Local measures of intermolecular free energies in solution

Towards Determination of Distances Between Nanoparticles and Grafted Paramagnetic Ions by NMR Relaxation

We developed an approach for determining distances between carbon nanoparticles and grafted paramagnetic ions and molecules by means of nuclear spin-lattice relaxation data. The approach was applied to copper-, cobalt- and gadolinium-grafted nanodiamonds, iron-grafted graphenes, manganese-grafted graphene oxide and activated carbon fibers that adsorb paramagnetic oxygen molecules. Our findings show that the aforementioned distances vary in the range of 2.7-5.4 Å and that the fixation of paramagnetic ions to nanoparticles is most likely implemented by means of the surface functional groups. The nuclear magnetic resonance data data are compared with the results of electron paramagnetic resonance measurements and density functional theory calculations.

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.

Overhauser dynamic nuclear polarization to study local water dynamics

Surface and internal water dynamics of molecules and soft matter are of great relevance to their structure and function, yet the experimental determination under ambient and steady-state conditions is challenging. One of the most powerful approaches to measure local water dynamics within 5 A distances is to utilize the modulation of the nuclear spin relaxation rate of water protons through their time-dependent dipolar coupling to paramagnetic probes, here nitroxide spin labels. We recently introduced a method to obtain local water dynamics through Overhauser dynamic nuclear polarization (DNP). This has a unique advantage over other related techniques available in that a highly amplified proton nuclear magnetic resonance signal carries the information, allowing the use of minute microliter sample volumes and 100 muM sample concentrations. The outcome of our approach is the quantitative determination of the key DNP parameter known as the coupling factor, which provides local translational diffusion dynamics of the solvent within 5 A of the spin label. In contrast to recent reports that the coupling factor for nitroxide radicals cannot be quantified due to the difficulty in determining the saturation factor for the spin label, we show the saturation factor can be accurately determined and for the first time present agreement between measurements and theory. We discuss the discrepancy between the related field cycling relaxometery technique and DNP in determining the coupling factor and present arguments in support of the DNP-determined value. DNP measurements of local hydration dynamics around nitroxides in bulk water and on the surface of proteins are presented.

Oxygen accessibility to ribonuclease a: quantitative interpretation of nuclear spin relaxation induced by a freely diffusing paramagnet

The nuclear spin relaxation induced by a freely diffusing paramagnetic center provides a direct measure of intermolecular accessibility. A number of factors are involved in a quantitative interpretation of relaxation data including excluded volume effects, solvation differences, and the details of the electron spin relaxation in the paramagnetic center. In the case where the electron relaxation time is short compared with correlation times describing the electron-nuclear coupling, the nuclear spin relaxation rates may be related to the effective local concentration of the paramagnetic center at different locations about the solute of interest. The local concentrations may in turn be related to differences in the local free energies of interaction between the diffusing paramagnet and the cosolute. We demonstrate this approach for the case of ribonuclease A and deduce surface free energy differences for a large number of protein proton sites. We find that the oxygen accessibility is poorly represented by hard-sphere models such as computed solvent or steric accessibility. There is a distribution of local intermolecular interactions with a width of the order of RT that dominates the report of the intermolecular exploration of the protein by this simple solute.

Spin relaxation measurements of electrostatic bias in intermolecular exploration

We utilize the paramagnetic contribution to proton spin-lattice relaxation rate constants induced by freely diffusing charged paramagnetic centers to investigate the effect of charge on the intermolecular exploration of a protein by the small molecule. The proton NMR spectrum provided 255 resolved resonances that report how the explorer molecule local concentration varies with position on the surface. The measurements integrate over local dielectric constant variations, and, in principle, provide an experimental characterization of the surface free energy sampling biases introduced by the charge distribution on the protein. The experimental results for ribonuclease A obtained using positive, neutral, and negatively charged small nitroxide radicals are qualitatively similar to those expected from electrostatic calculations. However, while systematic electrostatic trends are apparent, the three different combinations of the data sets do not yield internally consistent values for the electrostatic contribution to the intermolecular free energy. We attribute this failure to the weakness of the electrostatic sampling bias for charged nitroxides in water and local variations in effective translational diffusion constant at the water-protein interface, which enters the nuclear spin relaxation equations for the nitroxide-proton dipolar coupling.

The aqueous reference for ESR oximetry

The interaction of molecular oxygen with derivatives of nitroxide EPR spin labels has been investigated using nuclear spin-relaxation spectroscopy in aqueous and nonaqueous solvents. The proton spin-lattice relaxation rate induced by oxygen provides a measure of the local concentration of oxygen, which we find is dependent on solvent. In water, the hydrophobic effect increases the local concentration of oxygen in the nonpolar portions of solute molecules. For nitroxides reduced to the hydroxylamine in aqueous solutions, we find that the local concentration of oxygen is approximately twice that associated with a free diffusion hard sphere limit, while in octane, this effect is absent. These results show that nitroxide based ESR oximetry may suffer a reference concentration shift of order a factor of two if the aqueous nitroxide spectrum or relaxation is used as the reference.

Chromium(III) complexes as intermolecular probes

Metal ion complexes provide flexible paramagnetic centers that may be used to define intermolecular contacts in a variety of solution phase environments because both the charge and electronic relaxation properties of the complex may be varied. For most complex ions, there are several proton equilibria that may change the effective charge on the complex as a function of pH which in turn affects the efficacy of application for defining the electrostatic surfaces of co-solute molecules. We report here spectrophotometric and nuclear spin relaxation studies on aqueous solutions of chromium(III) complexes of EDTA, DTPA, and bis-amides of both. The effective charges available from these paramagnetic centers range from -3 to +1 and we report the pH ranges over which the effective charge is defined with confidence for application in magnetic relaxation experiments.