Analysis of the interplay among charge, hydration and shape of proteins through the modeling of their CZE mobility data

Abstract

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.

Estimation of global structural and transport properties of peptides through the modeling of their CZE mobility data

“…From the PLLCEM relevant basic peptide properties may be evaluated 13, 20, such as positive ${Z}_ +$ , negative ${Z}_ -$ , effective ${Z} = | {Z}_ + | -| {Z}_ - |$ and total $Z_{\rm T} = | {Z}_ + | + | {Z}_ -|$ charge numbers, and Stokes or equivalent hydrodynamic radius $a_{\rm H}$ , defining the total hydrodynamic peptide volume $V_{\rm H} = 4 {\rm {\pi}} a_{{\rm H}}^{3}/3$ . This volume is decomposed into the peptide compact volume $V_{\rm c} = Mv_{\rm p} /N_{\rm A} = 4 {\rm {\pi}} a_{\rm c}^3/3$ with compact radius $a_{\rm c}$ and the hydration volume $V_w$ .…”

“…Here, v w is the specific volume of the protocol solvent. In addition, estimations of peptide hydration number H =δ M /18 (number of water molecules per peptide chain) are obtained by summing each hydration number of ionizing, polar and non‐polar groups 13, 19 (these last expressions establish the PLLCEM convergence criterion 19, 20). In addition, this model provides the p K i values of ionizing groups yielding a shift $\Delta {\rm p}K_i$ in the reference ${\rm p}K_i^r$ reported in 34 as a result of the charge regulation phenomenon present in these particles 18, 35.…”

“…Therefore, the pH microenvironment ${\rm{pH}}_i$ around the i ‐ionizing group is also numerically available 19. This ${\rm{pH}}_i$ is a function of the mean field ${\rm pH}^*$ , designated the near‐molecule pH, and the electrical permittivity within the peptide domain ε′ (see the numerical procedure in 20 for their estimations). In this framework, the frequent assumption ε′≈ε is substituted by the expression ε′=εδ/(1+δ)+ε p /(1+δ), which uses the particle hydration as the weighing parameter between peptide ε p 36 and solvent ε electrical permittivities.…”

“…Then, they are used to infer global structural properties associated with the physics of peptide chains in dilute solution. In this framework, there are CZE models for peptides and proteins in the literature, covering different aspects and phenomena with varied degrees of complexity 5, 8–11, 13–20. By considering these works on the subject concerning either asymptotic analytical solutions and complex computational works, here we propose to add some theoretical developments to our previous studies 10, 13, involving the simple Perturbed Linderstrøm–Lang capillary electrophoresis model (PLLCEM), which has been applied previously to amino acids, peptides and proteins.…”

“…By considering these works on the subject concerning either asymptotic analytical solutions and complex computational works, here we propose to add some theoretical developments to our previous studies 10, 13, involving the simple Perturbed Linderstrøm–Lang capillary electrophoresis model (PLLCEM), which has been applied previously to amino acids, peptides and proteins. The description and development of this model may be found in detail with appropriate hypothesis and limitations in 18–20. In particular, this model allowed us to carry out studies of peptide characterizations through the “inverse problem” 10, 13, where the effective mobility was provided as one of the input data and then some basic peptide physicochemical properties were predicted.…”