There are three forms of incoherent neutron scattering (INS): elastic (EINS), quasi-elastic (QINS) and inelastic (IINS). Hydrogen has a large incoherent scattering cross-section and the incoherent measurements made result from fluctuations in the position, conformation and energy level of hydrogen atoms in particular in the sample. EINS results from atomic displacements on timescales of 0.1 femtosecond to 1 nanosecond. In this regime the dynamical behaviour of hydrated proteins is characterized by vibrational motions at low temperatures (<180 K) and by the onset of large-amplitude stochastic fluctuations as it passes through the glasslike transition temperature range 180-230 K. At 0 K only EINS occurs. As the temperature rises a broad IINS peak in the scattering intensity distribution due to vibrational or rotational transitions between well-defined energy levels is added to the spectrum. At higher temperatures still, a further contribution to the spectrum is made by EINS, arising from diffusive motions of (particularly) hydrogen atoms or jumps between conformational substates causing a small Doppler shift in the energy of the scattered neutron.

The figure shows a schematic INS spectrum. The x-axis is the energy transfer (omega is the energy, h Planck's constant) and the y-axis is the signal intensity S (as a function of momentum transfer [i.e. scattering angle] Q and energy omega). "Snapshots" from three different experiments performed at three distinct temperatures are shown. At 0 K only EINS occurs since very little molecular motion occurs and the sharp peak essentially arises from what limited vibrations occur near absolute zero. The peak is centred on omega = zero. At higher temperatures below the glasslike transition temperature both EINS and IINS occurs, with the spectrum again centred on zero energy. The IINS distribution arises from an increase with temperature in the amplitude of harmonic molecular vibrations. Above the transition temperature, the trend in EINS and IINS continues (i.e. elastic scattering events increasingly being replaced by inelastic ones). A new scattering event, QINS, arises from the onset of non-vibrational modes of motion, with the distribution of each of the three scattering modes in the spectrum being centred on zero omega.

Very little is known about the dynamics of biological molecules, which INS is a method for investigating. Unfortunately large amounts of sample (~100s of mg) are required for INS experiments and therefore those systems which have been investigated are naturally very abundant. The purple membrane bacteriorhodopsin-lipid array of Halobacterium salinarium is one such system, as are naturally highly abundant proteins such as lysozyme. Another application is to the global dynamic behaviour of proteins inside cells (Zaccai (2000) Science 288, 1604-1607). This review by Zaccai also provides an excellent introduction to incoherent neutron scattering. A PDF format version of Zaccai's review can be found here.

Case study: EINS of purple membrane
Zaccai and coleagues used EINS to reveal dynamical heterogeneity in the purple membrane. Deuterated purple membrane was labeled with hydrogenated retinal (the bacteriorhodopsin Schiff base), tryptophan and methionine. This permitted the monitoring of the motional properties of these important groups, which are clustered in the protein's functional centre, in the bacteriorhodopsin photocycle. The labeled groups were more rigid than the rest of the protein above the glasslike transition temperature. The authors conclude that the dynamical heterogeneity in bacteriorhodopsin thus revealed indicates that the majority of the molecule is highly dynamic, allowing important conformational changes during the photocyle, but that it simulataneously maintains a rigid core able to control the orientations adopted by retinal and thus regulate photocyclic turnover. Proc. Nat'l Acad. Sci. USA (1998) 95, 4970-4975. In another study the same authors studied the effect of hydration on the purple membrane's dynamics. Biophys. J. (1998) 75, 1945-1952. Zaccai has also written a review describing 25 years of research into purple membrane by neutron scattering, covering both INS and diffraction studies (Biophys. Chem. (2000) 86, 249-257).

Case study: QINS of purple membrane
Fitter and colleagues used QINS to monitor the effect of hydration and lipidation on bacteriorhodopsin flexibility and changes in the dynamics of bacteriorhodopsin and bovine rod cell rhodopsin upon light activation. FEBS Lett. (1998) 433, 321-325; Physica B (1999) 266, 35-40.

Case study: the role of hydration in the dynamic motion of parvalbumin
Parvalbumin, a typical EF-hand calcium-binding protein, was subjected to SANS, QINS, NMR and DSC by Zanotti et al.. A thorough description of the hydration-dependent motions of surface-exposed amino acids (lysines) contrasted with amino acids more buried in the core of the protein fold (alanines, isoleucines) was thereby formulated. Biophys. J. (1999) 76, 2390-2411.

Case study: truncation of a protein increases its dynamic nature
Kataoka et al. show that C-terminal truncation of staphylococcal nuclease results in an increased motional dynamic in its structure. Physica B (1999) 266, 20-26.

Case study: QINS of lysozyme
In the quasi-Laue neutron crystallographic structure of lysozyme reported elsewhere on this site, partial disordering of water molecules in the protein's hydration sphere was observed. This could arise from static disorder among crystallographic unit cells or dynamical disorder shared by all cells. These two possibilities cannot be distinguished between on the basis of crystallographic data, but can with IINS or QINS experiments. These experiments were carried out on IN5 and IN6 of the ILL and revealed that <5% of the hydrogen atoms in the sample were immobile while 60% had motional properties typical of solvent. Two major other populations of hydrogen atoms could be distinguished. One operated in a diffusion sphere of 3.6 +/- 0.4 Å with a typical shift of 1.6 Å and a residence time of 11 ps. This is five times slower than the motion of solvent water hydrogens. The other population had motional properties 50 times slower than solvent hydrogens. 3.6 Å is the sphere of occupation of a water molecule and 1.6 Å the distance to be travelled by a proton undergoing dynamic oscillation between neighbouring water molecules within a charge-relay network formed of the hydration layer covering the protein surface. This result strongly supports the idea that the indeterminacy in location of hydrogens arises from dynamical disorder shared by all unit cells in the crystal arising from protons in waters within hydrogen-bonding networks undergoing flip-flop transfer. Acta Crystallogr. (1999) D55, 978-987.

Case study: Dynamics of hydration water around plastocyanin
Paciaroni et al. (Phys. Rev. E. (1999) 60, R2476-R2479) use incoherent neutron scattering to detect the presence of an inelastic scattering peak around 3.5 meV in both plastocyanin and its hydration solvent. The simultaneous presence of this "boson peak" in both protein and hydration shell is interpreted to mean that there is a tight coupling between the solvent-exposed protein residues and the hydration water which gives rise to long range and collective molecular dynamics.

Case study: Dynamics of water around nucleic acid and proteolipid membrane systems
A further study that sought to investigate the dynamics of water around macromolecules suggests that in vivo most water is not in a bulk solvent-like state but part of a complex system, constrained in its dynamics through complex interactions with molecular surfaces and itself. Ruffle and colleagues (J. Am. Chem. Soc. (2002) 124, 565-569) estimate that approximately two layers of water molecules are perturbed from the bulk state in interaction with DNA, and four layers in the case of membranes. They estimate that in the mitochondrion, for example, all the water would be in purturbed superstructures rather than in a bulk state. An interesting methodology that these investigators seek to apply is the comparison of their vibrational spectra with those recorded for high-pressure forms of ice which may reproduce on the grand scale the localized interactions and perurbations of hydration water.

Molecular dynamics simulations appear to reproduce the experimentally oberved structural and dynamic chartacteristics of hydration water accurately.
 
 
 

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