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.

This work explores the validity of simple CZE models to analyze the electrophoretic mobilities of 102 peptides reported in literature. These models are based mainly on fundamental physicochemical theories providing analytical expressions amenable to relatively simple numerical analysis. Thus, the Linderstrøm-Lang capillary electrophoresis model (LLCEM) and its perturbed version (PLLCEM), proposed and applied previously to the CZE of globular proteins, are adapted and used here for peptides. Also the effects of pK-shifts on net charge, hydration and hydrodynamic size and shape of peptides are analyzed and discussed. Emphasis is placed on the fact that these parameters are physically coupled, and thus a variation in the net charge may produce an appreciable change in the hydrodynamic size of peptides. Within the framework of CZE, peptides may be assumed as having a hydrodynamic volume associated with either spherical or spheroidal particles. The effects on peptide net charge and hydrodynamic size, of electrostatic interaction between a pair of charged groups in the chain and electrical permitivitty around the peptide domain are studied. The predictions of the PLLCEM and LLCEM are in good agreement with results reported previously in the literature. Several limitations concerning these models and some needs for further research are also described.

Electrophoretic mobility data of four proteins are analyzed and interpreted through a physicochemical CZE model, which provides estimates of quantities like equivalent hydrodynamic radius (size), effective charge number, shape orientation factor, hydration, actual pK values of ionizing groups, and pH near molecule, among others. Protein friction coefficients are simulated through the creeping flow theory of prolate spheroidal particles. The modeling of the effective electrophoretic mobility of proteins requires consideration of hydrodynamic size and shape coupled to hydration and effective charge. The model proposed predicts native protein hydration within the range of values obtained experimentally from other techniques. Therefore, this model provides consistently other physicochemical properties such as average friction and diffusion coefficients and packing fractal dimension. As the pH varies from native conditions to those that are denaturing the protein, hydration and packing fractal dimension change substantially. Needs for further research are also discussed and proposed.

Peptide electrophoretic mobility data are interpreted through a physicochemical CZE model, providing estimates of the equivalent hydrodynamic radius, hydration, effective and total charge numbers, actual ionizing pK, pH-near molecule and electrical permittivity of peptide domain, among other basic properties. In this study, they are used to estimate some peptide global structural properties proposed, providing thus a distinction among different peptides. Therefore, the solvent drag on the peptide is obtained through a characteristic friction power coefficient of the number of amino acid residues, defined from the global chain conformation in solution. As modeling of the effective electrophoretic mobility of peptides is carried out in terms of particle hydrodynamic size and shape coupled to hydration and effective charge, a packing dimension related to chain conformation within the peptide domain may be defined. In addition, the effective and total charge number fractions of peptides provide some clues on the interpretation of chain conformations within the framework of scaling laws. Furthermore, the model estimates transport properties, such as sedimentation, friction and diffusion coefficients. As the relative numbers of ionizing, polar and non-polar amino acid residues vary in peptides, their global structural properties defined here change appreciably. Needs for further research are also discussed.

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.

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.

Effective electrophoretic mobility data of 20 amino acids reported in the literature are analyzed and interpreted through simple physicochemical models, which are able to provide estimates of coupled quantities like hydrodynamic shape factor, equivalent hydrodynamic radius (size), net charge, actual pK values of ionizing groups, partial charges of ionizing groups, hydration number, and pH near molecule (microenvironment-pH of the BGE). It is concluded that the modeling of the electrophoretic mobility of these analytes requires a careful consideration of hydrodynamic shape coupled to hydration. In the low range of pH studied here, distinctive hydrodynamic behaviors of amino acids are found. For instance, amino acids with basic polar and ionizing side chain remain with prolate shape for pH values varying from 1.99 to 3.2. It is evident that as the pH increases from low values, amino acids get higher hydrations as a consequence each analyte total charge also increases. This result is consistent with the monotonic increase of the hydrodynamic radius, which accounts for both the analyte and the quite immobilized water molecules defining the electrophoretic kinematical unit. It is also found that the actual or effective pK value of the alpha-carboxylic ionizing group of amino acids increases when the pH is changed from 1.99 to 3.2. Several limitations concerning the simple modeling of the electrophoretic mobility of amino acids are presented for further research.

The present work is motivated specifically by the need to find a simple interplay between experimental values of electrophoretic mobility and intrinsic viscosity (IV) of polypeptides. The connection between these two properties, as they are evaluated experimentally in a formulated dilute solution, may provide relevant information concerning the physicochemical characterization and separation of electrically charged chains such as polypeptides. Based on this aspect, a study on the relation between the effective electrophoretic mobility and the IV of the following globular proteins is carried out: bovine carbonic anhydrase, staphylococcal nuclease, human carbonic anhydrase, lysozyme, human serum albumin. The basic interpretation of the IV through polypeptide chain conformations involves two unknowns: one is the Flory characteristic ratio involving short-range intramolecular interactions and the other is the Mark-Houwink exponent associated with large-range intramolecular interactions. Here, it will be shown via basic and well-established electrokinetic theories and scaling concepts that the IV and global chain flexibility of polypeptides in dilute solutions may be estimated from capillary zone electrophoresis, in addition to classical transport properties. The polypeptide local chain flexibility may change due to electrostatic interactions among closer chain ionizing groups and the hindrance effect of their associated structural water.