Extreme-values statistics and dynamics of water at protein interfaces.

Immobilized proteins present a unique interface with water. The water translational diffusive motions affect the high-frequency dynamics and the nuclear spin-lattice relaxation as with all surfaces; however, rare binding sites for water in protein systems add very low-frequency components to the dynamics spectrum. Water binding sites in protein systems are not identical, thus distributions of free energies and consequent dynamics are expected. (2)H(2)O spin-lattice relaxation rate measurements as a function of magnetic field strength characterize the local rotational fluctuations for protein-bound water molecules. The measurements are sensitive to dynamics down to the kilohertz range. To account for the data, we show that the extreme-values statistics of rare events, i.e., water dynamics in rare binding sites, implies an exponential distribution of activation energies for the strongest binding events. In turn, for an activated dynamical process, the exponential energy distribution leads to a Pareto distribution for the reorientational correlation times and a power law in the Larmor frequency for the (2)H(2)O spin-lattice relaxation rate constants at low field strengths. The most strongly held water molecules escape from rare binding sites in times on the order of microseconds, which interrupts the intramolecular correlations and causes a plateau in the spin-lattice relaxation rate at very low magnetic field strengths. We examine the magnetic relaxation dispersion (MRD) data using two simple but related models: a protein-bound environment for water characterized by a single potential well and a protein-bound environment characterized by a double potential well where the potential functions for the local motions of the bound-state water are of different depth. This analysis is applied to D(2)O deuterium spin-lattice relaxation on cross-linked albumin and lysozyme, which is dominated by the intramolecular relaxation driven by the dynamical modulation of the nuclear electric quadrupole coupling. We also separate the intramolecular from the intermolecular contribution to water proton spin-lattice relaxation by isotope dilution and show that the intramolecular proton data map onto the deuterium relaxation by a scale factor implied by the relative strength of the quadrupole and dipolar couplings. The temperature and pH dependence of the magnetic relaxation dispersion are complex and accounted for by changing only the weighting factors in a superposition of contributions from single-well and double-well contributions. These experiments show that the reorientational dynamics spectrum for water, in and on a protein, is characterized by a strongly asymmetric distribution with a long-time tail that extends at least to microseconds.

Water-proton-spin-lattice-relaxation dispersion of paramagnetic protein solutions.

The paramagnetic contributions to water-proton-spin-lattice relaxation rate constants in protein systems spin-labeled with nitroxide radicals were re-examined. As noted by others, the strength of the dipolar coupling between water protons and the protein-bound nitroxide radical often appears to be larger than physically reasonable when the relaxation is assumed to be controlled by 3-dimensional diffusive processes in the vicinity of the spin label. We examine the effects of the surface in biasing the diffusive exploration of the radical region and derive a relaxation model that incorporates 2-dimensional dynamics at the interfacial layer. However, we find that the local 2-dimensional dynamics changes the shape of the relaxation dispersion profile but does not necessarily reproduce the low-field relaxation efficiency found by experiment. We examine the contributions of long-range dipolar couplings between the paramagnetic center and protein-bound-water molecules and find that the contributions from these several long range couplings may be competitive with translational contributions because the correlation time for global rotation of the protein is approximately 1000 times longer than that for the diffusive motion of water at the interfacial region. As a result the electron-proton dipolar coupling to rare protein-bound-water-molecule protons may be significant for protein systems that accommodate long-lived-water molecules. Although the estimate of local diffusion coefficients is not seriously compromised because it derives from the Larmor frequency dependence, these several contributions confound efforts to fit relaxation data quantitatively with unique models.

Water and backbone dynamics in a hydrated protein.

Rotational immobilization of proteins permits characterization of the internal peptide and water molecule dynamics by magnetic relaxation dispersion spectroscopy. Using different experimental approaches, we have extended measurements of the magnetic field dependence of the proton-spin-lattice-relaxation rate by one decade from 0.01 to 300 MHz for (1)H and showed that the underlying dynamics driving the protein (1)H spin-lattice relaxation is preserved over 4.5 decades in frequency. This extension is critical to understanding the role of (1)H(2)O in the total proton-spin-relaxation process. The fact that the protein-proton-relaxation-dispersion profile is a power law in frequency with constant coefficient and exponent over nearly 5 decades indicates that the characteristics of the native protein structural fluctuations that cause proton nuclear spin-lattice relaxation are remarkably constant over this wide frequency and length-scale interval. Comparison of protein-proton-spin-lattice-relaxation rate constants in protein gels equilibrated with (2)H(2)O rather than (1)H(2)O shows that water protons make an important contribution to the total spin-lattice relaxation in the middle of this frequency range for hydrated proteins because of water molecule dynamics in the time range of tens of ns. This water contribution is with the motion of relatively rare, long-lived, and perhaps buried water molecules constrained by the confinement. The presence of water molecule reorientational dynamics in the tens of ns range that are sufficient to affect the spin-lattice relaxation driven by (1)H dipole-dipole fluctuations should make the local dielectric properties in the protein frequency dependent in a regime relevant to catalytically important kinetic barriers to conformational rearrangements.

Dimensionality of diffusive exploration at the protein interface in solution.

The dynamics of water are critically important to the energies of interaction between proteins and substrates and determine the efficiency of transport at the interface. The magnetic field dependence of the nuclear spin-lattice relaxation rate constant 1/T(1) of water protons provides a direct characterization of water diffusional dynamics at the protein interface. We find that the surface-average translational correlation time is 30-40 ps and the magnetic field dependence of the water proton 1/T(1) is characteristic of two-dimensional diffusion of water in the protein interfacial region. The reduced dimensionality substantially increases the intermolecular re-encounter probability and the efficiency of the surface exploration by the small molecule, water in this case. We propose a comprehensive theory of the translational effects of a small diffusing particle confined in the vicinity of a spherical macromolecule as a function of the relative size of the two particles. We show that the change in the apparent dimensionality of the diffusive exploration is a general result of the small diffusing particle encountering a much larger particle that presents a diffusion barrier. Examination of the effects of the size of the confinement relative to the macromolecule size reveals that the reduced dimensionality characterizing the small-molecule diffusion persists to remarkably small radius ratios. The experimental results on several different proteins in solution support the proposed theoretical model, which may be generalized to other small-particle-large-body systems like vesicles and micelles.

Water molecule contributions to proton spin-lattice relaxation in rotationally immobilized proteins.

Spin-lattice relaxation rates of protein and water protons in dry and hydrated immobilized bovine serum albumin were measured in the range of (1)H Larmor frequency from 10 kHz to 30 MHz at temperatures from 154 to 302 K. The water proton spin-lattice relaxation reports on that of protein protons, which causes the characteristic power law dependence on the magnetic field strength. Isotope substitution of deuterium for hydrogen in water and studies at different temperatures expose three classes of water molecule dynamics that contribute to the spin-lattice relaxation dispersion profile. At 185 K, a water (1)H relaxation contribution derives from reorientation of protein-bound molecules that are dynamically uncoupled from the protein backbone and is characterized by a Lorentzian function. Bound-water-molecule motions that can be dynamically uncoupled or coupled to the protein fluctuations make dominant contributions at higher temperatures as well. Surface water translational diffusion that is magnetically two-dimensional makes relaxation contributions at frequencies above 10 MHz. It is shown using isotope substitution that the exponent of the power law of the water signal in hydrated immobilized protein systems is the same as that for protons in lyophilized proteins over four orders of magnitude in the Larmor frequency, which implies that changes in the protein structure associated with hydration do not affect the (1)H spin relaxation.

Changes in protein structure and dynamics as a function of hydration from (1)H second moments.

We report the proton second moment obtained directly from the Free Induction Decay (FID) of the NMR signal of variously hydrated bovine serum albumin (BSA) and hen egg white lysozyme (HEWL) and from the width of the NMR Z-spectrum of the cross-linked protein gels of different concentrations. The second moment of the proteins decreases in a continuous stepwise way as a function of increasing water content, which suggests that the structural and dynamical changes occur in small incremental steps. Although the second moment is dominated by the short range distances of nearest neighbors, the changes in the second moment show that the protein structure becomes more open with increasing hydration level. A difference between the apparent liquid content of the sample as found from decomposition of the FID and the analytically determined water content demonstrates that water absorbed in the early stages of hydration is motionally immobilized and magnetically indistinguishable from rigid protein protons while at high hydration levels some protein side-chain protons move rapidly contributing to liquid-like component of the NMR signal.

The magnetic field and temperature dependences of proton spin-lattice relaxation in proteins.

The nuclear magnetic relaxation dispersion profiles of lyophilized globular proteins were measured in the frequency range of 10 kHz-30 MHz at temperatures from 156 to 302 K. The existent theory of proton relaxation in immobilized protein systems was critically tested and expended to include contributions of rapid motions of protein side-chain groups. The new theory takes into account the strong coupling between the side-chain protons and the protein backbone, when correlation function cannot be written as a product of the contributions. The measurements showed that while the relaxation rate constant of the protein backbone protons is a linear function of the absolute temperature the side-chain groups exhibit an exponential temperature dependence corresponding to an activated process. Measurements carried out on simple homopolypeptides, polyglycine and polyalanine, provide strong support of the proposed new theory.

Nuclear magnetic relaxation dispersion study of the dynamics in solid homopolypeptides.

The (1)H nuclear magnetic relaxation dispersion profiles were measured from 10 kHz to 30 MHz as a function of temperature for polyglycine, polyalanine, polyvaline, and polyphenylalanine to examine the contributions of different side chain motions to the polypeptide proton relaxation rate constants. The spin-fracton theory for (1)H relaxation is modified to account for high frequency motions of side chains that are dynamically connected to the linear polymer backbone. The (1)H relaxation is dominated by propagation of rare disturbances along the backbone of the polymer. The side-chain dynamics cause an off-set in the field dependence of the (1)H spin-lattice relaxation rate constants which obey a power law in the Larmor frequency in the limit of low and high magnetic field strength.

Relaxation of protons by radicals in rotationally immobilized proteins.

Proton spin-lattice relaxation by paramagnetic centers may be dramatically enhanced if the paramagnetic center is rotationally immobilized in the magnetic field. The details of the relaxation mechanism are different from those appropriate to solutions of paramagnetic relaxation agents. We report here large enhancements in the proton spin-lattice relaxation rate constants associated with organic radicals when the radical system is rigidly connected with a rotationally immobilized macromolecular matrix such as a dry protein or a cross-linked protein gel. The paramagnetic contribution to the protein-proton population is direct and distributed internally among the protein protons by efficient spin diffusion. In the case of a cross-linked-protein gel, the paramagnetic effects are carried to the water spins indirectly by chemical exchange mechanisms involving water molecule exchange with rare long-lived water molecule binding sites on the immobilized protein and proton exchange. The dramatic increase in the efficiency of spin relaxation by organic radicals compared with metal systems at low magnetic field strengths results because the electron relaxation time of the radical is orders of magnitude larger than that for metal systems. This gain in relaxation efficiency provides completely new opportunities for the design of spin-lattice relaxation based contrast agents in magnetic imaging and also provides new ways to examine intramolecular protein dynamics.

Structural and dynamical examination of the low-temperature glass transition in serum albumin.

The nuclear magnetic transverse decay and the proton second moment of bovine serum albumin samples dry and hydrated with different water isotope compositions show that at temperatures around 170 K, there is a dramatic change in the dynamics of the water associated with the protein interface. By comparison, observation of the protein protons when hydrated with deuterium oxide provides no evidence for significant dynamical changes near 170 K. The proton second moment of the hydrated protein shows that the protein structure becomes more open with increasing hydration from the lyophilized condition and that the side chains extend from the protein surface into the solvent in the hydrated but not the dry cases. The proton second moment of serum albumin hydrated with H(2)O increases dramatically with decreasing temperature near 170 K, demonstrating that the water forms a rigid solid around the protein which effectively fills the surface irregularities created by the protein fold. Solvation with dimethyl sulfoxide yields small effects compared with water.

Observation of a deuteron nuclear magnetic resonance Knight shift in conductive polyaniline.

Solid state deuteron magic angle spinning nuclear magnetic resonance spectra of conductive ring-deuterated polyaniline consist of two peaks, one at the same chemical shift as the insulating form of the polymer and the second shifted by 5.8+/-1 ppm. The magnitude of the shift is field and temperature independent and is identified as a Knight shift. The deuterons undergoing a Knight shift originate from both the crystalline and amorphous regions of the sample, implying that conduction is mediated by delocalized polarons in both these regions. Spin count experiments demonstrate that in highly conductive samples, signal is lost not only by dephasing due to the proximity of localized unpaired electrons but also to high rf reflectance.