RESUMO
Kinetics of facilitated ion transport through planar bilayer membranes are normally analyzed by electrical conductance methods. The additional use of electrical relaxation techniques, such as voltage jump, is necessary to evaluate individual rate constants. Although electrochemical impedance spectroscopy is recognized as the most powerful of the available electric relaxation techniques, it has rarely been used in connection with these kinetic studies. According to the new approach presented in this work, three steps were followed. First, a kinetic model was proposed that has the distinct quality of being general, i.e., it properly describes both carrier and channel mechanisms of ion transport. Second, the state equations for steady-state and for impedance experiments were derived, exhibiting the input-output representation pertaining to the model's structure. With the application of a method based on the similarity transformation approach, it was possible to check that the proposed mechanism is distinguishable, i.e., no other model with a different structure exhibits the same input-output behavior for any input as the original. Additionally, the method allowed us to check whether the proposed model is globally identifiable (i.e., whether there is a single set of fit parameters for the model) when analyzed in terms of its impedance response. Thus, our model does not represent a theoretical interpretation of the experimental impedance but rather constitutes the prerequisite to select this type of experiment in order to obtain optimal kinetic identification of the system. Finally, impedance measurements were performed and the results were fitted to the proposed theoretical model in order to obtain the kinetic parameters of the system. The successful application of this approach is exemplified with results obtained for valinomycin-K(+) in lipid bilayers supported onto gold substrates, i.e., an arrangement capable of emulating biological membranes.
RESUMO
Selectivity between monovalent cations and its sequence of conductivity in lipid bilayers doped with the antibiotic Gramicidin D (GD) were examined using EIS. Experiments were performed using lipid bilayers obtained from a lipid mixture of phosphatidylcholine and dimethyldioctadecylammonium chloride (DODAC). Lipid bilayers were supported on gold surfaces modified with a mercapto-carboxylic acid. The bilayers were formed by chemisorption of this last species to form the first monolayer on gold and subsequent fusion of unilamellar vesicles to form an external bilayer attached by electrostatic interactions. A mathematical expression for the impedance of the membrane processes was derived. Some predictions of the presented model were checked after fitting the experimental results in various electrolyte compositions.