Bertil Halle

Interpretation of magnetic resonance data from water nuclei in heterogeneous systems

Nuclear magnetic resonance (NMR) data from water nuclei (1H, 2H, and 17O) can provide much information about the state of water in heterogeneous systems. In the present work, we present a theoretical framework for the interpretation of such data and discuss the implications of the theory. Due to the local anisotropy in heterogeneous systems, it is necessary to consider two components of water motion: a fast anisotropic reorientation superposed on a more extensive slow motion. On the basis of the experimentally verified assumption that these motions occur on different time scales, we develop a ’’two‐step’’ model of relaxation, showing that both motions may give important contributions to the relaxation. We derive a simple expression for the relevant correlation function, valid for isotropic systems. Anisotropic systems are also treated, making use of a new symmetry theorem for time correlation functions. The proof of this theorem is given in an Appendix. The magnitudes of the water 2H and 17O quadrupole co...

Flexibility and packing in proteins

Structural flexibility is an essential attribute, without which few proteins could carry out their biological functions. Much information about protein flexibility has come from x-ray crystallography, in the form of atomic mean-square displacements (AMSDs) or B factors. Profiles showing the AMSD variation along the polypeptide chain are usually interpreted in dynamical terms but are ultimately governed by the local features of a highly complex energy landscape. Here, we bypass this complexity by showing that the AMSD profile is essentially determined by spatial variations in local packing density. On the basis of elementary statistical mechanics and generic features of atomic distributions in proteins, we predict a direct inverse proportionality between the AMSD and the contact density, i.e., the number of noncovalent neighbor atoms within a local region of ∼1.5 nm3 volume. Testing this local density model against a set of high-quality crystal structures of 38 nonhomologous proteins, we find that it accurately and consistently reproduces the prominent peaks in the AMSD profile and even captures minor features, such as the periodic AMSD variation within α helices. The predicted rigidifying effect of crystal contacts also agrees with experimental data. With regard to accuracy and computational efficiency, the model is clearly superior to its predecessors. The quantitative link between flexibility and packing density found here implies that AMSDs provide little independent information beyond that contained in the mean atomic coordinates.

Protein hydration dynamics in aqueous solution

Water oxygen-17 and deuteron spin relaxation rates, measured as a function of resonance frequency, have been used to study the dynamics of protein hydration in aqueous solutions of ribonuclease A, lysozyme, myoglobin, trypsin and serum albumin. The relaxation data conform to the picture of protein hydration dynamics, proposed on the basis of previous studies of smaller proteins, where the long-lived water molecules responsible for the relaxation dispersion are identified with a small number of integrat water molecules seen in the crystal structures. These integral water molecules, with residence times in the range 10(-9)-10(-3) s, are either buried in internal cavities, trapped in narrow clefts or coordinated to metal ions. For the water molecules in the traditional hydration layer at the protein surface, the relaxation data suggest an average residence time in the range 10-50 ps, consistent with high-resolution 1H spectroscopy and computer simulations. The relaxation data also reveal some more specific features of protein hydration, relating to hydration of cavities that appear empty by crystallography, entrapment of water between structural domains of large proteins and subnanosecond 180 degrees flips in buried water clusters.

Hydration of denatured and molten globule proteins.

The hydration of nonnative states is central to protein folding and stability but has been probed mainly by indirect methods. Here we use water 17O relaxation dispersion to monitor directly the internal and external hydration of α-lactalbumin, lysozyme, ribonuclease A, apomyoglobin and carbonic anhydrase in native and nonnative states. The results show that nonnative proteins are more structured and less solvent exposed than commonly believed. Molten globule proteins preserve most of the native internal hydration sites and have native-like surface hydration. Proteins denatured by guanidinium chloride are not fully solvent exposed but contain strongly perturbed occluded water. These findings shed new light on hydrophobic stabilization of proteins.

Biomolecular hydration: From water dynamics to hydrodynamics

Thermally driven rotational and translational diffusion of proteins and other biomolecules is governed by frictional coupling to their solvent environment. Prediction of this coupling from biomolecular structures is a longstanding biophysical problem, which cannot be solved without knowledge of water dynamics in an interfacial region comparable to the dry protein in volume. Efficient algorithms have been developed for solving the hydrodynamic equations of motion for atomic-resolution biomolecular models, but experimental diffusion coefficients can be reproduced only by postulating hundreds of rigidly bound water molecules. This static picture of biomolecular hydration is fundamentally inconsistent with magnetic relaxation dispersion experiments and molecular dynamics simulations, which both reveal a highly dynamic interface where rotation and exchange of nearly all water molecules are several orders of magnitude faster than biomolecular diffusion. Here, we resolve this paradox by means of a dynamic hydration model that explicitly links protein hydrodynamics to hydration dynamics. With the aid of this model, bona fide structure-based predictions of global biomolecular dynamics become possible, as demonstrated here for a set of 16 proteins for which accurate experimental rotational diffusion coefficients are available.

Cell water dynamics on multiple time scales

Water–biomolecule interactions have been extensively studied in dilute solutions, crystals, and rehydrated powders, but none of these model systems may capture the behavior of water in the highly organized intracellular milieu. Because of the experimental difficulty of selectively probing the structure and dynamics of water in intact cells, radically different views about the properties of cell water have proliferated. To resolve this long-standing controversy, we have measured the 2H spin relaxation rate in living bacteria cultured in D2O. The relaxation data, acquired in a wide magnetic field range (0.2 mT–12 T) and analyzed in a model-independent way, reveal water dynamics on a wide range of time scales. Contradicting the view that a substantial fraction of cell water is strongly perturbed, we find that ≈85% of cell water in Escherichia coli and in the extreme halophile Haloarcula marismortui has bulk-like dynamics. The remaining ≈15% of cell water interacts directly with biomolecular surfaces and is motionally retarded by a factor 15 ± 3 on average, corresponding to a rotational correlation time of 27 ps. This dynamic perturbation is three times larger than for small monomeric proteins in solution, a difference we attribute to secluded surface hydration sites in supramolecular assemblies. The relaxation data also show that a small fraction (≈0.1%) of cell water exchanges from buried hydration sites on the microsecond time scale, consistent with the current understanding of protein hydration in solutions and crystals.

Dynamics at the Protein-Water Interface from 17O Spin Relaxation in Deeply Supercooled Solutions

Most of the decisive molecular events in biology take place at the protein-water interface. The dynamical properties of the hydration layer are therefore of fundamental importance. To characterize the dynamical heterogeneity and rotational activation energy in the hydration layer, we measured the (17)O spin relaxation rate in dilute solutions of three proteins in a wide temperature range extending down to 238 K. We find that the rotational correlation time can be described by a power-law distribution with exponent 2.1-2.3. Except for a small fraction of secluded hydration sites, the dynamic perturbation in the hydration layer is the same for all proteins and does not differ in any essential way from the hydration shell of small organic solutes. In both cases, the dynamic perturbation factor is <2 at room temperature and exhibits a maximum near 262 K. This maximum implies that, at low temperatures, the rate of water molecule rotation has a weaker temperature dependence in the hydration layer than in bulk water. We attribute this difference to the temperature-independent constraints that the protein surface imposes on the water H-bond network. The free hydration layer studied here differs qualitatively from confined water in solid protein powder samples.

The physical state of water in bacterial spores

The bacterial spore, the hardiest known life form, can survive in a metabolically dormant state for many years and can withstand high temperatures, radiation, and toxic chemicals. The molecular basis of spore dormancy and resistance is not understood, but the physical state of water in the different spore compartments is thought to play a key role. To characterize this water in situ, we recorded the water 2H and 17O spin relaxation rates in D2O-exchanged Bacillus subtilis spores over a wide frequency range. The data indicate high water mobility throughout the spore, comparable with binary protein–water systems at similar hydration levels. Even in the dense core, the average water rotational correlation time is only 50 ps. Spore dormancy therefore cannot be explained by glass-like quenching of molecular diffusion but may be linked to dehydration-induced conformational changes in key enzymes. The data demonstrate that most spore proteins are rotationally immobilized, which may contribute to heat resistance by preventing heat-denatured proteins from aggregating irreversibly. We also find that the water permeability of the inner membrane is at least 2 orders of magnitude lower than for model membranes, consistent with the reported high degree of lipid immobilization in this membrane and with its proposed role in spore resistance to chemicals that damage DNA. The quantitative results reported here on water mobility and transport provide important clues about the mechanism of spore dormancy and resistance, with relevance to food preservation, disease prevention, and astrobiology.

Does the dynamic Stokes shift report on slow protein hydration dynamics

The time-dependent fluorescence frequency shift of protein-attached probes has a much slower decay than that for the free probe. The decay times, ranging from 10 ps to several nanoseconds, have been attributed to hydration water motions several orders of magnitude slower than those in the hydration shell of small solutes. This interpretation deviates strongly from the prevailing picture of protein hydration dynamics. We argue here that the slow decay in the fluorescence shift can be explained by a ubiquitous solvent polarization mechanism, with no need to invoke slow water motions or a dynamic coupling with protein motions. This mechanism can be qualitatively understood with the aid of a dielectric continuum model. We therefore conclude that the long decay times measured with time-dependent fluorescence spectroscopy contain no information about protein hydration dynamics.

Nearly exponential quadrupolar relaxation. A perturbation treatment

Abstract Quadrupolar nuclear spin relaxation is treated by a perturbation method, which shows that the relaxation is nearly exponential provided that the effective spectral density is only weakly frequency dependent. Approximate analytical expressions for the relaxation rates are derived and tested against the experimentally accessible apparent relaxation rates, for a fast-exchange two-state model. The results for spin I = 5 2 and 7 2 indicate that the analytical expressions are accurate to within a few percent in most experimental situations.