A paramagnetic molecular voltmeter

We have developed a general electron paramagnetic resonance (EPR) method to measure electrostatic potential at spin labels on proteins to millivolt accuracy. Electrostatic potential is fundamental to energy-transducing proteins like myosin, because molecular energy storage and retrieval is primarily electrostatic. Quantitative analysis of protein electrostatics demands a site-specific spectroscopic method sensitive to millivolt changes. Previous electrostatic potential studies on macromolecules fell short in sensitivity, accuracy and/or specificity. Our approach uses fast-relaxing charged and neutral paramagnetic relaxation agents (PRAs) to increase nitroxide spin label relaxation rate solely through collisional spin exchange. These PRAs were calibrated in experiments on small nitroxides of known structure and charge to account for differences in their relaxation efficiency. Nitroxide longitudinal (R(1)) and transverse (R(2)) relaxation rates were separated by applying lineshape analysis to progressive saturation spectra. The ratio of measured R(1) increases for each pair of charged and neutral PRAs measures the shift in local PRA concentration due to electrostatic potential. Voltage at the spin label is then calculated using the Boltzmann equation. Measured voltages for two small charged nitroxides agree with Debye-Hückel calculations. Voltage for spin-labeled myosin fragment S1 also agrees with calculation based on the pK shift of the reacted cysteine.     

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.     

Length-Scale Dependence of Hydration Free Energy: Effect of Solute Charge

Size and curvature are important determinants of particle wettability, in addition to surface chemistry and texture. Hydration free energy of a nonpolar solute scales with volume for small solutes and with surface area for larger ones. If the solute acquires a surface charge, the scaling regimes can be affected, with size-dependence of the charge playing a critical role. For isolated particles grown at fixed surface charge density, the Born approximation gives scaling of hydration free energy with volume. We consider a distinctly different but practically important scenario, where the charged solute and surrounding counterions are dissolved together. For this process, our molecular simulations demonstrate the electrostatic contribution to the solvation free energy, calculated per unit area of the solute, to be virtually independent of solute size. We explain this behavior in terms of counterion shielding effect on the curvature-dependent solute energy in the dehydrated state, an effect closely balanced by the influence of dielectric screening in water. As a result, for moderate surface charge densities of the solute, the net electrostatic contribution is dominated by counterion solvation, and scales with solute surface area independently of the ionic strength in the solution.     

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.     

Revisiting the Poisson-Boltzmann theory: Charge surfaces, multivalent ions and inter-plate forces

The Poisson-Boltzmann (PB) theory is extensively used to gain insight on charged colloids and biological systems as well as to elucidate fundamental properties of intermolecular forces. Many works have been devoted in the past to study PB-related features and to confirm them experimentally. In this work we explore the properties of inter-plate forces in terms of different boundary conditions. We treat the cases of constant surface charge, constant surface potential and mixed boundaries. The interplay between electrostatic interactions, attractive counter-ion release, and repulsive van ’t Hoff contribution is discussed separately for each case. Finally, we discuss how the crossover between attractive and repulsive interactions for constant surface charge case is influenced by the presence of multivalent counter-ions, where it is shown that the range of the attractive interaction grows with the valency.     

Binding of oppositely charged membranes and membrane reorganization

We consider the electrostatic interaction between two rigid membranes, with different surface charge densities of opposite sign, across an aqueous solution without added salt. Exact solutions to the nonlinear Poisson-Boltzmann equation are obtained and their physical meaning discussed. We also calculate the electrostatic contribution to the free energy and discuss the renormalization of the area per head group of the charged lipids arising from the Coulomb interaction. Received 13 October 1998     

盐离子对蛋白质带电特性的影响

本文应用分子理论,研究盐离子对蛋白质带电特性的影响,理论模型考虑蛋白质与阴离子的结合作用。研究发现,由于蛋白质与阴离子的结合,距离蛋白质表面附近处的阴离子被吸附在了蛋白质表面,在距离蛋白质表面附近区域,阴离子分布较少。通过计算体系中的静电势,我们发现,在距离蛋白质表面附近,静电势呈现了较大的负值,带正电荷的阳离子感受到静电吸引,会出现在距离蛋白质表面附近的区域,这会使得在距离蛋白质表面附近的区域,阳离子数目增多。这样,在不同阴离子浓度、以及阴离子与蛋白质不同结合能条件下,阴离子会在不同程度上影响蛋白质的带电特性、影响体系中的静电特性。通过考察不同结合能条件下,蛋白质表面电荷面密度随阴离子浓度的变化关系还发现,较大的结合能会使得阴离子与蛋白质结合增快,蛋白质表面会呈现从正电荷态向负电荷态的转变。理论结果符合实验观测,由此表明,盐离子与蛋白质的结合导致蛋白质表面带电特性的改变,是盐离子影响蛋白质带电特性的本质。     

Molecular masking and unmasking of the paramagnetic effect of iron on the proton spin-lattice (T1) relaxation time in blood and blood clots

The contribution of hemolysis, proteolysis and the paramagnetic effect of iron on the proton spin-lattice (T1) relaxation time in blood was examined. Hemolysis induced by sonication resulted in a significant (10%) increase in the T1 relaxation time of whole blood. Proteolysis in both sonicated and unsonicated whole blood samples eventually yielded T1 values which correlated well with the relaxation times of free iron in plasma or water at concentrations comparable to the concentration of iron in whole blood. It is concluded that proteolysis allows the iron atom to express its paramagnetic effect on water relaxation by gradually destroying the hydrophobic nature of the pocket in which iron resides on the hemoglobin molecule. The contribution of various blood components to the T1 relaxation of whole blood was also studied. The T1 values for packed erythrocytes, intact whole blood, sonicated whole blood, plasma and serum proved to be significantly different from each other. Serum was found to have a significantly (12%) longer T1 relaxation time than plasma. Packed clotted blood in vitro showed no change in the T1 time for at least 13 days while packed erythrocytes showed a shortening of T1 time after 6-8 days.     

Missing 2k(F) response for composite fermions in phonon drag

The conventional approach to treat charged defects in extended systems in first principles calculations is via the supercell approximation using a neutralizing jellium charge. I explicitly show that errors in the resulting electrostatic potential surface are comparable to a band gap energy in semiconductors, for cell sizes typically used in simulations. I present a method for eliminating divergence of the Coulomb potential in charged supercell calculations that correctly treats the electrostatic potential in the local vicinity of a charged defect, via a mixed boundary condition approach.     

Evaluation of enthalpy of interfacial reactions from temperature dependency of interfacial equilibrium

Temperature dependency of equilibrium at metal oxide-aqueous electrolyte solution interface was analyzed by numerical simulation. Derivations of inner surface potential with respect to temperature were performed at constant values of several different parameters. When surface charge density in inner plane was kept constant the reasonable results were obtained, i.e. the electrostatic contribution to enthalpy of protonation of amphotheric surface sites was found to be positive in the pH region below the point of zero potential and negative above this point. All other examined possibilities produced opposite results. Derivation of empirical interfacial equilibrium constant at constant surface potential indicated that electrostatic effect on protonation entropy is negligible and that electrostatic contributions to reaction Gibbs energy and enthalpy are equal and directly related to the surface potential in the inner plane.     

Charge relaxation in polyampholytes of various statistics

We discuss theoretically the relaxation of charge fluctuations in polyampholyte solutions. It has been shown previously by some of us (J. Wittmer et al. Europhys. Lett. 24, 263 (1993)) that the charge distribution along the polyampholyte backbone has a dramatic influence on the polarization energy and hence on the solubility. Here it is demonstrated that a similar effect exists for the charge relaxation. The charge relaxation mechanism qualitatively depends on the statistics: for alternating polyampholytes the relaxation is mainly due to local dipole inversion and is not primarily driven by electrostatic interactions, whereas for random polyampholytes it is driven by electrostatic interactions. Intermediate statistics (with short-ranged (exponential) correlations) appear as a combination of these two limiting cases: short-wavelength modes are insensitive to the loss of correlations along the backbone, whereas long-wavelength modes correspond to a random statistics with renormalized charges. The relaxation of the dielectric constant is also calculated. Received: 20 December 2002 / Accepted: 13 March 2003 / Published online: 24 April 2003 RID="a" ID="a"e-mail: johner@ics.u-strasbg.fr     

On capillary motion of a viscoelastic liquid with a charged free surface

The structure of the capillary-relaxation motion spectrum in a liquid with a charged free surface has been investigated taking into account the viscosity relaxation effect. On the basis of numerical analysis of the dispersion equation for the wave motion in a viscoelastic incompressible liquid, it is shown that for a given wave number the range of characteristic relaxation times in which relaxation-type wave motion exists is limited and expands with increasing wave number. The growth rate of instability of the charged liquid surface markedly depends on the characteristic relaxation time and increases with its growth; in liquids with elastic properties, the energy dissipation rate of capillary motion is enhanced. At a surface charge density that is supercritical for the onset of Tonks-Frenkel instability, both purely gravitational waves and waves of a relaxational nature exist.     

Screened electrostatics of charged particles on a water droplet

We study the electrostatic properties of charged particles trapped at an interface in a water-in-oil microemulsion. The electrostatic potential and the counterion distribution in the water droplet are given in terms of the ratio of the Debye screening length κ^-1 and the droplet radius R. In the limit R→∞ we recover the well-known results for a flat interface. Finite-size corrections are obtained in terms of the small parameter 1/κR. Part of the counterions spread along the interface and form a charged layer of one Debye length thickness. In particular, there is a uniform surface charge contribution. We derive explicit expressions for the electric field, the mobile charge density, and the charge-induced pressure on the interface.     

Estimation of free copper ion concentrations in blood serum using T(1) relaxation rates

The water proton relaxation rate constant R(1)=1/T(1) (at 60 MHz) of blood serum is substantially increased by the presence of free Cu2+ ions at concentrations above normal physiological levels. Addition of chelating agents to serum containing paramagnetic Cu2+ nulls this effect. This was demonstrated by looking at the effect of adding a chelating agent-D-penicillamine (D-PEN) to CuSO4 and CuCl2 aqueous solutions as well as to rabbit blood serum. We propose that the measurement of water proton spin-lattice relaxation rate constants before and after chelation may be used as an alternative approach for monitoring the presence of free copper ions in blood serum. This method may be used in the diagnosis of some diseases (leukaemia, liver diseases and particularly Wilson's disease) because, in contrast to conventional methods like spectrophotometry which records the total number of both bound and free ions, the proton relaxation technique is sensitive solely to free paramagnetic ions dissolved in blood serum. The change in R(1) upon chelation was found to be less than 0.06 s(-1) for serum from healthy subjects but greater than 0.06 s(-1) for serum from untreated Wilson's patients.     

Interaction of a dielectric macroparticle with a point charge in plasma

The electrostatic interaction of a charged spherical dielectric macroparticle with a point charge in a plasma in the presence of an external uniform electric field is considered. The electrostatic force and the torque acting on the macroparticle have been determined, and the form of the interaction potential has been established for a nonuniform distribution of free charge on the macroparticle surface. A simple (for calculations) expression for the interaction potential that describes well the exact potential at all interparticle distances is proposed. The angular velocity of the spinning of dust particles caused by a nonuniform distribution of free charge over their surface has been estimated.     

The line shapes of the water proton resonances of red blood cells containing carbonyl hemoglobin, deoxyhemoglobin, and methemoglobin: implications for the interpretation of proton MRI at fields of 1.5 T and below

The 300 MHz (7 T) water proton resonances of suspensions of red blood cells containing paramagnetic deoxyhemoglobin or methemoglobin can be resolved into two broad lines assignable to intra- and extracellular water which undergoes rapid T2 relaxation by diffusion in magnetic field gradients induced by the intracellular paramagnets. The width of the resolved lines allowed an estimate of the maximum contribution that diffusion makes to T2 relaxation at 7 T. The dependence of the diffusion contribution on the square of the strength of the static magnetic field suggest that diffusion makes a small contribution to water proton T2 relaxation at 1.5 T compared to 7 T, and a negligible one at 0.5 T in early and intermediate hematomas containing deoxyhemoglobin or methemoglobin in intact red blood cells. At the lower field strengths, water proton T2 relaxation is apparently dominated by the rapid chemical exchange (mean lifetime tau = 10 msec) between the intra- and extracellular environments.     

Shape change of nanocontainers via a reversible ionic buckling

We demonstrate that small charged nanocages can undergo reversible changes of shapes by modifying the ionic conditions including salt concentration, pH, and dielectric permittivity of the medium. Using numerical simulations, we analyze structures with various charge stoichiometric ratios. At zero or low charge densities, the shape of the cage is determined by its elastic properties, and the surface charge pattern is dictated by the globally fixed geometry. As the charge density per molecule increases, the shape is strongly affected by the electrostatic forces. In this regime, the shape of the nanocage is controlled by the charge distribution.     

Nonlinear periodic waves on the charged surface of a finite-thickness ideal liquid layer

In the fourth order of smallness in the amplitude of a periodic capillary-gravitational wave travelling over the uniformly charged free surface of an ideal incompressible conducting liquid of a finite depth, analytical expressions for the evolution of the nonlinear wave, velocity field potential of the liquid, electrostatic field potential above the liquid, and nonlinear frequency correction that is quadratic in a small parameter are derived. It is found that the dependence of the amplitude of the nonlinear correction to the frequency on the charge density on the free liquid surface and on the thickness of the liquid layer changes qualitatively when the layer gets thinner. In thin liquid layers, the resonant wavenumber depends on the surface charge density, while in thick layers, this dependence is absent.     

A new constituent of electrostatic energy in semiconductors

The concept of electric energy is revisited in detail for semiconductors. We come to the conclusion that the main relationship used to calculate the energy related to the penetration of the electric field in semiconductors is missing a fundamental term. For instance, spatial derivate of the electrostatic energy using the traditional formula fails at giving the correct electrostatic force between semiconductor based capacitor plates, and reveals unambiguously the existence of an extra contribution to the standard electrostatic free energy. The additional term is found to be related to the generation of space charge regions which are predicted when combining electrostatics with semiconductor physics laws, such as for accumulation and inversion layers. On the contrary, no such energy is needed when relying on electrostatics only, as for instance when adopting the so-called full depletion approximation. The same holds for neutral and charged insulators that are still consistent with the customary definition, but these two examples are in fact singular cases. In semiconductors for instance, this additional energy can largely exceed the energy gained by the dipoles, thus becoming the dominant term. This unexpected result clearly asks for a generalization of electrostatic energy in matter in order to reconcile basic concepts of electrostatic energy in the framework of classical physics.     

Study of surface cell Madelung constant and surface free energy of nanosized crystal grain

Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be greatly beneficial to the analysis of surface states and the study of the dynamics of crystal nucleation and growth. A new approximative expression of the surface energy and relevant thermodynamic data are used in this calculation. New formula and computing method for calculating the Madelung constant α of any complex crystals are proposed, and the surface free energies and surface electrostatic energies of nanosized crystal grains and the Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized-crystal-grain TiO₂ and the surface electrostatic energy(absolute value) of nanosized-crystal-grain α -Al₂O₃ are found to be the biggest among all the crystal grains including those of other species.