Effect of background electrolyte on the estimation of protein hydrodynamic radius and net charge through capillary zone electrophoresis

Two physicochemical models are proposed for the estimation of both hydrodynamic radius and net charge of a protein when the capillary zone electrophoretic mobility at a given protocol, the set of pK of charged amino acids, and basic data from Protein Data Bank are available. These models also provide a rationale to interpret appropriately the effects of solvent properties on protein hydrodynamic radius and net charge. To illustrate the numerical predictions of these models, experimental data of electrophoretic mobility available in the literature for well-defined protocols are used. Five proteins are considered: lysozyme, staphylococcal nuclease, human carbonic anhydrase, bovine carbonic anhydrase, and human serum albumin. Numerical predictions of protein net charges through these models compare well with the results reported in the literature, including those found asymptotically through protein charge ladder techniques. Model calculations indicate that the hydrodynamic radius is sensitive to changes of the protein net charge and hence it cannot be assumed constant in general. Also, several limitations associated with models for estimating protein net charge and hydrodynamic radius from protein structure, amino acid sequence, and experimental electrophoretic mobility are provided and discussed. These conclusions also show clear requirements for further research.     

Global conformations of proteins as predicted from the modeling of their CZE mobility data

Estimations of protein global conformations in well-specified physicochemical microenvironments are obtained through global structural parameters defined from polypeptide-scale analyses. For this purpose protein electrophoretic mobility data must be interpreted through a physicochemical CZE model to obtain estimates of protein equivalent hydrodynamic radius, effective and total charge numbers, hydration, actual ionizing pK and pH-near molecule. The electrical permittivity of protein domain is also required. In this framework, the solvent drag on proteins is obtained via the characteristic friction power coefficient associated with the number of amino acid residues defining the global chain conformation in solution. Also, the packing dimension related to the spatial distribution of amino acid residues within the protein domain is evaluated and discussed. These scaling coefficients together with the effective and total charge number fractions of proteins provide relevant interpretations of protein global conformations mainly from collapsed globule to hybrid chain regimes. Also, protein transport properties may be estimated within this framework. In this regard, the central role played by the friction power coefficient in the evaluation of these properties is highlighted.     

From small charged molecules to oligomers: a semiempirical approach to the modeling of actual mobility in free solution

According to Stokes' treatment, the ionic mobility of particles, which are small with respect to Debye length, is usually considered to be proportional to the nominal charge and inversely proportional to the hydrodynamic radius. Experimentally, it is well known, however, that the ionic mobility of a small multicharged molecule does not depend linearly on its nominal charge in a wide range. This behavior can be accounted for by a condensation of the charge or a modification of the friction coefficient with the charge. This paper presents a semiempirical modeling of the actual mobility based on the assumption of additivity of frictional contributions pertaining to the uncharged molecular backbone and to each charged or uncharged moiety. Condensation of the charge was not considered. The model first appeared to be suitable for multicharged analytes having a characteristic dimension smaller than the Debye length, such as benzene polycarboxylic acids and polysulfated disaccharides. This approach was then adapted to account for the actual mobilities of singly and evenly charged oligomers (N-mers) having a dimension smaller than or similar to the Debye length. Rather good experimental agreement was obtained for polyalanines and polyglycines (N < or = 6), fatty acid homologs, fully sulfonated polystyrene oligomers (N < or = 13), and polycytidines (N < or = 10). Especially the influence of the polymerization degree on the mobility of oligomers having identical charge densities was clarified. It is also shown that the electrophoretic contribution to the overall friction coefficient increases linearly with the nominal charge but hardly depends on the chemical nature of the charged moieties. This model should be of interest to evaluate the role of various physicochemical phenomena (hydrodynamic and electrophoretic frictions, hydrodynamic coupling, charge condensation) involved in the migration of charged oligomers.     

Hydration, charge, size, and shape characteristics of peptides from their CZE analyses

A CZE model is presented for peptide characterization on the basis of well-established physicochemical equations. The effective mobility is used as basic data in the model to estimate relevant peptide properties such as, for instance, hydration, net and total electrical charge numbers, hydrodynamic size and shape, particle average orientation, and pH-microenvironment from the charge regulation phenomenon. Therefore 102 experimental effective mobilities of different peptides are studied and discussed in relation to previous work. An equation for the estimation of peptide hydration as a function of ionizing, polar, and non-polar amino acid residues is included in the model. It is also shown that the shape-orientation factor of peptides may be either lower or higher than one, and its value depends on a complex interplay among total charge number, molar mass, hydration, and amino acid sequence.     

Electrophoretic mobility equation for protein with molecular shape and charge multipole effects

We derive a simple formula for the free solution electrophoretic mobility of protein by including both molecular shape and charge distribution effects. The molecular shape of protein is described by a deformed sphere model, while the charge distribution is represented in terms of net charge, charge dipole, and charge quadrupole. The deformed sphere model approximates the radial coordinate of the protein surface as a simple quadratic equation based on the atomic coordinate data. Charge dipole does not affect the mobility of protein. Combined with the quadratic coefficients of the surface equation, charge quadrupole affects the mobility. When the charge quadrupole contribution is negligible, the mobility equation simplifies to the Henry equation in which the sphere radius is replaced with the hydrodynamic radius of protein. The deformed sphere model predicts correctly the hydrodynamic radius of protein from the atomic coordinate data. The hydrodynamic radius is not the radius of sphere of equal volume but the effective radius that correlates with the translational diffusivity of protein. To illustrate the utility of our mobility equation we study the electrophoresis of lysozyme and compare our results with previously published works.     

Separation of diadenosine polyphosphates by capillary electrophoresis

The influence of buffer composition and pH on the electrophoretic behavior of diadenosine polyphosphates with a phosphate chain ranging from two to five phosphate groups has been examined. The electrophoretic mobility in carbonate buffer increases according to the number of phosphates, whereas in borate buffer the mobility changes in an irregular way as a function of pH. This finding can be rationalized by a well-known interaction of borate with ribose rings, which modifies the charge and the hydrodynamic radius of each diadenosine polyphosphate in a different way. Our study shows that the best separation of diadenosine polyphosphates can be achieved at the highest pH values of the range examined both in borate and carbonate buffers.     

Prediction of Migration Times of Organic Ions in Capillary Zone Electrophoresis

The electrophoretic mobility ratio (R value) of any two ions is constant and independent of the capillary type and electrophoretic conditions if their electrical charges and hydration radii are constant. The use of strong acid salts and quaternary ammonium salts is therefore proposed for the determination of R values. Such analytes are called markers. The following determinations can be carried out: (i) the determination of the migration time corresponding to the electroosmotic flow (EOF) in any capillary under any electrophoretic condition by measuring the migration times of two markers in the condition studied (useful when the EOF is weak); (ii) the determination of the migration time of an analyte in any capillary by knowing the migration time of the markers in the capillary studied. If the pH is changed and the ionization of the analyte is pH dependent, the resulting migration time for the analyte can be calculated. The constancy of the mobility ratios of seven markers was checked experimentally at eight different pH values (between pH 3 and 10), at three temperatures, and for two buffer concentrations. The predicted and experimental migration times were also compared in two different types of capillaries.     

Potential of capillary zone electrophoresis for estimation of humate acid-base properties

Capillary zone electrophoresis (CZE) has been applied for fractionation and characterization of soil-derived humic acids (HAs). Humic acids from soddy-podzolic (HA(s)) and chernozem (HA(ch)) soils were studied as well as hydrophobic high-molecular-weight (HMW) and hydrophilic low-molecular-weight (LMW) HA(s) fractions obtained by salting-out with ammonium sulfate at a saturation of 0-40% and >70%, respectively. The possibility of CZE partial fractionation of HAs has been demonstrated. The shape of "humic hump" was shown to depend on the pH of running electrolyte. Almost the whole peak overlapping occurred if alkaline solutions were used for fractionation, but the peak resolution was improved at pH 5-7. Under appropriate fractionation conditions (pH 7), at least three humic acid subfractions with different electrophoretic mobilities were distinguished in the electropherograms of initial HA and HA(s) fractions. Such a high peak resolution has never been achieved for humic acids before. The presence of three subfractions in the HA is in agreement with gel-filtration analysis and was confirmed by comparison of the electrophoretic behavior of HA(s) with those of its HMW (hydrophobic) and the LMW (hydrophilic) fractions. The potentiometric titration of HA and its fractions was performed and the pK(a) of the functional groups were calculated. An attempt was made for the first time to relate the variation of electrophoretic mobility values with acid-base properties of humic acids. It was shown that changes in the humate charge resulting from the variation of the ionization degree of its functional groups as a function of pH can be estimated on the basis of electrophoretic mobility values. Potential of CZE in estimation of HA isoelectric point was demonstrated. The pH value corresponding to the lowest absolute electrophoretic mobility value of about 20 x 10(-5) cm(2) V(-1) s(-1) can be used for approximate estimation of HA isoelectric point. The data were discussed and agreement with the random coil structural model has been shown.     

Importance of electroosmotic flow and multiple ionic species on the electrophoresis of a rigid sphere in a charge-regulated zwitterionic cylindrical pore

The influence of electroosmotic flow (EOF) on the electrophoretic behavior of a particle is investigated by considering a rigid sphere in a charge-regulated, zwitterionic cylindrical pore filled with an aqueous solution containing multiple ionic species. This extends conventional analyses to a more general and realistic case. Taking a pore with pK(a) = 7 and pK(b) = 2 (point of zero charge is pH = 2.5) filled with an aqueous NaCl solution as an example, several interesting results are observed. For instance, if pH < 5.5, the particle mobility is influenced mainly by boundary effect, and is influenced by both EOF and boundary effects if pH ≥ 5.5. If pH is sufficiently high, the particle behavior is dominated by EOF, which might alter the direction of electrophoresis. The ratio of (pore radius/particle radius) influences not only the boundary effect, but also the strength of EOF. If the boundary effect is insignificant, the mobility varies roughly linearly with log(bulk salt concentration). These findings are of practical significance to both the interpretation of experimental data and the design of electrophoresis devices.     

Characterization of globular protein solutions by dynamic light scattering, electrophoretic mobility, and viscosity measurements

In this work, physicochemical properties of two globular proteinsbovine serum albumin (BSA) having a molecular weight of 67 kDa and human serum albumin (HSA) having a molecular weight of 69 kDawere characterized. The bulk characteristics of these proteins involved the diffusion coefficient (hydrodynamic radius), electrophoretic mobility, and dynamic viscosity as a function of protein solution concentration for various pH values. The hydrodynamic radius data suggested an association of protein molecules, most probably forming compact dimers. Using the hydrodynamic diameter and the electropheretic mobility data allowed the determination of the number of uncompensated (electrokinetic) charges on protein surfaces. The electrophoretic mobility data were converted to zeta potential values, which allowed one to determine the isoelectric point (iep) of these proteins. It was found to be at pH 5.1 for both proteins, in accordance with previous experimental data and theoretical estimations derived from amino acid composition and p K values. To determine further the stability of protein solutions, dynamic viscosity measurements were carried out as a function of their bulk volume concentration for various pH values. The intrinsic viscosity derived from these measurements was interpreted in terms of the Brenner model, which is applicable to hard spheroidal particles. It was found that the experimental values of the intrinsic viscosity of these proteins were in good agreement with this model when assuming protein dimensions of 9.5 x 5 x 5 nm3 (prolate spheroid). The possibility of forming linear aggregates of association degree higher than 2 was excluded by these measurements. It was concluded that the combination of dynamic viscosity and dynamic light scattering can be exploited as a convenient tool for detecting not only the onset of protein aggregation in suspensions but also the form and composition of these aggregates.     

On the application of CZE to the study of protein denaturation

Experimental mobilities obtained from CZE are used to study protein denaturation through a model based on known physicochemical theories. This model is able to provide additional information concerning the folded and unfolded protein states from mobility data. Its use comprises first the evaluation of relevant parameters of the protein microstates like the electrostatic free energy, apart from the classical conformational free energy, and second the expression of raw experimental data concerning the folding-unfolding transition into more specific physicochemical parameters like protein hydrodynamic radius, net charge number, and hydration. Spurious effects that are intrinsic to the experimental evaluation of the mobility of protein states, like BGE viscosity, pH, and ionic strength variations accompanying the changes of the denaturant agent intensity are eliminated. In order to illustrate the proposal of this work, two case studies are considered here. The first one concerns thermal and urea denaturations of horse heart ferricytochrome c and the second one involves thermal denaturation of hen egg-white lysozyme. Thus, relevant theoretical thermodynamic considerations of the folded-unfolded protein transition are presented, where the electrostatic free energy is included explicitly in the effective free energy. It is found that this transition involves sharp increases of hydrodynamic radius and protein hydration.     

Using electrophoretic mobility and bead modeling to characterize the charge and secondary structure of peptides

Using a modeling methodology developed in our laboratory previously, the free solution electrophoretic mobilities of several peptides are examined to see what they can tell us about: (i) the pK(a)s of specific side groups, and (ii) possible secondary structure. Modeling is first applied to mobility versus pH data of several small peptides (Messana, I. et al., J. Chromatogr. B 1997, 699, 149) where the only adjustable parameter associated with the charge state of the peptide is the pK(a )of the C-terminal. In addition to examining this parameter, the question of possible secondary structure is addressed. For two of the peptides considered, GGNA and GGQA, it is possible to account for the observed mobilities using "random" models with little restriction on the allowed range of Phi-Psi angles. For GGRA and RPPGF, "compact" models (possibly involving an I-turn) must be used to match modeling mobilities with experiment. Finally, three more complicated peptides ranging in size from 15 to 20 amino acids are also examined and characterized (Sitaram, B. R. et al., J. Chromatogr. A 1999, 857, 263). Here also, we find evidence of I-turns or some other "compact" structure in two of the three peptides examined.     

Fast high-throughput method for the determination of acidity constants by capillary electrophoresis. II. Acidic internal standards

A fast method for the determination of acidity constants by CZE has been recently developed. This method is based on the use of an internal standard of pK(a) similar to that of the analyte. In this paper we establish the reference pK(a) values of a set of 24 monoprotic neutral acids of varied structure that we propose as internal standards. These compounds cover the most usual working pH range in CZE and facilitate the selection of adequate internal standards for a given determination. The reference pK(a) values of the acids have been established by the own internal standard method, i.e. from the mobility differences between different acids of similar pK(a) in the same pH buffers. The determined pK(a) values have been contrasted to the literature pK(a) values and confirmed by determination of the pK(a) values of some acids of the set by the classical CE method. Some systematic deviations of mobilities have been observed in NaOH buffer in reference to the other used buffers, overcoming the use of NaOH in the classical CE method. However, the deviations affect in a similar degree to the test compounds and internal standards allowing thus, the use of NaOH buffer in the internal standard method. This fact demonstrates the better performance of the internal standard method over the classical method to correct mobility deviations, which together with its fastness makes it an interesting method for the routine determination of accurate pK(a) values of new pharmaceutical drugs and drug precursors.     

The free solution electrophoretic mobility of peptides by a bead modeling methodology

A bead modeling methodology, BMM, discussed previously to compute the free solution electrophoretic mobility of peptides [H. Pei, Y. Xin, S.A. Allison, J. Sep. Sci. 31 (2008) 554-564], is generalized to avoid the approximation of orientationally preaveraging hydrodynamic interaction. In general, peptide mobilities computed without preaveraging are lower by about 2%. The BMM is then used to study the free solution electrophoretic mobility of several insect oostatic peptides reported previously in a variety of different buffer systems ranging in pH from 2.25 to 8.1 [V. Solinova, V. Kasicka, D. Koval, J. Hlavacek, Electrophoresis, 25 (2004) 2299-2308]. With minor adjustment of the intrinsic pK(a0) of the N-terminal peptide, good agreement between modeling and experiment is achieved for peptide models with random secondary structures in the entire pH range. Model mobilities of these peptides appear to be relatively insensitive to the assumed secondary structure.     

Affinity capillary electrophoresis study of the linkage existing between proton and zinc ion binding to bacitracin A1

Measurements by capillary electrophoresis (CE) of bacitracin A(1) effective mobility at different pH values permitted to estimate the five acidic dissociation constants and the Stokes radii at different protonation stages of the macrocyclic dodecapeptide. The pK(a) values were 3.6 and 4.4 for the two carboxylic groups of the lateral chains of D-Asp-11 and D-Glu-4, respectively, 6.4 for the aza-atom of the imidazole ring of His-10, 7.6 for the amino group of N-terminal Ile-1 and 9.7 for the delta-amino group of D-Orn-7, very close to the values obtained by other researchers by titration experiments. In agreement with a rigid macrocyclic structure the Stokes radii of different protonated forms ranged only between 14.3 and 14.8 A. Best fitting procedures performed on experimental mobility measured at two different pH values (5.50 and 6.72) in the presence of increasing Zn(+2) concentration allowed confirming the model that assumes the binding of Zn(+2) to P(0) peptide form with a 1.5 x 10(3) M(-1) intrinsic association constant. Following to Zn(+2) binding, the pK(a) of the amino group of N-terminal Ile-1 is shifted from 7.6 to 5.9 and the Stokes radius is reduced of about 3 A. The mean charge of the bacitracin A(1)-Zn(+2) complex resulted +1.67 and +1.12 at pH 5.50 and 6.72, respectively. These results suggest that the amino group of N-terminal Ile-1 is not essential for Zn(+2) binding.     

Determination of dissociation constants of amino acids by capillary zone electrophoresis.

A method is proposed for the determination of dissociation constants of amino acids by capillary zone electrophoresis. According to the dissociation equilibrium of amino acids and the basic theory of electrophoresis, the nonlinear relationship between the pH value of the buffer and the effective electrophoretic mobilities of the analyte was obtained. The dissociation constants can be calculated from the pH values and the corresponding effective electrophoretic mobilities using the program written in C++. The dissociation constants, pKa1 and pKa2, of 11 kinds of amino acids were determined successfully by the proposed method. The determined dissociation constants were compared with values in the literature; the differences between them are in the range of -0.03 to 0.06. No significant differences were observed between the determined dissociation constants and the corresponding literature values.     

Nitromethane as solvent in capillary electrophoresis

Nitromethane has several properties that make it an interesting solvent for capillary electrophoresis especially for lipophilic analytes that are not sufficiently soluble in water: freezing and boiling points are suitable for laboratory conditions, low viscosity leads to favourable electrophoretic mobilities, or an intermediate dielectric constant enables dissolution of electrolytes. In the present work we investigate the change of electrophoretically relevant analyte properties - mobilities and pKa values - in nitromethane in dependence on the most important experimental conditions determined by the background electrolyte: the ionic strength, I, and the pH. It was found that the mobility decreases with increasing ionic strength (by, e.g. up to 30% from I = 0 to 50 mmol/L) according to theory. An appropriate pH scale is established by the aid of applying different concentration ratios of a buffer acid with known pKa and its conjugate base. The mobility of the anionic analytes (from weak neutral acids) depends on the pH with the typical sigmoidal curve in accordance with theory. The pKa of neutral acids derived from these curves is shifted by as much as 14 pK units in nitromethane compared to water. Both findings confirm the agreement of the electrophoretic behaviour of the analytes with theories of electrolyte solutions. Separation of several neutral analytes was demonstrated upon formation of charged complexes due to heteroconjugation with chloride as ionic constituent of the background electrolyte.     

Characterization of carboxylated nanolatexes by capillary electrophoresis

Poly(styrene-co-acrylic acid) (St/AA) and poly(styrene-co-methacrylic acid) (St/MA) nanolatexes with different acid contents were prepared by emulsion copolymerization and were analyzed by capillary electrophoresis (CE) and by laser doppler velocimetry (LDV). Due to the intrinsic differences in the methodologies, CE (separative technique) and LDV (zetametry, nonseparative technique) lead to very different electrophoretic mobility distributions. Beyond these differences, the variation of the electrophoretic mobility is a complex and nonlinear function of the hydrodynamic radius, the ionic strength, and the zeta potential. To gain better insight on the influence of the ionic strength and the acid content on the electrophoretic behavior of the nanolatexes, the electrophoretic mobility data were changed into surface charge densities using the O'Brien, White, and Ohshima modeling. This approach leads to the conclusion that the surface charge density is mainly controlled at high ionic strength (～50 mM) by the adsorption of anionic surfactants coming from the sample. On the contrary, at low ionic strength, and/or in the presence of neutral surfactant in the electrolyte, the acid content was the main parameter controlling the surface charge density of the nanolatexes.     

High‐resolution quantification by charge‐dominant electrophoretic mobility shift of quantum dots

Conjugation of biomolecules to colloidal nanoparticles, such as quantum dots (QDs), often leads to change in mobility. We discover that linking DNA molecules to quantum dots alters their surface charge density without significantly increasing the hydrodynamic radius, causing a prominent shift in electrophoretic mobility. In this study, a high‐resolution molecular quantification method named quantification by QDs electrophoretic mobility shift (qQEMS) is developed based on the charge‐dominant transformation that closely associates DNA quantity to QDs electrophoretic mobility. The versatility of qQEMS is demonstrated by a number of quantification assays in which DNA molecules functioned as enzyme substrates, target‐specific probes, and competitive charge carriers. qQEMS shows a great potential as a generic and versatile quantification platform for a wide range of applications.     

Modeling the electrophoresis of peptides and proteins: improvements in the "bead method" to include ion relaxation and "finite size effects"

A bead model methodology developed in our lab (Xin et al. J. Phys. Chem. B 2006, 110, 1038) and applicable to modeling the free solution electrophoretic mobility of peptides and proteins is generalized in two significant ways. First, an approximate account is taken of the relaxation effect, which makes the methodology applicable to more highly charged peptides and proteins than was previously possible. Second, a more accurate account is taken of the finite size of the beads making up the model structure. This improvement makes the method applicable at higher salt concentrations and/or to models consisting of larger sized subunits. The relaxation effect is accounted for by correcting "unrelaxed" mobilities on the basis of model size and average electrostatic surface, or zeta potential. Correction factors are estimated using those of spheres with the same hydrodynamic radius and zeta potential as the model structure. The correction factors of spheres are readily determined. The more general methodology is first applied to two sets of peptides (74 different peptides total) varying in size from 2 to 42 amino acids. The sets also cover a wide range of net charges. It is shown that accounting for finite bead size results in a small change in model mobilities under the conditions of the experiments (35 mM monovalent salt). The correction for ion relaxation, however, can be significant for highly charged peptides and improves agreement between model and experimental mobilities. Our correction procedure is also tested by examining the electrophoretic mobility of a particular protein "charge ladder" (Carbeck et al. J. Am. Chem. Soc. 1999, 121, 10,671), where the protein charge is varied over a wide range yet the conformation remains essentially constant. In summary, the effects of ion relaxation can be significant if the absolute electrophoretic mobility of a peptide exceeds approximately 0.20 cm2/(kV s).