We focus on the state-of-the-art theory of electromigration under single and multiple complexation equilibrium. Only 1:1 complexation stoichiometry is discussed because of its unique status in the field of affinity capillary electrophoresis (ACE). First, we summarize the formulas for the effective mobility in various ACE systems as they appeared since the pioneering days in 1992 up to the most recent theories till 2015. Disturbing phenomena that do not alter the mobility of the analyte directly but cause an unexpected peak broadening have been studied only recently and are also discussed in this paper. Second, we turn our attention to the viscosity effects in ACE. Change in the background electrolyte viscosity is unavoidable in ACE but numerous observations scattered throughout the literature have not been reviewed previously. This leads to an uncritical employment of correction factors that may or may not be appropriate in practice. Finally, we consider the ionic strength effects in ACE, too. Limitations of the current theories are also discussed and the tasks identified where open problems still prevail. Graphical Abstract A weak base (A) undergoes an acidic-basic equilibria (in blue) and migrates with an electrophoretic mobility of [Formula: see text]. Simultaneously, it interacts with a selector (sel) while the analyte-selector complex migrates with an electrophoretic mobility of [Formula: see text]. The strength of the interaction (in orange) is governed by the binding constant, K , and the concentration of the selector, c . This all gives the analyte an effective mobility of [Formula: see text] and moves it out of the zero position (EOF; right top insert). The interaction of the positively charged analyte with the neutral selector slows down the analyte with increasing selector concentration (right bottom insert).

Determination of thermodynamic acidity constants and limiting ionic mobilities of weak electrolytes by capillary electrophoresis using a new free software AnglerFishThermodynamic acidity constants (acid or acid-base dissociation constants, sometimes called also as ionization constants) and limiting ionic mobilities (both of them at defined temperature, usually 25°C) are the fundamental physicochemical characteristics of a weak electrolyte, that is, weak acid or weak base or ampholyte. We introduce a novel method for determining the data of a weak electrolyte by the nonlinear regression of effective electrophoretic mobility versus buffer composition dependence when measured in a set of BGEs with various pH. To correct the experimental data for zero ionic strength we use the extended Debye-Hückel model and Onsager-Fuoss law with no simplifications. Contrary to contemporary approaches, the nonlinear regression is performed on limiting mobility data calculated by PeakMaster's correction engine, not on the raw experimental mobility data. Therefore, there is no requirement to perform all measurements at a constant ionic strength of the set of BGEs. We devised the computer program AnglerFish that performs the necessary calculations in a user-friendly fashion. All thermodynamic pKa values and limiting electrophoretic mobilities for arbitrarily charged substances having any number of ionic forms are calculated by one fit. The user input consists of the buffer composition of the set of BGEs and experimentally measured effective mobilities of the inspected weak electrolyte.

CE determination of the thermodynamic pK a values and limiting ionic mobilities of 14 low molecular mass UV absorbing ampholytes for accurate characterization of the pH gradient in carrier ampholytes-based IEF and its numeric simulation Fourteen low molecular mass UV absorbing ampholytes containing 1 or 2 weakly acidic and 1 or 2 weakly basic functional groups that best satisfy Rilbe's requirement for being good carrier ampholytes ( pK a = pKa monoanion -pKa monocation < 2) were selected from a large group of commercially readily available ampholytes in a computational study using two software packages (ChemSketch and SPARC). Their electrophoretic mobilities were measured in 10 mM ionic strength BGEs covering the 2 < pH < 12 range. Using our Debye-Hückel and Onsager-Fuoss laws-based new software, AnglerFish (freeware, https://echmet.natur.cuni.cz/software/download), the effective mobilities were recalculated to zero ionic strength from which the thermodynamic pK a values and limiting ionic mobilities of the ampholytes were directly calculated by Henderson-Hasselbalch equation-type nonlinear regression. The tabulated thermodynamic pK a values and limiting ionic mobilities of these ampholytes (pI markers) facilitate both the overall and the narrow-segment characterization of the pH gradients obtained in IEF in order to mitigate the errors of analyte ampholyte pI assignments caused by the usual (but rarely proven) assumption of pH gradient linearity. These thermodynamic pK a and limiting mobility values also enable the reality-based numeric simulation of the IEF process using, for example, Simul (freeware, https://echmet.natur.cuni.cz/software/download). Abbreviations:3MHIS, 3-methylhistidine; DNS-Cl, dansylchloride; DNS-IDA, dansylated iminodiacetic acid; GLYHIS, glycyl-histidine; ICIEF, Imaging capillary isoelectric focusing; IDA, iminodiacetic acid; LAB, labetalol; LBB, Leucoberbelin blue I dye; SERO, serotonin compartment has to be filled with a base (the catholyte, e.g. 20 mM NaOH). Fourth, convective disturbances have to be absent or suppressed in the system (either by using an anti-convective medium or a capillary as the separation compartment). Fifth, a sufficiently large DC voltage has to be applied between the anode and the cathode for a sufficiently long period of time to allow any and all of the initially cationic and anionic carrier ampholytes in the mixture to migrate out of sections of the separation compartment in which the local pH value is different from their isoelectric point value. (Since Rilbe considered the isoelectric point value to be very close to the isoprotic point value-which he calculated as (pKa monocation + pKa monoanion )/2-the symbol pI, and the term pI value, became loosely-and interchangeably-used in the literature to designate either "iso" value.)Once all these conditions are fulfilled, adjacent, individual carrier ampholyte bands form across the separation compartment such that the pH in the successive bands increases Color online: See the article online to view Figs. 1, 3-5 in ...

The partial-filling affinity capillary electrophoresis (pf-ACE) works with a ligand present in a background electrolyte that forms a weak complex with an analyte. In contrast to a more popular mobility-shift affinity capillary electrophoresis, only a short plug of the ligand is introduced into a capillary in the pf-ACE. Both methods can serve for determining apparent stability constants of the formed complexes but this task is hindered in the pf-ACE by the fact that the analyte spends only a part of its migration time in a contact with the ligand. In 1998, Amini and Westerlund published a linearization strategy that allows for extracting an effective mobility of an analyte in the presence of a neutral ligand out of the pf-ACE data. The main purpose of this paper is to show that the original formula is only approximate. We derive a new formula and demonstrate its applicability by means of computer simulations. We further inspect several strategies of data processing in the pf-ACE regarding a risk of an error propagation. This establishes a good practice of determining apparent stability constants of analyte-ligand complexes by means of the pf-ACE.

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