Jana Svobodová

Simulation of the effects of complex‐ formation equilibria in electrophoresis: I. Mathematical model

Simul 5 Complex is a one‐dimensional dynamic simulation software designed for electrophoresis, and it is based on a numerical solution of the governing equations, which include electromigration, diffusion and acid–base equilibria. A new mathematical model has been derived and implemented that extends the simulation capabilities of the program by complexation equilibria. The simulation can be set up with any number of constituents (analytes), which are complexed by one complex‐forming agent (ligand). The complexation stoichiometry is 1:1, which is typical for systems containing cyclodextrins as the ligand. Both the analytes and the ligand can have multiple dissociation states. Simul 5 Complex with the complexation mode runs under Windows and can be freely downloaded from our web page http://natur.cuni.cz/gas. The article has two separate parts. Here, the mathematical model is derived and tested by simulating the published results obtained by several methods used for the determination of complexation equilibrium constants: affinity capillary electrophoresis, vacancy affinity capillary electrophoresis, Hummel–Dreyer method, vacancy peak method, frontal analysis, and frontal analysis continuous capillary electrophoresis. In the second part of the paper, the agreement of the simulated and the experimental data is shown and discussed.

Enhanced selectivity in CZE multi-chiral selector enantioseparation systems: proposed separation mechanism.

It has been reported many times that the commercial mixtures of chiral selectors (CS), namely highly sulfated β‐CDs (HS‐β‐CDs), provide remarkable enantioselectivity in CZE when compared with single‐isomer CDs, even single‐isomer HS‐β‐CDs. This enhanced enantioselectivity of multi‐CS enantioseparative CZE is discussed in the light of multi‐CS model that we have introduced earlier. It is proposed on a theoretical basis and verified experimentally that the two enantiomers of a chiral analyte under interaction with a mixture of CSs are very likely to differ in their limit mobilities, which is opposite to single‐CS systems where the two limit mobilities are likely to be the same. Thus while the enantioseparation is usually controlled by different distribution constants between the two enantiomers and CS used in single‐CS systems, an additional, electrophoretic, enantioselective mechanism resulting from different limit mobilities may play a significant role in multi‐CS systems. This additional mechanism generally makes the multi‐CS systems more selective than the single‐CS systems. The possible inequality of limit mobilities is also significant for optimization of separation conditions using mixtures of CSs. A practical example supporting our considerations is shown on enantioseparation of lorazepam in the presence of a commercial mixture of HS‐β‐CDs and a single‐isomer HS‐β‐CD, heptakis(6‐O‐sulfo)‐β‐CD.

Applicability and limitations of affinity capillary electrophoresis and vacancy affinity capillary electrophoresis methods for determination of complexation constants

ACE and vacancy affinity capillary electrophoresis (VACE) are the commonly used methods for determination of complexation constants by CE. The applicability and limitations of these methods were tested experimentally and by means of simulations using our simulation software Simul 5 Complex. It was shown that while the ACE method provides reliable and precise values of complexation parameters, those determined by VACE can be incorrect especially in the case of strong complexation. The effective mobilities of the system peaks in the VACE method, and consequently, the resulting complexation parameters were found to be a function of concentration of the analyte present in the BGE. Development of system peaks in VACE is discussed in the frame of the linear theory of electromigration. Dependence of mobility of system peaks on the composition of the BGE cannot be characterized by a simple analytical expression as in the case of ACE method. Thus, the VACE method fails and the resulting complexation constants might seriously differ from the reality.

Model of CE enantioseparation systems with a mixture of chiral selectors: Part I. Theory of migration and interconversion☆

Theory of equilibria, migration and dynamics of interconversion of a chiral analyte in electromigration enantioseparation systems involving a mixture of chiral selectors for the chiral recognition (separation) are proposed. The model assumes that each individual analyte-CS interaction is fast, fully independent on other interactions and the analyte can interact with CS in 1:1 ratio and that the analyte is present in the concentration small enough not to considerably change the concentration of free CSs. Under these presumptions, the system behaves as there was only one chiral selector with a certain overall equilibrium constant, overall mobility of analyte-selector complex (associate) and overall rate constant of interconversion in a chiral environment. We give the mathematical equations of the overall parameters. A special interest is devoted to the dynamics of interconversion. Interconversion in systems with mixture of chiral selectors is governed by two apparent rate constants of interconversion in the same way as in case of singe-selector systems. We propose the experimental design that allows to determine rates of interconversion in both chiral and achiral parts of the enantioseparation system separately. The approach is verified experimentally in the second part of the article.

Simulation of the effects of complex- formation equilibria in electrophoresis: II. Experimental verification

The complete mathematical model of electromigration in systems with complexation agents introduced in the Part I of this article (V. Hruška et al., Eletrophoresis, 2012, 33, this issue), which was implemented into our simulation program Simul 5, was verified experimentally. Three different chiral selector (CS) systems differing in the type of the CS, the magnitude of the complexation constants as well as in the experimental conditions were selected for verification. The experiments and simulations were performed at various concentrations of the CSs in order to discuss the influence of the concentration of the CS on the separation. The simulated and experimental electropherograms show very good agreement in the position, shape and amplitude of the analyte peaks.

Determination of stability constants of complexes of neutral analytes with charged cyclodextrins by affinity capillary electrophoresis.

A novel procedure for the determination of stability constants in systems with neutral analytes and charged complexation agents by affinity capillary electrophoresis was established. This procedure involves all necessary corrections to achieve precise and reliable data. Temperature, ionic strength, and viscosity corrections were applied. Based on the conductivity measurements, the average temperature of the background electrolyte in the capillary was kept at the constant value of 25°C by decreasing the temperature of the cooling medium. The viscosity correction was performed using the viscosity ratio determined by an external viscosimeter. The electrophoretical measurements were performed, at first, at constant ionic strength. In this case, the increase of ionic strength caused by increasing complexation agent concentration was compensated by changing of the running buffer concentration. Subsequently the dependence of the analyte effective mobility on the complexation agent concentration was measured without the ionic strength compensation (at variable ionic strength). The new procedure for determination of the stability constants even from such data was established. These stability constants are in a very good agreement with those obtained at the constant ionic strength. The established procedure was applied for determination of the thermodynamic stability constants of (R, R)‐(+)‐ and (S, S)‐(‐)‐hydrobenzoin and R‐ and S‐(3‐bromo‐2‐methylpropan‐1‐ol) complexing with 6‐monodeoxy‐6‐mono(3‐hydroxy)propylamino‐β‐cyclodextrin hydrochloride.

Complexation of Buffer Constituents with Neutral Complexation Agents: Part I. Impact on Common Buffer Properties

The complexation of buffer constituents with the complexation agent present in the solution can very significantly influence the buffer properties, such as pH, ionic strength, or conductivity. These parameters are often crucial for selection of the separation conditions in capillary electrophoresis or high-pressure liquid chromatography (HPLC) and can significantly affect results of separation, particularly for capillary electrophoresis as shown in Part II of this paper series (Beneš, M.; Riesová, M.; Svobodová, J.; Tesařová, E.; Dubský, P.; Gaš, B. Anal. Chem. 2013, DOI: 10.1021/ac401381d). In this paper, the impact of complexation of buffer constituents with a neutral complexation agent is demonstrated theoretically as well as experimentally for the model buffer system composed of benzoic acid/LiOH or common buffers (e.g., CHES/LiOH, TAPS/LiOH, Tricine/LiOH, MOPS/LiOH, MES/LiOH, and acetic acid/LiOH). Cyclodextrins as common chiral selectors were used as model complexation agents. We were not only able to demonstrate substantial changes of pH but also to predict the general complexation characteristics of selected compounds. Because of the zwitterion character of the common buffer constituents, their charged forms complex stronger with cyclodextrins than the neutral ones do. This was fully proven by NMR measurements. Additionally complexation constants of both forms of selected compounds were determined by NMR and affinity capillary electrophoresis with a very good agreement of obtained values. These data were advantageously used for the theoretical descriptions of variations in pH, depending on the composition and concentration of the buffer. Theoretical predictions were shown to be a useful tool for deriving some general rules and laws for complexing systems.

Simulation of the effects of complex‐formation equilibria in electrophoresis: III. Simultaneous effects of chiral selector concentration and background electrolyte pH

This paper describes the results of the second‐level testing of the simulation program Simul 5 Complex. We compare the published experimental results with the simulated migration behavior of the enantiomers at different pH and chiral selector concentration values and use the same optimization object function, separation selectivity, as the original papers. Simul 5 Complex proved to be a suitable tool for the prediction of the effective mobilities, separation selectivities, and migration order reversals in these pH‐dependent and CD concentration dependent enantiomer separations. In addition, by performing simulations of four different separations systems (both real and model systems), Simul 5 Complex revealed the existence of unexpected and hitherto unexplained electromigration dispersion effects that were caused by the complexation process itself and could significantly impair the quality of the separations.

Determination of thermodynamic values of acidic dissociation constants and complexation constants of profens and their utilization for optimization of separation conditions by Simul 5 Complex

In this paper we determine acid dissociation constants, limiting ionic mobilities, complexation constants with β-cyclodextrin or heptakis(2,3,6-tri-O-methyl)-β-cyclodextrin, and mobilities of resulting complexes of profens, using capillary zone electrophoresis and affinity capillary electrophoresis. Complexation parameters are determined for both neutral and fully charged forms of profens and further corrected for actual ionic strength and variable viscosity in order to obtain thermodynamic values of complexation constants. The accuracy of obtained complexation parameters is verified by multidimensional nonlinear regression of affinity capillary electrophoretic data, which provides the acid dissociation and complexation parameters within one set of measurements, and by NMR technique. A good agreement among all discussed methods was obtained. Determined complexation parameters were used as input parameters for simulations of electrophoretic separation of profens by Simul 5 Complex. An excellent agreement of experimental and simulated results was achieved in terms of positions, shapes, and amplitudes of analyte peaks, confirming the applicability of Simul 5 Complex to complex systems, and accuracy of obtained physical-chemical constants. Simultaneously, we were able to demonstrate the influence of electromigration dispersion on the separation efficiency, which is not possible using the common theoretical approaches, and predict the electromigration order reversals of profen peaks. We have shown that determined acid dissociation and complexation parameters in combination with tool Simul 5 Complex software can be used for optimization of separation conditions in capillary electrophoresis.

A nonlinear electrophoretic model for PeakMaster: Part III. Electromigration dispersion in systems that contain a neutral complex-forming agent and a fully charged analyte. Theory

We introduce a new nonlinear electrophoretic model for complex-forming systems with a fully charged analyte and a neutral ligand. The background electrolyte is supposed to be composed of two constituents, which do not interact with the ligand. In order to characterize the electromigration dispersion (EMD) of the analyte zone we define a new parameter, the nonlinear electromigration mobility slope, S(EMD,A). The parameter can be easily utilized for quantitative prediction of the EMD and for comparisons of the model with the simulated and experimental profiles. We implemented the model to the new version of PeakMaster 5.3 Complex that can calculate some characteristic parameters of the electrophoretic system and can plot the dependence of S(EMD,A) on the concentration of the ligand. Besides S(EMD,A), also the relative velocity slope, S(X), can be calculated. It is commonly used as a measure of EMD in electrophoretic systems. PeakMaster 5.3 Complex software can be advantageously used for optimization of the separation conditions to avoid high EMD in complexing systems. Based on the theoretical model we analyze the S(EMD,A) and reveal that this parameter is composed of six terms. We show that the major factor responsible for the electromigration dispersion in complex-forming electrophoretic systems is the complexation equilibrium and particularly its impact on the effective mobility of the analyte. To prove the appropriateness of the model we showed that there is a very good agreement between peak shapes calculated by PeakMaster 5.3 Complex (plotted using the HVLR function) and the profiles simulated by means of Simul 5 Complex. The detailed experimental verification of the new mode of PeakMaster 5.3 Complex is in the next part IV of the series.