Moment analysis method for the determination of permeation kinetics of coumarin at lipid bilayers of liposomes by using capillary electrophoresis.

A method was developed for studying mass transfer kinetics at lipid bilayers of liposomes. Elution peaks of coumarin were measured by liposome electrokinetic chromatography (LEKC). Four types of phospholipids having different alkyl chains were used for preparing liposomes, which were used as pseudo-stationary phases in LEKC systems. Rate constants of permeation across lipid bilayers of liposomes or of adsorption at lipid membranes were determined by analyzing the first absolute and second central moments of the elution peaks measured by LEKC. The rate constants of permeation or adsorption tend to decrease with an increase in the carbon number of the alkyl chains of phospholipids. It was demonstrated that the moment analysis of elution peak profiles measured by LEKC is effective for determining lipid membrane permeability or adsorption kinetics. Compared with other conventional techniques, the method has some advantages for studying mass transfer kinetics at lipid bilayers. Solute permeation across or solute adsorption at real lipid bilayers of liposomes is analyzed. The principle of the method is the analysis of separation behavior in LEKC, which is different from that of the other ones. It is expected that the method contributes to the kinetic study of mass transfer at lipid bilayers from various perspectives.

Moment equations for partial filling capillary electrophoresis.

Moment equations were developed for partial filling CE systems, in which solute dissolution phenomena by spherical molecular assemblies or intermolecular interactions take place. Because experimental conditions of partial filling CE are divided into five categories on the basis of the magnitude relationship between the migration velocity of solute molecules and that of molecular assemblies or ligand molecules, the moment equations were systematically developed for each case by using the Einstein equation for diffusion and the random walk model. In order to demonstrate the effectiveness of the moment equations, they were applied to the analysis of partial filling CE behavior, which is correlated with dissolution phenomena of small solute molecules into spherical molecular assemblies as specific examples. Simulation results only in the case that the migration velocity of solute molecules is faster than that of molecular assemblies were represented in this paper. Detailed explanations about the derivation procedure of the moment equations and the simulation results in other cases can be found in the Supporting Information. The moment equations are theoretical bases for applying partial filling CE to the study on solute permeation kinetics at the interface of spherical molecular assemblies and on reaction kinetics of intermolecular interactions.

Kinetic study on solute permeation at the interface of molecular aggregates by partial filling capillary electrophoresis.

Moment analysis method using partial filling CE was developed for the kinetic study on solute permeation at the interface of spherical molecular aggregates. Moment equations for partial filling CE were developed by classifying CE systems into five categories according to the migration velocities of solute and molecular aggregate. The method was applied to the study on the dissolution of electrically neutral solutes into SDS micelles. Elution peaks were measured by partial filling CE while changing the concentration of SDS and the filling ratio of SDS micellar zone to the capillary (ϕM ). Partition equilibrium constants (Kp ) and rate constants of interfacial solute permeation of SDS micelles (kin and kout ) were determined from the first absolute and second central moments of the elution peaks by using the moment equations. Their values were comparable irrespective of ϕM and were almost the same as those previously measured by complete filling CE. The positive correlation of Kp with the hydrophobicity of the solutes was explained in terms of the change in kin and kout . It was demonstrated that the moment analysis method using partial filling CE is effective for studying solute permeation kinetics at the interface of spherical molecular aggregates.

Moment analysis method for determination of rate constants of solute permeation across interface of spherical molecular aggregates by means of high-performance liquid chromatography.

A moment analysis method was developed for the study of solute permeation at the interface of spherical molecular aggregates. At first, new moment equations were developed for determining the partition equilibrium constant (Kp) and permeation rate constants (kin and kout) of solutes from the first absolute (µ1A) and second central (µ2C) moments of elution peaks measured by using high-performance liquid chromatography (HPLC). Then, the method was applied to the analysis of mass transfer phenomena of three solutes, i.e., hydroquinone, resorcinol, and catechol, at the interface of sodium dodecylsulfate (SDS) micelles. HPLC data were measured by using an ODS column and an aqueous phosphate buffer solution (pH = 7.0) as the mobile phase solvent. Pulse response experiments were conducted while changing SDS concentration (5 - 20 mmol dm-3) in the mobile phase under the conditions that the surface of ODS stationary phase was dynamically coated by SDS monomers. In order to demonstrate the effectiveness of the moment analysis method using HPLC, the values of Kp, kin, and kout were determined for the three solutes as 35 - 69, 2.4 × 10-8 - 1.4 × 10-6 m s-1, and 7.0 × 10-10 - 2.1 × 10-8 m s-1, respectively. Their values increase with an increase in the hydrophobicity of the solutes. The method has some advantages for the study of interfacial solute permeation of molecular aggregates. For example, neither immobilization nor chemical modification of both solute molecules and molecular aggregates is required when elution peaks are measured by using HPLC. Interfacial solute permeation takes place in the mobile phase without any chemical reaction or physical action on molecular aggregates. The values of Kp, kin, and kout were analytically determined from those of µ1A and µ2C by using the moment equations. The results of this study must contribute to the dissemination of an opportunity for studying the interfacial solute permeation of molecular aggregates to many researchers because of extremely high versatility of HPLC.

A study on attempt for determination of permeation kinetics of coumarin at lipid bilayer of liposomes by using capillary electrophoresis with moment analysis theory.

It was tried to develop a moment analysis method for the determination of lipid membrane permeability. The first absolute and second central moments of elution peaks measured by liposome electrokinetic chromatography (LEKC) are analyzed by using moment equations. As a concrete example, elution peak profiles of coumarin in a LEKC system, in which liposomes consisting of 1-palmitoyl-2-oleoyl-sn­glycero-3-phosphocholine (POPC) and phosphatidylserine (PS) are used as a pseudo-stationary phase, were analyzed. It seems that lipid membrane permeability of coumarin across the lipid bilayer of POPC/PS liposomes was measured by the moment analysis method because previous permeability measurements using parallel artificial membrane permeability assay (PAMPA) and Caco-2 cells indicated that coumarin is permeable across lipid bilayer. However, it was also pointed out that the moment analysis method with LEKC is not effective for the determination of lipid membrane permeability and that it provides information about adsorption/desorption kinetics at lipid bilayer of liposomes. Therefore, different moment equations were also developed for the determination of adsorption/desorption rate constants of coumarin from the LEKC data. It was demonstrated that permeation rate constants at lipid bilayer or adsorption/desorption rate constants can be determined from the LEKC data on the basis of moment analysis theory for the mass transfer phenomena of coumarin at the lipid bilayer of POPC/PS liposomes. Mass transfer kinetics of solutes at lipid bilayer should be determined under the conditions that liposomes originally be because they are self-assembling and dynamic systems formed through weak interactions between phospholipid monomers. The moment analysis method using LEKC is effective for the experimental determination of the mass transfer rate constants at the lipid bilayer of liposomes because neither immobilization nor chemical modification of liposomes is necessary when LEKC data are measured. It is expected that the results of this study contribute to the dissemination of an opportunity for the determination of permeation rate constants or adsorption/desorption rate constants at the lipid bilayer of liposomes to many researchers because capillary electrophoresis is widespread.

Moment theory of affinity capillary electrophoresis for analysis of reaction kinetics of intermolecular interactions.

A theoretical basis for affinity capillary electrophoresis (ACE) was systematically developed by applying the moment theory to the study on intermolecular interactions between solute (S) and ligand (L) molecules to form complex (X). Moment equations were developed for both complete filling and partial filling ACE systems, in which SLm or SnL forms as X. They are effective for the determination of equilibrium and kinetic constants of association between S and L and dissociation of X from the first absolute and second central moments of elution peaks measured by ACE. In order to demonstrate their effectiveness, simulative calculations of partial filling ACE behavior was conducted by assuming the stoichiometry of 1:1 between S and L. Because partial filling ACE systems are classified into five categories based on experimental conditions, calculation results for all the five cases are explained. The combination of ACE and moment theory is effective because there are some advantages concerning the accurate analysis of intermolecular interactions. The results of this study provide an opportunity for the study on intermolecular interactions to many researchers because CE is already versatile.

Moment Analysis of Mass Transfer Kinetics in Micellar Electrokinetic Chromatography Systems.

Moment equations were developed for quantitatively studying the separation characteristics of micellar electrokinetic chromatography (MEKC). They explain how the first absolute and second central moments of elution peaks are correlated with some fundamental parameters of the partition equilibrium and mass transfer kinetics in MEKC systems. In order to discuss the influence of the mass transfer kinetics on peak broadening, the moment equations were used to analyze the separation behavior in MEKC systems. Separation conditions were chosen on the basis of practical MEKC experiments previously conducted. It was quantitatively clarified that both the solute permeation at the interfacial boundary of surfactant micelles and axial diffusion of solute molecules in a capillary had a predominant contribution to the spreading of the elution peaks in MEKC systems. This is a preliminary study for the analytical determination of rate constants concerning solute permeation at the interface of surfactant micelles from elution peak profiles measured by MEKC. In addition, it was also indicated that the experimental conditions of MEKC systems could be controlled so that the interfacial solute permeation would have a predominant role for the band broadening. For example, the contribution of the interfacial permeation was about 33 times larger than that of the axial diffusion of solute molecules under the MEKC conditions in a previous study. This means that the rate constants could appropriately be determined for the interfacial solute permeation.

Numerical correction for asymmetrical peak profiles for moment analysis of chromatographic behavior.

A numerical correction method is proposed for the moment analysis of some properties of chromatographic columns, even when the profiles of their elution peaks exhibit some asymmetry. Information on the retention equilibrium and the mass transfer kinetics of a C18-silica gel packing material is derived by the moment analysis from the experimental data obtained under three different sets of conditions: (1) the tailing peaks eluted from the column used; they are not corrected by the numerical method; (2) the same peaks are corrected by the numerical method, which provides the information on the column radial heterogeneity and on the efficiency at its center; and (3) symmetrical peaks having nearly Gaussian profiles eluted from another column packed with the same material; these peaks are not corrected by the numerical method. The analytical results obtained under the three different conditions are compared. The results demonstrate that the numerical correction method allows the determination of the information on the chromatographic behavior of columns from asymmetrical peak profiles, i.e., column efficiency at radial center, order of the polynomial functions for representing the radial distributions of mobile phase flow velocity and column efficiency, ratio of the flow velocity near the wall to that at the column center, and ratio of the column efficiency near the wall to that at the column center.

Moment Analysis Theory for Size Exclusion Capillary Electrochromatography with Chemical Reaction of Intermolecular Interaction.

New moment equations were developed for size exclusion capillary electrochromatography (SECEC), in which intermolecular chemical reactions simultaneously took place. They explain how the first absolute and second central moments of elution peaks are correlated with some fundamental equilibrium and kinetic parameters of mass transfer and chemical reaction in SECEC column. In order to demonstrate the effectiveness of the moment equations, they were used to predict chromatographic behavior under hypothetical SECEC conditions. It was quantitatively studied how the association and dissociation rate constants of intermolecular interaction affected the position and spreading of elution peaks. It was indicated that both the intermolecular reaction kinetics and axial dispersion of solute molecules in a capillary column had a predominant contribution to the band broadening.