Moment theory for the analytical determination of rate constants for solute permeation 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-sn‑glycero-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 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 (ϕ_M ). Partition equilibrium constants (K_p ) and rate constants of interfacial solute permeation of SDS micelles (k_in and k_out ) 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 ϕ_M and were almost the same as those previously measured by complete filling CE. The positive correlation of K_p with the hydrophobicity of the solutes was explained in terms of the change in k_in and k_out . 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.