons scatter quasielastically from stochastic, diffusive processes, such as overdamped vibrations, localized diffusion and transitions between energy minima. In biological systems, such as proteins and membranes, these relaxation processes are of considerable physical interest. We review here recent methodological advances and applications of quasielastic neutron scattering (QENS) in biology, concentrating on the role of molecular dynamics simulation in generating data with which neutron profiles can be unambiguously interpreted. We examine the use of massively-parallel computers in calculating scattering functions, and the application of Markov state modeling. The decomposition of MD-derived neutron dynamic susceptibilities is described, and the use of this in combination with NMR spectroscopy. We discuss dynamics at very long times, including approximations to the infinite time mean-square displacement and nonequilibrium aspects of single-protein dynamics. Finally, we examine how neutron scattering and MD can be combined to provide information on lipid nanodomains. This article is part of a Special Issue entitled "Science for Life" Guest Editor: Dr. Austen Angell, Dr. Salvatore Magazù and Dr. Federica Migliardo.

Computational investigation of dynamical transitions in Trp-cage miniprotein powders

We investigate computationally the dynamical transitions in Trp-cage miniprotein powders, at three levels of hydration: 0.04, 0.26 and 0.4 g water/g protein. We identify two distinct temperatures where transitions in protein dynamics occur. Thermal motions are harmonic and independent of hydration level below T_low ≈ 160 K, above which all powders exhibit harmonic behavior but with a different and enhanced temperature dependence. The second onset, which is often referred to as the protein dynamical transition, occurs at a higher temperature T_D that decreases as the hydration level increases, and at the lowest hydration level investigated here (0.04 g/g) is absent in the temperature range we studied in this work (T ≤ 300 K). Protein motions become anharmonic at T_D, and their amplitude increases with hydration level. Upon heating above T_D, hydrophilic residues experience a pronounced enhancement in the amplitude of their characteristic motions in hydrated powders, whereas it is the hydrophobic residues that experience the more pronounced enhancement in the least hydrated system. The dynamical transition in Trp-cage is a collective phenomenon, with every residue experiencing a transition to anharmonic behavior at the same temperature.

Anomalous and anisotropic nanoscale diffusion of hydration water molecules in fluid lipid membranes

We have studied nanoscale diffusion of membrane hydration water in fluid-phase lipid bilayers made of 1,2-dimyristoyl-3-phosphocholine (DMPC) using incoherent quasi-elastic neutron scattering. Dynamics were fit directly in the energy domain using the Fourier transform of a stretched exponential. By using large, 2-dimensional detectors, lateral motions of water molecules and motions perpendicular to the membranes could be studied simultaneously, resulting in 2-dimensional maps of relaxation time, τ, and stretching exponent, β. We present experimental evidence for anomalous (sub-diffusive) and anisotropic diffusion of membrane hydration water molecules over nanometer distances. By combining molecular dynamics and Brownian dynamics simulations, the potential microscopic origins for the anomaly and anisotropy of hydration water were investigated. Bulk water was found to show intrinsic sub-diffusive motion at time scales of several picoseconds, likely related to caging effects. In membrane hydration water, however, the anisotropy of confinement and local dynamical environments leads to an anisotropy of relaxation times and stretched exponents, indicative of anomalous dynamics.

Motional displacements in proteins: The origin of wave-vector-dependent values

The average mean-square displacement, 〈r(2)〉, of H atoms in a protein is frequently determined using incoherent neutron-scattering experiments. 〈r(2)〉 is obtained from the observed elastic incoherent dynamic structure factor, S(i)(Q,ω=0), assuming the form S(i)(Q,ω=0) =exp(-Q(2)〈r(2)〉/3). This is often referred to as the Gaussian approximation (GA) to S(i)(Q,ω=0). 〈r(2)〉 obtained in this way depends on the value of the wave vector, Q considered. Equivalently, the observed S(i)(Q,ω=0) deviates from the GA. We investigate the origin of the Q dependence of 〈r(2)〉 by evaluating the scattering functions in different approximations using molecular dynamics (MD) simulation of the protein lysozyme. We find that keeping only the Gaussian term in a cumulant expansion of S(Q,ω) is an accurate approximation and is not the origin of the Q dependence of 〈r(2)〉. This is demonstrated by showing that the term beyond the Gaussian is negligible and that the GA is valid for an individual atom in the protein. Rather, the Q dependence (deviation from the GA) arises from the dynamical heterogeneity of the H in the protein. Specifically it arises from representing, in the analysis of data, this diverse dynamics by a single average scattering center that has a single, average 〈r(2)〉. The observed Q dependence of 〈r(2)〉 can be used to provide information on the dynamical heterogeneity in proteins.