Drew F. Parsons

Measurements and Theoretical Interpretation of Points of Zero Charge/Potential of BSA Protein

The points of zero charge/potential of proteins depend not only on pH but also on how they are measured. They depend also on background salt solution type and concentration. The protein isoelectric point (IEP) is determined by electrokinetical measurements, whereas the isoionic point (IIP) is determined by potentiometric titrations. Here we use potentiometric titration and zeta potential (ζ) measurements at different NaCl concentrations to study systematically the effect of ionic strength on the IEP and IIP of bovine serum albumin (BSA) aqueous solutions. It is found that high ionic strengths produce a shift of both points toward lower (IEP) and higher (IIP) pH values. This result was already reported more than 60 years ago. At that time, the only available theory was the purely electrostatic Debye-Hückel theory. It was not able to predict the opposite trends of IIP and IEP with ionic strength increase. Here, we extend that theory to admit both electrostatic and nonelectrostatic (NES) dispersion interactions. The use of a modified Poisson-Boltzmann equation for a simple model system (a charge regulated spherical colloidal particle in NaCl salt solutions), that includes these ion specific interactions, allows us to explain the opposite trends observed for isoelectric point (zero zeta potential) and isoionic point (zero protein charge) of BSA. At higher concentrations, an excess of the anion (with stronger NES interactions than the cation) is adsorbed at the surface due to an attractive ionic NES potential. This makes the potential relatively more negative. Consequently, the IEP is pushed toward lower pH. But the charge regulation condition means that the surface charge becomes relatively more positive as the surface potential becomes more negative. Consequently, the IIP (measuring charge) shifts toward higher pH as concentration increases, in the opposite direction from the IEP (measuring potential).

Why Direct or Reversed Hofmeister Series? Interplay of Hydration, Non-electrostatic Potentials, and Ion Size

A modified Poisson-Boltzmann analysis is made of the double layer interaction between two silica surfaces and two alumina surfaces in chloride electrolyte. The analysis incorporates nonelectrostatic ion-surface dispersion interactions based on ab initio ionic excess polarizabilities with finite ion sizes. A hydration model for the tightly held hydration shell of kosmotropic ions is introduced. A direct Hofmeister series (K > Na > Li) is found at the silica surface while the reversed series (Li > Na > K) is found at alumina, bringing theory in line with experiment for the first time. Calculations with unhydrated ions also suggest that surface-induced dehydration may be occurring at the alumina surface.

Possible origin of the inverse and direct hofmeister series for lysozyme at low and high salt concentrations

Protein solubility studies below the isoelectric point exhibit a direct Hofmeister series at high salt concentrations and an inverse Hofmeister series at low salt concentrations. The efficiencies of different anions measured by salt concentrations needed to effect precipitation at fixed cations are the usual Hofmeister series (Cl(-) > NO(3)(-) > Br(-) > ClO(4)(-) > I(-) > SCN(-)). The sequence is reversed at low concentrations. This has been known for over a century. Reversal of the Hofmeister series is not peculiar to proteins. Its origin poses a key test for any theoretical model. Such specific ion effects in the cloud points of lysozyme suspensions have recently been revisited. Here, a model for lysozymes is considered that takes into account forces acting on ions that are missing from classical theory. It is shown that both direct and reverse Hofmeister effects can be predicted quantitatively. The attractive/repulsive force between two protein molecules was calculated. To do this, a modification of Poisson-Boltzmann theory is used that accounts for the effects of ion polarizabilities and ion sizes obtained from ab initio calculations. At low salt concentrations, the adsorption of the more polarizable anions is enhanced by ion-surface dispersion interactions. The increased adsorption screens the protein surface charge, thus reducing the surface forces to give an inverse Hofmeister series. At high concentrations, enhanced adsorption of the more polarizable counterions (anions) leads to an effective reversal in surface charge. Consequently, an increase in co-ion (cations) adsorption occurs, resulting in an increase in surface forces. It will be demonstrated that among the different contributions determining the predicted specific ion effect the entropic term due to anions is the main responsible for the Hofmeister sequence at low salt concentrations. Conversely, the entropic term due to cations determines the Hofmeister sequence at high salt concentrations. This behavior is a remarkable example of the charge-reversal phenomenon.

Ion Specific Surface Charge Density of SBA-15 Mesoporous Silica

Potentiometric titrations were used to estimate the surface charge density of SBA-15 mesoporous silica in different salt solutions. It was found that surface charge depends both on cation type, following a Hofmeister series (Cs(+) < Guanidinium(+) < K(+) < Na(+) < Li(+)), and on salt concentration (in the range 0.05-1 M). The surface charge series is reproduced by theoretical calculations performed using a modified Poisson-Boltzmann equation that includes ionic dispersion forces with ab initio ion polarizabilities and hydrated ions. The hydration model assigns an explicit hydration shell to kosmotropic (strong hydrated) ions only. The Hofmeister series appears to be due to the combination of ion-surface dispersion interactions and ion hydration.

Importance of Accurate Dynamic Polarizabilities for the Ionic Dispersion Interactions of Alkali Halides

Ab initio quantum mechanical calculations of the dynamic polarizability of alkali metal and halide ions are performed as a function of imaginary frequency. Electron correlation is shown to provide a significant correction to ionic polarizabilities. Ab initio ion-surface dispersion coefficients are compared with single- and multimode London approximations. The commonly employed single-mode model with the characteristic frequency taken from the ionization potential of the ion is shown to be inadequate, underestimating dispersion forces with an average error around 40% or as high as 80% for halide ions. Decomposition of the polarizability data into five modes covers the major modes of each ion adequately (four modes for Li(+)). Illustrative calculations of surface potentials at the mica surface in aqueous alkali halide electrolytes are made. Charge reversal is obtained with the more polarizable cations, K(+) and Rb(+). The error in the single-mode ionization potential models is seen as a strong shift in the surface potential from negative toward positive values.

Ab initio molar volumes and gaussian radii

Ab initio molar volumes are calculated and used to derive radii for ions and neutral molecules using a spatially diffuse model of the electron distribution with Gaussian spread. The Gaussian radii obtained can be used for computation of nonelectrostatic ion-ion dispersion forces that underlie Hofmeister specific ion effects. Equivalent hard-sphere radii are also derived, and these are in reasonable agreement with crystalline ionic radii. The Born electrostatic self-energy is derived for a Gaussian model of the electronic charge distribution. It is shown that the ionic volumes used in electrostatic calculations of strongly hydrated cosmotropic ions ought best to include the first hydration shell. Ionic volumes for weakly hydrated chaotropic metal cations should exclude electron overlap (in electrostatic calculations). Spherical radii are calculated as well as nonisotropic ellipsoidal radii for nonspherical ions, via their nonisotropic static polarizability tensors.

Charge Reversal of Surfaces in Divalent Electrolytes: The Role of Ionic Dispersion Interactions

Surface potentials of alkali earth nitrates at a mica surface are calculated using a modified Poisson-Boltzmann approach that includes nonelectrostatic ion-surface dispersion interactions. New ab initio dynamic polarizabilities are used to determine dispersion interactions. A hydration model describing the hydration shell of cations is presented. Excellent agreement with experiment is achieved, including charge reversal at high electrolyte concentration without the need for site binding models. This suggests that specific ionic dispersion forces provide the mechanism for ion surface binding. An asymptotic surface potential is found in the limit of very high concentration. A Hofmeister series is predicted according to the strength of charge reversal, with Mg > Ca > Sr > Ba. The ion-surface dispersion adsorption energies of hydrated ions appear to explain the apparent repulsive secondary hydration forces observed experimentally between mica surfaces when taken with a surface hydration layer.

Hofmeister series reversal for lysozyme by change in pH and salt concentration: insights from electrophoretic mobility measurements

Hofmeister series reversal can occur with change in pH, or increase in salt concentration. The phenomena are a challenge for any theory of ion specific effects. Recent theoretical work predicts how a complex interplay between ionic sizes, hydration and dispersion forces explains Hofmeister series reversal. Electrophoretic mobility measurements on lysozyme suspensions reported here are consistent with the theory.

A continuum model of solvation energies including electrostatic, dispersion, and cavity contributions

Physically accurate continuum solvent models that can calculate solvation energies are crucial to explain and predict the behavior of solute particles in water. Here, we present such a model applied to small spherical ions and neutral atoms. It improves upon a basic Born electrostatic model by including a standard cavity energy and adding a dispersion component, consistent with the Born electrostatic energy and using the same cavity size parameter. We show that the well-known, puzzling differences between the solvation energies of ions of the same size is attributable to the neglected dispersion contribution. This depends on dynamic polarizability as well as size. Generally, a large cancellation exists between the cavity and dispersion contributions. This explains the surprising success of the Born model. The model accurately reproduces the solvation energies of the alkali halide ions, as well as the silver(I) and copper(I) ions with an error of 12 kJ mol(-1) (±3%). The solvation energy of the noble gases is also reproduced with an error of 2.6 kJ mol(-1) (±30%). No arbitrary fitting parameters are needed to achieve this. This model significantly improves our understanding of ionic solvation and forms a solid basis for the investigation of other ion-specific effects using a continuum solvent model.

Implications of rotation–inversion–permutation invariance for analytic molecular potential energy surfaces

A molecular potential energy surface has the symmetry properties of invariance to rotation of the whole molecule, inversion of all atomic coordinates, and permutation of indistinguishable nuclei. While some of this invariance character can be easily incorporated in a local description of the surface, a formal application of these symmetry restrictions is useful in considering the form of the globalsurface which must account for large amplitude changes of the atomic coordinates. The form of a global molecular potential energy surface as a properly symmetrized analytic function of Cartesian coordinates is derived by extending Molien’s theorem of invariants for finite groups to cover the continuous rotation–inversion group. O(3), and the product of O(3) with the complete nuclear permutation group. The role of so‐called redundant internal coordinates in molecular potential energy surfaces is clarified.